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CUREe-KAJIMA RESEARCH PROJECT
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SEISMIC PERFORMANCE OF A 30-STORY BUILDING
LOCATED ON SOFT SOIL AND DESIGNED ACCORDING TO UBC 1991
Amador Teran-Gilmore and Vitelmo V. Bertero
Earthquake Engineering Research Center
University of California. at Berkeley
July 15, 1991 - January 14, 1993
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SEISMIC PERFORMANCE OF A 30-STORY BUILDING
LOCATED ON SOFT SOIL AND DESIGNED ACCORDING TO UBC 1991
Amador Teran-Gilmore and Vitelmo V. Bertero
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Earthquake Engineering Research Center
University of California at Berkeley
July 15, 1991 - January 14, 1993
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ABSTRACT
Researchers and practitioners interested in the seismic design of buildings have expressed
serious concerns about the reliability and rationality of present building code methodology for
the Earthquake-Resistant Design (EQRD) of tall buildings, particularly those to be built on deep
soft soil. Therefore it was decided to conduct the studies reported herein, which have the
following main objective: to assess the adequacy of the U.S. Uniform Building Code (UBC)
methodology for tall buildings on soft soil.
To achieve the above main objective, it was decided to design a tall building on soft soil
using the UBC methodology, and then to analyze its performance under the critical Earthquake
Ground Motions (EQGMs) that could occur at the building site. First, a 30-story RC building
with identical configuration, structural system and structural layout as those of a building that
has been designed and built in Japan was selected. The 30-story building, assumed to be
located in the San Francisco Bay Area, is constituted by a three-dimensional assemblage of
Reinforced Concrete (RC) special moment-resisting frames. The following studies that were
conducted are reported herein.
In Chapter 2, a description of the function, configuration, structural system, and structural
layout of the selected building is given. In this chapter, some of the general requirements for
the design of the 30-story building according to UBC are presented, together with the methods
used for the preliminary design of the 30-story building.
A detailed discussion and interpretation of some UBC design guidelines is presented in
Chapter 3. In this chapter, the design procedure for obtaining the final design from the
preliminary design is presented, as well as a summary of the member sizes and reinforcement
for the final design of the 30-story building. Some considerations about the way accidental
torsion is accounted for in the UBC specifications are presented.
In Chapter 4, the studies conducted on the behavior of the designed 30-story building when
subjected to different levels of EQGM was studied. A summary of the results obtained from
the several analyses that were carried out on this building are presented: elastic response
spectra analyses (RSA) and elastic time-history analyses (THA) for service and safety limit
. , states; nonlinear pushover analyses, and nonlinear THA for service and safety. It should be
noted that the nonlinear THA were limited to plane (2D) models. The results obtained from the
elastic and nonlinear analyses, which include floor displacements, lnterstory Drift Indices (IDI),
maximum and cumulative plastic rotations at the ends of the members (emax and 8acJ, global
displacement ductility demands (~), story displacement ductiility demands (~story), local
rotational ductility demands (~, and finally, an estimate of local damage index to the
members of the building (DMI), provide information on which the assessment of the adequacy
of UBC specifications and design methodology in the design of the 30-story building can be
based for the service and safety limit states. In Chapter 4, only the performance of the 30-story
building is discussed; while the discussion of the possible reasons for i1s behavior are
presented in Chapter 5.
Chapter 5 provides information that complements that presented in Chapter 4. Additional
analyses of the 30-story building were carried out to complete the information on which the
assessment of the behavior of the building can be based: elastic analyses were carried out
to assess the adequacy of a 2D model of the building has for predicting the global three
dimensional (3D) behavior of the building; an extra nonlinear 2D THA was carried out to
assess the effect of P-~ on the dynamic nonlinear behavior of the building; and finally, the
nonlinear response of single-degree-of-freedom systems (SDOFS) is computed to study the
reliability of estimating nonlinear response from the linear elastic response of systems
subjected to EQGMs recorded in soft soils. Once the information regarding the behavior of the
building is completed, an assesment of the seismic performance of the building is made.
Finally, Chapter 6 presents a comparison of the seismic performance of three 30-story
buildings with exactiy the same structural layout, but designed according to three different
design philosophies: American practice, Japanese practice, and a newly developed Conceptual
Design Methodology. Based on the results obtained from this comparison and from those
discussed in Chapters 3 to 5, conclusions are drawn and recommendations are formulated for
improving present EQRD Code procedures and for the needed research to achieve such
improvements.
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ACKNOWLEDGEMENTS
The studies reported herein have been conducted as Task #5, .. Development of a
Preliminary Design Method,.. of a research project entitled .. Design of High-Rise
Reinforced Concrete Buildings on Soft Soils ... This project is part of a program of research
which is financially supported by Kajima Corporation and administered by CUREe, the
California Universities for Research in Earthquake Engineering. The financial support from
Kajima is gratefully acknowledged. The findings, observations, conclusions and
recommendations of this report are those of the authors alone.
The authors would like to express their gratitude to Professors James Anderson,
Graham Powell and Filip Filippou for their valuable input in discussions that were held
regarding the studies presented in this report.
Special thanks are due to Dr. Norio Inoue, Group Manager of the Kajima Team, and the
members of his team for their valuable comments during the meetings that we had to
discuss this work, as well as for the valuable information that they provided regarding the
Japanese design of the 30-story building selected for the studies reported herein.
Also, special thanks are due to Dr. Ashraf Habibullah of Computers and Structures,
Inc., who donated a free copy of the ETABS program, with which all the elastic analysis
I' on the 30-story building were carried out. The helpful information provided by Dr. Robert
Morris, and in general, the kindness of the people who work in Computers and Structures,
Inc. is greatly appreciated.
Thanks are also extended to Brad Young for editing this manuscript.
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TABLE OF CONTENTS
ABSTRACT
ACKNOWLEDGEMENTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii
TABLE OF CONTENTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iv
LIST OF FIGURES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii
LIST OF TABLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . XV
SYMBOLS AND ABBREVIATIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xvi
1. INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.1 STATEMENT OF THE PROBLEM . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 OBJECTIVES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.3 SCOPE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
2. THE 30-STORY BUILDING AND ITS PRELIMINARY DESIGN . . . . . . . . . . . 5 2.1 GENERAL REMARKS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.2 UBC EARTHQUAKE-RESISTANT DESIGN PHILOSOPHY AND
PROCEDURES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.2 GIVEN INFORMATION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2.3 THE STRUCTURE'S LOADS FOR PRELIMINARY DESIGN . . . . . . . . 10
2.3.1 DEAD LOAD ....... _. . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2.3.2 LIVE LOADS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 2.3.3 TRIBUTARY AREA FOR VERTICAL LOADS ............. 12 2.3.4 LATERAL LOADS ................................ 12
2.4 PRELIMINARY DESIGN . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 2.4.1 PRELIMINARY DESIGN FOR DRIFT . . . . . . . . . . . . . . . . . . 14 2.4.2 PRELIMINARY DESIGN FOR STRENGTH . . . . . . . . . . . . . . 16 2.4.3 REVISION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 2.4.4 COMMENTS ON FORCE PROCEDURE USED FOR
PRELIMINARY DESIGN . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 2.5 UBC WIND LOADS AND DRIFT REQUIREMENTS . . . . . . . . . . . . . . 20
3. DESIGN ACCORDING TO UBC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 3.1 LATERAL FORCE PROCEDURE ............................ 43
- 3.2 DESIGN SPECTRA FOR UBC DESIGN . . . . . . . . . . . . . . . . . . . . . . 45 3.3 STRUCTURAL ANALYSIS OF THE 30-STORY BUILDING
ACCORDING TO UBC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 3.3.1 30-STORY BUILDING PROPERTIES AND ANALYTICAL
MODELLING . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
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3.3.2 DRIFT CONTROL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 3.3.3 PROCEDURE OF ANALYSIS . . . . . . . . . . . . . . . . . . . . . . . . 60
3.4 PROPERTIES OF DEFINITIVE VERSION OF THE 30-STORY BUILDING . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
3.5 ELASTIC ANALYSIS OF ADOPTED PRELIMINARY DESIGN OF THE 30-STORY BUILDING . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65 3.5.1 PSEUDO-DYNAMIC APPROACH, RSA ANALYSIS TO
OBTAIN DESIGN FORCES ......................... 65 3.5.2 PSEUDO-DYNAMIC APPROACH, COMPUTATION OF
DRIFT AND REQUIRED STRENGTH OF MEMBERS . . . . . . 66 3.5.3 COMPARISON BETWEEN PSEUDO-DYNAMIC AND
DYNAMIC APPROACHES . . . . . . . . . . . . . . . . . . . . . . . . . . 68 3.6 REINFORCED CONCRETE DESIGN ACCORDING TO UBC . . . . . . . 74 3.7 MEMBER SIZES AND LONGITUDINAL REINFORCEMENT . . . . . . . . 79
4 ANALYSIS OF THE SEISMIC PERFORMANCE OF THE 30-STORY BUILDING DESIGNED ACCORDING TO UBC . . . . . . . . . . . . . . . . . . . . 133 4.1 INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133 4.2 ELASTIC RESPONSE SPECTRUM ANALYSIS (RSA) AND TIME
HISTORY ANALYSIS (THA) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134 -4.2.1 SERVICE LIMIT STATE ........................... 135 4.2.2 SAFETY LIMIT STATE ............................ 138
4.3 NONLINEAR ANALYSIS OF 30-STORY BUILDING .............. 140 4.3.1 MODEL OF 30-STORY BUILDING FOR NONLINEAR
ANALYSIS .................................... 140 4.3.2 ROTATIONAL CAPACITY OF BEAMS, DAMAGE INDEX . . . 147 4.3.3 PUSHOVER NONLINEAR ANALYSIS . . . . . . . . . . . . . . . . . 148 4.3.4 NONLINEAR THA FOR SERVICE . . . . . . . . . . . . . . . . . . . . 152 4.3.5 NONLINEAR THA FOR SAFETY . . . . . . . . . . . . . . . . . . . . 158 4.3.6 CONCLUDING REMARKS . . . . . . . . . . . . . . . . . . . . . . . . . 163
5 OVERALL EVALUATION ...................................... 221 5.1 GENERAL REMARKS .................................. 221 5.2 EFFECT OF AXIAL DEFORMATION IN COLUMNS ON THE
BEHAVIOR OF THE 30-STORY BUILDING . . . . . . . . . . . . . . . . . 221 5.3 EFFECT OF 2D MODELLING OF A 3D BUILDING . . . . . . . . . . . . . 228 5.4 SLAB STRENGTH INFLUENCE ON THE BEHAVIOR OF 30-
STORY BUILDING . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 229 5.5 INFLUENCE OF P-A EFFECTS . . . . . . . . . . . . . . . . . . . . . . . . . . . 230 5.6 NONLINEAR RESPONSE PREDICTION FROM LINEAR ELASTIC
ANALYSIS ......................................... 232 5.7 RELIABILITY OF RESULTS OBTAINED FROM 20 NONLINEAR.
ANALYSIS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233 5.8 SEISMIC PERFORMANCE OF THE 30-STORY BUILDING ....... 235
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6 FINAL REMARKS AND CONCLUSIONS ........................... 271 6.1 COMPARISON OF THE SEISMIC PERFORMANCE OF THE 30-
STORY BUILDING DESIGNED ACCORDING TO DIFFERENT DESIGN PHILOSOPHIES ............................. . 6.1.1 INTRODUCTORY REMARKS ...................... . 6.1.2 SOFT SOIL SPECTRA ........................... . 6.1.3 CHARACTERISTICS OF THE THREE DESIGNS OF THE
30-STORY BUILDING ........................... . 6.1 .3.1 WEIGHTS .............................. . 6.1.3.2 STIFFNESS ............................. . 6.1.3.3 DYNAMIC PROPERTIES ................... . 6.1.3.4 VISCOUS DAMPING ...................... . 6.1.3.5 STRENGTH AND DEFORMABILITY CAPACITY .. .
6.1.4 SEISMIC PERFORMANCE OF DIFFERENT DESIGNS OF THE 30-STORY BUILDING ....................... . 6.1.4.1 SEISMIC PERFORMANCE AT SERVICE LIMIT
STATE OF CONCEPTUAL AND UBC DESIGNS ... . 6.1.4.2 SAFETY LIMIT STATE ..................... . 6.1.4.3 COMPARISON OF PERFORMANCE OF THREE
DESIGNS BY THE STUDY OF THE BEHAVIOR OF SDOFS ................................. .
6.1.5 CONCLUSIONS ................................ . 6.2 FINAL CONCLUSIONS AND DESIGN RECOMMENDATIONS .... .
6.2.1 UBC DESIGN SPECIFICATIONS ................... . 6.2.2 DESIGN RECOMMENDATIONS FOR TALL BUILDINGS IN
SOFT SOIL SITES ............................. .
REFERENCES ............................................... .
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276 279 279 280 281 281
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283 287
291 296 298 298
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LIST OF FIGURES
FIGURE 2.1 UBC DESIGN METHODOLOGY . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 FIGURE 2.1 UBC DESIGN METHODOLOGY (contd.) . . . . . . . . . . . . . . . . . . . . . 28 FIGURE 2.2 LOCATION OF 30-STORY BUILDING ....................... 29 FIGURE 2.3 GEOTECHNICAL MAP OF THE SAN FRANCISCO BAY AREA 11
[Ref. 11] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 FIGURE 2.4 PLAN VIEW OF 30-STORY BUILDING . . . . . . . . . . . . . . . . . . . . . . 31 FIGURE 2.5 ELEVATION VIEW OF 30-STORY BUILDING . . . . . . . . . . . . . . . . . 32 FIGURE 2.6 IRREGULARITY TYPE B IN 30-STORY BUILDING . . . . . . . . . . . . . 33 FIGURE 2.7 SLAB THICKNESS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 FIGURE 2.8 LOCATION OF FRAME B . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 FIGURE 2.9 STORY SHEAR TAKEN BY FRAME B . . . . . . . . . . . . . . . . . . . . . . 36 FIGURE 2.10 PORTAL METHOD OF ANALYSIS ........................ 37 FIGURE 2.11 ESTIMATION OF DRIFT DUE TO FLEXURAL DEFORMATION OF
BEAMS AND COLUMNS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 FIGURE 2.12 PRELIMINARY DESIGN FOR GRAVITY LOADS .............. 39 FIGURE 2.13 CANTILEVER METHOD OF ANALYSIS .................... 40 FIGURE 2.14 PRELIMINARY SIZES OF MEMBERS OF FRAME B ........... 41 FIGURE 2.15 ESTIMATION OF DRIFT DUE TO AXIAL DEFORMATION OF 42 FIGURE 3.1 MEASURED SHEAR WAVE VELOCITY PROFILE FOR YOUNG BAY
MUD FOR SIX SAN FRANCISCO BAY SHORE SITES [11] . . . . . . . . . . . 86 FIGURE 3.2 SITE SPECTRA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 FIGURE 3.3 OBTAINING UBC FROM SITE SPECTRA . . . . . . . . . . . . . . . . . . . . 88 FIGURE 3.4 COMPARISON OF UBC SPECTRA FOR DIFFERENT SOIL
CONDITIONS AND SITE SPECTRA ............................ 89 FIGURE 3.5 COMPARISON OF UBC SPECTRA AND DESIGN SPECTRA FOR
CONCEPTUAL DESIGN ..................................... 90 FIGURE 3.6 DYNAMIC DOFS ASSOCIATED WITH FLOOR DIAPHRAGM . . . . . 91 FIGURE 3.7 FORMULA TO COMPUTE ROTARY INERTIA . . . . . . . . . . . . . . . . . 92 FIGURE 3.8 BASE SHEAR VS. TIP DISPLACEMENT CURVES FOR
MULTISTORY BUILDING AT DIFFERENT LIMIT STATES ............ 93 F:IGURE 3.9 PROCEDURE TO COMPUTE letr . . . . . . . . . . . . . . . . . . . . . . . . . . 94 FIGURE 3.10 PSEUDO-DYNAMIC APPROACH . . . . . . . . . . . . . . . . . . . . . . . . . 95 F:IGURE 3.11 DEFINITION OF CENTER OF MASS ACCOUNTING FOR er . . . . . 96 FIGURE 3.12 DEFINITION OF CENTER OF MASS ACCOUNTING FOR er+eacc . . 97 F:IGURE 3.13 COLUMN SIZES ..................................... 98 FIGURE 3.14 INTERIOR BEAM SIZES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
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FIGURE 3.15 EXTERIOR BEAM SIZES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100 FIGURE 3.16 PHYSICAL INTERPRETATION OF DOF COUPLING .......... 101 FIGURE 3.17 FLOOR DISPLACEMENTS OBTAINED FROM ELASTIC RSA
ACCOUNTING FOR er ..................................... 102 FIGURE 3.18 FLOOR FORCES AT CENTER OF MASS OBTAINED FROM
ELASTIC RSA ACCOUNTING FOR er . . . . . . . . . . . . . . . . . . . . . . . . . . 103
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FIGURE 3.19 FLOOR DISPLACEMENTS OBTAINED FROM PSEUDO-DYNAMIC APPROACH (er+e8c:J . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
FIGURE 3.20 COMPARISON OF FLOOR DISPLACEMENTS WHEN "-NEGLECTING AND ACCOUNTING FOR eacc USING PSEUDO-DYNAMIC · ,. APPROACH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 05
FIGURE 3.21 IDI OBTAINED FROM PSEUDO-DYNAMIC APPROACH (er+ e8c:J .. 106 FIGURE 3.22 DYNAMIC APPROACH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 07 FIGURE 3.23 COMPARISON OF FLOOR DISPLACEMENTS OBTAINED FROM
ELASTIC RSA ACCOUNTING FOR er AND FROM ELASTIC RSA ACCOUNTING FOR er + eacc . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 08
FIGURE 3.24 COMPARISON OF FLOOR DISPLACEMENTS RATIOS OBTAINED FROM ELASTIC RSA ACCOUNTING FOR er AND FROM ELASTIC RS A ACCOUNTING FOR er AND eacc ................... .
FIGURE 3.25 COMPARISON OF STORY SHEARS OBTAINED FROM ELASTIC RSA ACCOUNTING FOR er AND FROM ELASTIC RSA ACCOUNTING FOR er + eacc ............................................. .
FIGURE 3.26 RATIO OF STORY SHEARS OBTAINED FROM ELASTIC RSA ACCOUNTING FOR er AND FROM ELASTIC RSA ACCOUNTING FOR er+eacc .................................................. .
FIGURE 3.27 STORY SHEARS OBTAINED FROM ELASTIC RSA ACCOUNTING FOR er+eacc .................... · ... · · · · · · · · · · · ·
FIGURE 3.28 RATIO OF FLOOR TORSIONAL MOMENT TO FLOOR FORCE OBTAINED FROM ELASTIC RSA ACCOUNTING FOR er+eacc ........ .
FIGURE 3.29 COMPARISON OF FLOOR DISPLACEMENTS RATIOS OBTAINED FROM THE PSEUDO-DYNAMIC AND DYNAMIC APPROACHES ........................................... .
FIGURE 3.30 COMPARISON OF FLOOR DISPLACEMENTS OBTAINED FROM THE PSEUDO-DYNAMIC AND DYNAMIC APPROACHES ............ .
FIGURE 3.31 COMPARISON OF IDI OBTAINED FROM THE PSEUDO-DYNAMIC AND DYNAMIC APPROACHES ....................... .
FIGURE 3.32 DISPLACEMENT AT CENTER OF MASS AND AVERAGE DISPLACEMENT OF FLOOR DIAPHRAGM ....................... .
FIGURE 3.33 LOCATION IN PLAN OF DIFFERENT BEAM TYPES .......... . FIGURE 3.34 LOCATION IN PLAN OF DIFFERENT COLUMN TYPES ........ . FIGURE 3.35 PERCENTAGE OF STEEL ON BEAM TYPE B1 ............. . FIGURE 3.36 PERCENTAGE OF STEEL ON BEAM TYPE B2 ............. . FIGURE 3.37 PERCENTAGE OF STEEL ON BEAM TYPE B3 ............. . FIGURE 3.38 PERCENTAGE OF STEEL ON BEAM TYPE 84 ............. . FIGURE 3.39 PERCENTAGE OF STEEL ON BEAM TYPE B5 ............. . FIGURE 3.40 PERCENTAGE OF STEEL ON BEAM TYPE B6 ............. . FIGURE 3.41 PERCENTAGE OF STEEL ON BEAM TYPE B7 ............. . FIGURE 3.42 PERCENTAGE OF STEEL ON COLUMNS TYPE C1, C2 AND C3 FIGURE 3.43 PERCENTAGE OF STEEL ON COLUMNS TYPE C4, C5 AND C6 .
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117 118 119 120 121 122 123 124 125 126 127 128
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FIGURE 3.44 PERCENTAGE OF STEEL ON COLUMNS TYPE C8,C9 AND C10 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129
FIGURE 3.45 REQUIRED VS. SUPPLIED STRENGTH ON FIRST BEAM OF FRAME B ............................................... 130
FIGURE 3.46 REQUIRED VS. SUPPLIED STRENGTH ON SECOND BEAM OF FRAME B ............................................ 131
FIGURE 3.47 REQUIRED VS. SUPPLIED STRENGTH ON THIRD BEAM OF FRAME B ............................................... 132
FIGURE 4.1 BIDIRECTIONAL INPUT CONSIDERED IN 3D ELASTIC THA . . . . 168 FIGURE 4.2 SCT-EW GROUND MOTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169 FIGURE 4.3 FLOOR DISPLACEMENTS OBTAINED FROM ELASTIC
ANALYSES FOR SERVICE WITH UNIDIRECTIONAL INPUT . . . . . . . . . 170 FIGURE 4.4 IDI OBTAINED FROM ELASTIC ANALYSES FOR SERVICE
WITH UNIDIRECTIONAL INPUT ............... : . . . . . . . . . . . . . . 171 FIGURE 4.5 STORY SHEAR DISTRIBUTION OBTAINED FROM ELASTIC
AND NONLINEAR ANALYSES FOR SERVICE WITH UNIDIRECTIONAL INPUT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172
FIGURE 4.6 MAXIMUM FLOOR STRESS RATIOS FOR SERVICE ELASTIC RSA .................................................. 173
FIGURE 4.7 DEFINITION OF STRESS RATIO IN COLUMNS . . . . . . . . . . . . . 174 FIGURE 4.8 FLOOR DISPLACEMENTS OBTAINED FROM 3D ELASTIC THA
FOR SERVICE WITH BIDIRECTIONAL INPUT .................... 175 FIGURE 4.9 IDI OBTAINED FROM 3D ELASTIC THA FOR SERVICE WITH
BIDIRECTIONAL INPUT .................................... 176 FIGURE 4.10 STORY SHEAR DISTRIBUTION OBTAINED FROM 3D
ELASTIC THA FOR SERVICE WITH BIDIRECTIONAL INPUT . . . . . . . . 177 FIGURE 4.11 FLOOR DISPLACEMENTS OBTAINED FROM ELASTIC
ANALYSES FOR SAFETY WITH UNIDIRECTIONAL INPUT . . . . . . . . . . 178 FIGURE 4.12 IDI OBTAINED FROM ELASTIC ANALYSES FOR SAFETY
WITH UNIDIRECTIONAL INPUT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179 FIGURE 4.13 STORY SHEAR DISTRIBUTION OBTAINED FROM ELASTIC
AND NONLINEAR ANALYSES FOR SAFETY WITH UNIDIRECTIONAL INPUT ................................................. 180
FIGURE 4.14 MAXIMUM FLOOR STRESS RATIOS FOR SAFETY ELASTIC RSA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181
FIGURE 4.15 MODEL USED FOR NONLINEAR 2D THA . . . . . . . . . . . . . . . . . 182 FIGURE 4.16 DRAIN 2DX ELASTOPLASTIC MODEL FOR HYSTERETIC
BEHAVIOR OF RC MEMBERS ............................... 183 FIGURE 4.17 DRAIN 2DX YIELD INTERACTION SURFACE FOR RC
·COLUMNS .............................................. 183 FIGURE 4.18 DEFINITION OF CUMULATIVE PLASTIC DEFORMATIONS . . . . 184 FIGURE 4.19 BASE SHEAR VS. TIP DISPLACEMENT CURVE OBTAINED
FROM PUSHOVER ANALYSIS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185
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FIGURE 4.20 COMPARISON OF IDI DISTRIBUTION THROUGH HEIGHT OBTAINED USING DIFFERENT SECANT STIFFNESSES . . . . . . . . . . . 186
FIGURE 4.21 a FLOOR DISPLACEMENTS OBTAINED FROM PUSHOVER ANALYSES FOR DIFFERENT TIP DISPLACEMENTS . . . . . . . . . . . . . . 187
FIGURE 4.21 b FLOOR DISPLACEMENTS OBTAINED FROM PUSHOVER ANALYSES FOR DIFFERENT TIP DISPLACEMENTS . . . . . . . . . . . . . . 188
FIGURE 4.22a IDI OBTAINED FROM PUSHOVER ANALYSIS FOR DIFFERENT TIP DISPLACEMENTS ........................... 189
FIGURE 4.22b IDI OBTAINED FROM PUSHOVER ANALYSIS FOR DIFFERENT TIP DISPLACEMENTS . . . . . . . . . . . . . . . . . . . . . . . . . . . 190
FIGURE 4.23 MAXIMUM ROTATIONS OBTAINED FROM PUSHOVER ANALYSIS .............................................. 191
FIGURE 4.24 DIFFERENT STATES OF 30-STORY BUILDING COMPARED IN FIGURES 4.21 AND 4.22 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192
FIGURE 4.25 DISTRIBUTION OF PLASTIC HINGES IN PUSHOVER ANALYSIS FOR L\ = 0.30 m . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193
FIGURE 4.26 DISTRIBUTION OF PLASTIC HINGES IN PUSHOVER ANALYSIS FOR L\ = 0.45 m ......................................... 194
FIGURE 4.27 DISTRIBUTION OF PLASTIC HINGES IN PUSHOVER ANALYSIS FOR L\ = 0.60 m . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 195
FIGURE 4.28 DISTRIBUTION OF PLASTIC HINGES IN PUSHOVER ANALYSIS FOR L\ = 0.90 m .......................................... 196
FIGURE 4.29 DISTRIBUTION OF PLASTIC HINGES IN PUSHOVER ANALYSIS FOR L\ = 1 .20 m . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197
FIGURE 4.30 DISTRIBUTION OF PLASTIC HINGES IN PUSHOVER ANALYSIS FOR L\ = 1 .275 m . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 198
FIGURE 4.31 DISTRIBUTION OF PLASTIC HINGES IN PUSHOVER ANALYSIS FOR L\ = 1.35 m .......................................... 199
FIGURE 4.32 TIME HISTORY OF BASE SHEAR FOR 2D NONLINEAR THA FOR SERVICE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 200
FIGURE 4.33 TIME HISTORY OF TIP DISPLACEMENT FOR 2D NONLINEAR THA FOR SERVICE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 200
FIGURE 4.34 ENVELOPES OF FLOOR DISPLACEMENTS FROM 2D NONLINEAR THA FOR SERVICE ............................. 201
FIGURE 4.35 ENVELOPES OF IDI FROM 2D NONLINEAR THA FOR SERVICE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202
FIGURE 4.36 COMPARISON OF IDI FROM PUSHOVER ANALYSIS AND 2D NONLINEAR THA FOR SERVICE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203
FIGURE 4.37 MAXIMUM ROTATION ON A MEMBER OF A STORY FROM 2D NONLINEAR THA FOR SERVICE . . . . . . . . . . . . . . . . . . . . . . . . . . 204
FIGURE 4.38 DISTRIBUTION OF MAXIMUM ROTATION FROM 2D NONLINEAR THA FOR SERVICE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 205
FIGURE 4.39 MAXIMUM CUMULATIVE PLASTIC ROTATION ON A MEMBER OF A STORY FROM 2D NONLINEAR THA FOR SERVICE . . . . . . . . . . 206
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FIGURE 4.40 DISTRIBUTION OF CUMULATIVE PLASTIC ROTATIONS FROM 2D NONLINEAR THA FOR SERVICE ..................... 207
FIGURE 4.41 DISTRIBUTION OF DAMAGE INDEX FROM 2D NONLINEAR THA FOR SERVICE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 208
FIGURE 4.42 TIME HISTORY OF BASE SHEAR FOR 2D NONLINEAR THA FOR SAFETY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 209
FIGURE 4.43 TIME HISTORY OF TIP DISPLACEMENT FOR 2D NONLINEAR THA FOR SAFETY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 209
FIGURE 4.44 ENVELOPES OF FLOOR DISPLACEMENTS FROM 2D NONLINEAR THA FOR SAFETY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 210
FIGURE 4.45 ENVELOPES OF IDI FROM 2D NONLINEAR THA FOR SAFETY ................................................ 211
FIGURE 4.46 IDI VS. STORY SHEAR RELATIONSHIP FOR 7TH STORY OBTAINED FROM PUSHOVER ANALYSIS ...................... 212
FIGURE 4.47 COMPARISON OF IDI FROM PUSHOVER ANALYSIS AND 2D NONLINEAR THA FOR SAFETY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213
FIGURE 4.48 MAXIMUM ROTATION ON A MEMBER OF A STORY FROM 2D NONLINEAR THA FOR SAFETY . . . . . . . . . . . . . . . . . . . . . . . . . . . 214
FIGURE 4.49 DISTRIBUTION OF MAXIMUM ROTATIONS FROM 2D NONLINEAR THA FOR SAFETY ....................................... 215
FIGURE 4.50 MAGNITUDE OF ROTATIONS OF COLUMNS AS COMPARED TO ROTATIONS ON BEAMS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 216
FIGURE 4.51 MAXIMUM CUMULATIVE PLASTIC ROTATION ON A MEMBER OF A STORY FROM 2D NONLINEAR THA FOR SAFETY . . . . . . . . . . . 217
FIGURE 4.52 DISTRIBUTION OF CUMULATIVE PLASTIC ROTATIONS FROM NONLINEAR THA FOR SAFETY .............................. 218
FIGURE 4.53 DISTRIBUTION OF DAMAGE INDEX FROM 2D NONLINEAR THA FOR SAFETY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219
FIGURE 5.1 MODEL USED FOR SIMPLIFIED ANALYSIS OF 30-STORY BUILDING . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 242
FIGURE 5.2 BEAM MOMENT ENVELOPES FOR ANALYSIS NEGLECTING AXIAL DEFORMATION OF THE COLUMNS . . . . . . . . . . . . . . . . . . . . . . 243
FIGURE 5.3 BEAM MOMENT ENVELOPES FOR ANALYSIS ACCOUNTING AXIAL DEFORMATION OF THE COLUMNS . . . . . . . . . . . . . . . . . . . . . . 244
FIGURE 5.4 BEAM GRAVITY MOMENTS FOR ANALYSIS NEGLECTING AXIAL DEFORMATION OF THE COLUMNS . . . . . . . . . . . . . . . . . . . . . . 245
FIGURE 5.5 BEAM GRAVITY MOMENTS FOR ANALYSIS ACCOUNTING FOR AXIAL DEFORMATION OF THE COLUMNS . . . . . . . . . . . . . . . . . . 246
FIGURE 5.6 MOMENTS IN BEAMS DUE TO DIFFERENTIAL AXIAL DEFORMATION IN NEIGHBORING COLUMNS . . . . . . . . . . . . . . . . . . . 247
FIGURE 5.7 BEAM MOMENTS DUE TO LATERAL LOADS FOR ANALYSIS NEGLECTING AXIAL DEFORMATION OF THE COLUMNS . . . . . . . . . . 248
FIGURE 5.8 BEAM MOMENTS DUE TO LATERAL LOADS FOR ANALYSIS ACCOUNTING FOR AXIAL DEFORMATION OF THE COLUMNS . . . . . . 249
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FIGURE 5.9 AXIAL FORCES IN COLUMNS DUE TO LATERAL LOADS FOR ANALYSIS NEGLECTING AXIAL DEFORMATION OF THE COLUMNS . . 250
FIGURE 5.10 AXIAL FORCES IN COLUMNS DUE TO LATERAL LOADS FOR ANALYSIS ACCOUNTING AXIAL DEFORMATION OF THE COLUMNS 250
FIGURE 5.11 FREE BODY OF FIRST FLOOR OBTAINED FROM ANALYSIS NEGLECTING AXIAL DEFORMATION OF THE COLUMNS . . . . . . . . . . 251
FIGURE 5.12 FREE BODY OF FIFTH FLOOR OBTAINED FROM ANALYSIS NEGLECTING AXIAL DEFORMATION OF THE COLUMNS .......... 251
FIGURE 5.13 FREE BODY OF TENTH FLOOR OBTAINED FROM ANALYSIS NEGLECTING AXIAL DEFORMATION OF THE COLUMNS . . . . . . . . . . 252
FIGURE 5.14 FREE BODY OF FIFTEENTH FLOOR OBTAINED FROM ANALYSIS NEGLECTING AXIAL DEFORMATION OF THE COLUMNS . . 252
FIGURE 5.15 FREE BODY OF FIRST FLOOR OBTAINED FROM ANALYSIS ACCOUNTING FOR AXIAL DEFORMATION OF THE COLUMNS . . . . . . 253
FIGURE 5.16 FREE BODY OF FIFTH FLOOR OBTAINED FROM ANALYSIS ACCOUNTING FOR AXIAL DEFORMATION OF THE COLUMNS . . . . . . 253
FIGURE 5.17 FREE BODY OF TENTH FLOOR OBTAINED FROM ANALYSIS ACCOUNTING FOR AXIAL DEFORMATION OF THE COLUMNS . . . . . . 254
FIGURE 5.18 FREE BODY OF FIFTEENTH FLOOR OBTAINED FROM ANALYSIS ACCOUNTING FOR AXIAL DEFORMATION OF THE COLUMNS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 254
FIGURE 5.19 APPROXIMATE METHOD TO ESTIMATE THE MOMENT AT THE LEFT END OF THE BEAM ON LOCATED ON THE THIRD BAY . . . 255
FIGURE 5.20 EFFECT OF PERPENDICULAR BEAMS . . . . . . . . . . . . . . . . . . 255 FIGURE 5.21 SECOND MODEL USED FOR SIMPLIFIED ANALYSIS OF 30-
STORY BUILDING . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 256 FIGURE 5.22 EFFECT OF 2D MODELLING ON MAGNITUDE OF THE
MOMENT AT THE LEFT END OF THE BEAMS LOCATED IN THE THIRD BAY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 257
FIGURE 5.23 REDUCTION OF MOMENT DUE TO 2D MODELLING . . . . . . . . 258 FIGURE 5.24 EVOLUTION OF THE MOMENT AT THE LEFT END OF THE
BEAMS LOCATED IN THE THIRD BAY ACCORDING TO PUSHOVER ANALYSIS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 259
FIGURE 5.25 REDUCTION OF THE MOMENT AT THE LEFT END OF THE BEAMS LOCATED IN THE THIRD BAY ACCORDING TO PUSHOVER ANALYSIS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 260
FIGURE 5.26 EVOLUTION OF THE MOMENT AT THE RIGHT END OF THE BEAMS LOCATED IN THE THIRD BAY ACCORDING TO PUSHOVER ANALYSIS .............................................. 261
FIGURE 5.27 REDUCTION OF THE MOMENT AT THE RIGHT END OF THE BEAMS LOCATED IN THE THIRD BAY ACCORDING TO PUSHOVER ANALYSIS .............................................. 262
FIGURE 5.28 EFFECT OF P-~ ON TIME HISTORY OF BASE SHEAR FOR SAFETY ............................................... 263
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FIGURE 5.29 EFFECT OF P-d ON TIME HISTORY OF TIP DISPLACEMENT FOR SAFETY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 263
FIGURE 5.30 EFFECT OF P-d ON STORY SHEARS FOR SAFETY . . . . . . . . 264 FIGURE 5.31 EFFECT OF P-d ON IDI FOR SAFETY . . . . . . . . . . . . . . . . . . . 265 FIGURE 5.32 ACCELERATION SPECTRA OBTAINED FOR SCT-EW (; =
0.05) .................................................. 266 FIGURE 5.33 REDUCTION OF ACCELERATION FOR INELASTIC
RESPONSE ON SDOFS SUBJECTED TO SCT-EW (; = 0.05) . . . . . . . . 267 FIGURE 5.34 INELASTIC/ELASTIC DISPLACEMENT RATIOS FOR SDOFS . 268 FIGURE 5.35 TORSIONAL EFFECTS ON STORY DISPLACEMENTS . . . . . . . 269 FIGURE 5.36 COMPARISON OF MAXIMUM ROTATIONS OBTAINED FOR
THA FOR SAFETY VS. SUPPLIED ROTATIONAL CAPACITY ........ 270 FIGURE 6.1 SCHEMATIC STRENGTH AND DISPLACEMENT DEMAND
SPECTRA FOR EQGM RECORDED IN SOFT SOIL . . . . . . . . . . . . . . . 310 FIGURE 6.2 CHANGE IN DISPLACEMENT DEMAND DUE TO REDUCTION
OFT FOR EQGM RECORDED IN SOFT SOIL . . . . . . . . . . . . . . . . . . . . 311 FIGURE 6.3 EFFECT OF DAMPING ON LINEAR ELASTIC RESPONSE FOR
EQGM RECORDED IN SOFT SOIL . . . . . . . . . . . . . . . . . . . . . . . . . . . 312 FIGURE 6.4 PREDOMINANT GROUND PERIOD FOR VARIOUS SOFT SOIL
SITES ................................................. 313 FIGURE 6.5 COMPARISON OF RESPONSE OF SDOFSs WITH T OF 1.7
AND 2.53 SECS .......................................... 314 FIGURE 6.6 SIZES OF BEAMS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 315 FIGURE 6.7 SIZES OF COLUMNS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 316 FIGURE 6.8 STORY SHEAR VS. STORY DRIFT CURVES OBTAINED FROM
PUSHOVER ANALYSIS OF JAPANESE DESIGN ................. 317 FIGURE 6.9 BASE SHEAR VS. TIP DISPLACEMENT CURVES OBTAINED
FROM PUSHOVER ANALYSES OF CONCEPTUAL AND UBC DESIGN . 318 FIGURE 6.10 IDI FOR JAPANESE DESIGN CORRESPONDING TO THE
FIRST LEVEL OF DESIGN EARTHQUAKE FORCES ............... 319 FIGURE 6.11 IDI FROM PUSHOVER ANALYSES OF CONCEPTUAL AND
UBC DESIGN . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 320 FIGURE 6.12 STRENGTH AND DISPLACEMENT SPECTRA FOR SCT-EW
EQGM SCALED TO PGA OF 0.3G (; = 0.05) . . . . . . . . . . . . . . . . . . . . . 321 FIGURE 6.13 STRENGTH AND DISPLACEMENT SPECTRA FOR SENDAI
EW EQGM SCALED TO MAXIMUM ACCELERATION OF 0.4G (; = 0.03) .................................................. 322
FIGURE 6.14 ENVELOPE OF FLOOR DISPLACEMENTS FROM THA OF JAPANESE DESIGN (MAXIMUM ACCELERATION 0.4G) . . . . . . . . . . . . 323
FIGURE 6.15 ENVELOPE OF IDI FROM THA OF JAPANESE DESIGN (MAXIMUM ACCELERATION 0.4G) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 324
FIGURE 6.16 ENVELOPE OF STORY SHEARS FROM THA OF JAPANESE DESIGN (MAXIMUM ACCELERATION 0.4G) ..................... 325
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. .-··.
FIGURE 6.17 FLOOR DISPLACEMENTS FROM ELASTIC RSA FOR SERVICE (CONCEPTUAL DESIGN) . . . . . . . . . . . . . . . . . . . . . . . . . . . 326
FIGURE 6.18 IDI FROM ELASTIC RSA FOR SERVICE (CONCEPTUAL DESIGN) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 327
FIGURE 6.19 STRESS RATIOS FROM ELASTIC RSA FOR SERVICE (CONCEPTUAL DESIGN) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 328
FIGURE 6.20 FLOOR DISPLACEMENTS OBTAINED FROM ELASTIC ANALYSES FOR SERVICE (UBC DESIGN) . . . . . . . . . . . . . . . . . . . . . . 329
FIGURE 6.21 IDI OBTAINED FROM ELASTIC ANALYSES FOR SERVICE (UBC DESIGN) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 330
FIGURE 6.22 STORY SHEARS OBTAINED FROM ELASTIC ANALYSES FOR SERVICE (UBC DESIGN) ................................... 331
FIGURE 6.23 STRESS RATIOS OBTAINED FROM ELASTIC ANALYSES FOR SERVICE (UBC DESIGN) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 332
FIGURE 6.24 ENVELOPE OF FLOOR DISPLACEMENTS FROM 2D NONLINEAR THA FOR SERVICE (UBC DESIGN) . . . . . . . . . . . . . . . . . 333
FIGURE 6.25 ENVELOPE OF IDI FROM 2D NONLINEAR THA FOR SERVICE (UBC DESIGN) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 334
FIGURE 6.26 MAXIMUM PLASTIC ROTATIONS FROM 2D NONLINEAR THA FOR SERVICE (UBC DESIGN) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 335
FIGURE 6.27 CUMULATIVE PLASTIC ROTATIONS FROM 2D NONLINEAR THA FOR SERVICE (UBC DESIGN) . . . . . . . . . . . . . . . . . . . . . . . . . . . 336
FIGURE 6.28 ENVELOPE OF FLOOR DISPLACEMENTS FROM 3D ELASTIC THA FOR SERVICE (UBC DESIGN) . . . . . . . . . . . . . . . . . . . . . . . . . . . 337
FIGURE 6.29 ENVELOPE OF IDI FROM 3D ELASTIC THA FOR SERVICE (UBC DESIGN) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 338
FIGURE 6.30 ENVELOPE OF STORY SHEARS FROM 3D ELASTIC THA FOR SERVICE (UBC DESIGN) ............................... 339
FIGURE 6.31 ENVELOPE OF FLOOR DISPLACEMENTS FROM 2D NONLINEAR THA FOR SAFETY (CONCEPTUAL AND UBC DESIGNS) . 340
FIGURE 6.32 ENVELOPE OF IDI FROM 2D NONLINEAR THA FOR SAFETY (CONCEPTUAL AND UBC DESIGNS) . . . . . . . . . . . . . . . . . . . . . . . . . . 341
FIGURE 6.33 PLASTIC ROTATIONS IN BEAMS FROM 2D NONLINEAR THA FOR SAFETY (CONCEPTUAL AND UBC DESIGNS) . . . . . . . . . . . . . . . 342
FIGURE 6.34 PLASTIC ROTATIONS IN COLUMNS FROM 2D NONLINEAR THA FOR SAFETY (CONCEPTUAL AND UBC DESIGNS) . . . . . . . . . . . 343
FIGURE 6.35 ROTATIONS IN BEAMS AND COLUMNS OF UBC DESIGN . . . . 344 FIGURE 6.36 STRENGTH AND DISPLACEMENT SPECTRA FOR
EMERYVILLE 260 EQGM, SOUTH STATION (; = 0.05) . . . . . . . . . . . . . 345 FIGURE 6.37 STRENGTH AND DISPLACEMENT SPECTRA FOR FOSTER
CITY EQGM (; = 0.05) ..................................... 346
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FIGURE 6.17 FLOOR DISPLACEMENTS FROM ELASTIC RSA FOR SERVICE (CONCEPTUAL DESIGN) ........................... 326
FIGURE 6.18 IDI FROM ELASTIC RSA FOR SERVICE (CONCEPTUAL DESIGN) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 327
FIGURE 6.19 STRESS RATIOS FROM ELASTIC RSA FOR SERVICE (CONCEPTUAL DESIGN) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 328
FIGURE 6.20 FLOOR DISPLACEMENTS OBTAINED FROM ELASTIC ANALYSES FOR SERVICE (UBC DESIGN) . . . . . . . . . . . . . . . . . . . . . . 329
FIGURE 6.21 IDI OBTAINED FROM ELASTIC ANALYSES FOR SERVICE (UBC DESIGN) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 330
FIGURE 6.22 STORY SHEARS OBTAINED FROM ELASTIC ANALYSES FOR SERVICE (UBC DESIGN) ................................... 331
FIGURE 6.23 STRESS RATIOS OBTAINED FROM ELASTIC ANALYSES FOR SERVICE (UBC DESIGN) ............................... 332
FIGURE 6.24 ENVELOPE OF FLOOR DISPLACEMENTS FROM 2D NONLINEAR THA FOR SERVICE (UBC DESIGN) . . . . . . . . . . . . . . . . . 333
FIGURE 6.25 ENVELOPE OF IDI FROM 2D NONLINEAR THA FOR SERVICE (UBC DESIGN) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 334
FIGURE 6.26 MAXIMUM PLASTIC ROTATIONS FROM 2D NONLINEAR THA FOR SERVICE (UBC DESIGN) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 335
FIGURE 6.27 CUMULATIVE PLASTIC ROTATIONS FROM 2D NONLINEAR THA FOR SERVICE (UBC DESIGN) . . . . . . . . . . . . . . . . . . . . . . . . . . . 336
FIGURE 6.28 ENVELOPE OF FLOOR DISPLACEMENTS FROM 3D ELASTIC THA FOR SERVICE (UBC DESIGN) . . . . . . . . . . . . . . . . . . . . . . . . . . . 337
FIGURE 6.29 ENVELOPE OF IDI FROM 3D ELASTIC THA FOR SERVICE (UBC DESIGN) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 338
FIGURE 6.30 ENVELOPE OF STORY SHEARS FROM 3D ELASTIC THA FOR SERVICE (UBC DESIGN) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 339
FIGURE 6.31 ENVELOPE OF FLOOR DISPLACEMENTS FROM 2D NONLINEAR THA FOR SAFETY (CONCEPTUAL AND UBC DESIGNS) . 340
FIGURE 6.32 ENVELOPE OF IDI FROM 2D NONLINEAR THA FOR SAFETY (CONCEPTUAL AND UBC DESIGNS) . . . . . . . . . . . . . . . . . . . . . . . . . . 341
FIGURE 6.33 PLASTIC ROTATIONS IN BEAMS FROM 2D NONLINEAR THA FOR SAFETY (CONCEPTUAL AND UBC DESIGNS) . . . . . . . . . . . . . . . 342
FIGURE 6.34 PLASTIC ROTATIONS IN COLUMNS FROM 2D NONLINEAR THA FOR SAFETY (CONCEPTUAL AND UBC DESIGNS) . . . . . . . . . . . 343
FIGURE 6.35 ROTATIONS IN BEAMS AND COLUMNS OF UBC DESIGN . . . . 344 FIGURE 6.36 STRENGTH AND DISPLACEMENT SPECTRA FOR
EMERYVILLE 260 EQGM, SOUTH STATION (; = 0.05) . . . . . . . . . . . . . 345 FIGURE 6.37 STRENGTH AND DISPLACEMENT SPECTRA FOR FOSTER
CITY EQGM (s = 0.05) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 346
xiv
SYMBOLS AND NOTATIONS
20 =two-dimensional 30 = three-dimensional b = width of beam C8 = combined height, exposure and gust factor coefficient Cq = pressure coefficient C = base shear coefficient d = effective depth of RC member DOF = degree of freedom OM I = damage index er = real eccentricity eacc = accidental eccentricity E = modulus of elasticity EH = hysteretic energy EQ = earthquake EQRD = earthquake resistant design EQGM = earthquake ground motion f~ = compressive strength of concrete fy = yield strength of reinforcement F1 = force in ith story Ft = force in top story h = total depth of slab or beam he = total height of a column H = total height of a. building I = importance factor lb = moment of inertia of a beam lc = moment of inertia of a column I 01 = interstory drift index 18 =effective moment of inertia on a cross section of the beam lett=. moment of inertia of aRC beam accounting for flexural cracking 19 = moment of inertia of the gross section ~ = secant stiffness IP = length of plastic hinge on RC member L = total span of a beam NYR = number of yield reversals M = moment at end of column or beam OVS = overstrength P = design wind pressure or axial force in column PGA = peak ground acceleration q5 = wind stagnation pressure at standard height RC = reinforced concrete RSA = response spectrum analysis Rw = lateral force reduction factor. This value accounts for reduction of lateral
xvi
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forces due to fnelastic behavior and overstrength of the structure. S =site coefficients for soil characteristics . SDOFS = single degree of freedom system SEAOC = Structural Engineers Association of California SMRSF =special moment resisting space frame T = fundamental period of translation of a building in seconds T R = return period of an earthquake ground motion T
9 = predominant period of the soil
THA = time history analysis UBC = 1991 version of Uniform Building Code V b = base shear or shear force on a beam Vc = shear force on a column V1 =shear on ith story V oYN = base shear obtained by a RSA V5r =base shear obtained by UBC simplified static approach w1 = weight of ith story W = total weight of a building or USC seismic dead load Z = seismic zone factor. This value corresponds to the expected PEAK GROUND
ACCELERATION. B = parameter used to compute damage index bu = ultimate deformation a system can undergo under monotonic lateral
load bv = deformation of a system at yield ~ = top floor displacement e or emax =largest value between positive and negative plastic hinge rotation eacc = cumulative plastic rotation eP = plastic hinge rotation eu = ultimate rotational capacity of RC member under monotonic loading t-t = global displacement ductility ratio t-ta = cumulative ductility ratio J.lioca1 = RC member rotational ductility ratio J.lstorv = story displacement ductility ratio J.ltar = design target ductility ; = percent of critical viscous damping p :; ratio of tension reinforcement pb = balance ratio of tension reinforcement Pmax = maximum ratio of tension reinforcement <p = RC beam curvature
xvii
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1. INTRODUCTION
1.1 STATEMENT OF THE PROBLEM
In recent years, due to the high cost of land in big cities and other problems such as
those related to the extension of services, modern high-rise buildings are not only being
constructed in cities located in regions of high seismicity, but several of them have been
constructed on soft soil sites at these cities (Mexico City, San Francisco Bay Area, etc.).
Unfortunately, the significant advances that have been made in the technology of
construction of tall buildings have not been followed by studies that aim at understanding
tall building behavior, particularly considering their interaction with the soil when subjected
to intense ground mo~ion. There are several issues that need to be addressed to obtain
rational and sound designs of tall buildings in seismic zones, among which the following
can be mentioned: first, current seismic regulations, i.e., the 1991 Uniform Building Code
(UBC) [Ref. 1], pay very little attention to specific problems encountered in the design of
tall buildings subjected to intense ground motion; and second, given their high
slenderness ratios, tall buildings tend to have long periods that in several cases come
close to the predominant period of soft soils, so that large dynamic amplification of their
static elastic response can be expected due to engineering resonance. In view of these
problems, it was decided that it would be worthwhile to conduct a series of studies on the
design of tall reinforced concrete (RC) buildings to be built on deep soft soils. The main
purpose of this series of studies [Refs. 2, 3, 4, 5] was to provide information to help the
designer accomplish better designs of tall buildings on soft soil zones. To achieve this
purpose, it was decided that all these studies should be integrated and that attempts
should be made to try to design and compare the seismic performance of the same
building using different design methods:
• UBC Design: the building was designed according to current earthquake resistant
design (EQRD) provisions (1991 UBC). A series of linear and nonlinear analyses of the
behavior of the designed building were conducted to assess the adequacy of the obtained
~ design. The most important results obtained are evaluated, and a critical discussion of
the weaknesses and advantages of the UBC design is offered. Finally, main conclusions
1
are drawn and recommendations to improve code design procedures are offered.
Japanese Design: a second design of a building with exactly the same configuration
is available, and its seismic performance is summarized in Ref. 6.
Conceptual Design: a third design of a building with exactly the same configuration
was carried out by Bertero R.D. and Bertero V.V. using a conceptual design methodology
[Ref. 3].
Buildings with the same configuration were designed according to different philosophies
and practices for the purpose of assessing, by comparing the seismic performance of the
three designs, what design recommendations and what design philosophy should be
adopted for the adequate design of a tall building on soft soil. Thu~, the results reported
here are just part of a larger set of results, and their usefulness is considerably increased
when they are considered simultaneously with those reported elsewhere [Refs. 2, 3, 4,
5, 6]. An attempt is made in this report to compare and judge the designs obtained using
present code procedures in Japan and the U.S., and those developed for the conceptual
methodology.
1.2 OBJECTIVES
The ultimate goal of the studies reported herein is to assess the adequacy of UBC
methodology for EQRD of tall buildings on soft soil. To accomplish this goal, a series of
studies were conducted with the following objectives: to select a tall RC building whose
site is on the shores of the San Francisco Bay with deep soft soil; to design such building
according to current American design practice (1991 UBC); to assess the adequacy of
the design according to the general philosophy of EQRD that has been accepted
worldwide; and finally, to draw conclusions and offer recommendations for•improving
current design practices for such buildings.
1.3 SCOPE
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To achieve the above objectives, a 30-story RC building with identical configuration, r'
structural system and structural layout as those of a building that has been designed and
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built in Japan [Ref. 6] was selected. The 30-story building, located on the shores of the
San Francisco Bay, is constituted by a three-dimensional assemblage of RC special
moment-resisting frames. The following studies were conducted.
In Chapter 2, a description of the function, configuration, structural system, and
structural layout of the selected building is given. In this chapter, some of the general
requirements for the design of the 30-story building according to UBC are presented,
together with the methods used for the preliminary design of the 30-story building. Finally
the sizes of the members obtained from the preliminary design of the building are
summarized.
A detailed discussion and interpretation of some UBC design guidelines is presented
in Chapter 3. In this chapter, the design procedure for obtaining the final design from the
preliminary design is presented, as well as a summary of the member sizes and
reinforcement for the final design of the 30-story building. Some considerations about the
way accidental torsion is accounted for in the UBC specifications are presented.
The behavior of the designed 30-story building subjected to different ground motion
input was studied in Chapter 4. The results of elastic response spectra analyses for
service and safety limit states, as well as those of elastic and nonlinear time-history
analyses for service and safety that were carried out on the designed building are
presented. These analyses provide information on which the assessment of the adequacy
of UBC specifications and design methodology in the design of the 30-story building can
be based. In Chapter 4, the performance of the 30-story building is only judged as good
_,,_ or bad according to whether or not its behavior satisfies the current criteria for
earthquake-resistant design. Discussion of the possible reasons for the behavior of the
building is presented in Chapter 5.
Chapter 5 provides information that complements that presented in Chapter 4. Mainly,
additional elastic analyses of the 30-story building were carried out to complete the
3
information on which the assessment of the behavior of the building can be based. Once
the information regarding the behavior of the building has been completed, an · l
assessment of the seismic performance of the building is made. '
Finally, Chapter 6 summarizes some of the most important issues discussed in this
report and presents a critical discussion of some UBC earthquake-resistant design
provisions that could lead to unsatisfactory earthquake-resistant design of tall buildings
located in soft soil areas. This chapter ends with the main conclusions drawn from the
results of the studies conducted and with the formulation of recommendations for
improving present EQRD code procedures and for the needed research to achieve such
improvements.
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2. THE 30-STORY BUILDING AND ITS PRELIMINARY DESIGN
2.1 GENERAL REMARKS
In this chapter, general information regarding the site and the 30-story building is
presented. That is, the function, structural system, structural layout, structural material,
and non-structural components and contents of the 30-story building are presented. The
ways in which these characteristics of the building affect its design under UBC 1991
requirements is discussed. Also, the location of the construction site and the
characteristics of the soil at the site are discussed.
/
The procedure, design considerations and assumptions made and used to obtain an
acceptable preliminary design of the building are presented. For the preliminary design
phase, drift control as well as strength requirements were considered. A summary of the
member sizes at the end of this preliminary design phase is presented.
Important note: In this report the European (and Japanese) terminology for
numbering floors was used. The first floor in the above terminology corresponds
to the second floor in American terminology, etc.
2.2 UBC EARTHQUAKE-RESISTANT DESIGN PHILOSOPHY AND PROCEDURES
The best way to introduce UBC philosophy of design is by quoting the Tentative
Commentary to Recommended Lateral Force Requirements, 1988 edition (SEAOC
Commentary) [Ref. 7]. In Chapter 1, SEAOC Commentary states the following:
The primary function of these recommendations is to provide minimum
standards for use in building design regulation to maintain public safety in
extreme earthquakes likely to occur at the building's site. The SEAOC
recommendations primarilv are intended to safeguard against major failures
and loss of life, not to limit damage, maintain functions, or provide easv
repair. It is emphasized that the purpose of these recommended design
procedures is to provide buildings that are expected to meet this life safety
5
objective.
The procedures presented herein are based on many assumptions of
performance and utilize elastic analysis procedures ...
.. . Structures designed in conformance with these recommendations should,
in general, be able to:
1. Resist minor levels of earthquake ground motion without damage;
2. Resist moderate levels of earthquake ground motion without structural
damage, but possibly experience some nonstructural damage;
3. Resist major levels of earthquake ground motion having an intensity
equal to the strongest either experienced or forecast for the building site,
without collapse, but possibly with some structural as well as nonstructural
damage.
As shown above, UBC design philosophy coincides with the accepted world-wide
philosophy for EQRD. Before continuing this report, it is emphasized that UBC considers,
for the performance of buildings, three levels of earthquake ground motion. The first one
is associated with frequent minor levels of earthquake ground motion, and the
performance of the structure is considered adequate only if the structure does not suffer
damage (structural or nonstructural). In this report, such ground motion is denoted as
allowable stress ground motion, and the behavior of the building subjected to this
ground motion is the performance of the building at allowable stress limit state. The
second level of ground motion is associated with moderate levels of earthquake ground
motion, which can occur occasionally, and the performance of the structure is considered
acceptable if the structure has no structural damage, although some nonstructural
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damage is considered acceptable. In this report, such ground motion is denoted as first ·,
yield ground motion, and to the behavior of the building subjected to this ground motion
as the performance of the building at first yield limit state. Finally, the third level of
ground motion is associated with very intense earthquake ground motions, and the
performance of the structure is considered satisfactory if, in spite of structural as well as
6
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nonstructural damage, the structure can resist the ground motion without collapse. In this
report, such ground motion is denoted as safety ground motion, and the behavior of the
building subjected to this ground motion is the performance of the building at safety or
ultimate limit state.
In this report, the service limit state is limited by the first significant yielding of the
members of the structure, and the performance of the structure is considered acceptable
if the building has no structural damage. Thus the definition of the service limit state is
similar to that corresponding to first yield limit state. UBC specifications require
serviceability conditions (drift control) to be satisfied at allowable stress limit state. In this
report, the serviceability conditions need to be met at the service limit state, and thus it
is necessary to define appropriate serviceability conditions for UBC service limit state. For
this purpose, the drift conditions given by UBC for allowable stress limit state are
multiplied by the appropriate load factor to obtain the drift conditions corresponding to
UBC service limit state (as discussed in detail in Chapter 3, the ratio between strength
at first significant yield and strength at allowable stress due to lateral forces is 1.4 for RC
structures).
Continuation of Chapter 1 of SEAOC Commentary:
The SEAOC Recommendations provide minimum design criteria in
specific categories stated in broad general terms. It is the responsibility of
the structural engineer to interpret and adapt these basic principles to each
structure using experience and good judgement ...
... Where damage control is desired, the design must not only provide
sufficient strength to resist the specified seismic loads but also
provide the proper stiffness and rigidity. The control of damage is very
complex. Some elements are sensitive to acceleration, making floor
acceleration the key design consideration, while others are sensitive to
7
inters tory distortions, making drift the key design consideration ...
... It must be recognized that major earthquake ground motion can
cause interstory deformations several times larger than those
calculated with the seismic design loads given in these
recommendations.
From the above quotations, it can be concluded that designing a building according to
UBC specifications should result in a building with enough stiffness and strength to avoid
structural and non-structural damage when subjected to allowable stress ground motions,
with enough strength to avoid structural damage during first yield ground motions, and
with enough strength to survive a safety ground motion. In UBC specifications, stiffness
of the structure should be provided in such a way that the drift requirements specified for
the allowable stress limit state are met. Although there are other specifications related to . the maximum. displacement the structure can undergo at the safety limit state (the
structure should be stable up to story drifts obtained by multiplying the story drifts for
allowable stress limit state by 3Aw I 8), these specifications can not guarantee satisfactory
drift control when the structure is subjected to moderate or severe ground motions (i.e.,
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those which can be associated with service or safety limit states). Also, as clearly stated , 1
in the commentary, no assurance or guarantee is made about the amount or severity of
damage during intense ground motions.
Figure 2.1 summarizes in a simplified manner UBC design methodology for earthquake
resistant design of RC special moment-resisting space frames (SMRSF).
2.2 GIVEN INFORMATION
The design of the 30-story building is based on the following information.
Function. The building is an apartment building, and therefore can be classified as a
standard occupancy structure, which, according to table 23-K of UBC [Ref. 1], has a
standard occupancy category (IV). According to table 23-L [Ref. 1], this structure has an
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importance factor, I, equal to 1, for earthquake as well as for wind loading.
Site. The building is located in the San Francisco Bay Area, which, according to figure
23-2 [Ref. 1], corresponds to seismic zone 4. The seismic zone factor, Z, has a value of
0.40 according to table 23-1 [Ref. 1]. Figure 2.2 shows the location of the building within
the United States of America and within the San Francisco Bay Area.
Soli. The soil in this location can be classified, according to table 23-J [Ref. 1], as soil
type S4; that is, a soil profile containing more than 40 feet of soft clay characterized by
a shear wave velocity of less than 500 ft per second (for further discussion on this issue,
see section 3.1 ). For this type of soil, UBC specifies a value of site coefficient, S, equal
to 2.0. Figure 2.3 shows a map that summarizes the geotechnical conditions of the San
Francisco Bay Area.
Structural System. A RC special moment-resisting frame system is used to carry
gravity as well as lateral loads. According to table 23-0 [Ref. 1], Rw has a value of 12.
Structural Layout. The layout is the same as that of a building designed and built
in Japan. Basically, beam spans are 4.8 m and 5.3 m, with a story height of 2.85 m
(except for the first story, which has a height of 4.50 m). Figures 2.4 and 2.5 show plan
and elevation views of the Japanese building [Ref. 6].
Regularity Conditions. According to the requirements specified in tables 23-M and
23-N [Ref. 1], this building can be considered to be a regular structure in height, and
having a plan irregularity type B (reentrant corner), as can be seen from the dimensions
shown in Figure 2.6. Preliminary estimation of the ratio between the displacement at the
end frame and the average displacement of the diaphragm was obtained to check
whether the 30-story building has plan irregularity type A. Using the model shown in
Figure 2.9b for this purpose, a displacement at the end frame equal to 1 .146 the average
9
displacement of the diaphragm is obtained. Because UBC sets a limit of 1.2 for this ratio,
the structure can be considered as not having plan irregularity type A.
2.3 THE STRUCTURE'S LOADS FOR PRELIMINARY DESIGN
2.3.1 DEAD LOAD
To estimate the weight of the building, the depth (thickness) of the slab needs to be
estimated, and therefore its preliminary design has to be conducted. For this purpose, the
1989 version of the American Concrete Institute Code (ACI Code) [Ref. 8] was used.
Figure 2. 7 shows the provisions used to compute the minimum thickness of the slab
according to deflection control (ACI section 9.5.3). Using these provisions, a total
thickness, h, equal to 12 em is obtained. The slab for the Japanese design of a building
with the same configuration has a thickness of 15 em. For a total floor area around 1 000
m2 per story, the difference in weight per story due to the slab is about 70 tons. Thus,
accounting only for the reduction in the slab thickness, the American-designed building
weighs 21 00 tons less than the Japanese one.
Preliminary sizes of beams and columns were required to compute a preliminary weight
for the structure; thus for a typical floor, it was assumed that beams had 0.80 m x 0.40
m in dimension, and the columns 0.60 m x 0.60 m. For the first story, beams were
1.00 x 0.50, and columns 0.90 x 0.90. To compute the contribution of the columns to the
weight of a floor, it was assumed that half the weight of the columns on top and on the
bottom of the slab was tributary to the floor.
To estimate the weight of the reinforced concrete structural elements, a specific weight
equal to 2.3 ton/m3 was used.
In section 2334.(a) of UBC, the seismic dead load, W, is defined as the total dead load
of the structure plus applicable portions of other loads (the other loads are listed in that
same section). In this section, UBC states that where partition load is considered in the
floor design, a load not less than 1 0 psf shall be included for the design and analysis of
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the structure under lateral loads. To compute the weight of other nonstructural elements,
estimates of the weight per unit area were obtained from a design handbook. For
preliminary estimation of weight, a total floor area of 1000 m2 was used.
A summary of the preliminary weight of each type of element, as well as the total
preliminary story weight for a typical story and the first story, are shown in Tables 2.1 and
2.2.
Finally, the 30-story building has an appendage on the roof. As a preliminary estimate
of the roof's weight, information on the weight of the existing building was used. Table 2.3
shows the weights given by Fukuzawa [Ref. 6] for the Japanese 30-story building. The
roof weight for preliminary design was estimated as follows:
roof WeighfFukuzsws roof weightpretiminsry = 30 story weightpr9timinsry
30 StOry WeightFukuzsws
2.3.2 LIVE LOADS
1151 = 1385 791 952
USC sections 2304 to 2306 deal with the values of live load that need to be considered
in the design of a structure. According to table 23-A of USC, for residential use, live load
on floors can be considered using a distributed load of 40 psf and no concentrated loads.
In section 2306, USC allows reduction of live loads for any member of the floor system
supporting more than 150 ff. For the 30-story building, the largest tributary area for any
beam is [(5.3) 2/2] m2, which is equal to 151 ff. Thus, no reduction was considered for live
loads in beams. Reduction in the live loads should be considered in columns, given the
fact that the great majority of the columns have tributary areas larger than 150 ff:
nevertheless, no reduction in live load was considered in their design. Live load needs
to be considered in three different load cases (see cases i, ii and iv defined in section
2.4.2).
11
For roof loads, UBC specifies in section 2305A (Table 23-C) a value of 20 psf for
members with tributary areas less than 200 fe.
2.3.3 TRIBUTARY AREA FOR VERTICAL LOADS
For the design of beams due to gravitational loads, tributary areas were estimated for
them. To compute member forces, the beams were loaded with a uniform distributed load
computed as the weight of the tributary area divided by the clear span of the beam.
2.3.4 LATERAL LOADS
The lateral loads for preliminary design were estimated according to section 2334.{b)
of UBC (static force procedure), using the reactive weights computed in section 2.3.1.
Although the analysis and design of the 30-story building should be carried out using a
dynamic analysis as discussed in Chapter 3, it was considered sufficient to use the UBC
static force procedure to obtain an adequate preliminary sizing of the members of the
structure. It should be mentioned that the preliminary sizing was done parallel with the
development of site spectra. The site spectra were not available at the time the
preliminary design was carried out. Nevertheless, the use of the static force procedure
usually leads to conservative design of regular buildings. Section 2.4.4 presents a
discussion of this issue.
The procedure used for preliminary sizing of the building can be summarized as
follows:
BASE SHEAR
where
VST = z I c w = 0.051W Rw
V sr = static base shear
z = 0.4
I= 1.0
Rw = 12
12
(UBC formula 34-1}
C = 1.25 S I T213 < 2.75 (C/Rw > 0.075) (UBC formula 34-2)
S=2
T = 0.030 H314 = 2.1 sees
As shown above, the period of the structure was computed using Method A specified
by UBC code. This method provides predictions that are 80 to 90 percent of the lower
bound values of measured periods at deformation values near first yield of the structural
elements [Ref. 7]. For UBC static force procedure, using a lower bound for the period
leads to an upper bound of the value of the static design base shear. It was considered
appropriate to use the above value ofT to obtain a conservative estimate of the static
base shear for the preliminary sizing of the elements.
DISTRIBUTION OVER HEIGHT OF LATERAL FORCES
where
n VST = Ft + EFi
i=1 (UBC formula 34-6)
Ft = 0.07 T VST < 0.25 VsT (UBC formula 34-7)
(UBC formula 34-8)
w1 ,F1 = weight and equivalent lateral force in ith story
wx ,Fx =weight and equivalent lateral force in xth story
Ft = equivalent lateral force acting on the roof
n = total number of stories
2.4 PRELIMINARY DESIGN
In the preliminary design phase, only frame 8 was designed. Figure 2.8 shows the
location of the selected frame within the plan of the structure.
13
The total earthquake base shear induced in the structure was estimated as described
in section 2.3.4 of this paper. To estimate the percentage of base shear carried by frame
8, a simplified distribution of the total base shear among all the frames of the structure,
as shown in Figure 2.9, was carried out assuming infinitely stiff beams (the stiffness of
a frame in any given story is proportional to the number of columns that the frame has
in that story). In the first stage, direct shear as well as shear induced by torsion in the
frame was considered. Given the small real eccentricities, torsion was estimated
accounting only for accidental eccentricities estimated according to U8C code.
Once the base shear acting on frame 8 was estimated, it was distributed through
height using the formulas given in Section 2.3.4. Table 2.4 shows the story forces
computed for the frame.
2.4.1 PRELIMINARY DESIGN FOR DRIFT
First, the beams were sized to comply with the U8C drift requirements for earthquake
loading. U8C 1991 specifies in section 2334.(h) that, for earthquake loading, the
calculated drift shall not exceed 0.03/Rw nor 0.004 for structures having a fundamental
period of 0.7 sees or larger. In this case (Rw = 12), story drift should be limited to 0.0025.
The lateral forces used to compute story drifts do not need to be scaled up.
To estimate the required beam sizes to control drift, a simplified analysis (portal
method) of the frame was carried out. As shown in Figure 2.1 0, the main assumptions
of the portal method are: inflection points in columns and beams are located at mid-height
and midspan, respectively; the total earthquake story shear is distributed equally among
the interior columns and the shear taken by the exterior columns is half of that taken by
the interior ones. Once the shear in each column has been determined, the shears in the
beams due to lateral loads can be estimated as shown in Figure 2.1 0. Once the shears
in beams and columns are known, the moments at the end of the beams and columns
can be determined as well as the axial forces in the columns.
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The story deformation, !J., of the story can then be estimated by computing the flexural
deformations of the beams and columns of a subassemblage, as shown in Figure 2.11.
A span equal to 5.3 m was considered for the subassemblage. This assumption is not
correct, because there are 4 spans of 4.8 m and 2 spans of 5.3 in the frame.
Nevertheless, it was considered that assuming a span of 5.3 m would yield reasonable
results, given that the difference in spans is small. Because at this stage the sizes of the
columns and beams are usually not known, the ratios hJic and L/lb in Figure 2.11 are not
known. To be able to solve for Elb, it is necessary to assume that a certain percentage
of the story displacement is due to the flexural deformation of the beams and the rest due
to column flexural deformation. It is well known that, for framed structures, the size of the
beams play a larger role than do the columns for drift control. As shown in Figure 2.11,
it was assumed that 75% of the story displacement is due to the deformation of the
beams [Ref. 9]. Also, a moment of inertia of the beams equal to 70% of the gross
moment of inertia of the beams was considered to account, in a simplified way, for
cracking of the RC sections.
Table 2.5 summarizes the information obtained using the approach illustrated in Figures
2.10 and 2.11. The table shows the required compressive strength of the concrete, f~, and
gross moment of inertia of the beams, 19
, to provide adequate drift control under the
assumptions previously made. The fifth, sixth and seventh columns give the preliminary
sizes of the beams, height and width (hand b), and the provided 19
• The eighth column
(Drift A) gives the value of the story drift computed using the proposed sizes of the
beams and the method summarized in Figures 2.10 and 2.11.
At this stage, drift due to axial deformation of the columns was ignored because the
sizes of the columns were still not known. Column sizes were defined by strength
requirements, as discussed in Section 2.4.2. Once column sizes were estimated, the drifts
due to axial deformation of columns were computed and accounted for, as discussed in
Section 2.4.3.
15
2.4.2 PRELIMINARY DESIGN FOR STRENGTH
Gravitational as well as lateral loads were considered in the preliminary analysis phase.
According to sections 2609.(c) and 2625.(c).4 of USC [Ref. 1], the following load cases
should be considered in the design of a building:
i. 1.4 D + 1.7 L
ii. 1 .4 ( D + L + E )
iii. 0.9 D ± 1.4 E
iv. 0.75 ( 1.4 D + 1.7 L + 1.7 W)
v. 0.9 D + 1.3 W
Load combinations iv and v were not accounted for in the design because, for the 3D
story building, strength requirements for earthquake are higher than those for wind. A
portal method analysis of frame S was carried out to estimate the bending moments and
shear forces induced in the beams and columns by the equivalent lateral loads.
The sizes of the beams obtained in Section 2.4.1 were checked for strength. Figure
2.12 shows how vertical loads were considered in them for their preliminary design. As
shown in Figure 2.12a, the moments at the ends of the beams were computed using the
expressions given by USC (section 2608.(d)) for the simplified design of continuous
beams under uniform distributed gravity loads. Once the load combinations were carried
out, it was checked that no beam would require a steel percentage above that specified
as the maximum by USC for beams without compression reinforcement ( Pmax < 0.025 and
Pmax < 0.75 Pb).
Figure 2.12b shows how vertical loads were considered to estimate preliminary axial
forces for the design of columns. As shown in the figure, half the weight of the beam and
its tributary gravity load were assigned to each one of the two columns that support the
beam, i.e., the beams were assumed to be simply supported by the columns. Although
this assumption is not strictly correct due to the different end conditions at both end of the
16
beams, the values of axial load in the columns obtained from this assumption are
reasonable. Moments at the ends of the columns due to gravity loads were estimated in
such a way that the gravity moments at the ends of the beams are equilibrated at the
joint.
To estimate the earthquake-induced axial forces in the interior columns, a cantilever
method analysis of frame B was carried out. As shown in Figure 2.13, the main
assumptions of the cantilever method are: inflection points in columns and beams are
located at mid-height and midspan, respectively; the total story overturning moment is
assumed to be resisted by the axial forces in the columns, and the value of the axial force
in a column is assumed to be proportional to the distance of the column to the centroid
of the building. Once the axial force in each column has been determined, all the forces
and moments in the beams and columns can be determined.
It should be noted that in the design for strength requirements of beams and exterior
columns, the results obtained from the portal method of analysis were used. Typical
framed buildings tend to have a "portal" type of behavior, but for taller buildings, some
type of "cantilever" behavior can be expected. Thus, the global elastic behavior of the 3D
story building can be estimated reasonably well from the portal method, given the fact that
the stiffness of the beams is not large enough to enforce "cantilever" behavior.
Nevertheless, the axial forces and axial deformations on the columns can not be
estimated correctly using the portal method, due to the cantilever component of behavior
of the 30-story building. The main problem with the portal method is that it yields the
following results when used to analyze a building under lateral loads: axial forces due to
lateral loads are concentrated in the exterior columns, while the axial forces in the interior
columns are zero. Thus, the portal method tends to overestimate the axial forces in the
exterior columns while it underestimates the axial forces in the interior columns. Although
the design for the exterior columns would be conservative when using the results from
the portal method, it is unreasonable to assume that the earthquake-induced axial load
in the interior columns is zero when carrying out an elastic analysis. To obtain a
17
reasonable and conservative estimate of the axial forces induced by earthquake in the
interior columns, the cantilever method was used. It should be noted that this was done
to obtain a reasonable upper-bound estimate of the axial forces in the interior columns,
and not to assess the real behavior of the building. Thus, although the cantilever method
of analysis will not give better results than the portal method, the distribution of axial
forces in the interior columns using this method seemed more reasonable than that
obtained using the portal method.
From load cases ii and iii, it can be seen that the earthquake design forces used to
compute strength requirements for members have to be scaled up by 1 .4. For a RC
building, UBC requires drift to be satisfied under allowable stress lateral forces, while
elastic strength requirements need to be satisfied at a factored load level, which is
defined as the allowable stress earthquake multiplied by 1.4.
2.4.3 REVISION
Figure 2.14 shows the preliminary sizes obtained from satisfying drift {without
accounting for axial deformation of columns) and strength requirements. Before carrying
out a more refined structural analysis of the building, the effect of axial deformation of the
columns in the drift of the building was estimated. To estimate this effect the building was
idealized as a cantilever beam, as shown in Figure 2.15, and the deflection of the beam
was computed at every story. Table 2.5 shows the expected drifts {Drift B) in the frame,
accounting for axial deformation of the columns. As shown in Table 2.5, the total
expected drifts {accounting for axial deformation of the columns) were very close to the
maximum value required by UBC (0.0025), and thus the preliminary design was
considered satisfactory for drift control.
It should noted that the drift due to the flexural deformation of the beams and columns
was computed from the results obtained from a portal method analysis. Then these drifts
are superimposed on those obtained using a cantilever method to account for the axial
deformation of the columns. Although this superimposition can not be justified if the real
18
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behavior of the structure needs to be estimated, this superimposition was done to
account, in a conservative way, for the story drifts of the 30-story building due to the axial
deformation of the columns.
It was also checked that the dimensions of the members were such that they could
carry the maximum possible shear (computed according to the plastic moments at the
member ends) on the member. Given the large number of load cycles that a structure,
located in soft soil and subjected to severe ground motions, has to undergo, it was
considered important to limit the shear stresses on the RC members to avoid degradation
of the stiffness and strength of the concrete members. It was considered that limiting the
shear stress on the RC members to 4 V"f; (psi) would help to avoid such degradations.
It has been observed experimentally [Ref. 1 0] that when the average shear stress at a
critical region (plastic hinge) of a flexural member exceeds a value of 3.5 VT;" (psi), with
a load reversal exceeding the flexural yielding value, a significant degradation in the
energy absorption and energy dissipation capacities occur.
2.4.4 COMMENTS ON FORCE PROCEDURE USED FOR PRELIMINARY DESIGN
Figure 3.4 compares the USC spectra that need to be used with the USC static and
dynamic force procedures of a building located on soil type 4. For the design of a building
with T greater than 0. 7 sees, a dynamic analysis of the building needs to be carried out.
As explained in Chapter 3, the spectrum used with dynamic force procedure has to be
derived specifically accounting for the dynamic characteristics of the site. The static force
procedure spectrum is obtained using the expressions given in this chapter to estimate
preliminary lateral forces. As shown in Figure 3.4, the dynamic spectrum ordinate is larger
than that of the static spectrum for a T of 2.1 sees. The initial assumption that the use of
the static force procedure spectrum would have a larger ordinate than the one
corresponding to the site spectra was not correct. Nevertheless, it was decided not to
redo the preliminary analysis of the building for the following reasons:
• The difference between the values of the ordinates for the two spectra is not large. It
19
also should be considered that the whole mass of the building is used to obtain the static
base shear. If a dynamic analysis of the building is carried out, the mass of the first mode
of a frame would be around 70 to 80% of the total mass of the building.
• Figure 3.18 shows the comparison of the forces obtained from the dynamic analysis of
the definitive design of the building and those specified by USC static force procedure
(both force distributions, shown with discontinuous lines, lead to a base shear of 1 020
ton). As shown, USC static force procedure leads to considerably larger force in the top
story, while it underestimates the forces in the rest of the stories. Thus, using the static
force procedure leads to larger story shears and overturning' moments, which in turn
would be reflected in a conservative design.
For the 30-story building, it was believed the use of the static force procedure led to
a reasonable and conservative preliminary design, and thus this design was not repeated
when the site spectra was obtained. By comparing the preliminary design of the building
with the definitive design of the building (presented in Chapter 3), it can be seen that the
change in the dimensions of the members from preliminary to definitive design was not
significant.
The fact that the building is regular in plan and elevation was important to obtain a
reasonable design from the static force procedure. The use of this method for preliminary
design is attractive due to its simplicity. Nevertheless, the results shown in Figures 3.4
and 3.18 lead to the conclusion that the static force procedure led to a reasonable design
because of complementing errors rather than because of the soundness of the method.
Thus, it is recommended that dynamic methods be used in order to obtain better
preliminary designs.
2.5 UBC WIND LOADS AND DRIFT REQUIREMENTS
In this section, a summary of the USC specifications (sections 2314 to 2318) used to
compute wind lateral forces is presented followed by a comparison of the story lateral
20
forces due to wind and earthquake.
From Figure 23-1 of UBC, the minimum basic wind speed is 70 mph. Because the 30-
story building is located in the San Francisco Bay Area, it has exposure type C, which
corresponds to terrain which is flat and generally open, extending one mile or more from
the site. According to section 2316 of UBC, the design wind pressure can be estimated
as:
where P is the design wind pressure; C8 the combined height, exposure and gust factor
coefficient (given in Table No.23-G of UBC); cq is the pressure coefficient for the structure
(given in Table No.23-H of UBC); qs is the wind stagnation pressure at standard height
of 33ft (given in Table No.23-F of UBC); and finally, I is the importance factor (given in
Table No.23-L of UBC).
To estimate the lateral forces due to wind, the normal force method [as specified in
section 2317(b) of UBC] was used. For the 30-story building, qs = 12.6 psf, I = 1, cq is 0.8
inward for windward wall and 0.5 outward for leeward wall. The value of C8 depends on
the height above the ground and was obtained from Table No.23-G of UBC.
Section 2318 of UBC states: .. For outward acting forces the value ofce shall be obtained
from Table No.23-G based on the mean roof height and applied for the entire height of
the structure ...
UBC lateral forces due to wind were computed following the above specifications. Table
2.4 shows a comparison between the unfactored equivalent lateral forces due to
earthquake and the unfactored lateral forces due to wind. As shown, the lateral forces
due to earthquake are significantly larger than those for wind, and thus earthquake lateral
forces control the design for lateral loads. It should also be noted that the fact that the
lateral force in the 30th story is considerably larger for earthquake than for wind would
21
make the design for earthquake much more conservative (as compared to the design for
wind) than would be suggested by only comparing the base shears produced by
earthquake and wind, respectively (1247 and 395 ton, respectively).
22
Dead load for gravity load Component analysis
(ton)
Beams (0.8 m x 0.4 m) 248
Columns (0.6 m x 0.6 m) , , , Slab (0. 12m width) 285
Partitions 9711 )
Ceiling 4913)
Others 4914)
TOTAL 839
(1) weight per unit area of 20 psf (UBC section 2304.(d)) (2) weight per unit area of 10 psf (UBC section 2334.(a))
Dead load for lateral load analysis (reactive weight)
(ton)
248 , , , 285 4912)
4913)
4914)
791
(3) weight per unit area of 10 psf for hung ceiling, metal lath, gypsum, fiber plaster and equipment (4) weight per unit area of 10 psf for reactive live load
TABLE 2.1 TOTAL WEIGHT OF TYPICAL FLOOR FOR PRELIMINARY DESIGN
Dead load for gravity load Component analysis
(ton)
Beams (1 .0 m x 0.5 m) 401
Columns (0.9 m x 0.9 m) 322 Slab (0. 1 2 m width) 285
Partitions 9711 )
Ceiling 49{J)
Others 4914)
TOTAL 1203
(1) weight per unit area of 20 psf (UBC section 2304.(d)} (2) weight per unit area of 10 psf (UBC section 2334.(a))
Dead load for lateral load analysis (reactive weight)
(ton)
401
322
285 4912)
49{J)
4914)
1153
(3) weight per unit area of 10 psf for hung ceiling, metal lath, gypsum, fiber plaster and equipment (4) weight per unit area of 1 0 psf for reactive live load
TABLE 2.2 TOTAL WEIGHT OF FIRST FLOOR FOR PRELIMINARY DESIGN
23
Story height f' weight c (m) (kg/em~ (ton)
=
30 2.85 240 1385 29 2.85 240 952 28 2.85 240 952 27 2.85 270 967 26 2.85 270 964 25 2.85 270 961 24 2.85 300 945 23 2.85 300 945 22 2.85 300 945 21 2.85 300 945 20 2.85 330 945 19 2.85 330 945 18 2.85 330 945 17 2.85 330 945 16 2.85 360 945 15 2.85 360 945 14 2.85 360 945 13 2.85 360 945 12 2.85 360 981 11 2.85 360 981 10 2.85 360 981 9 2.85 360 981 8 2.85 390 981 7 2.85 390 981 6 2.85 390 981 5 2.85 390 981 4 2.85 420 981 3 2.85 420 981 2 2.85 420 981 1 4.50 420 1399
TOTAL 87.15 29711
TABLE 2.3 WEIGHT OF JAPANESE BUILDING [Ref. 6]
24
Story story force for preliminary total story force due to total story force due to design of Frame B (ton) earthquake (ton) wind (ton)
1 0.85 4.93 13.54
2 0.94 5.52 10.98
3 1.31 7.66 11.34
4 1.68 9.80 11.65
5 2.05 11.94 11.90
6 2.41 14.08 12.15
7 2.78 16.22 12.36
8 3.15 18.36 12.56
9 3.51 20.50 12.74
10 3.88 22.64 12.90
11 4.25 24.78 13.04
12 4.62 26.92 13.16
13 4.98 29.06 13.29
14 5.35 31.20 13.41
15 5.71 33.34 13.54
16 6.08 35.48 13.66
17 6.45 37.62 13.77
18 6.81 39.76 13.86
19 7.18 41.90 13.94
20 7.55 44.04 14.02
21 7.92 46.18 14.11
22 8.28 48.33 14.18
23 8.65 50.47 14.26
24 9.01 52.61 14.33
25 9.38 54.75 14.41
26 9.75 56.89 14.49
27 10.11 59.03 14.56
28 10.48 61.17 14.64
29 10.85 63.31 14.71
30 47.03 278.55 7.39
TABLE 2.4 STORY FORCES FOR 30-STORY BUILDING
25
Story f' leff lg h c (1) (1) (1) (2)
1 420 938885 1341264 80 2 420 554156 791651 70 3 420 551700 788144 70 4 420 548279 783255 70 5 390 564422 806317 70 6 390 558865 798378 70 7 390 552332 789046 70 8 390 544796 778280 70 9 360 558155 797364 70
10 360 548251 783216 70 11 360 537305 767578 70 12 360 525314 750448 70 13 360 512279 731287 70 14 360 498228 711755 70 15 360 483134 690191 70 16 360 467024 667177 70 17 360 449870 642671 65 18 330 450867 644095 65 19 330 430799 615427 65 20 330 409640 585200 65 21 300 406300 580428 65 22 300 381822 545459 65 23 300 356231 508901 65 24 300 329497 470709 65 25 270 317967 454238 65 26 270 287408 410583 65 27 270 255644 365205 65 28 240 236216 337452 65 29 240 200003 285719 65 30 240 162511 232159 65 , .z fc = compressive strength of concrete 1n kg/em
1.11 =effective moment of inertia in cm4 = 0.7 lg lg = gross moment of inertia in cm4 = b x h3 1 12 h,b = total depth and width of beam in em
b lg IDIA IDI 8 (2) (2) 40 1706667 .0020 .0000 35 1000417 .0020 .0000 35 1000417 .0020 .0001 35 1000417 .0020 .0001 35 1000417 .0020 .0001 35 1000417 .0020 .0002 35 1000417 .0020 .0002 35 1000417 .0019 .0002 35 1000417 .0020 .0002 35 1000417 .0020 .0002 35 .1000417 .0019 .0003 35 1000417 .0019 .0003 35 1000417 .0018 .0003 35 1000417 .0018 .0003 35 1000417 .0017 .0003 35 1000417 .0017 .0004 30 686563 .0023 .0004 30 686563 .0023 .0004 30 686563 .0022 .0004 30 686563 .0021 .0004 30 686563 .0021 .0004 30 686563 .0020 .0004 30 686563 .0019 .0004 30 686563 .0017 .0004 30 686563 .0017 .0005 30 686563 .0015 .0005 30 686563 .0013 .0005 30 686563 .0012 .0005 30 686563 .0010 .0005 30 686563 .0008 .0005
IDI A= lnterstory Drift Index A= story drift due to flexural deformation of members IDI 8 = lnterstory Drift Index 8 = story drift due to axial deformation of columns (1) required by analysis (2) proposed
Total IDI
.0020
.0020
.0021
.0021
.0021
.0022
.0022
.0021
.0022
.0022
.0022
.0022
.0021
.0021
.0020
.0021
.0027
.0027
.0026
.0025
.0025
.0024
.0023
.0021
.0022
.0020
.0018
.0017
.0015
.0013
TABLE 2.5. PRELIMINARY BEAM SIZES FOR BEAM CONTROL
26
I Define Location (Z) I
1 Define Site Geology and
site characteristics (S)
l Define Occupancy
Category of building (I)
1 Define if structure is regular
or irregular
l Define structural system
SMRSF, R .. = 12
l \ Estimate T, \
l
I Get Preliminary Design!
Form Analytical Model of building .. 8 l
Compute static base shear '\.foT , formulas (34-1) and (34-2)
Static Force Procedure
.1
Height of
building and type
Dynamic Force Procedure
FIGURE 2.1 UBC DESIGN METHODOLOGY
27
Static Force Procedure
l Distribute forces through height
Dynamic Force Procedure
l Define allowable stress
design spectra
formulas (34-6) and (34-7) Response Spectrum or Time History Analysis Get Dynamic base
shear, VovN
! I Static Analysis I
.. maximum displacement
larger than 1.2 average displacemen
of diaphragm
.l Scale dynamic response by
factor k VST VovN
where k = 0 .. 9 for regular bldg and 1.0 for irregular bldg.
Increase Accidental ~ Torsion formula (34-9)
Redo analysis
NO l-----------"J I Check drift for allowable stress I ----.. •~!
l not satisfactory
satisfactory
,-----------------,not satisfactory Get member forces by superposing
appropiate factored load cases ADJUST DESIGN
satisfactory ! f ,----D-e-si_g_n_R_C_m_e_m_b_e-rs_f_o_r-fi-rs-t -y-ie-ld-_, not satisfactory
according to RC SMRSF specifications --~ .. ~
satisfactory J I FINAL DESIGN
FIGURE 2.1 UBC DESIGN METHODOLOGY (contd.)
28
a) Map of the U.S.
\ \
0 ·-·-
0
.0
0 0
FIGURE 2.2 LOCATION OF 30-STORY BUILDING
29
.,. zr -
EXPLANATION -Bay mud
~ Allomam
~ L:.;j
.... . . . . . . . . . .
U'l-v-r
i
\
...... I
I --
FIGURE 2.3 GEOTECHNICAL MAP OF THE SAN FRANCISCO BAY AREA [Ref. 11]
30
0 I~' ..;I
01 I
gl ''" .... A~~~~~~~~-
4.800 14.800 I I I
TYPICAL FLOOR PLAN
•.sao 5. cOO 5. cOO 4.800 I, .sao I I I I I Z9. BOO
6 cb 0 8 8 I
0 0 29TH,30TH AND ROOF FLOOR PLAN
FIGURE 2.4 PLAN VIEW OF 30-STORY BUILDING
31
e "'' :1 c:
. .. '' '' .... . .. ~ ..... _ .. __ ... ... ..
l..J .. ~ .. J .. J .... I ..... I I I I n.
1,. I I I
I A I 'I~ CD l..V ® 0
A FRAME SECTION C FRAME SECTION
Z6F
0 ,... "' I u ...
:J~ _1_7F_]~
0
~ . u ...
00 .... 0 "',.., . . u u ....... X -' Q ... - -< - ::z :; E Q = ~ .. Q -< = ~ :. ..
--M"' ;~ ~~ - .... ...
FIGURE 2.5 ELEVATION VIEW OF 30-STORY BUILDING
32
I @)
················· ®
®
®
@)
r I @) 4.8 reentrant corner
+ 0 1-- 4.8 -1- 4.8 -I- 5.3 --1-- 5.3 -t--- 4.8 -1- 4.8 -1
units in m
4.8 = 0.161 > 0.15 (USC limit) 4 X 4.8 + 2 X 5.3
FIGURE 2.6 IRREGULARITY TYPE B IN 30-STORY BUILDING
33
Two way beam-supported slab system:
Required: MINIMUM THICKNESS FOR DEFLECTION CONTROL
Data:
Geometry of slab and beams
18
= moment of inertia of slab
I b = moment of inertia of beam
ex m = average value of ex for all beams
at the edges of the panel
In = fr88-~psn
p = ratio of clear spans in the two
directions
ACI s.s.3
In ( 0.8 + fy ) h = 200,000
MIN 1 36 + sp ( l%m - 0.12 ( 1 + -))
p
(9-11)
(9-12)
(9-13)
I
f
FIGURE 2.7 SLAB THICKNESS
34
b
,---.....J' ~h~ r h
~
~r---~-~--.--~~-~ Minimum Thickness !nlf
( Grade 60 Reinforcement ) · sr---~--+·-~·--+--~
35 t----7-!Y'-6oo.JC
32.7 r~-:-....---l--___;'---...!.---1
0.5 1.0 1.5 2.0 2.5
.,.
!- 4.8 -+- 4.8 -1- 5.3 --+- 5.3 -t- 4.8 -+- 4.8 -I
Frame selected for predimensioning
FIGURE 2.8 LOCATION OF FRAME B
35
@
®
®
@)
@)
®
0
v
v
5k
K;
6k
7k
7k
7k
7k
6k
a) DIRECT SHEAR, ~ = V EK;
1- --1
eacc
5k
6k
7k
7k
---_J_ aaa:
5k
6k 7k 7k 7k 7k 6k
K;d;
7k
7k
6k
b) TORSION SHEAR, V; = L K; d~ eacc 1.3 V
FIGURE 2.9 STORY SHEAR TAKEN BY FRAME 8
36
rigid .
(:Jc:zz:dzz:>~':ZiJ{Jz::=2.==0{Jn===O,Cv • " " " • O(:Jz==.zQOz=zz>:z:z:::zO, T hi+f2
+ h;/2 ...L
-~ -~ -~ -~ -~ -~ -~ 2 2
L f---2
-vc L
2
vb f
--j
T h;.,
-2
+ h; 2
l
FIGURE 2.10 PORTAL METHOD OF ANALYSIS
37
-!J.b = VbL 3 = 2 24Eib
I- -1
+ vb f
he 2
l f----
L L ---j """2"" """2""
where u = 0.75
lb ,/c = moment of inertia of beam and column respectively
E = modulus of elasticity
FIGURE 2.11 ESTIMATION OF DRIFT DUE TO FLEXURAL DEFORMATION OF BEAMS AND COLUMNS
38
M~ M~ M~ M~ M~ M~ M~ M~ M~ M~ M~ M~
I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I ~ wu E Z Z Z Z Z L
M: M; M; M; M; M:
+- L1 -+- L 1 -1- L2 -+- L2 -t- L 1 -+- L1-+
UBC Section 2608.d:
a) Predesign of beams for gravity loads
I I I I I I I I I
L L
b) Predesign of columns for gravity loads
FIGURE 2.12 PRELIMINARY DESIGN FOR GRAVITY LOADS
39
rigid
Storyi
L1•4.8m
Lz• 5.3 m f-- l1 -t- L1 -t- Lz -f- L2 -t- L1 -t- L 1 --j
• .. ·· ~ r t [~~:T ~T / c centroid of sro~ columns
distribution of axial forces in columns
FIGURE 2.13 CANTILEVER METHOD OF ANALYSIS
40
Story BEAMS COLUMNS
30 r------.-----r--,---~-----.--,------,
50x50 25
+ 65x30
20 60x60
15 t 70x70
10
+ 70x35
5 SOx 80
80x40 -- ---- --
UNITS in em
FIGURE 2.14 PRELIMINARY SIZES OF MEMBERS OF FRAME 8
41
-'--
-
'-- - '-- - '-- - - - -
Elevation view
Plan view
centroid of story columns
A1 "" area of ith column
d1 = distance of ith column to centroid of story columns
le~~ = equivalent moment of inertia = I: A, cf
UBC Lateral Loads·~., -"""' flexural deflection of beam gives conservative drift due to axial deformation of columns
beam with laq
FIGURE 2.15 ESTIMATION OF DRIFT DUE TO AXIAL DEFORMATION OF COLUMNS
42
3. DESIGN ACCORDING TO UBC
3.1 LATERAL FORCE PROCEDURE.
According to UBC [Ref. 1], the type of analyses that need to be performed on a
structure depend on parameters such as the total height, regularity and occupancy
category of the structure, as well as the type of soil it is built on. Section 2333.(h).3.A of
UBC states that the dynamic lateral force procedure shall be used for structures which
are 240ft or more in height. The 30-story building roof has a height of 286ft (87.15 m),
and thus, a dynamic analysis of the building need to be carried out.
In section 2335.(d), UBC requires that, for design purposes, the dynamic analysis of
the structure can be either a response spectrum analysis (RSA) or a time-history analysis
(THA). For the design of the 30-story building, a RSA analysis was selected. For UBC
design, the shape of the design spectra varies with the type of soil on which the building
is located; and thus, the soil at the site needs to be classified as one of the four types
defined by UBC. For the purposes of this research, it is considered that the building is
located on the shores of the San Francisco Bay. The soil along the shores, as shown in
Figure 2.3, is composed mainly of bay mud with a depth between 0 and 40 m (0 to 131
ft). Shear wave velocities for the bay mud, measured from samples taken in different
locations, are shown in Figure 3.1 [Ref. 11]. As shown, shear wave velocities are less
than 500 fps for soil depths of 60 ft or less on all locations. The characteristics of the bay
mud match those required by UBC in its table 23-J for soil profile S4: "A soil profile
containing more than 40 ft of soft clay characterized by shear wave velocity less than 500
ft per second'.
Some insight into the reason why a soil profile type S4 was included in UBC can be
found in SEAOC commentary [Ref. 7], section 1.D.8.b.{4): "Because there are many
similarities between the soft clay deposits in Mexico City with certain Soil Profile Type S4
areas in California, there is concern about the possible occurrence of extensive damage
to structures on such deposits due to similar resonance type response ... ".
43
Seed [Ref. 11], after commenting on the properties of the bay mud and performing
analytical estimates of the damage potential of ground motions filtered through the bay
mud concludes that there is cause for concern about a type of damage potential in bay
mud similar to that estimated for the 1985 Mexican earthquakes (for discussion about '
damage potential of the 1985 Mexican ground motions see Refs. 2 and 12). Thus, it
seems appropriate to consider bay mud as soil type S4.
According to UBC, section 2333.(h).3.D, a dynamic analysis should be performed on
structures, regular or irregular, which are located on soil profile type S4 and have a period
greater than 0.7 seconds. The analysis shall include the effects of the soil at the site and
shall conform to section 2335.(b).4 of UBC. Continuing with SEAOC commentary [Ref.
7], section 1.D.8.b.(4):
.. . therefore, special dynamic analyses have been adopted for certain
classes of structures judged to be susceptible to such damage. The
purpose of the provisions of this section is to define the conditions for which
these special analysis are to be applied. From evaluation of the observed
damage in Mexico City, it is judged that damage to structures on Type 54
soils is unlikely if the natural period of the structure is short or long
compared to that of the site. Therefore, structures with natural periods less
than or equal to 0. 7 seconds have been excluded as candidates for these
special analysis procedures ...
The importance of the above requirement is not the need to perform a dynamic
analysis, because this has already been required because of the height of the building.
The issue is in the definition of the design spectra. For this purpose, section 2335.(b) .4
of UBC requires that the ground motion representation shall be one having, as a
minimum, a 1 0 percent probability of being exceeded in 50 years. Also, for structures on
soil profile type S4, the following requirements shall apply:
44
I
A. The ground motion shall be developed in accordance with a site-specific response
spectrum based on the geologic, tectonic, seismologic and soil characteristics associated
with the specific site. The spectrum shall be developed for a damping ratio of 0.05.
Ground motion time histories developed for the specific site shall be representative of
actual earthquake motions. Response spectra from time histories, either individually or
in combination, shall approximate the site design spectrum described above.
B. Possible amplification of building response due to effects of soil structure interaction
and lengthening of building period caused by inelastic behavior shall be considered.
C. The base shear determined by these procedures may be reduced to a design base
shear, V, by dividing by a factor not greater than the appropriate Rw factor for the
structure.
According to the above requirements, an elastic design spectrum needs to be
developed specifically for the site, and then a dynamic analysis of the structure should
be performed using design spectra obtained by reducing the elastic design spectra by the
appropriate Rw factor.
3.2 DESIGN SPECTRA FOR UBC DESIGN
For the purpose of making a conceptual design of a building with the same
configuration as that designed in this report, site spectra were determined in Ref. 5 using
several ground motions recorded in soft soil. For the conceptual design of the building,
two spectra were developed for the site, an elastic one that is associated with service limit
state and a second one associated with safety limit state and developed for a 11 of 2.5
(Figure 3.2). For the design of the 30-story building according to UBC, a third spectrum
(elastic associated with safety limit state) developed for the site by Goucha and Bertero
was used (Figure 3.2). The last spectrum satisfies all the requirements made by UBC for
the site elastic design spectra.
45
To satisfy drift requirements, USC forces are computed for the allowable stress limit
state. These forces can be estimated by performing a RSA of the structure. For this
purpose, the elastic site spectra for safety can be reduced by Rw, as illustrated in Figure
3.3.
The lateral forces used in the design of concrete members are obtained by using the
USC allowable stress spectra scaled up by a factor of 1.4. Recall that USC requires an
elastic analysis to compute the design forces and moments in the building's members,
and thus the above-mentioned factored lateral forces are associated with the first
significant yielding strength of the RC members. Thus, the spectra used for the design
for strength at first yield can be obtained by scaling up the allowable stress spectra 1.4
times, as shown in Figure 3.3. At this stage it is important to emphasize the definitions
given for USC spectra, because they are used several times in future discussions. The
UBC allowable stress spectra, associated with allowable stress limit, are defined as the
elastic safety site spectra divided by Rw. The UBC design spectra, associated with the
building's first significant yielding, are defined as the UBC allowable stress spectra scaled
up by 1.4.
It should be noted that the allowable stress spectra obtained by reducing the elastic
spectra developed for the site is significantly different from that obtained following USC
requirements for other types of soil. Figure 3.4 compares the UBC spectra (without
reduction) required for dynamic analysis of structures located on soils type 3 and 4, with
that required by UBC for use with static force procedure and soil type 4. As shown, the
dynamic spectra for soil type 3 and the static spectra for soil type 4 are conservative in
the short-period range; nevertheless, in the large-period range (tall buildings have large
fundamental period of translation) they tend to underestimate the response of a structure.
It should be noted that for all values ofT, the static spectra for soil type 4 ordinates are
larger than those corresponding to the dynamic spectra for soil type 3. By comparing both
dynamic spectra, it can be concluded that the use of the dynamic spectra for soil type 3
can lead to significant underdesign when used in tall buildings located in soft soil. Note
46
I
I--
that the same is not true for short- and medium-rise buildings.
According to section 1.E.2.a of SEAOC commentary [Ref. 7], the reduction factor, Rw,
represents the ability of the structural system to accommodate loads and absorb energy
in excess of its allowable stress limit without collapse. It also states the following: ., The
reduction in force is comparable to previous recommendations where the K factor was
used. Experience indicates that buildings designed to these reduced levels perform
adequately . ., The problem with this approach is that the above-mentioned ability is
quantified in an irrational way, so that UBC approach can lead to unconservative design.
Figure 3.5 shows the comparison between the spectra used for the conceptual design of
the building and those used for UBC design. Although a direct comparison of the spectra
can not be established because of the different purposes of each one, a very useful
indirect comparison can be established. On a first approach to the problem, it can be
seen that the UBC design spectra have significantly smaller ordinates than their
conceptual design counterparts. SEAOC commentary gives some insight in section
1.E.2.a:
For a given structural system having a design level as determined by the
Rw value, the following factors produce a structure having a total yield
mechanism resistance which is significantly larger than the specified
design base shear value. The contributors to this resistance are: the
working stress design basis; multiple load combinations; system
redundancy; participation of other structural and non-structural elements in
resisting lateral forces; strain hardening; and the as-built member
configurations ...
Figure 3.5 shows a comparison of the UBC design spectra for first significant yielding
(considering different overstrength, OVS, values) with the design site spectra for safety
and ~ = 2.5 used in the conceptual design. As shown, the ordinates of the UBC design
spectra accounting for an OVS of 200% come close, in the long period range (T > 1.8
sees), to those corresponding with the safety design spectra for ~ of 2.5. Nevertheless,
in this case, because of the different shape of both spectra, higher-mode effects can vary
47
significantly for both spectra. Given the height of the 30-story building (T would range
from 2 to 3 sees), its OVS would be somewhere around 100%, which would lead to a
building with about 60% of the minimum strength required by the design site spectra for
safety {J..l = 2.5). The main problem with the UBC approach is that the drift of a building
needs to be controlled for design forces associated with the allowable stress spectra. As
shown in Figure 3.5, the UBC design spectrum {equal to 1.4 times the allowable stress
spectrum) has very low ordinates when compared with the service spectrum obtained for
the site {for conceptual design, service drift was controlled using this spectra; while for
UBC, drift is controlled using the UBC allowable stress spectrum). ForT greater than 1
second, the ordinates of the allowable stress UBC spectra are about 25% of those
corresponding to the service site spectrum. Thus, it can be concluded that the UBC forces
consi_dered to estimate serviceability drifts and those considered to design the strength
of the members of a building can be significantly smaller than those that need to be
considered to obtain an appropriate design for strength and drift control. Using the UBC
spectra leads to a very large underdesign for service and to a significant underdesign for
safety if the OVS is close to 100%. Only if the resulting OVS is larger than 200% can the
design of the building be considered adequate from a ultimate strength perspective.
3.3 STRUCTURAL ANALYSIS OF THE 30-STORY BUILDING ACCORDING TO UBC
A structural analysis of a tridimensional model of the 30-story building was carried out
following UBC specifications. For this purpose, ETABS-PLUS computer program [Ref. 13]
was used. This section describes, step by step, the procedure used to develop the model
and the estimation of the forces acting on it.
3.3.1 30-STORY BUILDING PROPERTIES AND ANALYTICAL MODELLING
• Foundation. The building was modelled on a fixed base. Figure 2.5 shows the
foundation system used for the real Japanese building. Given the large stiffness of the
perimeter walls used in the foundation, it is assumed that the deformations at the
foundation level are small. Further studies need to be carried out to assess the accuracy
of this assumption. Soil-structure interaction needs to be studied, and two issues need
48
to be considered: first, the magnitude of the displacement of the foundation as a rigid
body has to be assessed; and second, the magnitude of the dissipation of input energy
at the foundation level due to soil damping and radiation damping must also be assessed.
• Diaphragms. Rigid in-plane diaphragms were considered for the model of the building.
This assumption is realistic given that: holes on the slab are not large, as shown in Figure
2.4; the plan of the building is square (for elongated buildings it is possible for this
assumption to be incorrect); the thickness of the slab is 12 em (for thin slabs this
assumption can be incorrect). Each diaphragm has 3 dynamic degrees of freedom (DOF):
two translational and one rotational displacement. As shown in Figure 3.6, all 3 DOF are
associated with only one point in the diaphragm. The mass properties of the structure are
lumped at this location and are associated with the above mentioned DOFs.
• Mass Properties. The weight of the reactive mass of each floor was estimated as the
sum of the weight of the reactive mass computed according to specifications of UBC
section 2334.(a) plus a portion of the live load (it was considered that a portion of the live
load corresponding to furniture, equipment, etc., was likely to generate inertia forces, and
thus their mass should not be neglected when computing the story masses). An outline
of UBC requirements is presented in section 2.3 of this report. Table 3.1 shows the story
weights estimated for the final design of the 30-story building. The weights were adjusted
several times during the design process. The weight of the 30-story building designed
according to USC is about 25% smaller than that estimated by Fukuzawa for the building
designed according to Japanese practice [Ref. 6], as shown in Table 3.2. Both sets of
weights include a portion of the live load that was considered to be part of the reactive
mass. For the design of the Japanese building, the following typical non-structural loads
were_ considered [Ref. 14]: finish 35 kg/m2, ceiling 15 kg/m2
, wall separating each
apartment 115 kg/m2 and effective live load for earthquake 60 kg/m 2• For USC design the
following non-structural loads were considered: partitions 50 kg/m2, ceiling plus equipment
50 kg/m2, reactive live load 50 kg/m2 (which is slightly smaller than the value given in Ref.
17). This leads to a total load of 225 kg/m2 for Japanese design vs. 150 kg/m2 for USC
49
design. The main difference between the designs is the weight associated with the walls
separating each apartment, with 115 kg/m2 for Japanese design and 50 kg/m2 in UBC
design. Note that for the floor design, section 2304.(d) of UBC requires that the weight
of the separating walls (partitions) be estimated using a value of 1 00 kg/m2 (20 ps~, while
to estimate the seismic dead load, section 2334.(a) of UBC, the weight of the separating
walls should be estimated using a value of 50 kg/m2 (10 ps~.
One of the reasons for the smaller weight of the UBC design is the smaller sizes of
beams, columns and slab of the UBC 30-story building with respect to these elements in
the Japanese building.
To perform a dynamic analysis, translational masses computed as wJg were assigned
to the translational DOFs; while a rotary mass, computed according to Figure 3.7, was
assigned to th1;3 rotational DOF.
Eccentricities. Real eccentricities for each story were estimated. For this purpose, the
center of mass for each slab was computed, taking into account the holes in them,
assuming a uniform distribution of mass throughout the entire slab. Table 3.3 shows a
summary of the values obtained for all the stories of the building. As shown, there is a
significant variation of the accidental eccentricity in theY direction. This variation can be
explained by the fact that the shape of the slabs for each story vary over height. Figure
2.4 shows the plan view of the slabs of a typical story as compared with that of the 3 top
stories. It can be clearly seen that the eccentricity in the direction parallel to the frames
1 to 7 (Y direction) changes considerably for these two slabs.
UBC, in its section 2334.(e), states the following:
To account for the uncertainties in locations of loads, the mass at each
level shall be assumed to be displaced from the calculated center of mass
in each direction a distance equal to five percent of the building dimension
at that level perpendicular to the direction of the force under consideration.
50
The effect of this displacement on the story shear distribution shall be
considered.
Also, for a dynamic analysis, in section 2335.(e).5, UBC states:
The analysis shall account for torsional effects ...
.. . Where three dimensional models are used for analysis, effects of
accidental torsion shall be accounted for by appropriate adjustments in
the model such as adjustments of mass locations, or by equivalent
static procedures ...
In section 1 .F.S.e of the SEAOC commentary, the following is stated:
Accidental torsions prescribed in section 1 E6 (UBC 2334.(f)) are also
required for dynamic analysis procedures ...
.. . To account for such effects, torsional moments due to accidental torsion
can be computed using the static procedures given in section 1 E6, and then
distributed to the various members of the building's lateral force resisting
system to obtain the corresponding member forces. This distribution can
be accomplished by either an EQUIVALENT STATIC LOAD METHOD
OR A DYNAMIC ANALYSIS METHOD. In the STATIC METHOD, the
accidental torsional moments at each level may be calculated as the
product of the equivalent static force from sect~on 1 E4 (UBC 2334.d)
times the 5 percent eccentricity specified in section 1 E5b. The resulting
moments are applied as pure couple loadings, all of the same sense, at
their corresponding levels. The effects of these couple loads are then
added, as an increase, TO THE RESULTS OF THE DYNAMIC
ANALYSIS.
SEAOC commentary gives another option to account for accidental eccentricity in the
same section:
51
For the DYNAMIC METHOD and nonflexible diaphragms, it is required to
displace the mass in the dynamic model to alternate sides of the
calculated center of mass and use a a three dimensional analysis to
calculate the effects directly ...
• Options to Account for Accidental Eccentricities. From the above statements, it can
be seen that there are two possible approaches to considering accidental eccentricity
within the USC earthquake design specifications:
-Pseudo-dynamic approach. A response spectrum analysis of the building is carried out,
using the reallocation of the center of mass in each story, and using the USC allowable
stress spectra. As a result of the analysis, story forces and story torsional moments are
obtained for each level. Then story torsional moments (coupling loads), computed as
static story forces times the accidental eccentricity, are added to the dynamic story
torsional moments, previously obtained, with the purpose of analyzing the building and
determining design forces for the members.
- Dynamic approach. A response spectrum analysis of the building is carried out,
accounting for the real and accidental eccentricities to locate the center of mass in each
story, and using the USC allowable stress spectra.
Two different models were prepared, one for each approach. For the design of the
building, the results obtained from the pseudo-dynamic approach were used. The results
obtained from both approaches are compared in section 3.5.3, and the reasons why the
results from the pseudo-dynamic approach were used are discussed in that section.
• Model. Section 2335.(d) of USC states:
A mathematical model of the physical structure shall represent the spatial
distribution of the mass stiffness of the structure to an extent which is
52
adequate for the calculation of the significant features of its dynamic
response ...
Given the fact that axial deformations of columns are significant and that lateral forces
need to be considered in two orthogonal directions, it was considered necessary to carry
out a full-scale tridimensional analysis enforcing complete deformation compatibility for
every member.
Response Spectrum Analysis. As mentioned earlier, it was decided to perform a
dynamic RSA of the building. UBC section 2335.(e).1 states:
The requirement of Section 2335. (d). 1 that all significant modes be included
may be satisfied by demonstrating that for the modes considered, at least
90 percent of the participating mass of the structure is included in the
calculation of response for each principal horizontal direction.
The first 15 modes were considered in the analysis: there were roughly 5 in each
translational direction and 5 for torsional DOF. It should be noted that only 9 modes would
have been enough to satisfy UBC requirements. For the three directions, the sum of the
participating mass was greater than 90% of the total reactive mass of the structure in that
direction, as shown in Table 3.4.
UBC section 2335.(e).2 states:
The peak member forces, displacements, story forces, story shears and
base reactions for each mode shall be combined by recognized methods.
When three-dimensional models are used for analysis, modal
interaction effects shall be considered when combining modal
maxima.
Given the fact that the stories were allowed to rotate in plan, as well as the closeness
of the fundamental periods computed for each one of the three dynamic directions (two
53
translations plus one rotation), the results were combined using a CQC rule.
• Scaling of Results. On the USC approach, there is one interesting limitation set on
section 2335.(e}.3, which states:
The base shear for a given direction determined using these procedures
(dynamic procedures), when less than the values below, shall be scaled
up to these values.
A. The base shear shall be increased to the following percentage of the
values determined ·from the procedures of section 2334 (static force
procedure):
(i) One hundred percent for irregular buildings.
(ii) Ninety percent for regular buildings, except that the base shear shall not
be less than 80 percent of that determined from section 2334 (which is the
static method) using the period, T, calculated from method A.
All corresponding parameters, including deflections, member forces
and moments, shall be increased proportionately.
B. The base shear on a given direction determined by using this
procedures need not exceed that required by Item A above. All
corresponding parameters may be adjusted proportionately.
The above is a very important and limiting requirement of the UBC approach. The
base shear for the building, carefully obtained from a dynamic RSA analysis, shall be
scaled up or down to a certain percentage of that estimated using the simplified static
procedure of USC section 2334. Deflections, and member forces and moments should
be scaled proportionately. On one hand, UBC requires site spectra that reflect the
dynamic characteristics of the construction site, but on the other hand, it allows for the
computed dynamic base shear to be scaled up or down to the static base shear.
SEAOC commentary explains this apparent contradiction in its section 1 D.B.a:
In these Recommendations, the results of a dynamic analysis are
54
normalized or scaled (Section 1 F5c) to the levels required by the static
force procedure of section 1 E. Therefore the basic information provided
by dynamic analysis consists of the particular distributions of forces
and deformations as they might differ from those provided by the static
load distribution of Section 1 E.
Also, in section 1 F.2:
This subsection describes the types of representation of seismic ground
motion, principally by a response spectrum, that can be used in a dynamic
analysis. The dynamic results of a dynamic analysis are normally sensitive
to the estimated intensity and frequency content of the seismic ground
motion. The spectrum can be considered to have two characteristics: shape
and amplitude. For the design of structures using these
Recommendations, the shape of the response spectra is more
important than the magnitude because the structural response is
scaled as noted in section 1 F5c ....
Finally, in section 1 f.5.c. (2) of the commentary :
This is a permissive section in that the engineer is permitted to
decrease the dynamic base shear to that required by section 1f5c(1).
However, there are cases where the engineer or owner may wish to use
force levels above the minimums established by these Recommendations
to provide more damage control or continuity of operation. Note that there
are special requirements for 54 sites, see 1 F2d.
Although the USC code establishes special requirements for S4 sites, there are no
provisions in it to override the possibility of a reduction in the computed dynamic base
shear.
It can be concluded from the above commentaries that there is a design philosophy
55
hidden under the various code statements which implies that the design of a structure for
the static base shears yield satisfactory results. To approach the design of the 30-story
building, it was considered adequate to scale up the dynamic base shear if necessary.
Nevertheless, it was considered poor practice to scale down the results from a dynamic
RSA. Thus, scaling is considered adequate only if it increases the values of the story
drifts and design forces of the members of the 30-story building. Section 2333.(e).3.C of
USC states: "Structures having one or more of the features listed in table No. 23-N shall
be designated as having plan irregularity." Because the 30-story building has plan
structural irregularity type 8 (reentrant corner), which is included in table No. 23-N of
USC, the 30-story building needs to be considered as an irregular building according to
section 2335.(e).3.A of USC. Thus, for the 30-story building, the dynamic base shear,
VovN' was scaled to a 100% of the static base shear, Vsr· All corresponding parameters
(deflections, member forces, etc.) are adjusted proportionately.
Directional Effects. USC deals with this aspect in its sections 2335.(e).4, 2334.(a) and
2337.(a). In section 2334.(a), USC requires that the structure should be designed for
seismic forces coming from any horizontal direction. For this purpose USC states:
The design seismic forces may be assumed to act nonconcurrently in the
direction of each principal axis of the structure, except as required by
section 2337. (a).
In section 2337.(a), USC states:
A column of a structure forms part of two or more intersecting lateral force
resisting systems.
EXCEPTION: if the axial load in the column due to seismic forces acting
in either direction is Jess than 20% of the column allowable axial load.
The requirement that orthogonal effects be considered may be satisfied
by designing such elements for 100 percent of the prescribed seismic
forces in one direction plus 30 percent of the prescribed forces in the
56
I
perpendicular direction. The combination requiring the greater component
strength shall be used for design. Alternatively, the effects of the two
orthogonal directions may be combined on a square root of the sum of the
squares (SRSS) basis ....
Given the fact that the 30-story building lateral load carrying system is constituted by
special moment-resisting frames, bidirectional effects were considered in its analysis.
Bidirectional effects were considered for the design of every column, although due to the
low axial forces induced in them, columns on top floors could have been spared this
requirement.
Member Geometric Properties. SEAOC Commentary, in section 1.F.3 states the
following:
Section Properties. The selection of section properties for the structural
model is complex and requires considerable judgement to properly
understand and represent the structure's expected performance. Reinforced
concrete and masonry are particularly difficult ...
.. . For concrete and masonry, a first approximation would be to use gross
uncracked section properties and the code modulus of elasticity. Assuming
cracked sections and transformed steel area throughout, or using the
moments of inertia specified in the ACI code for deflection
calculations may be an excessive refinement.
Although UBC considers as an acceptable practice the use of gross moment of inertia
of the members to model the stiffness of the structure, in some cases this type of
idealization will not be able to capture the real behavior of a building [Ref. 15]. To
compute the story drifts, it was considered important to model a reasonable value of the
secant stiffness of the structure under allowable stress loads to obtain reasonable
estimate of drift. This reflects the fact that there is nonlinear behavior in the structure
57
even before yield is reached due to the cracking and inelastic action which occurs on
concrete members. However, simplifying assumptions need to be considered given the
complexities involved in computing a different stiffness for all the members of the 30-story
building.
As shown in Figure 3.8, the value of the secant stiffness can change depending on
what limit state of the structure needs to be considered. For the 30-story building, the
secant stiffness for the allowable stress state was chosen, because according to UBC,
drift must be satisfied at this state. As shown in Figure 3.8, the selected secant stiffness,
k8 , does not represent adequately the behavior of the structure throughout the entire base
shear Nb) vs displacement at the top story (L\) curve: it only gives a good estimate of the
building's behavior at the allowable stress state. In other words, because the design
process only requires drifts to be satisfied at allowable stress state, the selected k8 gives
a reasonable estimate of the behavior of the structure; nevertheless, the selected k8
would not give reasonable estimates of drift at other limit states, as shown in the figure.
The following considerations were made in modelling the members, under allowable
stress loads, of the 30-story building:
I. Modulus of elasticity of concrete was obtained from UBC:
Ec = 15100 {t[ (f~ units are kg/em~
II. Columns were modeled using their gross moment of inertia, 19
• Given that practically
every column of the structure is under compression axial loads (superposing effects of
vertical and lateral loads), it was considered that the effect of cracking was not significant.
Ill. Beams were modeled using an effective moment of inertia, left. The value of the
moment of the inertia of the beams affects considerably the computed values of story
drift. For this reason, it was considered important to have a reasonable estimate of the
58 I
1a11 for the beams. Figure 3.9 illustrates the procedure used to compute leff for the beams.
Basically, the procedure is based on computing the cracked and gross moments of inertia
at both ends and on the middle of the beams. Depending on the shape and amplitude of
the bending moment diagram of the beam, obtained by superposing gravity and lateral
loads, effective moments of inertia for each one of these locations are obtained using
UBC formulas 9-7 to 9-9:
t, lg M =-
cr Yt
where Ia is the effective moment of inertia on a cross-section of the beam; Mer and Mathe
cracking and the maximum moments, respectively, on the section at which Ia is being
computed; lg the gross concrete section moment of inertia about the centroidal axis
neglecting the contribution of the longitudinal reinforcement; lcr the cracked section
moment of inertia accounting the longitudinal reinforcement in the beam; fr the modulus
of rupture; and Yt the distance from the centroidal axis of the gross section to the extreme
fiber in tension. In the above expression, f~ is in kg/cm2• 1811 for the whole beam is obtained
by computing a weighted average, as shown in Figure 3.9, of the effective moments of
inertia for these three locations.
lv. Joint size. It was assumed that for allowable stress limit, the joint would not show
significant cracking or nonlinear behavior, i.e., it was assumed that the joint deformability
was not significant. Thus, rigid zones with a length of 100% of the members' total depth
were used in the analysis. Because of the large sizes of the members of the structure,
the free span of the members is significantly smaller than their total span, and thus rigid
zones should be considered to get a better estimate of the stiffness of the structure.
59
3.3.2 DRIFT CONTROL
Section 2334.(h).1 of USC states: 11 Story drift is the displacement of one level relative
to the level above or below due to the design lateral forces. Calculated drift shall
include translational and torsional effects11• UBC defines what it means by design lateral
forces in section 2334.(h).4. Basically, in this section, USC requires that for drift
calculation the forces need not be scaled up with the use of a load factor; and thus, as
commented several times before, drift needs to be satisfied for allowable stress limit
state.
Section 2334.(h).2 of UBC states: 11 ... For structures having a fundamental period of
0. 7 seconds or greater, the calculated story drift shall not exceed 0. 03/Rw or 0. 004 times
the story height'. For the 30-story building, this limits the value of interstory drift ratio to
0.0025.
Also, UBC 2334.(i). states that II ... In seismic zones 3 and 4 (30-story located in zone
4), P-!1 need not be considered where the story drift ratio does not exceed 0.02/Rw"· In
the analysis of the 30-story building, P-11 effects were accounted for because in several
stories the values of drift exceeded the above limit.
3.3.3 PROCEDURE OF ANALYSIS
As mentioned before, computing the drifts on the structure, emphasis was put on
capturing an appropriate stiffness for the structure. The problem with this approach is that
a member stiffness depends on the shape and amplitude of its moment diagram under
gravity and lateral load which, in turn, depends on the value of its stiffness. Thus, an
iterative scheme was used in the analysis of the building. As shown in Figure 3.10
(Figures 3.11 and 3.12 aid the understanding of Figure 3.10), the main steps taken to
perform the analysis of the structure can be summarized as follows.
a. Create or redefine the model of the structure, according to the effective moment of
inertia of beams, which depend on the size and reinforcement of the beams, and gross
60
~ ,:
I
\
I·
I I
moment of inertia of columns, which depend on the size of the columns.
b. Obtain dynamic properties of the building.
c. Perform a RSA of the building's model using the USC allowable stress spectra.
Account for real eccentricities, er, only.
d. With the value ofT estimated in step b, compute V5r according to section 2334.(b)
of USC.
e. From the analysis carried out in step c, obtain dynamic base shear, VovN·
f. If needed (V0vN < V5r}, scale all dynamic response forces and displacements by a
factor V5rNovN·
g. Statically superpose story torsional moments (coupling loads) computed as static
forces times the accidental eccentricity. Compute member forces and story displacements
considering the dynamic story shears and the superposition of dynamic and static
torsional moments (bidirectional input needs to be considered, 100% in one direction and
30% in the perpendicular direction).
h. From the results obtained from g, compute 101 for the stories and reinforcement for
beams and columns. Check that sizes of beams and columns are satisfactory from a drift
and strength perspective. If required, change dimensions of some members according to
the following criteria:
- increase beam sizes for drift control
- increase column sizes (or reinforcement) if axial forces are excessive.
i. If results obtained in h are similar to results obtained in previous cycle and all USC
61
drift and strength requirements are met, proceed to final design. If not, go to j.
j. With the member end moments obtained by using the allowable stress spectra, and
with longitudinal reinforcement of beams computed in h, estimate leff for the beams. The
leff of the beams are assumed to be equal in both translational directions.
k. Go to a.
3.4 PROPERTIES OF DEFINITIVE VERSION OF THE 30-STORY BUILDING
As remarked in section 3.3.3, an iterative scheme was used for the analysis and design
of the 30-story building. In this section, the properties and characteristics of what was
considered as the adopted preliminary design of the building are discussed.
Figures 3.13 to 3.15 summarize the column and beam sizes for the final design of the
30-story building. Basically, all the columns in a story have the same cross-section.
However, there are two types of beam on each story: the interior beams, which belong
to the internal frames, and the exterior beams, which belong to the external frames. The
first version of the building had the same size for all the beams within a story; however,
given the large axial forces induced in the columns at the ends of the external frames,
it was considered convenient to control the axial forces by reducing the sizes of the
beams in the external frames. UBC requires RC members to be designed using the
results obtained from an elastic analysis of the building; in this case, a RSA. Thus, the
exterior beams were reduced so that the stiffness of the external frame was diminished
in such a way that the axial forces induced in the columns of this frame were reduced.
Note that if a capacity analysis is made, it is not enough to reduce the stiffness of the
exterior beams, but it is also necessary to reduce the strength of these beams according
to the reduction in stiffness. By comparing Figure 2.14 with Figures 3.13 to 3.15, the size
adjustment of the different elements on the structure can be seen.
Table 3.1 summarizes the weights of the definitive version of the 30-story building. The
62
I I
. ) total weight of the building is about 22650 tons, which is about 75% of the weight
computed for this same building designed according to Japanese practice. An important
percentage of the weight reduction in the American design is due to the smaller sizes of
the columns and beams. The weight reduction due to smaller beams and columns is 4055
tons or 13.6% the weight of the Japanese building .. Nevertheless, a very important
I
I
~\
contributor to the reduction of the weight can be found in the reduction of the slab
thickness. The reduction in the weight of the building due to the thinner slab is about
2034 tons, or 6.8% the weight of the Japanese building. The total reduction due to
smaller structural elements is 13.6 + 6.8 = 20.4%. The rest of the reduction, 25 - 20.4 = '
4.6% is attributed to the smaller nonstructural element loads considered in the UBC
design (see section 3.3.1 ).
Table 3.3 summarizes the real eccentricities computed for each story. To compute
these eccentricities, the center of mass of each story was computed accounting for the
existence of holes in the diaphragm. The real eccentricity is defined as the distance
between the center of mass and the center of stiffness (whose location coincides with that
of the geometric centroid of the diaphragm assuming no hole exists).
Figure 3.11 shows the definition of real eccentricity. In general, it was found that the
values of real eccentricities are small compared to the plan dimension of the diaphragm.
As shown in Table 3.3, the larger eccentricities can be found in story 1 (0.496 m) and in
stories 2 to 12 (0.33 m). The eccentricities are small in the middle of the building and
grow again (up to 0.22 m) in the upper stories. This can be explained by the change in
the slab shape throughout the height of the building, as shown in Figure 2.4. It should be
noted that the floor real eccentricities were computed accounting only for the slab and
ignoring the other structural and non-structural elements in the story.
The dynamic properties of the building were estimated considering the real eccentricity
of the center of mass in each floor. The computed values are summarized in Table 3.4.
In it, the periods of the first 15 modes of the structure (5 in each plan direction: two
63
translations and 1 rotation) are included, as well as the participating mass for each mode.
By observing the effective weight factors in the table, it can be concluded that the modes
are practically associated with one direction, that is, there is little coupling between the
3 DOFs in plan. It can also be observed that the value of the fundamental mode of
vibration associated with each of the 3 directions (two translations and one rotation) is
very similar. The similitude for the translational periods can be explained by the fact that ,-
the building has practically the same structural layout in both directions, and that the real
eccentricity in both directions is small compared to the plan dimensions. Usually, for
regular buildings, the fundamental period of rotation has a similar value than those
corresponding to the translational DOFs.
Also, the dynamic properties of the building were estimated accounting for real plus
accidental eccentricity, as shown in Figure 3.12. These values are summarized in Table
3.5. As shown by the effective mass factors for each mode, a strong coupling exists
between the 3 DOFs when accidental eccentricity is accounted for. The consequence of
this coupling is discussed in section 3.6.3. As can be concluded from the comparison
between Tables 3.4 and 3.5, there is a significant change in the behavior of the building
when eacc is incorporated in the model.
Figure 3.16 shows a physical interpretation of the DOFs coupling in the first mode of
the model of the building that accounts for accidental eccentricity. As shown in the figure
and in the first mode of Table 3.5, there is a significant coupling of the 3 DOFs in the
diaphragm when the distance from the center of mass of the structure to the center of
stiffness of the structure is large. When the diaphragm rotates it will have significant
displacements in the two translational DOFs. Similar conclusions can be obtained for
each one of the translational DOFs, i.e., if the diaphragm translates in X direction, it will
have significative rotational and even translational displacements in the Y direction, etc.
64
I
\
) '
3.5 ELASTIC ANALYSIS OF ADOPTED PRELIMINARY DESIGN OF THE 30-STORY
BUILDING
In this section, the results of the various elastic analyses performed on the model of
the 30-story building are discussed. The analysis were carried out using the ETABS
PLUS computer program [Ref. 13].
3.5.1 PSEUDO-DYNAMIC APPROACH, RSA ANALYSIS TO OBTAIN DESIGN
I ! FORCES
To obtain the story forces, a RSA of the structure was carried out using the UBC
allowable stress spectra shown in Figure 3.3 (which was deriyed by reducing Rw times
the elastic site spectra for safety). The RSA was carried out accounting for the values of
1 ) the real eccentricity, and the ground motion was considered acting simultaneously in two
directions (1 00% in one direction and 30% in the other).
The results of the analysis are summarized in Figures 3.17 and 3.18. Figure 3.17
J shows the floor displacement obtained throughout the height of the building. In the same
figure, the displacement at the center of mass is compared with that obtained at the end
frame for each floor. Note that the center of mass displacement is not given for the same
( I
location in plan throughout the height of the building, because the location in plan of the
center of mass varies from floor to floor. Figure 3.11 defines the location of the center of
mass for the model of the building accounting for real eccentricity only. As shown in Table
3.3, the real eccentricities change through height (mainly in theY direction}, and thus the
center of mass has different locations throughout the height of the building.
The displacement at the tip of the building is 0.1144 m at the center of mass and
0.1174 m at the end frame. As shown in the figure, the effects of torsion due to real
eccentricity are not significant.
Figure 3.18 shows the force distribution obtained through the height of the building. The
forces shown in the figure are applied at the center of mass of the floor diaphragms. The
65
base shear obtained from the RSA, VovN• was equal to 936 ton or .041 W. From the
simplified static method proposed in section 2334.(b) of UBC, a base shear of 1020 ton
or .045 W was obtained. As discussed in section 3.3.1, UBC requires for VovN to be
scaled up to V sr· Such scaling is shown in Figure 3.18 for the floor forces, along with the
distribution of forces obtained using UBC static force procedure. As shown, for this
building and these design spectra, the scaling up of the forces is not significant. Also, it 1 ,
should be noted that the UBC static force procedure to compute the distribution of forces
over height leads to considerably larger lateral force on the top story, while it leads to ' '
smaller forces in stories 1 to 29. Thus, it can be concluded that the use of force
distribution obtained from UBC static method would lead to larger story shears and story
overturning moments for the 30-story building.
3.5.2 PSEUDO-DYNAMIC APPROACH, COMPUTATION OF DRIFT AND REQUIRED
STRENGTH OF MEMBERS
To obtain the design forces on the members and the story displacements of each
( I
frame, the scaled up dynamic response (V5rNovN), obtained assuming the scaled up I lateral RSA forces acting at the center of mass (Figure 3.18), was superposed on the
effects of the statically computed coupling loads to account for accidental eccentricity.
The earthquake input was considered simultaneously in two orthogonal directions
(1 00% in one direction and 30% in the other). The results from this analysis are
summarized in Figures 3.19, 3.20 and 3.21.
Figure 3.19 shows the floor displacements obtained in the center of mass and the end
frame for every floor when eacc is accounted for using the pseudo-dynamic approach.
Figure 3.12 shows how the center of mass is defined for a floor diaphragm when the
accidental eccentricity is accounted for. By comparison with Figure 3.11, it can be seen
that the center of mass has different locations in plan when accounting for and when
neglecting the accidental eccentricity in the floor diaphragm. Also note that the center of
mass of the diaphragms vary throughout the height of the building.
66
I \
, __
When accounting statically for accidental eccentricity, the tip displacement is equal to
0.1271 m at the center of mass and equal to 0.1498 m at the end frame. The effect of
the accidental eccentricities can not be assessed from the displacement at the center of
mass, because when accidental eccentricity is accounted for, the location of the center
of mass varies with respect to the location of the center of mass when only real
eccentricity is accounted for. Nevertheless, the effect of accidental eccentricity can be
studied from the displacements at the end frame (whose location does not vary).
Comparing the displacements for the end frame, it can be seen that when a RSA was
carried accounting only for real eccentricity, a tip displacement of 0.1174 was obtained;
while when the effects of accidental eccentricity were superposed, the tip displacement
increased to 0.1498, which represents an increase in the displacement of 27.6% for the
end frame. Nevertheless, it should be recalled that the dynamic forces and displacements
obtained in the former case were scaled up by V srI V ovN (1 020/936 = 1 .0897) before
superposing the effects of the accidental eccentricity, and thus the real increase due to
real eccentricity is given by 1 .276/1.0897 = 1 .171. Figure 3.20 compares the
displacements at the end frame obtained by neglecting and accounting for eacc using the
pseudo-dynamic approach. As shown, the torsional moments produced by the accidental
eccentricity of the center of mass result on a lateral displacement increase of 17%, which
is signi'ficant.
Figure 3.21 shows the IDI computed for the end frame throughout the height of the
building. As shown, all the stories comply with the UBC limit of 0.0025. Also, it can be
noticed that the larger values of IDI can be found in the lower stories, particularly stories
4 to 15, while stories 16 to 23 have slightly smaller values. The IDI diminishes
considerably towards the upper stories and becomes very small for the 30th story. This
distribution of IDI can be explained because the member sizes on the top stories were
not reduced, and also because the ratio between the effective and gross moments of
inertia are smaller for the lower stories and tend to grow in the upper stories (recall that
"'- a secant stiffness has been used to model the beams of the building). As shown in
Figures 3.19 to 3.21, the 30-story building shows a shear beam type of behavior.
67
3.5.3 COMPARISON BETWEEN PSEUDO-DYNAMIC AND DYNAMIC APPROACHES
As discussed in section 3.3.1, UBC gives two options for accounting for the accidental , ;
eccentricity in a building. These two options were termed in that section the pseudo-
dynamic approach and dynamic approach, respectively. In this section, a comparison
between the results obtained using both approaches is made. Figures 3.10 and 3.22
summarize the procedures used to analyze the building using these two approaches. A
detailed description of the pseudo-dynamic approach is given in section 3.3.3.
Before comparing the results obtained from the pseudo-dynamic and dynamic
approaches, two RSA analyses were carried out on the building: one accounting only for
real eccentricity, and the other accounting for real plus accidental eccentricity. It was
considered useful to carry out these two analyses to identify the influence of accounting
for the accidental eccentricity in the RSA of the building. To simplify the discussion of the
comparison between the results of both analyses, the ground motion was input on.ly on
the X translational direction of the building. Figure 3.23 compares the floor displacements
in the X direction obtained from both RSAs at the center of mass and at the end frame
of each floor. Note that the location of the center of mass for both analyses is different
(compare Figures 3.11 and 3.12).
As shown in the Figure 3.23, when accidental eccentricity was considered in the RSA,
the following was observed: the displacement of the center of mass on each story is
significantly diminished with respect to that obtained when the accidental eccentricity was
not considered in the RSA; while the displacement at the end frame increases with
respect to that obtained when no accidental eccentricity is considered in the RSA. The
displacements at the top story for the RSA accounting only for real eccentricity are 0.1144
m at the center of mass and 0.117 4 m at the end frame. These two values for the RSA
accounting for real plus accidental eccentricities are 0.0992 m and 0.1292 m, respectively,
representing a 13% decrease in the displacement at the center of mass and a 10%
increase in the displacement at the end frame. As shown in Figure 3.24, where the center
of mass and end frame displacement ratios through height are plotted for both RSA, the
68
....
/'
r I
torsional effects are increased considerably when accidental eccentricity is accounted for
r , in the RSA.
\_I
To explain the decrease of the floor displacements at the center of mass and the
increase of the floor displacements at the end frames, several aspects of the behavior of
the 30-story building need to be considered. Figure 3.25 shows a comparison of the story
shear distribution through height, in the X direction, for both RSA analyses (recall that
ground motion is input only in the X direction). As shown, when real eccentricity, er, plus
accidental eccentricity, eacc• are considered in the RSA, there is a significant reduction
in the values of the story shears in the X direction throughout the height of the building.
Figure 3.26 shows the ratio between both sets of story shears. As shown, the story
shears computed in the RSA that accounted for real plus accidental eccentricities are
about 85% of those computed in the RSA that only accounted for real eccentricity. The
story shear reduction helps explain the reduction in the center of mass floor
displacements for the RSA accounting for real plus accidental eccentricities, as compared
with that in which only real eccentricity was accounted for. To help explain the decrease
in story shear, Tables 3.4 and 3.5 must be compared. Table 3.4, which summarizes the
dynamic properties of the building accounting for real eccentricity only, shows the
behavior of a building whose modes are associated mainly with 1 DOF, that is, the
dynamic DOFS are practically uncoupled. In this type of building, if the ground motion is
input in any of the 3 principal directions, say X for example (as in the current RSA), the
response of the building is associated almost exclusively with that direction, while the
response in the perpendicular directions ( Y and rotation) is very small.
Table 3.5, which summarizes the dynamic properties of the model of the building that
accounts for eacc in the location of the center of mass of the floor diaphragms, shows a
structure with strong coupling of its 3 dynamic.DOF. Comparing all the modes of both
tables, it can be seen that when accounting for eacc• the translational modal mass tends
to be distributed evenly in the two translational DOFs (X and Y) for all modes. Other
consequences of accounting for eacc can be seen in the first mode of Table 3.5. As shown
69
by the effective mass factors, when the diaphragm rotates it also translates in the X and
Y directions, as shown in Figure 3.16, indicating that there is a strong coupling between
the 3 DOFs of the diaphragm. As a consequence the coupling, a ground motion that is
input in one of the principal directions, say X for example, would lead to a significant
response not only in that direction, but in the perpendicular directions as well \{ and
rotation). Figure 3.27 summarizes the story shear distribution obtained from the RSA
where er plus eacc were accounted for. Recall that for this analysis the ground motion was
input in the X direction. As shown, there is a significant response in the Y direction. Now
it can be concluded that, for the RSA accounting for er + eacc' the story shears in the
direction of the ground motion input, X direction, decrease with respect to the RSA where
only er is accounted for, because for the former model of the building a very important
percentage of the modal masses is associated with the perpendicular directions, Y and
rotation, where a significant response can be observed.
Simultaneously with a reduction of the response in the direction of the ground motion
input and the increase in the response associated with the Y direction, there is a
considerable increase in the torsional response of the building when eacc is accounted for,
as shown in Figure 3.28. The accidental eccentricity of the building, computed as 0.05
B, is about 1.50 m. Figure 3.28 shows floor torsional moment to floor force ratio at the
center of mass of the floors (defined in Figure 3.12) ranging from 7 m at the top stories
to 5 min the lower ones, i.e., 4.67 and 3.33 times the value of eacc· This elastic dynamic
amplification of the torsional effects have been identified and discussed elsewhere for
SDOFS [Ref. 16].
The problem with the above identified dynamic amplification of torsion is that, because
of the lack of UBC provisions to regulate this issue, the two options given by UBC to deal
with the accidental eccentricity in the analysis of a building lead to very different results.
Figures 3.29 to 3.31 summarize the results obtained from analyzing the building using the
pseudo-dynamic and dynamic approaches. Note that for this comparison, both
approaches result in the same location for the center of mass of the diaphragms (see
70
\ I
I_ i
' :
/ I
'-
' I
I
" I '
_,...,_
I ~
Figure 3.12). By comparing the results obtained using the two approaches, the following
observations can be made.
• As shown in Figure 3.29, the ratio between the displacement of a floor at its end frame
and at its center of mass varies considerably, depending on which approach is used. As
shown for the pseudo-dynamic approach, this ratio is slightly less than 1 .2 for every story,
while for the dynamic approach, the ratio is larger than 1 .3. According to UBC, this fact
is very significant because, as UBC states in its Table 23 N, the value of the ratio
between the displacement at the end and the average displacement of the diaphragm
must be limited to 1 .2, otherwise the building would have plan irregularity type A. At this
stage, it needs to be considered that the displacement at the center of mass is slightly
larger than the average displacement of the diaphragm, as shown in Figure 3.32. Thus,
the average displacement of the diaphragm was computed and Figure 3.29 shows the
corrected displacement ratios. The 30-story building, which has small values of er and
symmetrical stiffness and strength with respect to the geometric centroid of the
diaphragms, can be considered as not having torsional irregularity (USC plan irregularity
type A) when using the pseudo-dynamic approach; nevertheless, if the dynamic approach
is used, the structure needs to be defined as torsionally irregular. This fact leads to a
definition problem when using USC specifications, because the torsional irregularity of a
building is dependent not only on the properties of the building itself, but on the procedure
used to account for eacc·
• As discussed in section 3.3.1, the base shear obtained from a dynamic analysis has to
be scaled up to a given percentage of the static base shear. Other parameters, such as
displacements and member forces and moments, need to be scaled up by the same ratio.
What this means is that, although the base shear obtained for both approaches is
significantly different, as shown in Figures 3.25 and 3.26, both have to be scaled up to
the same base shear value. The static base shear is 1020 ton, while the dynamic base
-- shears are 936 ton and 788 ton in the direction of the input ground motion, for the RSAs
ignoring and accounting eacc respectively. To scale up the forces for the pseudo-
71
dynamic approach, the story forces have to be multiplied by a factor of 1 020/936 = 1.09
(9% increase). To scale up the forces in the dynamic approach, it must be noticed
that, as shown in Figure 3.27, there are significant story shears in the direction
perpendicular to that of the inputted ground motion. The base shears are 788 ton in the
direction of the input and 328 in the perpendicular direction. If the structure needs to be
analyzed simultaneously in two directions, 1 00% and 30%, a problem arises for the
dynamic approach: should the results of the RSA considering ground motion in only one
direction be scaled up before superposing the bidirectional effects, that is, use a scale
factor of 1 020/788 = 1 .23, and then after scaling superpose the bidirectional effects; or
should the bidirectional effects need to be superposed first and then scaled up, that is,
use a scale factor of 1 020/(788+0.3(328}} = 1.15. The latter approach would lead to a fair
comparison, because then, the base shear after superposing the bidirectional effects
would be practically 1020 ton for both approaches.
These two approaches lead to completely different results for the design of some
members, mainly of those that belong to the end frame. Figure 3.30 compares the end
frame displacements for the pseudo-dynamic and dynamic approaches. As shown, the
displacement at the top story, accounting for earthquake input in two perpendicular
directions, computed for the pseudo-dynamic approach is 0.1498 m, while that obtained
for the dynamic approach is 0.1721 m, which would be reflected in about 15% larger
design forces for the end frame (assuming the same stiffness for the frame for both set
of results). It can also be seen that the displacements at the center of mass of the floors
are very similar for both approaches. Figure 3.31 shows the comparison of the IDI
distribution over height computed at the end frame for both approaches. As shown, the
use of the dynamic approach leads to larger IDI. For the 30-story building, the pseudo
dynamic approach gives a maximum IDI of 0.0021, while the dynamic approach gives
0.0025, which is equal to the limit for IDI given by USC. This fact leads to problems in the
USC approach, because the adequacy of the structure for drift requirements does not
only depend on the structure itself, but depends significantly on the procedure used to
account for eacc in the structural analysis of the building.
72
' I i
! .
'•-
' '
·~
t •
In this work, the pseudo-dynamic approach was used for the design and revision of the
30-story building. Selecting which procedure to use to account for accidental eccentricity
is not easy. At this stage, the following should be considered:
Pseudo-dynamic approach. It is not correct to compute the design forces using a
RSA accounting for real eccentricities and then complete the analysis by superposing
static torsional moments to estimate the effects produced by the existence of accidental
eccentricities. In this way, the possible benefits of performing a dynamic analysis are lost,
particularly for buildings that are irregular in plan.
Dynamic Approach. Although at first glance this would appear to be a correct
procedure, the use of real plus accidental eccentricities in a RSA leads to results that are
difficult to interpret using the UBC Code. Due to the large amplification of torsion when
accounting for accidental eccentricity, two important defects can be observed when using
this procedure: first, in the majority of the cases where the fundamental translational and
rotational periods of the structure are close (which is very common), the torsion
amplification would usually lead to displacement ratios (displacement at the end frame to
the average displacement in the diaphragm) larger than 1.2. Even if the structure is
perfectly symmetrical, this fact would lead to a structure with plan irregularity type A
Secondly, the amplification of torsion in structures which are highly redundant in torsion,
have a symmetrical layout of mass and yielding strengths and possess high ductility
would only be observed in the elastic range, and thus the torsion amplification would be
considerably reduced if the structure were to go into its inelastic range of behavior.
The value of 0.05 B for the accidental eccentricity was adopted a long time ago, and
was developed considering the behavior of one-story buildings. With the development of
powerful computer programs with 3D analysis capabilities, the possibility of performing
a purely dynamic approach has brought several problems when trying to apply the code
requirements for eacc· None of the above procedures are rational: on one hand the
pseudo-static approach is irrational, while on the other hand the dynamic approach has
73
a rational basis but sometimes leads to results that are not only difficult to interpret, but
also to justify. The probability of having the same specified large eacc through the whole
height is very low. There is a need to determine values of eacc for multistory buildings
which are a function of the number of stories of the building. That is, it is necessary to
assess how probable it is for eacc to have the same value and orientation with respect to
the real center of mass, for all diaphragms in a multistory building. Finally, the
amplification of torsional response needs to be considered only for the strength of the
members at first yielding. For safety limit state, torsion should be assessed using different
procedures [Ref. 5].
In this work, the pseudo-dynamic approach was adopted, not based on its rationality,
but because it was considered that the majority of American engineers would choose to
use this method of analysis given that it leads to smaller displacements and member
forces in the structure, particularly at the end frames, and thus to a more economical
design. Currently, there is a need to come up with consistent method(s) to deal with eacc
in the USC approach.
3.6 REINFORCED CONCRETE DESIGN ACCORDING TO UBC
For the design of the beams and columns, guidelines from section 2625 of USC were
used. A summary of the most important USC RC earthquake design requirements follows:
• Strength Reduction Factors: Strength reduction factors are the same as those given
for non-earthquake design, except that the strength reduction factor for axial compression
and flexure shall be 0.5 for columns whose transverse reinforcement does not confine the
section properly for ductile behavior.
• Concrete Strength: Compressive strength f~ shall no be less than 3000 psi.
• Reinforcement: Steel with grades 40 and 60 should be used. The ratio of the actual
ultimate tensile stress to the actual tensile yield strength is not less than 1.25.
74
' ' '
• Flexural Members (I.e. Beams):
SCOPE
• Factored axial compressive force on member shall not exceed A/c/1 0
• Clear span for the members shall not be less than 4 times its effective depth
• The width to depth ratio shall not be less than 0.3
• The width shall not be less than 10 inches nor more than the width of the supporting
member
LONGITUDINAL REINFORCEMENT
• For single reinforced beams, the amount of positive and negative reinforcement shall
not be less than 200 bwdlfv. The reinforcement ratio, p, shall not exceed 0.025. At least
two bars shall be provided continuously at both top and bottom .
• Positive moment strength at joint face shall not be less than one half of the negative
moment strength provided at the face of the joint. Neither the negative nor the positive
moment strength at any section along the member length shall be less than one fourth
th~ maximum moment strength provided at the face of either joint.
TRANSVERSE REINFORCEMENT
• Hoops shall be provided over a length equal to twice the member depth measured
from the face of the supporting member toward midspan, at both ends of the flexural
members
• the first hoop should be located not more than 2 inches from the face of the •
supporting member
• maximum spacing of these hoops shall not exceed (1) d/4, (2) 8 times the diameter
of the smallest longitudinal bar, (3) 24 times the diameter of the hoop bar, and (4) 12
inches
• where the above hoops are not required, stirrups with 135 degree seismic hooks shall
be spaced at no more than d/2 throughout the length of the member
75
Members Subjected to Bending and Axial Loads (I.e. Beam and Columns):
SCOPE
• Factored axial compressive force on member exceeds Agf'J1 0
• Shortest cross sectional dimension, measured on a straight line passing through the
geometric centroid, shall not be less than 12 inches
• The ratio of the shortest cross-sectional dimension to the perpendicular dimension
shall not be less than 0.4
MINIMUM FLEXURAL STRENGTH
• The flexural strengths of the columns shall satisfy the following:
~M> 6 ~M L..., c 5L..., g
where
}: Me = sum of moments, at the center of the joint, corresponding to the design flexural
strength of the columns framing into that joint. Column flexural strength shall be
calculated for the factored axial force resulting in the lowest flexural strength.
}: M9 = sum of moments, at the center of the joint, corresponding to the design
flexural strength of the beams framing into that joint.
LONGITUDINAL REINFORCEMENT
• The 'reinforcement ratio, p9
, shall not be less than 0.01 and not more than 0.06
TRANSVERSE REINFORCEMENT
• Transverse reinforcement as specified below shall be provided unless a larger amount
is required by strength:
(i) The volumetric ratio of spiral or circular hoop reinforcement, p5 , shall not be less
than
76
(A ) r:
Ps = 0.45 ___p_ - 1 ~ Ac fyh
(ii) the total cross-sectional area of rectangular hoop reinforcement shall not be less
than
In the above expressions, s is the spacing of transverse reinforcement measured along
the longitudinal axis, he the cross sectional dimension of column core measured center-to
center of confining reinforcement, fyh the yield strength of the transverse reinforcement,
A9
the net area of concrete section bounded by web thickness and length of section in
the direction of the shear force considered, Ach the cross sectional area of the structural
member measured out-to-out of transverse reinforcement, and Ac the area of core of
spirally reinforced compression member measured to outside diameter of spiral.
* Transverse reinforcement shall be spaced at distances not exceeding 4 inches
* Crossties or legs of overlapping hoops shall not be spaced more than 14 inches on
center in the direction perpendicular to the longitudinal axis of the structural member
* Transverse reinforcement in the amount specified above shall be provided over a
length 10 from each joint face and on both sides of any section where flexural yielding may
occur. The length 10
shall not be less than (1) the depth of the member at the joint face
77
or at the section where flexural yielding may occur, (2) one sixth of the clear span of the
member, and (3) 18 inches .
• The remaining length of the column shall contain spiral or hoop reinforcement with
center to center spacing not exceeding the smaller of six times the diameter of the
longitudinal column bars or 6 inches.
Joints of Frames
GENERAL REQUIREMENTS
• Forces in the longitudinal beam reinforcement at the joint face shall be determined by
assuming that the stress in the flexural tensile reinforcement is 1.25 fy.
TRANSVERSE REINFORCEMENT
• Same amount specified for columns in the length 10 shall be provided in the joint
unless the joint _is confined by structural members as follows:
- within the depth of the shallowest framing member, transverse reinforcement equal
to at least one half of the amount required above where members frame into all four sides
of the joint and where each member width is at least three fourths the column width. At
these locations, the spacing may be increased but shall not exceed 6 inches;
-transverse reinforcement as required in length 10 of columns shall be provided through
the joint to provide confinement for longitudinal beam reinforcement outside the column
core if such confinement is not provided by a beam framing into the joint
SHEAR STRENGTH
• The nominal shear strength at the joint shall not exceed the forces specified below:
-for joints confined on all four faces ................................................................ 20 Vf?.J - for joints confined on three faces or on two opposite faces ........................ 15 v'1: Ai
- for others ..................................................................................................... 12 VJ; Ai
where Ai is the effective cross sectional area within the joint in a plane parallel to the · .,
plane of the reinforcement generating shear in the joint. The joint depth shall be the
overall depth of the column. Where a beam frames into a support of larger width, the
78
effective width of the joint shall not exceed the smaller of (1) beam width plus the joint
depth, (2) twice the smaller perpendicular distance from the longitudinal axis of the beam
to the column side
A joint is considered to be confined if such confining members frame into all faces of
the joint. A member that frames into a face is considered to provide confinement to the
joint if al least three fourths of the face of the joint is covered by the framing element.
Transverse Reinforcement in Frame Members.
* For determining the required transverse reinforcement in frame members in which the
earthquake-induced shear force represents one half or more of total design shear, the
quantity Vc shall be assumed to be zero if the factored axial compressive force including
earthquake effects is less than A9f~ /20.
3.7 MEMBER SIZES AND LONGITUDINAL REINFORCEMENT
Figures 3.13 to 3.15 and 3.33 to 3.4 7 summarize the design of beams and columns of
the 30-story building. In Figures 3.13 to 3.15 the sizes of the members are shown. Figure
3.33 shows the location in plan of the different types of beams according to their
reinforcement. As shown, there are 7 different types of beams in a story, according to
their size and reinforcement. Figure 3.34 shows the location in plan of the different types
of columns in a story according to their size and reinforcement. The different types of
columns and beams define 3 different types of frames in all the structure: frames A and
G are the same; frames B, C, E and F are the same; and finally frame D.
Figures 3.35 to 3.41 summarize the percentage of steel of the beams, while Figures
3.42 to 3.44 do so for the different types of columns.
All columns in a story have the same size, and their sizes through height are shown
in Figure 3.13. Figures 3.42 to 3.44 summarize the steel ratios for the different types of
columns. As shown in these figures, the steel ratios in the bottom columns are close or
79
equal to 0.06, which is the maximum steel percentage allowed by U8C. The steel
percentage decreases rapidly starting at columns located in the 6th to 8th floor, until they
reach very low percentage of steel in story 13. Some jumps in the value of steel
reinforcement can be seen in the 2th, 5th and 18th stories. This can be explained by
noticing, in Figure 3.13, the change in columns sizes in these floors with respect to these
sizes in the story below them.
For the design of the beam reinforcement, the contribution of the slab to the strength
of the beams was neglected. Figures 3.14 and 3.15 show the variation of beam sizes
throughout the height of the building. As shown, there are two sizes of beams in a story.
Figure 3.15 shows the sizes of the beams in the perimeter frames, which correspond to
beam types 81 and 82 in Figure 3.33; while Figure 3.14 shows the sizes of the interior
beams, which correspond to beam types 83 to 87. In some bays, as shown in Figures
3.35, 3.37 and 3.40, the percentage of steel is practically constant for the bottom 15
stories, and in other cases it increases over height in the first 15 stories. As shown in
Figures 3.14 and 3.15, the beam sizes are constant from story 2 to 15, which, combined
with the fact that the steel ratio is almost constant through these stories, implies that the
strength of the beams is practically constant throughout the first 15 stories, and in some
cases it increases over height. Figures 3.45 to 3.47 show a comparison between the
required end moments obtained from the elastic analysis of the structure and the supplied
moments (which were computed including a 0.9 reduction factor and neglecting for the
contribution of the slab to the strength of the beam) in the beams of the first 3 bays of
frame 8 (refer to Figure 3.33 for location of frame B). As shown, the strength of the
beams is practically constant in the 15 bottom floors, ~nd then decreases slowly towards
the top of the building. The reasons for these unusual strength requirements of beams
over height are discussed in Chapter 5.
80
Story Beams Column Slab (1) (2) (3)
30 223.7 104.0 316.4
29 169.9 106.2 280.7
28 172.5 106.2 280.7
27 165.4 106.2 277.8
26 165.4 106.2 275.5
25 160.4 106.2 272.6
24 160.4 106.2 270.3
23 160.4 106.2 270.3
22 160.4 106.2 270.3
21 160.4 106.2 270.3
20 176.3 106.2 270.3
19 176.3 106.2 270.3
18 176.3 106.2 270.3
17 176.3 124.6 270.3
16 176.3 124.6 270.3
15 176.3 124.6 270.3
14 176.3 124.6 270.3
13 176.3 124.6 270.3
12 171.0 124.6 264.8
11 171.0 124.6 264.8
10 171.0 124.6 264.8
9 171.0 124.6 264.8
8 171.0 124.6 264.8
7 171.0 124.6 264.8
6 171.0 124.6 264.8
5 171.0 124.6 264.8
4 171.0 124.6 264.8
3 171.0 144.5 264.8
2 171.0 144.5 264.8
1 206.4 213.0 273.8
Total 5197.4 3624.8 8134.4
(1) does not include slab nor joint weight (2) includes weight of joint (3) for a slab thickness of 12 em (4) for a 10 psf distributed weight
Partition Ceil. Other Perlm. Total (4) (4) (5) (6)
56.0 56.0 409.4 18.1 1183.6
49.7 49.7 49.7 27.2 733.1
49.7 49.7 49.7 27.2 735.8
49.2 49.2 49.2 27.2 724.1
48.8 48.8 48.8 27.2 720.7
48.3 48.3 48.3 27.2 711.3
47.9 47.9 47.9 27.2 707.7
47.9 47.9 47.9 27.2 707.7
47.9 47.9 47.9 27.2 707.7
47.9 47.9 47.9 27.2 707.7
47.9 47.9 47.9 27.2 723.6
47.9 47.9 47.9 27.2 723.6
47.9 47.9 47.9 27.2 723.6
47.9 47.9 47.9 27.2 742.0
47.9 47.9 47.9 27.2 742.0
47.9 47.9 47.9 27.2 742.0
47.9 47.9 47.9 27.2 742.0
47.9 47.9 47.9 27.2 742.0
46.9 46.9 46.9 27.2 728.4
46.9 46.9 46.9 27.2 728.4
46.9 46.9 46.9 27.2 728.4
46.9 46.9 46.9 27.2 728.4
46.9 46.9 46.9 27.2 728.4
46.9 46.9 46.9 27.2 728.4
46.9 46.9 46.9 27.2 728.4
46.9 46.9 46.9 27.2 728.4
46.9 46.9 46.9 27.2 748.3
46.9 46.9 46.9 27.2 748.3
46.9 46.9 46.9 27.2 748.3
48.5 48.5 238.7 32.5 1061.4
1440.2 1440.2 1983.8 812.2 22653.7
(5) for a 10 psf distributed weight, except on 30 story, where masonry walls, water deposit and elevator machinery are considered, and for first story, where weight of annex building is included [ref. 14].
(6) includes weight of perimeter beam plus glass wall
TABLE 3.1 ESTIMATED WEIGHTS, in tons, FOR UBC DESIGN
81
Story Japanese Design UBC Design Conceptual Design
30 1385 1183.6 905.5
29 952 733.1 817.3
28 952 735.8 819.3
27 967 724.1 833.6
26 964 720.7 830.5
25 961 711.3 821.3
24 945 707.7 818.2
23 945 707.7 860.3
22 945 707.7 860.3
21 945 707.7 860.3
20 945 723.6 860.3
19 945 723.6 860.3
18 945 723.6 860.3
17 945 742.0 876.1
16 945 742.0 876.1
15 945 742.0 876.1
14 945 742.0 876.1
13 945 742.0 876.1
12 981 728.4 862.2 11 981 728.4 862.2
10 981 728.4 884.1
9 981 728.4 884.1
8 981 728.4 884.1 7 981 728.4 884.1
6 981 728.4 884.1
5 981 728.4 884.1
4 981 748.3 884.1
3 981 748.3 884.1
2 981 748.3 884.1
1 981 1061.4 1084.6 TOTAL 29711 22653.7 26095.1
TABLE 3.2. COMPARISON OF WEIGHT IN TONS OF BUILDINGS WITH SAME CONFIGURATION DESIGNED ACCORDING TO DIFFERENT GUIDELINES
82
Story TOTAL AREA Eccentricity Eccentricity (m2> In X (m) In V (m)
30 1146.6(1) 0.004 -0.215
29 1017.2 -0.009 -0.216
28 1017.2 -0.009 -0.216 27 1006.4 -0.010 -0.164
26 998.3 -0.010 -0.126 25 987.8 -0.010 -0.081 24 979.4 -0.010 -0.048 23 979.4 -0.010 -0.048 22 979.4 -0.010 -0.048 21 979.4 -0.010 -0.048 20 979.4 -0.010 -0.048 19 979.4 -0.010 -0.048
18 979.4 -0.010 -0.048 17 979.4 -0.010 -0.048 16 979.4 -0.010 -0.048 15 979.4 -0.010 -0.048 14 979.4 -0.010 -0.048 13 979.4 -0.010 -0.048 12 959.5 -0.010 -0.333 11 959.5 -0.010 -0.333 10 959.5 -0.010 -0.333 9 959.5 -0.010 -0.333
8 959.5 -0.010 -0.333 7 959.5 -0.010 -0.333 6 959.5 -0.010 -0.333 5 959.5 -0.010 -0.333 4 959.5 -0.010 -0.333 3 959.5 -0.010 -0.333 2 959.5 -0.010 -0.333 1 991.9 0.063 -0.496
(1) includes area of penthouse
TABLE 3.3 STORY ECCENTRICITIES FOR 30-STORV BUILDING
83
EFFECTIVE MASS FACTORS (AS % OF Mode Period TOTAL MASS)
Number (sees) X-translation Y -translation Z-rotation
1 2.53 65.92 9.73 0.31 2 2.53 9.76 66.18 0.00 3 2.37 0.28 0.02 76.27 4 0.84 11.99 0.55 0.10 5 0.84 0.56 12.08 0.00 6 0.78 0.09 0.00 11.63. 7 0.46 4.18 0.10 0.03 8 0.46 0.10 4.24 0.00 9 0.43 0.06 0.00 4.36
10 0.32 2.02 0.01 0.02 11 0.32 0.01 2.03 0.00 12 0.30 0.02 0.00 2.04 13 0.24 1.29 0.02 0.01 14 0.24 0.02 1.30 0.00 15 0.23 0.01 0.00 1.32
TOTAL 96.30 96.30 96.10
TABLE 3.4 DYNAMIC PROPERTIES OF MODEL OF 30-STORY BUILDING WHEN eacc IS NOT INCLUDED
84
EFFECTIVE MASS FACTORS (AS % OF Mode Period TOTAL MASS)
Number (sees) X-translation Y -translation Z-rotation
1 2.71 28.00 25.44 22.80
2 2.53 36.25 39.70 0.00
3 2.22 11.70 10.79 53.80 4 0.90 4.97 4.18 3.23
5 0.84 5.80 6.84 0.00
6 0.73 1.86 1.62 8.50 7 0.49 1.66 1.38 1.21
8 0.46 1.97 2.37 0.00
9 0.40 0.70 0.59 3.19
10 0.34 0.81 0.67 0.57 11 0.32 0.94 1.11 0.00 12 0.28 0.28 0.25 1.53 13 0.26 0.55 0.45 0.32 14 0.24 0.60 0.72 0.00 15 0.21 0.12 0.11 1.09
TOTAL 96.20 96.20 96.20
TABLE 3.5 DYNAMIC PROPERTIES OF MODEL OF 30-STORY BUILDING WHEN eacc IS INCLUDED
85
..... -60
80
100
120
Shear Wave Velocity, fps
\ \ \ \ ,......__~
I ' \ I \ - ·-·- -·-·-.,
\ \
\ \ \ \ \ \
i i i
\ \ \ \
Son Mateo (Bridgewoy Pork) Ravenswood Redwood Point Son Mateo (Audubon School) Coyote Hill Embarcadero Center
1 40 L-.L_J.._.J...._.J...._...J.......J.....~~--'---'---L..--L.---L.--..1.~--L..-----.1...-..L..-..1
0 500 1000 1500 2000
FIGURE 3.1 MEASURED SHEAR WAVE VELOCITY PROFILE FOR YOUNG BAY MUD FOR SIX SAN FRANCISCO BAY SHORE SITES [11]
86
I
Sa/g 1
0.9
0.8
0.7
0.6
0.5
Site Spectra Service (~=0.02} and Safety (~=0.05}
. ..-.... ---.... ........ . I ...... , . .....,
/ -...... . ....._ ~fety ~ = 1 // ·~ ... · ... ···~---·~·· ........ · ······~·~ ........... . I , f ···· ...... I ·---..........,\\
. ~------ .... 0.4 J.. ...... ··· -·,······ .... safety ~ = 2.5
:, ............ __ 0.3 i' ----- -------- ........ -- ..... __
0.2
0.1
o~~--~~~~~~~~~~--~~~~ 0 0.4 0.8 1.2 1.6 2.0 2.4 2.8
Period (sees}
FIGURE 3.2 SITE SPECTRA
87
Sa/ UBC Spectra and Elastic Site Spectra for Safety g 1 ~ = 0.05
0 9 ...-. ...--..... .. . . ~~
/' .... ~.~,....._, site safety f.L = 1 0.8 1 '..... .. ................. ~.'"'-
.l. ....._ ____ ... • ••
0.7 .1 ·· ..................... . ~ ....
~:: I reduce R.,. ~ 12 times ~\\\ :
0 f .4 I
0.3
0.2 0.1 UBC design
0 ----------------- ------------·-usc-ailowat>lesiiess·-----------------o 0.4 0.8 1.2 1.6 2.0 2.4 2.8
Period (sees)
FIGURE 3.3 OBTAINING UBC FROM SITE SPECTRA
88
UBC Spectra Sa/g Safety for~= 1 and ~=0.05
1.1
1 ;------------------- ..... soil type 4 static
soil type 3 dynamic . . . .
0.9 i .--··--·.......... "\ ' .... '······-. .....:_", : / ""
08 I l ".;-, . : ... ·· ", ·-......
0 : !.... " ...... _ .. .._ ...
7 ' : ~ . : i .......... . : .. 0.6 i / "' .... ,
i j ••••• ...... 0.5 i! -.. 0
.4 !,,1 ., ____ _
-c- soil type 4 dynamic ....... -... ...... ..... -· ···· ... .... , ... ,
-...............-...-.._, . ·· ..
·········------. 0.3 ! ·-.....
0.2
0.1
o~~~~~~~~~~~~~~~~~~~
0 0.4 0.8 1.20 1.60 2.00 2.40 2.80 Period (sees)
FIGURE 3.4 COMPARISON OF UBC SPECTRA FOR DIFFERENT SOIL CONDITIONS AND SITE SPECTRA
89
Sa/g 0.45
0.4
0.35
Comparison between UBC and Site Spectra .--···· ..... . . . . · ·· .
• / saf~)y.site w=2.5 .: '· .. : ··. . '· . ' : ..
/ UBC design ~% OVS ................. .. 0.3 . . . .. ..
0.25
0.2
0.15
0.1
0.05
UBC design .. -·······················-------·-···········----
UBC allowable stress
·:···-···-:-..... , ..... ---
______ ......
o~--~~~~~--~~~~--r-~~~--~.-0 0.4 0.8 1.2 1.6 2.0 2.4 2.8
Period (sees}
FIGURE 3.5 COMPARISON OF UBC SPECTRA AND DESIGN SPECTRA FOR CONCEPTUAL DESIGN
90
y
--·~X
e
-$- center of mass
I FIGURE 3.6 DYNAMIC DOFS ASSOCIATED WITH FLOOR DIAPHRAGM
91
y
X center of mass X
y
- General diaphragm - Uniformely distributed mass per unit area - Total mass of diaphragm = M - Area of diaphragm = A - Moment of inertia about XX and YY = lx and ly respectively
FIGURE 3.7 FORMULA TO COMPUTE ROTARY INERTIA
92
v2 t-- ks for ultimate
v1 . : ~ ks for first yield
/Lf- k8 for allowable stress
t/ L\t
V1 =base shear for allowable stress limit state
v2 = base shear at first yield
FIGURE 3.8 BASE SHEAR VS. TIP DISPLACEMENT CURVES FOR MULTISTORY BUILDING AT DIFFERENT LIMIT STATES
93
cracks
I = eft
leftR+ ~ftL 2
a) Bottom Stories
~ ... I/
I = eft
b) Top Stories
( .
I /~
/ '
FIGURE 3.9 PROCEDURE TO COMPUTE leu
94
Set model of the building
RSA y ground motion in two perpendicular directions
(100% in X and 30% inY)
superpose static coupling loads
'Fxs -+-te '~ + +ry \~
-r-e+
static torsional mome due to e"""
IT
forces in center of mass
scale dynamic response by _'!_g_
VovN
-t- +
apply load fact ors and ations load combin
End Moments in Sizes and longitudinal Beams and Columns reinforcement in members
NO
Compute Moment of Inertia of Beams and Columns Compute Story Mass
YES
GO TO ANAL DESIGN I
FIGURE 3.10 PSEUDO-DYNAMIC APPROACH
95
-$- center of mass
-+- geometric centroid of diaphragm
ery real eccentricity in y direction
en: real eccentricity in x direction
FIGURE 3.11 DEFINITION OF CENTER OF MASS ACCOUNTING FOR e,
96
+- -t-
erx + eaccx
-$- center of mass
• geometric centroid of diaphragm
e ry real eccentricity in y direction
e rx real eccentricity in x direction
e accy accidental eccentricity in y direction
eaccx accidental eccentricity in x direction
FIGURE 3.12 DEFINITION OF CENTER OF MASS ACCOUNTING FOR e, + eacc
97
Story 30
25
20
15
10
5
1
Sizes of Columns
1 0 20 30 40 50 60 70 80 90 1 0 Size (em)
FIGURE 3.13 COLUMN SIZES
98
Floor
30
25
20
15
10
5
1
Sizes of Interior Beams
,
width height
0 1 0 20 30 40 50 60 70 80 90 1 00 Size (em)
FIGURE 3.14 INTERIOR BEAM SIZES
99
Floor Sizes of Exterior Beams
30
' 25
20
width height
15
10
5
1 0 10 20 30 40 50 60 70 80 90 100
Size (em)
I
FIGURE 3.15 EXTERIOR BEAM SIZES
100
-$- center of mass
• geometric centroid of diaphragm
(location of center of stiffness)
FIGURE 3.16 PHYSICAL INTERPRETATION OF DOF COUPLING
101
Floor 30
25
20
15
10
5
1
Elastic RSA Real Eccentricities Only
J /
Center of Mass ... ...-.. /
·' .. / ./ .. End Frame
·' ' ,•"' .,. .. · ... , . .... ...
,"."
.•.. .--····· ...... •··•····•·
0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 Floor Displacement (em)
,~ FIGURE 3.17 FLOOR DISPLACEMENTS OBTAINED FROM ELASTIC RSA "~ ACCOUNTING FOR er
', ',
----102
i i
/ I
Elastic RSA Sto~
Real Eccentricities Only
------~:·~---------~-~~~-~~~~i:-~==~~re 25 ' I
/ i'--Scaled Up Vsr/ VoYN
20 From RSA
15
10
5
1 50 100 150 200 250
Story Force (ton)
FIGURE 3.18 FLOOR FORCES AT CENTER OF MASS OBTAINED FROM ELASTIC RSA ACCOUNTING FOR er
103
Floor 30
25
20
15
10
5
Pseudo-dynamic Approach Real + Accidental Eccentricities
0.04 0.06 0.08 0.1 0.12 0.14 0.16 Floor Displacement (m)
FIGURE 3.19 FLOOR DISPLACEMENTS OBTAINED FROM PSEUDODYNAMIC APPROACH (er + eacc>
104
Floor 30
25
20
15
10
5
1
Pseudo-dynamic Approach Effect of Accounting for Accidental Eccentricity
0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 Floor Displacement (m}
FIGURE 3.20 COMPARISON OF FLOOR DISPLACEMENTS WHEN NEGLECTING AND ACCOUNTING FOR eacc USING PSEUDODYNAMIC APPROACH
105
Story
30
25
20
15
10
5
1
Pseudo-dynamic Approach Real + Accidental Eccentricities
0.0005 0.001 0.0015 0.002 0.0025 101
FIGURE 3.21 IDI OBTAINED FROM PSEUDO-DYNAMIC APPROACH (er + e.cJ
106
Set model of the bulldi!"Q using properties of definitive preliminary design
RSA j} ground motion In two perpendicular dlractlons (100% In X and 30% In Y)
Fys
+- -+-
erx + eaccx
J}scala dynamic response by Vsr
VDYN
I FINAL DESIGN I
FIGURE 3.22 DYNAMIC APPROACH
107
0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 Floor Displacement (m)
FIGURE 3.23 COMPARISON OF FLOOR DISPLACEMENTS OBTAINED FROM ELASTIC RSA ACCOUNTING FOR e, AND FROM ELASTIC RSA ACCOUNTING FORe,+ eacc
108
Elastic RSA Floor Effect of Accounting for Accidental Eccentricities
30 i l l l
25 i i l ! l
~ l i i
without e ! with e acc 15 i
l ! ! !
10 i l ! ! !
5 l ! f ' '
0.2 0.4 0.6 0.8 1 12 1.4
Displacement end frame 1 displacement center of mass
FIGURE 3.24 COMPARISON OF FLOOR DISPLACEMENTS RATIOS OBTAINED FROM ELASTIC RSA ACCOUNTING FOR e, AND FROM ELASTIC RSA ACCOUNTING FOR e, + eacc
109
Elastic RSA Sto~ Effect of Accounting for Accidental Eccentricity
25
20
without eiCC 15
10
5
0 100 200 300 400 500 1000 . Story Shear (ton)
FIGURE 3.25 COMPARISON OF STORY SHEARS OBTAINED FROM ELASTIC RSA ACCOUNTING FOR e, AND FROM ELASTIC RSA ACCOUNTING FOR e, + eecc
110
Elastic RSA Sto&b Effect of Accounting for Accidental Eccentricity
25
20
with/without 15
10
5
0 0.2 0.4 0.6 0.8 1 Story Shear RATIO
FIGURE 3.26 RATIO OF STORY SHEARS OBTAINED FROM ELASTIC RSA ACCOUNTING FOR er AND FROM ELASTIC RSA ACCOUNTING FOR er + eacc
111
Elastic RSA StorY. Effect of Accounting for Accidental Eccentricity
30 '"" \\
\ 25
\\ 20
15 \ Y direction
10
5
0 100
\ \
~ i
\ \ !
500 600 700 800 900 1000 Story Shear (ton)
FIGURE 3.27 STORY SHEARS OBTAINED FROM ELASTIC RSA ACCOUNTING FOR er + eacc
112
Elastic RSA Floor Effect of Accounting for Accidental Eccentricity
30
25
20
15
10
5
0 2 4 6 8 10 [Floor Torsional Moment I Floor Force J (m)
FIGURE 3.28 RATIO OF FLOOR TORSIONAL MOMENT TO FLOOR FORCE OBTAINED FROM ELASTIC RSA ACCOUNTING FOR er + eacc
113
Floor 30
25
20
15
10
5
0
Pseudo-dynamic and Dynamic ~P.roaches Real + Accidentaf Eccentricities
Pseudo-dynamic Dynamic
I
\ 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6
Displ. End Frame I Average Displacement
FIGURE 3.29 COMPARISON OF FLOOR DISPLACEMENTS RATIOS OBTAINED FROM THE PSEUDO-DYNAMIC AND DYNAMIC APPROACHES
114
Floor 30
25
20
15
10
5
Pseudo-dynamic and Dv.namic ~~)roaches Real + Accidental Eccentricities
Dynamic
- center of mass
----· end frame
Pseudo-dynamic
········· center of mass
-·-·· end frame
0 0.025 0.05 0.075 0.1 0.125 0.15 0.175 0.2 Floor Displacement (m)
FIGURE 3.30 COMPARISON OF FLOOR DISPLACEMENTS OBTAINED FROM THE PSEUDO-DYNAMIC AND DYNAMIC APPROACHES
115
Sto~
25
20
15
10
5
Pseudo-dynamic and D~namic AP.proach Real + Accidental Eccentric1t1es
........ -...::::::: .. ........ .....
.............. ......... ..... ...... ....
)
z \.
\
Pseudo-dynamic\ ·.
--~ ·--···········--······.,.
I F.,/
.,../
0 0.0005 0.001 0.0015 0.002 0.0025 0.003 IDI
FIGURE 3.31 COMPARISON OF IDI OBTAINED FROM THE PSEUDODYNAMIC AND DYNAMIC APPROACHES
116
I
r························································· ·················································· ......... 1
•• +- X1+
X1 average displacement in x direction
~ center of mass displacement in x direction
-$- center of mass
-+- geometric centroid of diaphragm
(location of center of stiffness)
FIGURE 3.32 DISPLACEMENT AT CENTER OF MASS AND AVERAGE DISPLACEMENT OF FLOOR DIAPHRAGM
117
81 B2 B2 •- 81
B3 B4 B5 B5 B4 B3
·~ •• ·~ I
B3 B4 85 85 B4 ~
B3 ~
•
Be B7 .. B7 B8 •• ----------------~
B3 B4 85 ~
85 B4 B3 ~
B3 B4 B5 B5 B4 B3 •
B1 B2 B2 B1
~ ) -I- ) --+- · ( _J_ S.J m -+-6.8 m-+- 4.8 m--1
....... _) "-"'"" ... Second Bay
····----·-··········-@
0
FIGURE 3.33 LOCATION IN PLAN OF DIFFERENT BEAM TYPES
118
\.
I
.. ·~~
C1 C2 C3 C3 C2 C1 0 ---------------------
cs ce C7
0 ---------------------
C5 ce C7
0 ---------------------
C8 C9 C10 C9 C8
0 --------------------------------------···
C4 cs C8 C7 C8 C5 C4 0 ---------------------
cs ce C7 0 ---------------------
C2 C3
0 ---------------------
_J_ 5.3 m -f--4.8 m-+- 4.8 m-1
First COlumn Fourth Column
Second COlumn Third COlumn
' '
FIGURE 3.34 LOCATION IN PLAN OF DIFFERENT COLUMN TYPES
119
Floor
30
25
20
15
10
5
i !
Design of Beams Beam Type B1
........... .... 1
:.. ........... _ ....... , ! ! i
Positive I ............... ,
1 /
Negative
0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 p
FIGURE 3.35 PERCENTAGE OF STEEL ON BEAM TYPE 81
120
I \
-' I
I '·
r I
Floor
30
25
20
15
10
5
1 0
I !
Design of Beams Beam Type B2
................ ______________ ,
l l l i I ~--....... ...
Positive
.. ··"
Negative
0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 p
FIGURE 3.36 PERCENTAGE OF STEEL ON BEAM TYPE 82
121
Floor 30
25
20
15
10
5
1
! !
Design of Beams Beam Type B3
....... --........ -.. ..... , i ' · ... ~ ..... ,
\ ! ....... __ ···--..... ~
i i i
Positiv~ i ! i i
! !
,,.; (
I _...... ........
Negative
0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 p
FIGURE 3.37 PERCENTAGE OF STEEL ON BEAM TYPE 83
122
I I
, \
-' I I
Floor
30
25
20
15
10
5
1 0
!
Design of Beams Beam Type B4
..... -............ ______ , i ' ............. ....
i i
\ ' Positive I i ! ~ ................ ______ 1
! I
! i I ....
r_.::::: .. ----.......... .........
0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 p
FIGURE 3.38 PERCENTAGE OF STEEL ON BEAM TYPE 84
123
Floor
30
25
20
15
10
5
1 0
: i
Design of Beams Beam Type B5
...... __ ·····--·····! i L-.........
l ! !
'·l ····--···---••• 1
--
i ;,..., . ._
.... ! ; : !
Positive! i ; : ! i i !
............ -·· _ .......
Negative
0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 p
FIGURE 3.39 PERCENTAGE OF STEEL ON BEAM TYPE 85
124
I
I I
I
.--·-
I .
I i
Floor
30
25
20
15
10
5
1 0
! i
I
Design of Beams Beam Type 86
""···············--············~
i \
i ! ! I
Positive ! Negative i ! i i ! ! ! ! .................
...... 1 ! .,.,....,. ...... ..
0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 p
FIGURE 3.40 PERCENTAGE OF STEEL ON BEAM TYPE 86
125
Floor 30
25
20
15
10
5
1
i
Design of Beams Beam Type B7
""'···--....... .._ ..... , I ;...._, .... ,
i i : .... r ..
! .. ........ ., f .............. ..._ ... ,
! i
Positive! ! ......... ...-• ,... ....
:
i : "··-·-... -·· ! ~ .......... ..
Negative
0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 p
FIGURE 3.41 PERCENTAGE OF STEEL ON BEAM TYPE 87
126
,-
( I
I I
Design of Columns Story Columns Type C1 ,C2,C3
30
25
20
15
10
5
1 C1
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1 p
FIGURE 3.42 PERCENTAGE OF STEEL ON COLUMNS TYPE C1, C2 AND C3
127
Design of Columns Story Columns Type C4,C5,C6,C7
30
25
0.09 0.1 p
FIGURE 3.43 PERCENTAGE OF STEEL ON COLUMNS TYPE C4, CS AND C6
128 ,.-
Design of Columns story Columns Type C8,C9,C1 0
30
25
20
15
10
5 C9 and C10 c:_:::·········~·
1 ..... ?
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1 p
FIGURE 3.44 PERCENTAGE OF STEEL ON COLUMNS TYPE C8,C9 AND C10
129
-E I c:::
0 ~ -c::: CD E 0 ::e
100
80
60
40
20
0
-20
-40
-60
-80
Comparison of Required and Supplied Strength Frame B, First Beam
....... -····-····---,.-····-····· , .... /·
•.........• / . /
//····--··-... ...... ;·-····-·········-····-····-····-····-····-····-····-····/ · Supplied - ·
-1 00 -'-r--~.....-r--r--1.---r-..--.--r--r--r-.--r--r-r--r--r......,..-~....-.---.--.---r--r-r--r-,-1 5 10 15 20 25 30
Floor
FIGURE 3.45 REQUIRED VS. SUPPLIED STRENGTH ON FIRST BEAM OF FRAME 8
130
·- r
100
80
- 60 E
I
40 c::: 0 e
20 -c::: CD E 0 0 :E -20
-40
-60
-80
Comparison of Required and Supplied Strength Frame B, Second Bay
Supplied+
.,. ......... / R "red ,. ............. /·
equ1 - .~················-·····-..... ....•...... / ~-~······"\!, " .............................. .... .. ·-....~·
Supplied-
1 5 10 15 20 25
........ //
30 Floor
FIGURE 3.46 REQUIRED VS. SUPPLIED STRENGTH ON SECOND BEAM OF FRAME 8
131
Comparison of Required and Supplied Strength Frame B, Third Bay
100
80 Supplied + "·, /··-·-·-·········-····-·········-·········-····-····-.._ 60 ...... ..... .......... ... -E Required+
C: 40 0 e - 20 c: CD
.•.... , ., '········-··-··
'·····-·····~ .. ~. .___..,-.,
E 0+------------------------------------o :::! -20
-40
-60 Required -
-80 Supplied-
-1 00 ....,_,.-,-,..........-,---,,.........,..._.,---,....,..,-,-,.-,-,......,--r--~---r-,.--,---.---T-r-r-r-...--r~ 1 5 10 15 20 25 30
Floor
FIGURE 3.47 REQUIRED VS. SUPPLIED STRENGTH ON THIRD BEAM OF FRAME B
132
4 ANALYSIS OF THE SEISMIC PERFORMANCE OF THE 30-STORY BUILDING
DESIGNED ACCORDING TO UBC
4.1 INTRODUCTION
As mentioned earlier, UBC approach for seismic design is based on just one EO design
level: the safety level. For this level, UBC defines a very large reduction factor, Rw, which
accounts mainly for the structure's capacity to dissipate energy in the inelastic range and
a certain overstrength (OVS). One of the problems with this UBC approach is thatthe
present trend in the seismic design of buildings is to attempt to design them just for the
strength required by the code, which results in a constructed building with relatively small
OVS (particularily tall buildings). This trend leads to the possibility of considerably
underdesigning the structure due to the large values of Rw that are allowed to be used
(12 for SMRSF).
Over the years, several issues have been raised about some of the EQ design
provisions of UBC. In this chapter, some of these issues are brought up by discussing the
performance of the 30-story building designed according to UBC specifications when
subjected to:
• Equivalent lateral loads obtained from design spectra developed for the site. Response
spectra analyses (RSA) were carried with the purpose of studying the performance of the
building at different limit states, in this case, at service and safety limit states. For this
purpose, site spectra were developed, as discussed in Ref. 5, by averaging the response
spectra obtained from several earthquake ground motions (EQGM) recorded at soft soil
sites. The service limit state was defined for a EQGM with a return period (T R) of 10
years. For this T R• a PGA of 0.07g was obtained for the San Francisco Bay Area [Ref.
5]. The safety limit state was defined for a EQGM with a T R of 450 years, which led to a
PGA of 0.30g [Ref. 5]. It should be noted that the service limit state design ground motion
was defined as that which produces first significant yielding rather than that inducing
allowable stresses.
133
Time-history analyses (THA) were carried out using the SCT-EW EQGM scaled to a
PGA of 0.07g for service limit state and 0.3g for safety limit state. The SCT-EW EQGM
was recorded during the 1985 Mexico City events. After studying several recorded
EQGMs in soft soil, it was observed that the one with largest damage potential and
amplification of elastic response for the 30-story building was the SCT-EW EQGM. A
detailed discussion of the characteristics of this EQGM can be found elsewhere [Ref. 2].
It was considered appropiate to study the behavior of the 30-story building under the
worst case scenario. It should be noted that according to Seed [Ref. 11], EQGMs
generated in the San Francisco Bay Area can have dynamic characteristics and damage
potential that are similar to those corresponding to the recorded motions in the soft soil
zone of Mexico City during the 1985 events (i.e., SCT-EW EQGM).
In this chapter, the seismic performance at different limit states of the building is
discussed and judged according to whether or not this performance satisfies the
philosophy of earthquake-resistant design summarized in section 2.2 of this report.
Discussion of the possible reasons of the observed performance is left to Chapter 5.
4.2 ELASTIC RESPONSE SPECTRUM ANALYSIS (RSA) AND TIME HISTORY
ANALYSIS (THA)
Some elastic analyses of the building were carried out using the ETABS program [Ref.
13] to obtain and estimate of the behavior of the building when subjected to the service
and safety EQGMs. First, the input EQGM in each analysis was considered only in one
direction, in such a way that the results obtained from the elastic analyses could be
compared with those obtained from the two dimensional (2D) nonlinear analyses of the
building carried out with the Drain 2DX program. Second, a tri-dimensional (3D) analysis
was carried out on the building considering components of the EQGM in two
perpendicular directions. Unfortunately, the ETABS program only allows for the EQGM
to be input in one direction, and thus it was not possible to use simultaneously the EW
and NS component of the SCT EQGM. Both components of the SCT EQGM were added
as vectors. The largest ground acceleration was obtained in a direction forming an angle
134
of 28° with respect ·to the EW direction. This acceleration was equal to 1.18 the PGA of
the SCT-EW ground motion. It was decided to scale up by 1.18 the 0.07g and 0.3g PGA
associated with the service and safety limit state EQGMs, respectively. Then, the EQGM
was input in the direction in which the maximum ground acceleration was obtained, as
shown in Figure 4.1 .
4.2.1 SERVICE LIMIT STATE
To study the performance of the building at the service limit state, two elastic analyses
(RSA and THA with EQGM input in one direction) were carried out. Figure 3.3 shows the
site spectra for service, while Figure 4.2 shows the SCT-EW EQGM. The main objectives
of these analyses were: to check the IDI for service limit state (defined at first yielding),
and to check that the members of the structure remain elastic.
In the modelling of the 30-story building for the elastic RSA and THA with unidirectional ·
input, the following considerations were made:
Only real eccentricity was considered to estimate the torsional induced effects.
P-.:l effects are included.
The spectra used for the RSA for service were obtained using a; of 0.02 [Ref. 5]. For
the THA analysis, a; of 0.05 was used.
CQC modal combination was used in the RSA analysis, accounting for the effects of
the first 15 modes: 5 translational modes in two perpendicular directions and 5 rotational
modes
The moments of inertia of beams and columns of the final design of the building were
considered. In section 3.3.1 a detailed description on how these properties were obtained
is presented.
Shear deformations were considered for beams and columns
The story masses were computed from the story weights shown in Table 3.1. To
compute the gravity load, a live load of 12 psf (about 0.06 ton/m2) was used. This value
corresponds to the mean value obtained from load surveys in real buildings [Ref. 17].
135
Figure 4.3 shows the envelope of floor displacements for the elastic RSA and THA with
unidirectional input. Note that the story displacements obtained from the THA of the
building are significantly larger than those obtained from the RSA. This clearly shows that
the SCT-EW record can be considered as a critical EQGM for elastic drift control. To get
a better idea of how the obtained floor displacements affect the behavior of the structure,
Figure 4.4 shows the envelope of IDI for both analyses. As shown, in both cases, the IDI
exceeds considerably the 0.0025 limit set by UBC for allowable stress state (1.4 x
0.0025 = 0.0035 for first significant yielding, i.e., the service limit state considered herein),
and the limit of 0.003 to avoid damage to nonstructural elements [Ref. 5]. It can be
concluded that the building has inadequate performance for IDI control for service, and
heavy non-structural damage is expected .
It should be noted that for the THA all the values of displacements and IDI that
correspond to the positive envelopes were produced simultaneously, i.e., all the maximum
positive displacements and IDI were reached at the same time. The same observation
can be made for the negative envelope of displacements and 101. It can be concluded
that the first mode dominates the elastic response of the building, that is, the SCT-EW
EQGM particularly excites the first mode of the structure.
Figure 4.5 shows the envelope of story shears from both analyses and the story shear
distribution used in the design of the building. As shown, the story shears exceed
considerably those used in the design. The base shear for these story shear distributions
are summarized in Table 4.1. Nonlinear response is expected in the 30-story building for
service limit state (which would be reflected as damage to the structural elements). A
confirmation of this observation can be found in Figure 4.6, where the maximum stress
ratios for columns and beams of Frame B are shown. The stress ratios shown in the
figure were obtained from the results obtained in the elastic RSA. For beams, the stress
ratio is computed as the ratio of the end moments of the beams obtained from the RSA
to the moment strength provided at that location (computed without strength factor and
accounting for the contribution of the slab). For the columns, the computation of this ratio
136
is more complicated because the moment strength (first significant yielding or usable
strength) provided at the end of the column is a function of the axial load acting on that
column. Figure 4.7 shows how the stress ratio is computed for a column: first, the pair
consisting of the axial force (P) and moment (M) at end of the column due to gravity is
located within the interaction diagram, second, the pair consisting of the total axial force
and moment (computed by superposing gr(lvity and lateral load effects) is located in the
P vs. M plane; third, a line is drawn between these two points; and finally, the moment
strength provided at the end of column, used in the stress ratio computation, is obtained
by intersecting this line and the curve that defines the P vs. M interaction diagram of the
column without strength reduction factor. As shown in Figure 4.6, there is a maximum
stress ratio of about two for beams throughout the height of the building, while the stress
ratio is less than one for columns in the lower stories and increases up to 1.5 in upper
stories. From the stress ratios, it can be concluded that inelastic behavior of some
elements is expected under the service EQGM, and that inelastic behavior tends to
concentrate in the beams.
From the observed behavior, it can be concluded that the 30-story building designed
according to UBC specifications has inadequate performance at service limit state as far
as drift control and strength requirements are concerned. Damage is expected in
nonstructural as well as structural elements.
Finally an elastic THA with bidirectional input was carried out in the building to assess
how adequately the unidirectional input analyses are able to predict the overall response
of the building. The model of the building used in this analysis was practically the same
as that used in the elastic THA with unidirectional input, except for the following.
• Real plus accidental eccentricities were considered to estimate the torsional induced
effects. The accidental eccentricities were oriented in the direction in which the torsional
effects due to accidental eccentricity were the largest.
137
The results obtained from the 30 elastic THA are summarized in Figures 4.8 to 4.1 0.
By comparing Figures 4.8 and 4.3, and Figures 4.9 and 4.4, it can be concluded that the
displacements and 101 obtained in the 30 elastic THA are larger than those obtained in
the elastic THA with unidirectional input. The plots shown in Figures 4.3 to 4.5 correspond
to the EW direction. It can also be seen in Figures 4.8 and 4.9 that the response in the
NS direction is not negligible when compared to that of the EW direction. Figure 4.10
shows the story shear distribution through height obtained from the 30 elastic THA. As
shown, the story shears in the EW direction are about 80% of those shown in Figure 4.5
for unidirectional input. Nevertheless, the story shears in the NS direction are about 50
to 60% those shown for EW direction in Figure 4.1 0. The vector sum of the EW and NS
story shear components shown in Figure 4.1 0 result in story shears that are very similar
to those shown in Figure 4.5. It can be concluded from the above discussion that a 20
analysis can not capture the 30 behavior of the building.
4.2.2 SAFETY LIMIT STATE
To study the performance of the building at the safety limit state, two elastic analyses
(RSA and THA with EQGM input in one direction) were carried out. Figure 3.3 shows the
site spectra for safety, while Figure 4.2 shows the SCT-EW EQGM. The main objectives
of these analyses were to estimate the 101 of the structure for safety, get an estimate of
the nonlinear response of the building (i.e., ductility demands), and to assess the
adequacy of the global nonlinear behavior of the building by studying, through the values
and the distribution of stress ratios in its members, the severity and distribution of the
inelastic response throughout the structure.
The modelling considerations used for these analyses are the same as those discussed
in the previous section, except that as of 0.05 was considered in the elastic RSA and
THA.
Figure 4.11 shows the envelope of floor displacements for the elastic RSA and THA
with unidirectional input. As shown in the figure, the floor displacements are very large.
138
Note that the floor displacements obtained from the THA are significantly larger than
those obtained from the RSA. To get a better idea of how these large floor displacements
affect the behavior of the structure, Figure 4.12 shows the envelope of IDI for both
analyses. As shown, the maximum IDI for the RSA analysis is about 0.02, which can be
considered to be acceptable for ultimate state (although very heavy structural and
nonstructural damage damage can be expected). The maximum IDI given by the THAis
about 0.04, which is excessive.
It should be noted that for the THA for safety, all the values of displacements and IDI
that correspond to the positive envelopes were produced simultaneously, that is, all the
maximum positive displacements and IDI were reached at the same time. The same
observation can be made for the negative envelope of displacements and 101. It can be
concluded that the first mode dominates the response of the building, that is, the SCT -EW
EQGM particularly excites the first mode of the structure.
Figure 4.13 shows the envelope of story shears from both analyses. As shown, story
shears exceed considerably those used in the design of the structure, as also shown by
the base shear in Table 4.1. As shown in this table, the base shears obtained from the
RSA, 0.5W, and the THA, 0.94W, are very large. To estimate the magnitude of the
nonlinear response of the structure, stress ratios for columns and beams were computed.
Figure 4.14 shows the maximum stress ratios for columns and beams of every story. The
stress ratios shown in the figure, computed from the safety RSA, were obtained using the
procedure described in the previous section. As shown in Figure 4.14, there is a
maximum stress ratio ranging from 6 to 7.5 for beams throughout the height of the
building, while the stress ratio is less than three for columns in the lower stories and
increases up to 4.5 in upper stories. Figure 4.14 clearly shows that very high ductility
demands (mainly in the beams) can be expected throughout the entire height of the
building.
Given the very high stress ratios computed, it can be concluded that the 30-story
139
building would have very large ductility demands which would very likely lead to the
failure of several of its members, which in turn would lead to the collapse of the structure,
while the IDI computed from the THA are extremely large and clearly not acceptable.
An elastic THA with bidirectional input was not carried out for safety limit state. The
results shown in Figures 4.8 to 4.1 0 for service limit state can be scaled up by a factor
of 0.30/0.07 to obtain the response corresponding to the elastic THA for safety with
bidirectional input.
4.3 NONLINEAR ANALYSIS OF 30-STORY BUILDING.
A series of nonlinear analyses were carried out on the 30-story building to get more
reliable information regarding the behavior of the structure at service (as remarked in
section 4.2.1, nonlinear behavior is expected even for service EQGM) and ultimate limit
states. For this. purpose, 2D nonlinear analyses of the structure were carried out using
the Drain 2DX p·rogram [Ref. 18].
In this section, a detailed description of how the structure was modelled to carry out the
nonlinear analyses is presented. The assumptions made to model the building are
discussed. Next, a pushover. analysis of the structure was carried out to study the
behavior of the structure under lateral monotonically increasing loads. Then, the results
obtained from nonlinear 2D THA for service and safety are presented and the
performance of the structure is judged according to them.
4.3.1 MODEL OF 30-STORY BUILDING FOR NONLINEAR ANALYSIS
Because the analysis of the 3D building had to be carried out on a 2D model, torsional
effects on the response of the building were not studied. As shown in Figure 4.15, there
are three different types of frames on the structure according to sizes and reinforcement
of columns and beams. To save time in the analysis, the seven frames of the structure
in a given direction were merged into these three frames, as shown in Figure 4.15. In a
3D building, torsional effects are larger in the frames near or at the end of the building
140
(i.e., frames A and G). When analyzing the 2D model, these effects are not considered, -
and thus the response of the frames at or near the end is likely to be underestimated.
• Material Properties. The stress-strain relationship for confined and unconfined concrete
in the beams are described by the following equations [Ref. 19]:
where
k=1 +p fyh z - 0.5 s I m ~
I 0.0207 + € 0 fc Esou 1
fc - 6.8966
f Esou + Esoh - Eon c
~ e50h = 0.75 Ps ~ s units; [MN,m]
and fc=longitudinal concrete stress, Ec= longitudinal concrete strain, fyh= yield stress for the
hoop reinforcement, h1= width of the concrete core measured to the outside of the hoops,
S= center-to-center spacing of the hoops, and E0 = 0.002 is typically assumed.
The maximum concrete strain is given by
- fyh Eanax-0.004+0.9 Ps 300
where Ps= ratio of the volume of hoop reinforcement to volume of concrete core measured
to the outside of the hoops.
Th~ modulus of elasticity, Ec , and the modulus of rupture, f1 , were assumed to be [Ref.
20]:
141
f,=0.63 {t! Units; [MN,m]
The steel reinforcement behavior was modeled by a straight line with slope Es in its
elastic range of behavior, by an horizontal straight line for plastic yield plateau and by a
parabola once it strain-hardens:
and
fs=Ett-s. lesl ~ey f8 =fy sgn(eJ ey< I e. I ~e.,
f5 =(&z e!+~ lesl +So) sgn(eJ e.,< le.l ~eu
where
{
=1ife>O sgn(eJ = -1 if ;s < 0
=Oife =0 s
For a reinforcement bar, an effective length of s/V2 was assumed to be laterally
supported by stirrups. The critical buckling stress, fer , is given by the_ following relation
[Ref. 21]:
where ~(EJ is the tangent modulus of the steel stress-strain relationship.
The following values for steel Grade 60 were considered [Ref. 22]:
Nominal yielding stress, fvn=420 MN/m2
Mean yielding stress, fv= 490 MN/m2
Mean ultimate stress,
142
Strain at onset of strain-hardening
Strain at ultimate,
Modulus of Elasticity,
E8h= 0.006
Eu = 0.10
E8 = 200000 MN/m2
Beams. To model the beams, the moment of inertia was computed using a weighted
average of the effective moment of inertia computed according to formula 9-7
(summarized in section 3.3.1 of this report) of UBC at different locations in the beam.
Figure 3.11 illustrates how the moment of inertia for a beam is computed. In the UBC
expression, the maximum moment acting on a beam was replaced with the yielding
moment of the beam.
The strength and stiffness of the beams were estimated by accounting for the
contribution of the slab. The strength was computed without the use of a strength
reduction factor. Miranda and Bertero [Ref. 23] remark that experimental results have
shown that when the beam gets further and further into its inelastic range of behavior, the
reinforcement of the slab outside the effective width starts contributing more and more
to the negative flexural strength of the beam. The amount of reinforcement of the slab
that needs to be considered to compute the flexural strength of the beam depends on the
level of inelastic deformation suffered by the beam, and thus it is very difficult to capture
adequately the flexural behavior of the beam. For the present analysis, the
recommendations made by French and Moehle [Ref. 24] were used: the effects that the
slab has on the stiffness and strength of the beams can be accounted for by accounting
for the steel in the slab inside an effective flange width (ACI318-89), which is defined as
the least of: a) the web width plus 16 times the slab thickness, b) the transverse
separation between beams, and c) one fourth the span of the beam . It should be noted
that, because of limitations on the modelling capacity of DRAIN 2DX, the beams have
equal stiffness for positive and negative moments. These two values will usually b~
different due to different ratios of positive and negative steel and due to the fact that for
positive moment, the beams behave like T beams, while for negative moments they
behave as a rectangular beam. To estimate the stiffness of a beam, an average of the
143
positive and negative stiffnesses was used.
To model the hysteretic behavior of the beams, an elasto-plastic model was used, as
shown in Figure 4.16. This type of behavior is the only option currently provided by
DRAIN 2DX to model a beam. Although a stiffness degrading model can be considered
reasonable to estimate the response of reinforced concrete structures, usually
elasto-plastic models lead to the same maximum responses. It is unlikely that the use of
the elasto-plastic model would change the response of the members of the building (and
of the building itself) as compared with that computed using a stiffness degrading model.
Also, the elasto-plastic model provides an easy way to compute the hysteretic energy
dissipated in the member, and thus provides a way to estimate local damage.
The moment-curvature relationships for the beams were computed using the material
properties described above and using the assumptions that plane sections remain plane
after flexural deformation, and that there exists complete compatibility of strains between
steel and concrete. The moment-curvature relationship was approximated by a bilinear
curve in such a way that it could be used by the DRAIN 2DX computer program. For this
purpose, the beam yield moment, My, and yield curvature, cpv, were defined as the
moment and curvature at which any bar of the section reaches first yielding. The ultimate
bending moment, Mu, was defined as the moment when a) the maximum strain is reached
in the concrete, b) the ultimate strain is reached in any bar, or c) the buckling stress is
reached in any bar. The ultimate curvature, cpu, was defined as the curvature when Mu is
reached. By connecting the origin to the point defined by (My,<py) with a straight line, and
then this point to the point defined by (Mu,cpu) with another straight line, the bilinear
moment curvature diagram was defined.
Using the above method, a strain-hardening value of about 0.02 was obtained for the
majority of the beams in the building. Thus, a value of 0.02 was used for the strain
hardening of all the beams in the model of the 30-story building.
144
Shear deformations were accounted for in the behavior of the beams. For this purpose,
the cracked shear area of the beam was estimated as Avf3, where Av = gross area/1.2,
according to the recommendations given by Park and Paulay [Ref. 25]. It should be noted
that the shear stiffness will remain constant throughout the analysis due to limitations of
the modelling capacity of DRAIN 2DX.
Rigid joints equal to half the dimension of the column parallel to the plane of the frame
were used to account for cracking and nonlinear behavior in the joint region.
DRAIN 2DX models members with lumped plasticity, i.e., all the inelastic deformation
of a member is concentrated at discrete points, usually at the ends of the member. For
the model of the 30-story building, the inelastic behavior was lumped at the ends of the
members. This is a reasonable modelling assumption for the beams of a structure
subjected to lateral loads, where the maximum moments are usually concentrated at the
ends. Caution should be used when modelling the top stories of a structure, because the
largest moment can occur at locations near the midspan of the beams.
• Columns. To model the columns, the moment of inertia was computed using the gross
section of the columns. This assumption seems reasonable, considering that the great
majority of the columns remain under axial compression even under the effect of lateral
loads. Small axial tension forces are expected only in the columns at the ends of the
frames when the building is subjected to lateral loads. With the above idealization, the
stiffness in the column remains constant for the entire THA. Any redistribution of forces
in the columns due to possible changes in their stiffness (which varies depending on the
value of the axial force induced in the column) can not be captured by this model. This
effect needs to be modelled when large tension forces are expected in some columns,
because then the shears induced to the columns that remain in compression can increase
significantly. It should be noted that the program DRAIN 2DX does not allow accounting
for this in the model of the building.
145
Because of the low span/depth ratio of the columns (ranging from about 2.5 to 3.5), it
was considered important to account for shear deformations in the behavior of the
columns. For this purpose, the cracked shear area was estimated as Avf3. As in the case
of beams, shear stiffness remains constant throughout the nonlinear analysis.
Rigid joints with lengths equal to the total depth of the beam were considered on the
top end of the columns. The strengths of the columns were computed using UBC 1991
provisions for flexural axial behavior without using a strength-reduction factor. Figure 4.17
shows the idealization of the P vs. M interaction diagram of columns that has to be made
for the columns of the model of the 30-story building. Given the large simplification that
has to be made on this diagram, it was considerefd unnecessary to estimate the P vs.
M curve using more refined procedures. One of the largest problems when modelling the
strength of a column lies in the value assigned for its strain hardening modulus, because
this value depends on the detailing of the confinement steel in the column and on the
axial force acting on the column. Because the axial force can change considerably in
some columns, their post-elastic stiffness can vary significantly through time as a function
of the axial load acting on them. DRAIN 2DX only allows one value of strain-hardening
for the analysis, and thus the real inelastic behavior of the column can not be captured.
Given the good confinement required by UBC for the end of the columns, no significant
degradation in the strength of the column is expected even under high axial loads, and
thus a strain hardening of zero was found reasonable. It should be noted that although
the program DRAIN 2DX allows the flexural stiffness of the column to vary according to
the state of the column (elastic or yielded), it does not allow the axial stiffness of the
column to vary (which is not realistic, given that the concrete cover can spall off, etc.). As
for the beams, columns were modelled using lumped plasticity at their ends.
• Story weights. The story masses were computed from the story weights shown in
Table 3.1. To compute the gravity load, a live load of 12 psf (about 0.06 ton/m~ was
used. This value corresponds to the mean value obtained from load surveys in real
buildings [Ref. 17].
146
4.3.2 ROTATIONAL CAPACITY OF BEAMS, DAMAGE INDEX
The plastic rotation capacity for beams was estimated [Ref. 26] as follows:
h 1=p 2
where his the total depth of the RC member. It should be considered that, although the
above method is a common way of computing the rotational capacity of the beams, it
usually leads to conservative estimates of this capacity because it neglects the effects of
deformation hardening and the effect of shear (which usually increases the length of the
plastic hinge beyond the assumed h/2).
For the beams of the 30-story building, the supplied monotonic rotational capacities
(estimated analytically) ranged from 0.035 to 0.058. It has been shown experimentally that
stable hysteretic behavior can be achieved up to inelastic rotations of 0.035 [Ref. 1 0].
Thus, the values obtained for the monotonic plastic rotation seem reasonable when
compared to those obtained in experimental tests, although the value of 0.058 seems
slightly high.
Given that an elastoplastic model was used to model the behavior of beams and
columns, the output of the THA analysis can be directly used to estimate the magnitude
of local damage in the members of the building [Ref. 5]. An estimate of the positive and
negative hysteretic energy dissipated at each plastic hinge can be obtained as:
EH + = M/ l:~ep + = M/ eacc + and EH. = My" l:~ep· = My" eacc-
where M/ and M/ are the positive and negative bending moments at yield; eP• and eP· the positive and negative plastic hinge rotations; and eacc + and eacc- the cumulative plastic
hinge rotations. Figure 4.18 shows how the cumulative plastic hinge rotations are defined.
The total hysteretic energy can be estimated as EH= EH • +EH- and local damage can be
estimated by using the damage index defined by Park and Ang:
147
where e is the maximum of eP• and eP-, Bu is the plastic hinge rotation as defined in this
section, and B is a model parameter. In this report, a B of 0.15 was used [Ref. 27]. It
should be noted that the above definition is slightly different than that given by Park and
Ang: in the traditional definition, e is the maximum rotation (including elastic and
maximum plastic hinge rotation); while in the above definition, e is the maximum plastic
hinge rotation. The above definition of DMI was used to obtain estimates of local damage
from values of DMI that are normalized in such a way that a value of DMI equal to zero
would be obtained if the member remains elastic (note that this same definition of DMI
has been used in Ref. 5).
4.3.3 PUSHOVER NONLINEAR ANALYSIS
Before carrying out a nonlinear THA of the building, which is time consuming and
therefore costly, it is convenient to estimate if the attained preliminary design is promising
(i.e., has a chance of satisfying all the design criteria). To do this, it is convenient to carry
out a pushover analysis of the building to assess the following.
Obtain a lateral load vs. displacement curve for the structure. For this purpose, the base
shear in the structure is plotted vs. the tip (30th floor) displacement of the building.
• Estimate the first yielding as well as the ultimate strength of the structure under
monotically increasing lateral loads, and the corresponding nominal drift index, Dl, and
IDI at different stages of loading.
• Assess the influence of P-i\ effects on the behavior of the structure when subjected to
lateral loads.
• Determine the formation of plastic hinges in the members of the structure and their
distribution throughout the building. Follow the maximum rotations at the ends of the
beams as a function of the displacement of the top story to estimate the maximum global
displacement ductility as a function of the flexural failure of the structural members.
Confirm that the building is capable of dissipating energy in a controlled way by means
148
of an acceptable plastic mechanism, that is, dissipating energy mainly in the beams as
opposed to in the columns, and particularly if the design has eliminated local mechanisms
such as a soft story mechanism.
For the pushover analyses, the building was modelled as described in section 4.3.1.
The distribution of lateral forces applied through the height of the building was determined
from the force distribution obtained from the elastic RSA for safety described in section
4.2.2 and shown in Figure 4.13. It should be noted that the distribution of forces obtained
from the RSA for safety is very similar in shape to that obtained from the THA for safety,
and thus its use was considered appropriate for the nonlinear analysis.
Figure 4.19 shows the tip displacement (L\) vs. base shear ty b) curve obtained from the
pushover analyses. Tables 4.2 and 4.3 summarize the most important points of this
curve. It can be seen in Table 4.2 that the tip displacement at UBC allowable stress is
0.152 m, which is different from the value of 0.117 m given in Table 4.1. The reason for
the observed difference lies in the fact that the building was modelled differently for each
analysis. As shown in Figure 3.8, the secant stiffness of the structure depends on the
state of the structure that needs to be analyzed. Figure 4.20 shows the difference of 101
distribution through height at UBC allowable stress limit state loads for the two models
of the building, i.e., one curve is associated with the secant stiffness computed for
allowable stress limit state while the other is associated with stiffness corresponding to
the safety limit state.
As shown in Figure 4.19 and Table 4.2, when P-~ effects are considered in the
analysis, the tip displacement and base shear at which the first element of the structure
yields are 0.266 m and 1785 ton., which is 1.25 the base shear for UBC design for first
significant yield. The maximum base shear the structure develops under the current
monotonic loading is 2451 ton, which is 1.75 times the UBC base shear for first yield.
Thus, the structure has a OVS of 75%, which is lower than the OVS of 1 00% considered
typical for an American building of this height. Figure 4.19 shows that when P-~ effects
149
are considered in the analysis, the ultimate base shear of the structure diminishes
considerably with respect to that when no P-6 effects are considered. The results shown
in Table 4.3 are discussed later.
Figures 4.21 and 4.22 show the displaced shape of the structure and the story 101 at
different tip displacements. As shown in both figures, the displaced shape of the structure
changes considerably as the tip displacement increases. After the tip of the structure
reaches a value of about 0.266 m (yield of first member), the lateral deformation of the
building starts concentrating in its lower 15 stories (with the exception of the first story)
while the upper stories show little increase in their 101. This tendencies can be observed
in Figures 4.21 to 4.23. Figure 4.21 b and 4.22b show a comparison of the floor
displacements and 101 obtained from two analyses, one considering P-6 effects and the
other neglecting them. Figures 4.21 band 4.22b need to be interpreted carefully, because
they do not compare the same state of the building. Figure 4.24 aids the interpretation
of Figures 4.21 b and 4.22b. As shown, the comparison of floor displacements and 101 are
made at six values of the tip displacement. From Figure 4.24, it can be seen that when
the tip displacement of the building is the same, when accounting and neglecting for P-6,
the base shear is significantly different, and thus the state of the building is different.
Nevertheless, useful information can be obtained from the indirect comparison established
between the results of the two analyses. It can be clearly seen that when the tip
displacement is larger than 0.30 m, the displaced shape of the building changes
considerably due to P-~ effects. Thus, part of the behavior observed in Figures 4.21 a and
4.22a can be attributed to P-~ effects: nevertheless, as clearly shown in Figures 4.21 b
and 4.22b for the curves obtained from the analysis without accounting for P-~ effects,
this behavior can not be attributed exclusively to P-~ effects. Further discussion of this
issue can be found in Chapter 5.
Figure 4.23 shows the maximum plastic rotation found in the beams of a given story.
As shown, the rotations follow a tendency similar to that discussed for the 101: as the tip
displacement increases, rotations are increased considerably in the bottom stories (with
150
the exception of the first two stories). The maximum rotational capacity computed
analytically for the beams range from 0.035 to 0.058. As shown in Figure 4.23, for a tip
displacement of about 1 .65 m, the monotonic rotational capacity of the beams in the lower
stories is reached. Nevertheless, the maximum base shear for the structure is reached
at a~ of 1.35 m, and thus the building is capable of developing its maximum strength
before any member fails. By idealizing the ~ vs. Vb curve obtained in the pushover
analysis with an elasto-perfectly plastic single degree of freedom system (SOOFS), it can
be seen in Figure 4.19 that the yield displacement of the SOOFS is about 35 em and that
ultimate global displacement ductility (~J is about 4.7 (1.65/0.35). Table 4.3 shows the
global, story and local ductility demands (~global,~story and ~local' respectively) on the 30-story
building as a function of the tip displacement.
~global is defined as the tip displacement divided by the tip displacement at yield (yield
tip displacement equal to 0.35 m according to the elasto-perfectly plastic idealization of
the ~ vs. Vb curve shown in Figure 4.19); ~story is defined as the 101 of the 7th story
divided by the 101 at yield of the 7th story (yield 101 equal to 0.0045 according to an
elasto-perfectly plastic idealization of the 101 vs story shear curve corresponding to the
7th story shown in Figure 4.46); and finally, ~ocai is defined as the maximum rotation
demand divided by the rotation at yield of the RC members. ~tory and ~ocai were computed
in the 7th story because the largest values of these two parameters were located in this
story according to the results of the nonlinear THA for service and safety limit states. It
should be noted that in the pushover analysis, the largest values of ~tory and ~local tend
to be located in the 7th story as the value of the tip displacement is increased.
As. shown in Table 4.3, for~ less than 0.266 m, i.e., prior to the yielding of the first
RC member in the building, the values of ~global and ~story are very similar to and slightly
smaller than those corresponding to ~local· Nevertheless, after the yielding of some RC
members, the value of ~ocal tends to increase relative. to the value of ~story' which in turn
increases relative to the value of ~global because of the concentration of lateral deformation
shown in Figures 4.21 to 4.23. Due to the significant change in the deformed shape of
151
the building as ~ increases, ~global is not a good parameter to characterize the local
ductility demands in the members of the building. For a~ of 1 .35 m (at which the building
reaches its ultimate strength), the value of ~ocaJ its about twice the value of ~story• which
in turn is about twice the value of ~global'
Figures 4.25 to 4.31 show the plastic hinge distribution for the building at different tip
displacements. As shown in Figure 4.25 for a tip displacement of 0.30 m, plastic hinges
have developed at the left end of several beams, where the lower part of the beam is in
tension (positive moment), while no hinges have appeared on the right end (subjected to
negative moments) of any beam. The observed behavior can be explained by the fact that
the strength of the slab has been considered for the nonlinear analysis while neglected
in the design of the beams, and thus there is a higher OVS in the negative flexural
capacity of the beams as compared with their positive flexural capacity. It also can be
seen that plastic hinges tend to concentrate in the interior bays of the frames.
Figure 4.26 shows the plastic hinge distribution for a tip displacement of 0.45 m. As
shown, the formation of plastic hinges extends to the right end of the beams in the lower
stories, while the positive hinges spread to the upper stories mainly in the interior bays.
Plastic hinges appear in the beams located in the first floor. Figures 4.27 and 4.28, for
tip displacements of 0.60 and 0.90 m show the same tendencies. As shown in Figure
4.29 for a tip displacement of 1 .20 m, hinges appear at the bottom ends of some tension
columns. In Figure 4.30, for a tip displacement of 1.275 m, it can be seen that plastic
hinges on columns have spread to several columns in the first story. Figure 4.31 shows
the state of the structure at 1 .35 m, at which the building develops its maximum base
shear for the pushover analysis. As shown, hinges have not spread to the beams located
in the upper stories of the building.
4.3.4 NONLINEAR THA FOR SERVICE
As discussed in section 4.2.1, nonlinear behavior is expected for the building subjected
to service EQGM input. Thus, a 20 nonlinear THA of the structure was carried out using
152
the same model used for the pushover analysis. As remarked before, the SCT -EW
EQGM, scaled to a PGA of 0.07g, was used for this purpose. Figures 4.32 to 4.41 and
Table 4.1 and 4.3 summarize the results obtained from this analysis.
By comparing the values summarized in Table 4.1 for all analyses for service, it can
be seen that the maximum base shear obtained from the nonlinear analysis is 0.59
(0.1 03/0.176) and 0.47 (0.1 03/0.22) the base shears obtained from the elastic RSA and
THA, respectively. Figure 4.5 shows a comparison between the envelope of story shears
obtained from the elastic RSA and THA with unidirectional input and the 20 nonlinear
THA. As shown, elastic analyses considerably overestimate the story shears. The
nonlinear maximum tip displacement is 0.85 and 0.66 the tip displacement obtained from
the elastic RSA and THA, respectively. A system with a Tof 2.5 sees (fundamental mode
of 30-story building), would be considered to be located in the preserved or constant
displacement range of behavior. As shown, the response obtained from the elastic
analysis tends to overestimate the nonlinear response. As discussed in detail in Chapter
5 for SDOFS, this results suggest that in soft soil, the elastic response does not always
give an accurate estimate of the nonlinear response.
Figures 4.32 and 4.33 show the time history of the base shear and the tip
displacement. In the pushover analysis, the yielding of the first element occurred at a tip
displacement of 27.5 em. As shown in the Figure 4.33, there are several cycles between
the 25th and 45th second of the analysis in which small inelastic demands can be
expected in the members of the building. The harmonic nature of the response of the
building can be seen in both figures. As shown, the building oscillates around its
undeformed configuration.
Figure 4.34 shows the envelopes of maximum story displacements. As shown, the
maximum negative and positive displacements are similar, except at stories 4 to 13. It
needs to be mentioned that all the displacements in these envelopes were obtained in an
very small interval of time. This fact suggests (as also suggested by the results obtained
153
from the elastic analysis) that the fundamental mode of the building dominates the global
response of the building.
A nonlinear THA of a SOOFS model of the building was carried out. The SOOFS has
an elasto-perfectly plastic behavior, aT corresponding to the first translational mode (2.53
sees) of the building, an equivalent height equal to the ratio of the first mode base
overturning moment and first mode base shear obtained from the elastic RSA and equal
to 0.67 the total height of the building, and finally, with a strength of 0.11W (same
strength/unit weight corresponding to the ultimate strength of the 30-story building
obtained from the pushover analysis as shown in Table 4.2). The small circles in Figure
4.34 shows the maximum displacements of the SOOFS. As shown, the results obtained
in the SOOFS match reasonably well those obtained in the 30-story building. Table 4.4
summarizes the results obtained in the SOOFS.
Figure 4.35 shows the envelope of 101 of the 30-story building and the drift index (01)
obtained in the SOOFS. The average 101 for all stories in the positive and negative
envelopes is about 0.005, which is similar to the value of the SOOFS 01, and
considerably larger than the 0.0025 required by the UBC code for allowable stress
(0.0035 for first significant yielding) and the limit of 0.003 to avoid significant damage to
nonstructural elements. Unlike the displacement envelopes, the 101 shown in the
envelopes were obtained at different times. This fact suggests that, although the
fundamental mode dominates the global behavior of the building, higher modes need to
be considered to assess correctly the behavior of the structure, mainly in the upper
stories. Figure 4.36 compares the negative 101 envelope obtained from the nonlinear THA
with the 101 distribution obtained from the pushover analysis with a tip displacement of
0.45 m. The value of 0.45 m was selected because it is similar to 0.4220 m, the
maximum tip displacement computed from the nonlinear THA. As shown, the 101
distributions over height for both analyses show concentration of the larger values of IDI
in stories 3 to 10. As shown the pushover analysis tends to overestimate this
concentration, as compared with that obtained from the nonlinear THA. This
154
overestimation is in part due to the overestimation of the P-~ effects in the pushover
analysis.
Table 4.3 shows the llglobal• 1-tstory and ~ocaJ obtained from the nonlinear THA for service.
The largest value of 1-tstory and ~ocal were located in the 7th floor. As shown in the table,
the values of llglobal• 1-tstory and ~ocaJ corresponding to the pushover analysis and a~ of 0.45
m (similar to the 0.4220 m maximum tip displacement in service nonlinear THA) are
similar to those obtained in the nonlinear THA for service. The. pushover analysis tends
to overestimate the value of ~ocaJ and give a good estimate of the value of 1-tstory· As shown
by the values above, moderate ductility demands are expected for the service EQGM.
It should be noted by comparing Tables 4.3 and 4.4 that there is no good agreement
between the 1-t obtained in the SDOFS and the llglobal obtained in the 30-story building
(1 .64 vs. 1 .20)_. This can be explained in part by the fact that llglobal is not a good
parameter to quantify the nonlinear behavior of the building due to the significant change
in the deformed shape of the building as~ increases (including a significant concentration
of deformation in a few stories). The value of llglobal computed from the lateral
displacements of the building corresponding to the equivalent height of the SDOFS (20th
story) is 0.34/0.24 = 1 .42, which is a reasonable estimate of the 1-t of 1 .64 obtained from
the SDOFS.
In Figure 4.37 the largest hinge rotation (maximum plastic rotation) for all members
located in a given story is plotted. All columns in the building remained elastic. The larger
hinge rotations in the beams ranged from 0.003 to 0.006 radians for stories 2 to 25, and
then they diminish to practically 0 from story 25 to story 30. Again, a large concentration
· of deformation can be observed in a few stories. Figure 4.37 only provides the largest
hinge rotation for all members on a given floor. Figure 4.38 provides an idea of how the
hinge rotation values are distributed throughout all of the members of the building. In this
figure, the magnitude of the hinge rotation is proportional to the radius of the shadowed
circles drawn at the ends of the members. As shqwn, in the lower stories the hinge
155
rotations are fairly evenly distributed in all beams of the story, while in the upper stories,
larger values of hinge rotations tend to be located in the interior bays.
In Figure 4.39, the largest cumulative plastic rotation for all members located in a given
story is plotted. In Figure 4.39, the larger value between the positive, eacc+, and the
negative cumulative plastic rotation, eacc·, is plotted. Beams show values of cumulative
plastic rotations ranging from 0.008 to 0.011 from story 5 to story 22. For beams, values
of maximum cumulative plastic rotation diminish to almost zero when going from story 22
to 30 and from story 5 to 1. Figure 4.40 provides an idea of the distribution of values of
cumulative plastic rotations (the figure shows the larger value between eac/ and eacc- for
the ends of all members of the building). As shown in both figures, the larger values of
cumulative plastic rotations tend to concentrate in stories 5 to 22 and in the interior bays.
Note that in the central frame of Figure 4.40 (which represents the exterior frames in the
real structure), the demands are significantly smaller than in the other two frames,
because torsion is not being considered in the 20 nonlinear THA (although it was
considered in the design of the building).
Finally, Figure 4.41 shows local damage (to compute local damage, the sum of Sac/
and eacc- was used to estimate the EH dissipated in the beam) to the members of the
building. Damage index (DMI) values, as discussed in section 4.3.2, were computed to
estimate the magnitude of such damage. As shown, main structural damage is
concentrated in the beams, and, as expected from the distribution of the maximum and
cumulative plastic rotations throughout the building, damage is concentrated in stories 5
to 22 and in the interior bays. As shown in Figure 4.41, the maximum value of DMI is
0.18, which according to Park and Ang corresponds to reparable structural damage. To
give an idea of how the above OMI was obtained, the computation of the damage index
on a beam located in the sixth floor follows:
156
The above computatio~ corresponds to a specific beam located on the sixth floor, which
corresponds to the beam with the largest hinge rotation {8 = 0.0057 as shown in Figure
4.38); nevertheless, the largest cumulative plastic rotations were located on a different
beam. For the beam for which the DMI was computed, the cumulative plastic rotation
demands in the positive and negative direction obtained from the THA were 0.0101 and
0.0075, respectively.
Figure 4.1 0 compares the story shear distribution obtained from the 2D nonlinear THA
(plane of analysis corresponds to EW direction) and those obtained from the elastic 3D
THA with bidirectional input. As shown, the story shears in the N-S directions are similar
to those obtained in the 2D nonlinear THA. Thus, it seems that nonlinear behavior can
be expected in the EW direction as well as in the NS direction (perpendicular to the plane
of the 2D nonlinear THA). The 2D nonlinear analysis is not able to capture some very
important characteristics of the 3D behavior of the building.
It can be concluded that the 30-story building does not perform satisfactorily for service.
Its large flexibility leads to IDI that are considerably Jarger than the limits specified by
USC for drift control and what is usually accepted in practice to avoid nonstructural
damage. Thus, extensive nonstructural damage can be expected for service limit state.
Furthermore, for service limit state the members of the building are supposed to remain
elastic. Because there is moderate structural damage in the beams of the structure and
significant damage is expected on nonstructural elements, it can be concluded that the
building does not have enough lateral strength and stiffness to perform adequately for
service limit state.
157
4.3.5 NONLINEAR THA FOR SAFETY
For safety or ultimate limit state, a nonlinear 20 THA of the structure was carried out
using the same model used for the pushover analysis. As remarked before, the SCT -EW
ground motion, scaled to a PGA of 0.30g, was used for this purpose. Figures 4.42 to 4.53
and Table 4.1 and 4.3 summarize the results obtained from this analysis.
By comparing the values summarized in Table 4.1 for all analyses for safety, it can be
seen that the maximum base shear obtained from the nonlinear THA is 0.27 and 0.14 the
base shears obtained from the elastic RSA and THA. Figure 4.13 shows the comparison
between the envelope of story shears obtained from the elastic RSA and THA with
unidirectional input and the 20 nonlinear THA. As shown and expected, elastic analysis
overestimate considerably the story shears when nonlinear behavior occurs, but not as
much as it is assumed in UBC (Aw is specified as 12). The nonlinear maximum tip
displacement is 0.79 and 0.40 the tip displacement obtained from the elastic RSA and
THA displacement. As discussed in detail in Chapter 5, this result suggests that in soft
soil the elastic response does not always give an accurate estimate of the nonlinear
response, and for tall buildings on soft soil it can overestimate it significantly, i.e., will lead
to too conservative designs.
Figures 4.42 and 4.43 show the time history of the base shear and the tip
displacement. In the pushover analysis, the yielding of the first member of the building
occurs at a tip displacement of 27.5 em. As shown in Figure 4.43, there is a large number
of cycles in which the tip displacement exceeds 27.5 em, and thus nonlinear behavior is
expected on several cycles. Although the maximum displacement of the structure is not
large, heavy damage to the building can be expected due to the large number of load ·
cycles and thus large value of cumulative plastic deformations. Thus, on a motion like the
SCT-EW record, damage can not be estimated exclusively from maximum plastic
deformations. The large cumulative plastic deformation demand needs to be considered
to estimate damage to the RC members. As shown in Figure 4.43, the building has a very
large positive displacement at the 25th second of the analysis and starts drifting in the
158
positive direction. Figure 4.43 shows that towards the end of the analysis (after the 45th
second) the building is not oscillating around its undeformed configuration (which
corresponds to its initial state of equilibrium, i.e., to a tip displacement of zero). Thus, it
can be concluded that the building has suffered a large and permanent deformation in the
positive direction (i.e., does not return to its initial undeformed configuration after the
earthquake ground motion).
Figure 4.44 shows the envelope of maximum story displacements of the building and
the displacements obtained from a SDOFS. As shown, the maximum positive
displacements are considerably larger than the negative ones for both sets of results, and
thus it can be concluded that the structure shows a significant permanent deformation
after the earthquake. The displacements obtained for this envelope were obtained in a
small interval of time, which suggests that the fundamental mode of the building
dominates the global response of the building. The results obtained from the SDOFS
match reasonably well with those obtained in the analysis of the whole building.
Figure 4.45 shows the envelopes of IDI of the building and the Dl computed from the
SDOFS. As shown, the positive and negative envelopes of IDI reflect the tendency of the
structure to yield in the positive direction. The maximum IDI is about 0.025 and
corresponds to the 7th story. This value of IDI can be considered as acceptable from a
structural point of view as shown in Figure 4.46, where it can be seen that no instability
is expected in this story for the given IDI (also, the maximum rotation on the beams was
equal to 0.026 which is considerably smaller than the ultimate rotational capacity of the
beams at this story). Nevertheless, very heavy damage can be expected in non-structural
components and contents, and from this point of view, the IDI is excessive.
Unlike the displacement envelopes, the IDI shown in the envelopes were obtained at
different times. This fact shows that although the fundamental mode dominates the global
behavior of the structure, higher modes need to be considered to assess correctly the
behavior of the structure, mainly in the upper stories. Figure 4.47 compares the positive
159
101 envelope obtained from the nonlinear THA with the 101 distribution obtained from the
pushover analysis with a tip displacement of 1.125 m. The value of 1.125 was selected
because it is similar to the 1.114 m maximum tip displacement computed from the
nonlinear THA. As shown, the 101 distribution over height for both analyses show
concentration of large values of 101 on stories 3 to 1 0. Nevertheless, the 101 for stories
16 to 30 are larger for the nonlinear THA with respect to those obtained from the
pushover. This suggests again the influence of higher modes in the behavior of the
structure that the pushover analysis can not capture. Table 4.3 summarizes the results
obtained from the nonlinear THA of the SOOFS.
Table 4.3 shows the ~global• ~story and ~ocal obtained from the nonlinear THA for safety.
The largest values of ~story and ~local were located on the 7th floor. As shown in the table,
the values of ~global• ~tory and ~ocal corresponding to the pushover analysis and a L\t of
1 .125 m (similar to the 1 .114 m maximum tip displacement obtained in the safety
nonlinear THA) are larger than those obtained in the nonlinear THA for safety. The
pushover analysis tends to overestimate the values of ~story and ~oca1· As shown by the
values above, large ductility demands are expected for the service EQGM. It also can be
concluded by analyzing Table 4.3 that, as the value of~ increases, the pushover analysis
tends to further overestimate the values of ~tory and ~ocal as compared with those
obtained from a nonlinear THA (i.e., the overestimation of these parameters is larger for
the THA for safety). Thus, these results suggest that the pushover analysis tends to
further overestimate the P-L\ effects as~ increases.
It should be noted by comparing Tables 4.3 and 4.4 that there is no good agreement
between the ~ obtained in the SOOFS and the ~global obtained in the 30-story building
(4.59 vs. 3.17). This can be explained in part by the fact that ~global is not a good
parameter for quantifying the nonlinear behavior of the building due to the significant
change in the deformed shape of the building as ~ increases (including a significant
concentration of deformation in a few stories). The value of ~global computed from the
lateral displacements of the building corresponding to the equivalent height of the SOOFS
160
\ i
I
I I
(20th story) is 0.96/0.24 = 4.00, which is a reasonable estimate of the ~of 4.59 obtained
from the SDOFS.
In Figure 4.48, the distribution of hinge rotation (maximum plastic rotation) for all the
members located in a given story is plotted. In general, columns have significantly smaller
hinge rotations than beams. As shown in the figure, the columns in the 3 lower stories
and 1 0 upper stories have small hinge rotations, while those in the other stories have
practically no rotation. The largest hinge rotation in the beams is about 0.026. As shown,
the distribution over height of hinge rotations is similar to that of 101, that is, there is a
very large concentration of large values of the rotation in a few stories. Figure 4.48 only
provides the largest hinge rotation in all the members located on a given floor. Figure
4.49 provides an idea of how the hinge rotation values are distributed throughout all the
members of the building. In this figure, the magnitude of the hinge rotation is proportional
to the radius of the shadowed circles drawn at the ends of the members. As shown, the
larger hinge rotations are fairly distributed in all the beams of stories 4 to 1 0. Also, it can
be seen that practically no rotation occurred in the columns. This observed behavior may
be due mainly to the combination of: first, the fact that the columns of the building are
overdesigned in comparison to the beams in such a way that no hinging occurs in the
columns (except at their bases); and second, the fact that columns are flexible in such
a way that their lateral deformation, once hinges appear in the beams, are large. Figure
4.50 summarizes this considerations.
In Figure 4.51, the distribution of the largest cumulative plastic rotations in all the
members located in a given story is plotted. As shown, columns have very small values
of cumulative plastic rotations. Only at the bottom end of the columns of the first story is
t~is value significant, with a cumulative plastic rotation of about 0.013 radians. The
maximum value for beams is about 0.13 radians. Figure 4.52 provides an idea of the
distribution of the cumulative plastic rotations throughout the whole building. As shown
in both figures, the larger values of cumulative plastic rotations of the beams tend to
concentrate in stories 3 to 25, while practically no rotation occurs in stories 1 and 2 and
161
from stories 26 to 30. Note that in the central frame in Figure 4.52 (which represents the
exterior frames in the real structure), the demands are smaller than in the other two
frames.
Finally, Figure 4.53 shows local damage to the members of the building. Damage index
(DMI) values were computed to estimate the magnitude of such damage. As shown, main
structural damage is concentrated in the beams, and as suggested by the distribution of
the maximum and cumulative plastic rotations throughout the building, damage is
concentrated in stories 5 to 22. The maximum value of damage index is 1.35. To give an
I I
idea of how the above DMI was obtained, the computation of the damage index for a 1 beam located in the seventh floor follows:
The above computation corresponds to a specific beam located on the seventh floor,
which corresponds to the beam with the largest hinge rotation (8 = 0.0262 as shown in
Figure 4.48). Nevertheless, the largest cumulative plastic rotation was located in a
different beam. For the beam for which the DMI was computed, the cumulative plastic
rotations in the positive and negative direction obtained from the THA were 0.1247 and
0.1169, respectively.
According to Park and Ang, a damage index of 1 corresponds to failure of the member.
As shown by the sizes of the circles at the end of the beams in Figure 4.53, failure of
several beams is expected; mainly those beams located in stories 6, 7, 8 and 9.
Although the value of 0.025 computed for the maximum 101 in the building is large and
heavy damage is expected on nonstructural elements and contents of the building, if the
structure is designed and detailed adequately, there should be no reason for collapse if . . it is subjected to just monotonically increasing lateral force, as it is shown in Figure 4.46. 1
162
i ' )
I
From an energy dissipation capacity point of view, it has been shown that practically all
beams in stories 6 to 9 would have failed, and thus it is very probable the building would
collapse under these circumstances. Nevertheless, it can be seen that the largest value
of damage index, 1.35, is not far away from 1.0, which represents the boundary between
failure and no failure. Thus, a judicious change in the detailing of the beams (i.e.,
increasing the value of eu by diminishing the separation of ties at the end of the beams)
and a small increase in the flexural strength of the beams (i.e., decreasing the maximum
and cumulative plastic deformation demands as shown for SDOFS in Table 4.4) would
be enough to avoid failure of these members (see equation to compute DMI). From the
1 above results, it can be said that the beams are underdesigned for safety level. One of ' I
the main reasons for the failure of the beams in stories 4 to 10 is the unexpected and
very noticeable concentration of plastic deformation in these stories. To qualify the
performance of the building as good or bad, it is necessary to explain this concentration.
At this point, it is not well understood why the larger values of 101, maximum and
cumulative plastic rotations at the end of the beams, tend to concentrate so noticeably
in stories 4 to 10. As shown in Figures 3.45 to 3.47, the ratio between supplied strength
and required strength (obtained from an elastic analysis) is similar for all stories in the
structure, with the exception of the top 5 stories. Also, as shown in Figure 4.14, the
elastic stress ratios are almost constant throughout the height of the building, which points
to the fact that no concentration of inelastic behavior should occur. No large variations
in the elastic stiffness from one story to the next can be observed in the 30-story building.
In Chapter 5, the possible reasons for this unexpected concentration of plastic
deformation in few stories is discussed.
4.3.6 CONCLUDING REMARKS
From the above discussion of the results obtained, it can be concluded that: the design
based on UBC requirements is inadequate under service EQGMs; and the UBC design
for safety level seems inadequate for drift control, not from a structural point of view but
because of the extensive and excessive damage to nonstructural elements and contents
of the building. From a strength point of view, it seems that a design based on just UBC
163
( \ ' I
seismic requirements does not provide enough strength to the structure to avoid its
collapse when subjected to the safety EQGM. The detailing of the beams has to be ,--\,
enhanced, and their strength has to be increased to avoid failure in them from an energy
dissipation point of view. Note that the maximum rotations on the beams are not
excessive: the failure in the beams is produced mainly by the large cumulative rotations
in them. From the example given for the computation of DMI for safety, damage due to
maximum rotation is 0.0262/0.048 = 0.55, and damage due to cumulative plastic rotation
is 0.15 (0.124 7 + 0.1169}/0.048 = 0. 76.
164
r
r \
I
I -I
Roof Results normalized to Pseudo-dynamic Base Shear displacement at UBC allowable stress results
Type of Analysis tons % ofW end Frame Base Shear (m)
Pseudodynamic 1020 4.5 .1174 1.00 UBC at allowable stress
Elastic RSA for 3948 17.6 .4980 3.87 Service!1H2l
Elastic THA for 4919 22.0 .6401 4.82 Service!1l(3l
Elastic RSA for 11206 50.0 1.4047 10.99 Safety!1H4l
Elastic THA for 21082 94.0 2.7928 20.67 Safety!1H5l
Inelastic THA for 2308 10.3 0.4220 2.26 Service(3H6l
Inelastic THA for 2932 13.5 1.1143 2.87 Safety!SH6l
{1) unidirectional input with real eccentricities only {2) for elastic site spectra determined for a return period of 10 years {3) for SCT scaled down to 0.07 PGA (4) for elastic site spectra determined for a return period of 450 years (5) for SCT scaled up to 0.30 PGA {6) without considering torsion
Displacement
1.00
4.24
5.45
11.97
23.79
3.59
9.49
TABLE 4.1 BASE SHEAR AND TIP DISPLACEMENT OF 30-STORY BUILDING OBTAINED FROM ANALYSES WITH UNIDIRECTIONAL INPUT
165
(
State of Building Tip displacement Base Shear Base Shear (m) (ton) Coefficient
UBC allowable stress 0.152 1020 0.045 t -
UBC design for first 0.213 1428 0.063 yield
First yield 0.266 1785 0.079 I I
Formation of 120 p.h. 0.300 1992 0.088
Formation of 460 p.h. 0.900 2405 0.106 base shear
Maximum base shear 1.350 2451 0.108 (640 p.h.)
Maximum base shear 1.114 2932 0.129 from 20 nonlinear THA
TABLE 4.2 SUMMARY OF TIP DISPLACEMENT VS. BASE SHEAR I RELATIONSHIP OBTAINED FROM PUSHOVER ANALYSIS OF 30-STORY BUILDING ACCOUNTING FOR P-~ EFFECTS
166
I .
I , r
Type of tip J.l.global J.l.story J.l.iocal J.l.iocal Analysis displacement (7th story) (maximum) (7th story)
(m)
Pushover 0.152 0.43 0.44 0.56 0.55
0.213 0.61 0.61 0.79 0.78
0.266 0.76 0.77 0.98 0.97
0.300 0.86 0.89 1.32 1.30
0.450 1.29 1.91 3.48 3.26
0.900 2.57 5.09 9.45 9.45
1.125 3.21 6.40 12.04' 12.04
1.350 3.85 7.60 14.50 14.50
THA for 0.422 1.20 1.76 2.90 2.90 service
THA for 1.114 3.17 5.58 10.82 10.82 safety
TABLE 4.3 DUCTILITY DEMANDS FROM NONLINEAR 2D THA ANALYSES OF 3Q-STORY BUILDING
Ground Motion PGA Yielding JL=l:!.max/11y J.l.a=llacc /11y Shear
Strength
SCT-EW 0.07 g 0.11 w 1.64 3.41 SERVICE
SCT-EW 0.30 g 0.11 w 4.59 38.35 ULTIMATE
0.12W 4.55 34.06
0.13 w 4.44 30.48
0.15W 4.12 24.84
TABLE 4.4 SUMMARY OF RESULTS OF SDOFS SUBJECTED TO SCT-EW GROUND MOTION
167
NS
direction of ground motion
EW
FIGURE 4.1 BIDIRECTIONAL INPUT CONSIDERED IN 3D ELASTIC THA
168
·-/
' \
/~
Ace. (g) 0.18.-------------------------------~~------------~
0.09
o.o~~~~~~~~~~~~~iT~Tt~HiiTtnTtit~~~ -0.09
-O.l8oL _______ 1_0----------------------~4~o~----~s~o------~6o 20
Time fs~cond)
Pseudo-Velocity (in/sec)
500
100
50
10
5
1
0.1
Fourier Amplirude Spectrum
3 4 5 6 Frequency (Hz)
7 8 9
0.5 1 5 10 50
Period (Second)
FIGURE 4.2 SCT-EW GROUND MOTION
169
10
Floor 30
25
20
15
10
5
Elastic Analyses for Service Comparison of Floor Displacements
THA
1 ~~--~--~--~--~--~--~--~--~~ ~ ~ ~ ~ ~ ~ M M U
Displacement (m)
FIGURE 4.3 FLOOR DISPLACEMENTS OBTAINED FROM ELASTIC ANALYSES FOR SERVICE WITH UNIDIRECTIONAL INPUT
170
f'. I I
P'~
I I
I '
Story 30
25
20
15
10
5
Elastic Analyses for Service Comparison of IDI
' ' '
' '
\
'
0.003 IDI
' '
:
' '
' '
' ' '
J
THA
0.009 0.012
FIGURE 4.4 IDI OBTAINED FROM ELASTIC ANALYSES FOR SERVICE WITH UNIDIRECTIONAL INPUT
171
storxo
25
20
15
10
5 (
Elastic and Nonlinear Analyses for Service Comparison of Story Shears
I I I I
I I I I
. •' ,
.· / .• I
I
:
:
·, ··· ... ' · .. ', · ....
\
· .. Elastic -... . .JHA
RSA\\ \ ...
Nonlin~r THA
' '
1 \ r-~--~--~--~--~--~--~--~--~~
-5000 -4000 -3000 -2000 -1000 1000 2000 3000 4000 5000 Shear(ton)
FIGURE 4.5 STORY SHEAR DISTRIBUTION OBTAINED FROM ELASTIC AND NONLINEAR ANALYSES FOR SERVICE WITH UNIDIRECTIONAL INPUT
172
-
I I
\ I
·'
,. \
I
,- \
i ;
Story
30
25
20
15
10
5
columns
Elastic RSA Analysis for Service Stress Ratios in Members
.• .···
' ~s
(
) '
4 5 7 10
Stress Ratio
FIGURE 4.6 MAXIMUM FLOOR STRESS RATIOS FOR SERVICE ELASTIC RSA
173
Compression
p
M and P due to gravity
( MgP Pgr)
Tension
Linear elastic M and P due to total load
( MT' PT)
M
Stress ratio "' ~:
FIGURE 4.7 DEFINITION OF STRESS RATIO IN COLUMNS
174
I I
, I
·" ' '
f I
FIGURE 4.8 FLOOR DISPLACEMENTS OBTAINED FROM 3D ELASTIC THA FOR SERVICE WITH BIDIRECTIONAL INPUT
175
Sto
30
25
20
15
10
5
30 ELASTIC THA for Service Real + Accidental Eccentricities
/
/
/
JDJ
'
_,
E-W
' ' '
0.003 0.006 0.009 0.012
FIGURE 4.9 IDI OBTAINED FROM 3D ELASTIC THA FOR SERVICE WITH BIDIRECTIONAL INPUT
176
~\ .'\:
"'L
'
,, ! '
\ '
--_,.-
/
Sto 30
25
20
15
10
5
30 Elastic THA for Service Real + Accidental Eccentricities
Nonlinear THA
N-S----'
E-W
1000 2000 3000 4000 5000 Shear(ton}
FIGURE 4.10 STORY SHEAR DISTRIBUTION OBTAINED FROM 3D ELASTIC THA FOR SERVICE WITH BIDIRECTIONAL INPUT
177
Elastic Analyses for Safety Floor Comparison of Floor Displacements
30
25 RSA
THA 20
FIGURE 4.11 FLOOR DISPLACEMENTS OBTAINED FROM ELASTIC ANALYSES FOR SAFETY WITH UNIDIRECTIONAL INPUT
178
I
,.·-, I
I :
..........
.....
,-" '
Story 30
25
20
15
10
5
Elastic Analyses for Safety Companson of IDI
) RSA
. ' ' .
' ' '
:
'
. . . . . I
THA
FIGURE 4.121DI OBTAINED FROM ELASTIC ANALYSES FOR SAFETY WITH UNIDIRECTIONAL INPUT
179
Story 30
25
20
15
10
5
1 -21000
Elastic and Nonlinear Analyses for Safety Comparison of Story Shears
··· .. ·,_
'· ·· .. ·. ·.
Elastic
'
' ' ' ' ' ' ' ' ' ' ' '
-14000
: :
: :
·-....... THA
. RSA ' '
Nonlinear\ THA ~
'
'
'
7000 1 Shear( ton)
\
f\.
. I
FIGURE 4.13 STORY SHEAR DISTRIBUTION OBTAINED FROM ELASTIC AND NONLINEAR ANALYSES FOR SAFETY WITH .f"·
UNIDIRECTIONAL INPUT
180
~' '
~·
' '
Story
30
25
20
15
10
5
Elastic RSA for Safety Stress Ratios in Members
columns ·······:.- beams
· .. ·-.. .::~
... ··
FIGURE 4.14 MAXIMUM FLOOR STRESS RATIOS FOR SAFETY ELASTIC RSA
181
Interior Frame Exterior Frame Central Frame
FIGURE 4.15 MODEL USED FOR NONLINEAR 2D THA
182
MOMENT,M .
-----------------r-I
I I
I I
I
CURVATURE.'~!
( a )
M M
FIGURE 4.16 DRAIN 2DX ELASTOPLASTIC MODEL FOR HYSTERETIC BEHAVIOR OF RC MEMBERS
8 A
My- M
FIGURE 4.17 DRAIN 2DX YIELD INTERACTION SURFACE FOR RC COLUMNS
183
FORCE OR MOMENT
ACCUMULATED POSITIVE DEFORMATION = SUM OF POSITIVE YIELD EXCURSIONS
A~,.... __
\_M~XIMUM POSITIVE
DEFORMATION
EXTENSION OR ROTATION
YY ~TED NEGATIVE DEFORMATION
= SUM OF NEGATIVE YIELD EXCURSIONS
FIGURE 4.18 DEFINITION OF CUMULATIVE PLASTIC DEFORMATIONS
184
I
Base Shear (ton) 3500
3000
2500 ............................. .
Pushover Analysis Base Shear/W
without P-~
• 460 p.h. ·································· 0.108
640 p.h. with P-~
2000 120 p.h . ...................... ........................................................................................................... ·································· 0.079
1500 ·················· ... ··········································································································· .................................. 0.063
500 fonnation of first p.h. first failure on a beam
0 0.3 0.6 0.9 1.2 1.5 1.8 2
Tip Displacement (m)
FIGURE 4.19 BASE SHEAR VS. TIP DISPLACEMENT CURVE OBTAINED FROM PUSHOVER ANALYSIS
185
Sto 30
25
20
15
10
5
Elastic Analyses for Allowable Stress Comparison of IDI
··· .....
K8 for allowable stress
···-..
<
' K8
for safety
' .•
0.0005 0.001 0.0015 0.002 0.0025 0.003 IDI
FIGURE 4.20 COMPARISON OF IDI DISTRIBUTION THROUGH HEIGHT OBTAINED USING DIFFERENT SECANT STIFFNESSES
186
I
Floor 30
25
20
15
10
0.25
Pushover Analysis P-a Effects Included
0.5
I
I
I
I
I
I
I
.' /
./
i /
! ! i :
:
1.25 1.5 Floor Displacement (m}
FIGURE 4.21 a FLOOR DISPLACEMENTS OBTAINED FROM PUSHOVER ANALYSES FOR DIFFERENT TIP DISPLACEMENTS
187
Floor 30
25
20
15
10
5
Pushover Analysis Effect of P-a on Floor Displacements
... ·····
1 1.25 1.5 Floor Displacement (m)
FIGURE 4.21 b FLOOR DISPLACEMENTS OBTAINED FROM PUSHOVER ANALYSES FOR DIFFERENT TIP DISPLACEMENTS
188
Story 30
25
20
15
5
1
Pushover Analysis P-a Effects Included
FIGURE 4.22a IDI OBTAINED FROM PUSHOVER ANALYSIS FOR DIFFERENT TIP DISPLACEMENTS
189
Story 30
25
20
15
10
5
Pushover Analysis Effect of P-a on IDI
no P-A effects
·· ..
P-A effects
FIGURE 4.22b IDI OBTAINED FROM PUSHOVER ANALYSIS FOR DIFFERENT TIP DISPLACEMENTS
190
Story
30
5
1
Pushover Analysis Maximum Rotations in Beams
0.035 0.04 0.045 0.05 0.055 0.06 emax
FIGURE 4.23 MAXIMUM ROTATIONS OBTAINED FROM PUSHOVER ANALYSIS
191
Base Shear (ton) 3500
3000
2500
2000
1500
1000
500
0 0.3
Pushover Analysis
without P-A
with P-A
0.6 0.9 12 15 1~ 2 Tip Displacement (m)
FIGURE 4.24 DIFFERENT STATES OF 30-STORY BUILDING COMPARED IN FIGURES 4.21 AND 4.22
192
...... co (,:)
Floor
30
25
20
15
10
5
FIGURE 4.25 DISTRIBUTION OF PLASTIC HINGES IN PUSHOVER ANALYSIS, L\ = 0.30 m
Floor
30
25
20
15
10
5
FIGURE 4.26 DISTRIBUTION OF PLASTIC HINGES IN PUSHOVER ANALYSIS, 6, = 0.45 m
Floor
30
25
20
15
10
5
FIGURE 4.27 DISTRIBUTION OF PLASTIC HINGES IN PUSHOVER ANALYSIS, ~ = 0.60 m
Floor
30
25
20
15
10
5
FIGURE 4.28 DISTRIBUTION OF PLASTIC HINGES IN PUSHOVER ANAL VSIS, ~ = 0.90 m
Floor
'30
25
20
15
10
5
FIGURE 4.29 DISTRIBUTION OF PLASTIC HINGES IN PUSHOVER ANALYSIS, L\ = 1.20 m
Floor
30
25
20
15
10
5
~
FIGURE 4.30 DISTRIBUTION OF PLASTIC HINGES IN PUSHOVER ANALYSIS, L\ = 1.275 m
..... co co
Floor
30
25
20
15
10
5
FIGURE 4.30 DISTRIBUTION OF PLASTIC HINGES IN PUSHOVER ANALYSIS, l\ = 1.35 m
25001~------------------------------------~
2000 ························································· .......... ··································································
1500 ··········································· ...................... ······························································
c 1000 .............................................................. ·····························································
~ 500 ······················n··-~v-·· ··/······ .......... ......... / ... 1·········{--n .. .;. ... f ..... ..f ... ~·-····· ~ . o~\l- \J'I ~ -500 ························~···· ····V····· ·· · · · · · ·· · ·· · ·· · · · · ···\ ········· ··· ·· ~ ··· ·· ·· ·· · ·· ·········· rn m -1000 ········································· ·· · ·· ··· ·· · ·· · ·· · ·· ···························································
.......... E --c Q.)
-1500 ············································· ········ ......... ································································
-2000 ······················································· .............. ································································
-2500 0 10 20 30 40 50 60 70 80
Time (sees)
FIGURE 4.32 TIME HISTORY OF BASE SHEAR FOR 20 NONLINEAR THA FOR SERVICE
0.4-.---------------------------------------~
0.3 ················································-········· ......... ·························-·-·········-·······························
0.2 ····-········································· ............... ·······················-·····-····----···----·--·--·--·······--·
E 0 Q.) (.) rn c.. -0.1 ................................................. . CJ)
0 c. -0.2 ············································· ... ··- .. .. .. .. . . --·····-·······-··---·-··-··-·--··-·--·--··----····--·-·····-·· F -0.3 ....................................................................... ······-························································
-0.4 ······································································ ... ···········-··························-·····························
-0.5-t-----r----,----r----,-------.----,------r----j 0 1 0 20 30 40 50 60 70 80
Time (sees)
FIGURE 4.33 TIME HISTORY OF TIP DISPLACEMENT FOR 20 NONLINEAR THA FOR SERVICE
200
Floor 30
25
20
15
10
5
Nonlinear THA for Service Envelope of Floor Displacements
/SDOFS 30-story building
1 r-~~~--~--~---+--~--~--~--~~ ..0.5 ..0.4 ..0.3 . -0.2 ..0.1 0.1 0.2 0.3 0.4 0.5
Displacement·(m)
FIGURE 4.34 ENVELOPES OF FLOOR DISPLACEMENTS FROM 20 NONUNEAR THA FOR SERVICE
201
Story 30
25
20
15
10
5
Nonlinear THA for Service Envelope of IDI
v- SDOFS drift index
0.012
IDI
FIGURE 4.35 ENVELOPES OF IDI FROM 20 NONLINEAR THA FOR SERVICE
202
I
Story 30
25
20
15
10
5
Nonlinear THA vs. Pushover Analysis I Dl for Service
·· ...
,; I
Pushover ... \ ... ...,j THA
,,
:· •. -
·!/ 1t-----~--,---.--.:.__---r-__ __:_,.. __ -----, __ --,
0.002 0.004 0.006 0. 0.012
FIGURE 4.36 COMPARISON OF 101 FROM PUSHOVER ANALYSIS AND 20 NONLINEAR THA FOR SERVICE
203
Story 30
25
20
15
10
5
Nonlinear THA for Service Maximum Rotations in Members
no plastic behavior in columns
0.006 0. Maximum Rotation
FIGURE 4.37 MAXIMUM ROTATION ON A MEMBER OFA STORY FROM 20 NONLINEAR THA FOR SERVICE
204
N 0 01
Floor 30
-------- ---r---·r---~~--~~~-------·~-~~--~ ~--~r-~r---~--- -- ---
-- --·-r--~-,
-- -- ---r---t
FIGURE 4.38 DISTRIBUTION OF MAXIMUM ROTATION FROM 20 NONLINEAR THA FOR SERVICE
Story
30
25
20
15
10
5
Nonlinear THA for Service Maximum Accumulated Rotations in Members
no plastic behavior in columns
0.006 0.008 0.01 0.012 Maximum accumulated rotation
FIGURE 4.39 MAXIMUM CUMULATIVE PLASTIC ROTATION ON A MEMBER OF A STORY FROM 20 NONLINEAR THA FOR SERVICE
206
1\) 0
"""'
Floor 30
25
20
15
10
5
--- ---~---~--~
--- --- ----~~----~--~--~ ~--~---~-------+----+---~ --- --- --· -+---~
~---1--~·--· -- ---+---1 ~---+·---· ·--· --· ·--+---1 --- ,_ :--· e--· ·--+---~ r---+----1 --- ·---; :::~::: ::--::: :;:-· ---
-----·--- ·------ , __ _
:~--~ 1--~1·
~---11·-
r---··-·
---.::r--::
·---.:: =---::·
·-::;.-:;
·---.:: --::
--- , __ :--+---~ ~--J.-----1 1-----1-· ·--. ---
1--·--
1----·
::=-$:~-~~:
·---:: ·---::.
---~: ---:::
==FF1-j ~ ~----~?_;~~t-·--. ::: ~t: ;::r==. •. ,J; T ·~··r~::::r~ .. r-:= ::=------<::·t:;-~~=r~·-~=r-----4:::.1
1;~_.4$~f:WP (f--=!?t ·::~:::---.c:r:$J: :~~1~~1~;~{1~~=~:# I. r... ,,,.,,. »··•· J
:.,:.__........,: ::--:~ :~.-:: ·---::
:---: :--: :--· ·---~·+---+~------~--4
~F:;~~FR:F::~~lf~' . -·
apace max (beams) = 0.9108 apace max (columns>= 9.0099
FIGURE 4.40 DISTRIBUTION OF CUMULATIVE PLASTIC ROTATION FROM 20 NONLINEAR THA FOR SERVICE
1\) 0 Q)
Floor 30
- - -- ---.J-.---+----1 ~--1--+----+---+---1 ~---4--+--+-- -- --
~--+--+·--· -- -- -- -- --25 ·-· ·--· ·--' '--+---t
- ,_, :--· ::--· ·--+----i ~--+---~
-- -- --+----1
- , __ ::---1---~ - ,_; :::-· -·~:::--· :::-·- ~---4--~~--~---'---··~--~
20
1---· ~::-::::::-:::·:::-::::~::~:-:- - ,_ 15 1---· :::-c.::)'-:::.:::-:::.::::-::. - ,_
-:-::::-:::;•:;;~::· ;:--::::~:-::: ·--. :%~:.::--~. ::-:::.:'-:::-
1---· :=:-::::::--:=::::--:= ,,,_,,,-10
5
f-·1·
f-·+---i -:~-:
:-.~--.:·
=-=~=· :-::~:
.-;;.-:;
t-C.:t-:<
f--,_
-1:-
1--··-·
·-::.-.:.
~··+----+---------+---·+-----,
Dl1 max = 0.18
1---~·--· :;:--: ,_
1----1:>.--,: ,, __ ,, ·-
-··::~·;;-.-.:;.-·
1----1:::-::: ·--:: -·
k· ~,.,:. ~,: ;, ;,!,. ,;. .--.~·~:-{:~i::-i:~-:,-~~
:~:;;~,~~;1;,:i,l.f:.=:: ... .. ~-:: .,_,,,,,_,f~··=-=: ·::-:: ::--::· :;:-:: .--:; , __ , , __ , :--· ·-·
. -
FIGURE 4.41 DISTRIBUTION OF DAMAGE INDEX FROM 20 NONUNEAR THA FOR SERVICE
3000~------------------~-----------------.
2000 ...................................................... ·················· ................................... .
§ 1000 ··········· ............................................ ···;J ........................... .
~ N ~ oW···································································
lli v v ag -1000 .......................................................... .
-2000 ........................ ··············· ..................................................................... .
-3000+------.-------,-----.-------,-------.----...-------.-----i 0 1 0 20 30 40 50 60 70 80
Time (sees)
FIGURE 4.42 TIME HISTORY OF BASE SHEAR FOR 20 NONLINEAR THA FOR SAFETY
-
1.2.------------------------------------,
1 ···································································· ··········································································
0.8 ·································-························ ........ ···································································
i ::: :::::·:::::·::::::·::::::.:::::: ·. ·~:: ·:. :·:.: .. :·.·. :.·~.: .. ::. [.·:· .·:·. :.·nA c.. 0.2 ·············~····· .. ··f\··· .... .. . . .. . .. . . ... . . . . . . .. ........ . . .. . .. .. . .. . .. . .. ..v. ... \;. .~ h-A.f\ .. l IJ u
~ -0.~ l~;i~·········· ·~···· .................. · ................................... . -0.4 ········································· ······································································································
-0.6+----.----,---..----..,..------,----.------.----J 0 1 0 20 30 40 50 60 70 80
Time (sees)
FIGURE 4.43 TIME HISTORY OF TIP DISPLACEMENT FOR 20 NONLINEAR THA FOR SAFETY
209
Floor 30
25
20
15
10
5
Nonlinear THA for Safety Envelope of Floor Displacements
SDOFS~
30-story building
1 ~--~--~--~--~--~--~--~--~~ -o.e -o.4 -o.2 0.2 o.4 o.e o.a 1 1.2
Displacement (m)
FIGURE 4.44 ENVELOPES OF FLOOR DISPLACEMENTS FROM 20 NONLINEAR THA FOR SAFETY
210
Story
30
25
20
15
10
5
1 -0.03 -0.02
Nonlinear THA for Safety Envelope of 101
~ SDOFS drift index
0.03 101
FIGURE 4.45 ENVELOPES OF 101 FROM 20 NONLINEAR THA FOR SAFETY
211
Pushover Analysis 2500~------------------------------------~
2000 ........................................................................................................................................... .
'-rn Q) 1500 ··:···· ................................................................................................................................... . .c (/) .
~ 0 ....... (/) .c 1000 .......................................................................................................................................... . ~
500 ................................ , .......................................................................................................... .
0 0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.045 0.05
7th story I D I
FIGURE 4.46 IDI VS. STORY SHEAR RELATIONSHIP FOR 7TH STORY OBTAINED FROM PUSHOVER ANALYSIS
212
~
Story
30
25
20
15
10
5
1
Nonlinear THA vs. Pushover Analysis . IDI for Safety
0.005 0.01 0.015 0.02 0.025
101 0.03
FIGURE 4.47 COMPARISON OF IDI FROM PUSHOVER ANALYSIS AND 20 NONLINEAR THA FOR SAFETY
213
Nonlinear THA for Safety Story Maximum Rotations in Members
30 .. · ·:-.. ) {
25 '··--.. , •, .. •
~,..~
20 >>columns
15
10
5
~:> 1 ..................... _
0.005
beams
0.01 0.015 0.02 0.025 0.03
Maximum Rotation
FIGURE 4.48 MAXIMUM ROTATION ON A MEMBER OF A STORY FROM 20 NONLINEAR THA FOR SAFETY
214
1\) ...... (11
Floor 30
--~--+-- ,__ --- ----- ·--· ··---. , __ , .,_ -- --+--+-----11---t----1 1----4·--·· ·--.1~-~ 1---4··- , __ ·---+ --+----1 1---+---1 -- --- -- .-- :--·f------1 -- ··-: ·--· ·--... - ·-- 1·- ·-· ·-- -- :::--· ··--... -
25 ·-: .,_, :--. ,,, __ . :;:-... - 1·-·-· ,_,- , __ , ::;-: , __ ···-
20
15
10
5
··- ·--· :=:-· :::-~ :::-~ ~-: ·- ._,
:-·· :::-· :::--: ::.....,___: ::·-: :-: ::- ,_,
:::-·:~-:::
:::-.:=:-:::
::~· -·:::-:;:
.. -.-- .. -.--·· ::-. _, ·-· ·-· :::-· ·--· :::--:· :::--·::= :-:
:::~:·::-=
;::,_,__,~:. :;:,____:::.
:::-::::::-.::
~-t-':-·_·:==:~-=:==:~-=:==:==: ~ t= ~-t ' :____-:~::~:;:-----.<;:::=: ep max (beams) = 0.0262 ep max (columns)= 0.0010
FIGURE 4.49 DISTRIBUTION OF MAXIMUM ROTATION FROM 20 NONLINEAR THA FOR SAFETY
' ' ' ' ' ' ~- --------: ' ' ' ' ' ' ' ' '
• plastic hinge
FIGURE 4.50 MAGNITUDE OF ROTATIONS OF COLUMNS AS COMPARED TO ROTATIONS ON BEAMS
216
Story 30
:> 25 1,
'i
Nonlinear THA for Safety Maximum Accumulated Rotations in Members
I
\ columns 20/
15
10
5
11-----r------.-----....-------r-----, 0.03 0.08 0.09 0.12 0.15
Maximum accumulated rotation
FIGURE 4.51 MAXIMUM CUMULATIVE PLASTIC ROTATION ON A MEMBER OF A STORY FROM 20 NONLINEAR THA FOR SAFETY
217
1\) ....... (X)
Floor 30
25
20
15
10
5
---+---+---- --- -- --
-- -- -- -. - ---·t----i
--- ··-· ·--· ·--· ·-· -- :::~ ---·t-----1 -- -- -- ;:;-: :--:;:f------1 1---1---~ 1----f:::-::. :=-=:=t---i
:---·:-: ·-· ·-·: ·-· :::-::::~:· -·::: :---: :=--··-·
;::-.;::-:::
::-· -·:::-:;:
=:-·--::;~:::
·---: =-~::
·-::;;::-:::
··-:=::::-:::
:::-::::::-:::
::-· -:;::;:-:;:
apace max (beams) = 0.1265 apace max (columns)= 0.0131
FIGURE 4.52 DISTRIBUTION OF CUMULATIVE PLASTIC ROTATION FROM 20 NONLINEAR THA FOR SAFETY
1\) ...... (0
••
Floor 30
25
20
15
10
5
~----~--~~--·+--- --- ---1----t·-- , ___ . ·---t---t--; ~----..,r----t --- .. _, ·---· ·--· ·-·+------1 ~---..,r----t t----1"'--' ,,_. :;:--· --· ··- t----+··-,._ ·--· :::-.::: :::-:;: :;:-, ·--
::;-..,::-.
:::-·:::-:::
:::-.:::-:::
::-· -·:::-:::
--- --- --- , __ --·t--~ -- ,,, __ ·--·t------1
, __ ,__ --- ,,;_, :--:;: ·.. - ·-- .::-~ ::-::: , __ ·-· ·-. ·--· :::--:::::~:: -. --: !$_ .. _,
:::------:::· :::~o--::
;::~::. ;;:,.___;;:.
;::-.::·:=:-· ~::
:::-:::.;:-.;:
:::-::::::
;;:,..__,;;: :;:,____,:;:
:;:-:;::::-~:
Dl1 max = 1. 35
FIGURE 4.53 DISTRIBUTION OF DAMAGE INDEX FROM 2D NONLINEAR THA FPR SAFETY
5 OVERALL EVALUATION
r·~ 5.1 GENERAL REMARKS
\ ; In this chapter, an overall evaluation of the seismic performance of the 30-story building
' .
I I
\
designed according to UBC is carried out. The evaluation is based on the study of the
results obtained from the analysis summarized in Chapter 4. Before attempting to judge
the performance of the 30-story building, it was considered important to explain why the
structure shows a concentration of deformations in a few stories when it enters its
inelastic range of behavior. In sections 5.2 to 5.5, the possible reasons for this behavior
are summarized.
As briefly discussed in section 4.2, the results obtained from elastic THA of the 30-story
building using the SCT-EW ground motion do not give a good estimate of the inelastic
response of the building when subjected to the same ground motion. In section 5.6, a
brief discussio_n of the reasons for the observed discrepancy between the elastic and
nonlinear response is presented. For this purpose, the response of a SDOFS is studied.
In section 5.7, the reliability of the results presented in Chapter 4 is discussed based
on the observations presented in sections 5.2 to 5.6
Finally, in section 5.8, the performance of the 30-story building designed according to
UBC is discussed for serviceability and safety limit states.
5.2 EFFECT OF AXIAL DEFORMATION IN COLUMNS ON THE BEHAVIOR OF THE
30-STORY BUILDING
To explain the concentration of deformation of the 30-story building, several parameters
were studied. One of the aspects of the behavior of the 30-story building that was difficult
to explain was the distribution over height of the bending moment at the ends of the
beams, as shown in Figures 3.45 to 3.47 for the beams located at three different bays
of Frame B. In some cases, as shown in Figure 3.47, the required moment at the ends
of the beams remains practically constant for the beams located from the first to the
221
twentieth story. In other cases, as shown in Figure 3.45, the required bending moment ;
increases with height, that is, in some cases a beam has larger end moments than those
corresponding to the beams located exactly below it. This abnormal distribution of beam
end moments over height was thought to be related in some way to the concentration of
inelastic deformation in the lower levels. Thus, in this section, an attempt to explain this
unusual distribution of end moments over height is carried out.
At an early stage, the axial deformation of the columns was identified as the main
parameter influencing the shape and distribution over height of bending moments
(obtained from the elastic analysis) at the ends of the beams. Nevertheless, given that
the results from the analysis of the 30-story building were difficult to interpret due to the
complexity of the model used, elastic analyses were carried out on simplified models of
the building using the ETABS program. The following simplifications were implemeted in
·~·
\ j
the model: I Moment of inertia of the beams. It was considered convenient to use the gross
moment of inertia rather than the effective moment of inertia of the beams, given the
fact that the latter parameter varies over height, and, for a given frame and story, from
bay to bay. The use of the effective moment of inertia of the beams, on the other hand,
produces a redistribution of forces among the members which makes it difficult to
identify exactly what influence the axial deformations of the columns have on the
behavior of the building. Therefore it was decided to use the gross moment of inertia .
of the beams in such a way that the patterns in the behavior of the 30-story building
could be easily identified.
Floor diaphragm rotation. Because of the floor diaphragm rotation, the distribution of
story shear between all the resisting elements of a story varies from that obtained if no
floor rotation is considered. When floor diaphragm rotation was considered, it was
difficult to interpret the exact influence of the axial deformation of the columns, and thus
it was decided to simplify the model of the building by fixing the rotational degree of
freedom of the diaphragm.
Lateral loads. As discussed in Chapter 3, the building was designed using a distribution
222
1
(,
' ' '•.
I
of equivalent lateral forces obtained from a RSA of the building. The simplified analysis
was carried by performing a static analysis of the building using the distribution of story
shears obtained from the RSA.
Figure 5.1 shows a plan of the building, the degree of freedom associated with each
diaphragm and the direction in which the lateral load was applied. As shown, a 20
analysis was carried out on a 30 model of the building.
In order to discuss the influence of the axial deformation of the columns of the building
in its overall behavior, Frame B was studied. Figure 5.1 shows the location of Frame B
within the structure and the definition of its first, second and third bays. Figure 5.2 shows
the required positive and negative design moments at both ends of the beams of the first,
second and third bays of Frame B, when the columns are not allowed to deform axially.
These moments were obtained from a moment envelope obtained by considering all
appropiate load combinations specified by the UBC code (section 2.4.2). Figure 5.3
shows similar results when the columns are allowed to deform axially. By comparing both
figures, it can be seen that the distribution through height of the required moments at the
ends of the beams changes significantly. The graphs in Figure 5.2 show tendencies that
can be considered normal, that is, the moments diminish monotonically from the lower
stories to the upper stories; nevertheless, the graphs shown in Figure 5.3 show the
unexpected tendencies described in. the first paragraph of this section. To explain such
: } tendencies, it is necessary to study the effects of gravitational loads separately from those
~\
! \
due to lateral loads.
Figure 5.4 shows the required design moments due to factored dead and live loads
when no axial deformation of columns is allowed. As expected, the moments at both ends
are negative, almost equal, and practically constant over height in the 3 bays. In contrast,
the moments obtained when the columns are allowed to deform axially deviate
considerably from these tendencies, as shown in Figure 5.5. By comparing both figures,
it can be seen that the moments at the first bay are significantly different when allowing
223
and neglecting the axial deformation of the columns. Also, it can be seen that these
effects diminish in the second bay, and further reduction can be observed in the third bay.
The above behavior can be explained as follows: first, the computer program used in the
analysis needs to assemble a global stiffness matrix and load vector for the structure; and
once these two have been assembled, it solves the system of equations defined by them.
Thus, the computer program considers that the structure is entirely built first, and once
it is built, all the gravity and lateral loads are applied to the building.
At this stage, the discussion on whether this is a realistic assumption or not should not
obscure the issue that is being dealt with, because it is a fact that practically all analyses I (if not all) carried out on structures are made in this way. Because of the construction
procedures used in real life, this assumption would not be realistic for the dead load due
to the slab and the structural members, since the gravity loads due to their weight are
applied in steps. That is, when the nth floor is being built, gravity loads due to dead load
have been already applied in the n-1 floors below it, and any possible differential in the
axial deformation of the columns due to this dead load at the nth floor is eliminated when
this floor is built. Nevertheless, other portions of the gravity load, such as the live load,
can be considered to be applied after the entire building has been built. Thus, a careful
consideration of the sequence in which the gravity loads are applied should be considered
in order to obtain reasonable end moments at the ends of the members due to gravity
loads.
For the analysis of the 30-story building, the end moments used in the design of the
members of the building were obtained by applying all the gravity loads after the stiffness
matrix of the structure was assembled. Because the axial forces due to gravity vary from
one column to another, so does the axial deformation of the columns. This effect is not
important in short and medium rise buildings, but in a tall building the difference in the //'
axial deformation of the columns becomes important. Figure 5.6 shows how the difference
in the axial deformation of two neighboring columns induces an initial deformation in the
beams and thus an initial state of stresses (or bending moments). The axial force and the
224
l ,,
axial deformation in the exterior columns due to gravity loads are usually considerably
\-, smaller than those corresponding to the interior columns, and thus, the above-mentioned
effect is larger on the first bay. Going back to Figure 5.3, it can be seen that the shift
observed in the values of the moments at the both ends of the beams, when considering
axial deformation of the columns, can be attributed to the effects of axial deformation of
columns when the building is subjected to gravity loads.
·-\ Nevertheless, the change in the distribution of the moments at the ends of the beams
can only be explained by studying the behavior of the building subjected to lateral loads.
1 \ Figures 5.7 and 5.8 compare the factored design moments at the ends of the beams due
to lateral loads. As shown, the distribution through height of the moments at the ends of
I
l
.
i \
\
the beams changes considerably when accounting and neglecting for the axial
deformation of the columns in the analysis. This effect is considerable on the beams that
belong to the third bay, where a large increase in the moments in the beams can be
observed. By comparing Figures 5.7 and 5.8, it can be seen that the difference between
the moments shown in these figures. increases through height. As shown in Figures 5.9
and 5.1 0, the axial forces acting on the columns of Frame B change significantly;
nevertheless this variation per se does not help explain the large increase of moments
observed in the third bay. Figures 5.9 and 5.1 0 show axial forces in 4 of the 7 columns
of Frame B. The fourth column corresponds to the middle column of the frame, while the
first column corresponds to the end column. The axial force in the fourth column is zero
(due to the symmetry of the frame) and large axial forces are induced in the first column.
As expected, when the axial deformations of the columns are neglected the axial forces
in the first column are larger than those corresponding to the case where columns are
allowed to deform axially.
Figures 5.11 to 5.18 were prepared to facilitate the understanding of the behavior of
the building. These figures show free bodies required to compute the moment at the left
end of the beam located in the third bay of Frame B. Given the complexity of these free
bodies, an alternate way of interpreting their results was sought. Figure 5.19 shows how
225
the moment at the ends of the beam can be estimated from the shear force acting on the
beam: first, the shear M in the beam can be computed by establishing equilibrium of
vertical forces, and then the moment at the end of the beam (M) can be estimated as
VLJ2. Note that for this estimate of the moment to be close to the real value of the
moment, the inflection point on the beam has to be close to its midspan (i.e. the
magnitudes of the moments at both ends of the beam, obtained from the analysis of the
building, have to be similar).
Figures 5.11 to 5.14 show free bodies obtained for the third bay beam located at floors
I \ .. i
1, 5, 10 and 15 when axial deformation of columns was neglected in the analysis. Figures /
5.15 to 5.18 show the same free bodies corresponding to the case when axial
deformation of the columns was accounted for.
Table 5.1 summarizes and compares the values of the left end moment at the third bay
beam. The title .. exact.. corresponds to the value of the moment obtained from the
analysis, and the title VL/2 corresponds to the value obtained by using the method shown
in Figure 5.19. As shown, the exact and approximate methods yield practically the same
values: thus the discussion on the observed behavior can be focused exclusively on the
equilibrium of vertical forces on Figures 5.11 to 5.18.
Table 5.2 summarizes the results obtained from analysing the free bodies of Figures
5.11 to 5.18. On one hand, as shown in Figures 5.11 to 5.14, the only vertical forces
contributing to the shear force in the beam are the axial forces in the columns. The values
of the shear in these free bodies are summarized in the second column of Table 5.2. On
the other hand, as shown in Figures 5.15 to 5.18, when the axial deformation of the
column is accounted for, not only the axial force in the columns, but also the shear forces
in the beams perpendicular to the plane of the frame, contribute significantly to the shear
in the beam. Figure 5.20 shows the effect of the perpendicular beams. Given the different
stiffness corresponding to the different frames of the building, the story shear that each
frame carries is different and so are the axial forces and the axial deformation
226
I l_
I '
I
I ~
f
' I
\
\
I '
corresponding to the columns in each frame. As shown in the figure, the axial deformation
on the columns of Frame A are smaller than those of their neighboring columns that
belong to Frame B, which in turn are smaller than those of Frame C. Thus, a deformation
is induced to the perpendicular beams that connect Frame B to both its neighboring
Frames (A and C). These deformations induce shears and moments in the perpendicular
beams (the magnitude of the shear forces in the perpendicular beams can be seen in
Figures 5.15 to 5.18). This phenomenon could not be seen in Figures 5.11 to 5.14
because there is no axial deformation of the columns, and thus no differential deformation
between neighboring columns.
The third column of Table 5.2 summarizes the shear force in the third bay beam due
to the axial forces in the columns when their axial deformation is accounted for. The fifth
column of Table 5.2 summarizes the shear produced by the shear forces in the
perpendicular beams. As shown, when the effect of the perpendicular beams is neglected
(fourth column in the table}, the shears in the beams of the third bay of Frame B are very
similar when neglecting and accounting for axial deformation. Nevertheless, when the
effect of the perpendicular beams is accounted for, as shown in the sixth column of the
table, the value of the shear at the end of the beam (and thus the value of the end
moment) changes considerably. It can be seen that the variation in the value of the shear
force at the beam increases considerably with height, i.e., the shear in the 15th story
increases by 58.4% while that in the 5th story increases by 25.2%. It can be concluded
from the above discussion that the effect of the axial deformation of the columns is
twofold:
• Within the plane of the frame it produces variation in the columns axial force and axial
deformation distributions, which in turn produces deformations in the beams of the frame
that alter the force distribution throughout the frame.
• Perpendicular to the plane of the frame, it induces deformations in the beams
perpendicular to the plane, which in turn create internal forces in these beams that alter
the force distribution throughout the building.
227
5.3 EFFECT OF 2D MODELLING OF A 3D BUILDING
From the last section, it was found that one of the ways in which the axial deformation
of the columns influences the behavior of the 30-story building is by inducing deformation
in the beams perpendicular to the frame. Although the results found in section 5.2 are
helpful for interpreting the behavior of the 30-story building, they are insufficient for fully
understanding the behavior of the building. It should be noted that the nonlinear behavior
of the building (pushover analysis and THA for service and safety) was studied by
analyzing a 2D model of the building using the program DRAIN 2DX. Although DRAIN
2DX allows the model of the building to account for axial deformation of the columns, it
does not allow the modelling of the effect of the perpendicular beams. In this section, the
effect of using a 2D model to study a 3D building (designed according to the results
obtained from of a 3D linear elastic analysis) is studied.
Two models of the building were analyzed using the ETABS program. The first model
is the same as the one used in section 5.2 where the columns are allowed to deform
axially. The second model was obtained from the first by eliminating the beams
perpendicular to the direction of loading, as shown in Figure 5.21. The second model tries
to simulate the type of analysis that would be carried out using DRAIN 2DX: ground
motion is only input in one direction, no torsional effects are considered and the effects
of the beams perpendicular to the plane of loading are neglected.
Figure 5.22 shows the comparison of the moments obtained, from the analysis of both
models of the building, for the left end moment of the beam located in the third bay of
Frame B. As shown in the figure, the moments at the lower stories are similar, and the
differences between them tend to increase in the upper stories. Figure 5.23 is provided
to complement Figure 5.22 by providing the ratios between the values of the moments
\ '
I I
(
I
r
plotted in Figure 5.22. Figure 5.23 clearly illustrates that the value of the moment obtained , ,
from the 20 model is further reduced with respect to the value obtained from the 3D
model when going from the lower to the upper stories. )
228
I, '
'\
\
The above observations can be confirmed by studying the results obtained from the
nonlinear 2D pushover analysis carried out with DRAIN 2DX. Figure 5.24 shows the
evolution of the moment at the left end of the beam located at the third bay of Frame B.
Figure 5.25 helps to interpret Figure 5.24. Figure 5.25 shows two sets of moment ratios;
the first corresponds to the supplied real yield moment of the beam to the moment
obtained by DRAIN 2DX when ~ = 0.225 m (at this ~1, no element of the building has
yielded); and the second corresponds to the elastic moment used to design the beams
to the moment obtained by DRAIN 2DX when ~ = 0.225 m. As shown in Figure 5.25, the
computed ratios follow trends similar to that shown in Figure 5.23, with the exception that
, 1 in the first story the moment ratio diminishes considerably. This can be explained using
Figure 5.24, where it can be seen that the supplied yield strength in the first story is much
larger than the required design moment of the beam (obtained from elastic 3D analysis
\
l \
using UBC requirements). Thus, due to modelling effects, the moments in the beams of
the upper stories obtained using DRAIN 2DX are not as large as the moments obtained
from a 30 analysis, and therefore the nonlinear 20 analysis will underestimate these
moments. As a consequence, the formation of plastic hinges in the beams located on the
upper stories will be delayed or even eliminated. This can be clearly seen in Figure 5.24
and Figures 4.25 to 4.31 (which correspond to the nonlinear pushover analysis), where '
it can be seen that the plastic hinges tend to form in the lower stories first, and then start
spreading gradually to the upper stories. Also, it should be noted that, due to the higher
OVS of the first story beam (which can be considered a mistake in the design), this beam
tends to form plastic hinges later than the other beams corresponding to the lower stories.
5.4 SLAB STRENGTH INFLUENCE ON THE BEHAVIOR OF 30-STORV BUILDING
Trends similar to those described in Figures 5.24 and 5.25 can be seen in Figures 5.26
and 5.27. The last two figures are similar to the first two, but they were obtained from the
moments at the right end of the beam. These two last figures were included to assess
the effect of the overstrength in the beams provided by the contribution of the slab.
Figures 5.24 and 5.25 correspond to the case where the slab is in compression, while
Figures 5.26 and 5.27 correspond to the case where the slab is in tension. The
229
contribution of the slab to the strength of the beam is considerably higher when the slab
is tension than that when the slab is in compression (for slab in compression, a small
increase in the internal lever arm can be expected; nevertheless, when the slab is in
tension, the reinforcement of the slab increases significantly the ultimate or plastic
strength of the beam). The effect of the contribution of the slab to the strength of the
beams can be assessed by comparing Figures 5.24 and 5.26, and 5.25 and 5.27.
The contribution of the slab to the strength of the beam was not considered in the
design of the longitudinal steel of the beams. The reinforcement and thickness of the slab
is constant through height. Although the depth of the beams is larger in the lower stories,
so that the increase in strength is higher in these beams (they have a larger lever arm),
the relative increase in strength is higher in the upper stories: the OVS is larger in the
upper stories because, while the steel content of the beams tends to diminish in the upper
stories (as shown in ·Figures 3.35 to 3.41), the steel in the slab is the same throughout
the height and provides larger OVS to the beams with smaller steel content. By
comparing Figures 5.25 and 5.27, it can be seen that, due to the effect of the slab (larger
OVS in the upper stories), the beams in the upper stories are less likely to yield. That is,
the tendency shown in Figures 5.24 and 5.25 becomes more noticeable when the
contribution of the slab to the strength of the beam is accounted for.
5.5 INFLUENCE OF P·A EFFECTS
Figures 4.21 b and 4.22b show the influence of the P-A effects on the behavior of the
building. These figures were plotted from the results obtained from the pushover analysis
of the building. The concentration of the deformation in a few stories can not be attributed
exclusively to P-A effects. As shown in the figures, the curves obtained from the analysis
where P-A effects were not accounted for clearly show a concentration of deformation in
(
a few stories. By comparing these curves with those obtained from the analysis /
considering P-A effects, it can be seen that P-A effects increase the concentration of
deformation.
230
/" I
\ I
From the above discussion, it can be concluded that P-~ effects are important for the
behavior of the building, and thus they can not be neglected. Three issues need to be
addressed to explain the large effect of the P-~ effects:
• low strength of the structure;
• low stiffness of the structure; and
• concentration of deformation in a few stories.
It was considered important to assess the P-~ effects on the behavior of the building
subjected to an earthquake ground motion. Thus, the nonlinear 20 THA for safety was
repeated ignoring the P-~ effects. Figures 5.28 to 5.31 summarize the P-~ effects on the
nonlinear dynamic behavior of the building. In Figures 5.28 and 5.29, the solid and dotted
curves represent the response of the building when P-~ are neglected and accounted for,
respectively, in the THA. As shown in Figure 5.28, P-~ does not alter the time history of
the base shear; nevertheless, as shown in Figure 5.29, there is a significant change in
the time history of the tip displacement. As shown, between the 35th and 40th second,
the building suffers a considerable permanent deformation when P-~ effects are
accounted for, and moves to a new deformed position around which it continues
oscillating; meanwhile the structure keeps oscillating around its undeformed configuration
when P-~ effects are not accounted for. As shown in Figure 5.30, P-~ effects are not I I \ significant in the values of the story shears; nevertheless, as shown in Figure 5.31 (and
previously by Figure 5.29), when P-~ effects are accounted for the building starts drifting
to the positive side while it keeps oscillating around its undeformed configuration when
P-~ effects are neglected. When P-~ effects are neglected, the 101 demands diminish
considerably in the positive direction while they increase in the negative direction, but
overall the demands on 101 are considerably smaller when P-~ effects are neglected. Due
to the excessive flexibility of the building and the inadequate concentration of deformation
, ", in a few stories, P-~ effects are significant and detrimental to the response of the building.
<::: As discussed in sections 4.3.4 and 4.3.5, the pushover analysis tends to overestimate
the P-~ effects when compared to the results obtained from the THA for service and
231
safety. Figures 4.36 and 4.47 compare the 101 obtained from the pushover analysis and
the THA for service and safety. As mentioned in section 4.3.5, it seems that the larger
the tip displacement, the larger this overestimation is.
5.6 NONLINEAR RESPONSE PREDICTION FROM UN EAR ELASTIC ANALYSIS
In the past, approximate methods have been used to estimate the inelastic response
of a system from the elastic response of that same system. For example, for structures
with large T, it is assumed that the inelastic displacement (independently of the strength,
and thus of f..t of the system) is equal to the elastic displacement of the system. Also, it
is assumed that the strength of a system that develops a displacement ductility ratio, f..t,
can be obtained from the strength obtained from the elastic analysis divided by f..t.
The above methods of estimating inelastic response have yielded reasonable results
for a large collection of different ground motions. Nevertheless, as shown by the
comparison of the elastic and nonlinear analysis of the 30-story building, these methods
tend to overestimate significantly the nonlinear response of systems subjected to SCT-
EW. Figure 5.32 shows the acceleration spectra obtained from the SCT -EW ground
motion. As shown, the reduction in the response of a system with aT around 2 sees is
much larger than that predicted by approximate methods when the system undergoes
inelastic behavior. Figure 5.33 shows ratios of elastic/inelastic acceleration response for
f..t of 2, 3 and 4. As shown, the reduction in the response for a system with a T of 2.5
sees is much larger than f..t, and thus the elastic acceleration divided by f..t will
overestimate significantly the nonlinear acceleration. Also, as shown in Figure 5.34, for
a large range of periods (1.8 to 2.8 sees), the displacements obtained from nonlinear
systems are considerably smaller that that obtained from the elastic analysis, which
contradicts the widely held assumption that the elastic displacement of a system is a
lower bound to its displacement when the system undergoes nonlinear behavior. Again,
the elastic response overestimates significantly the nonlinear response. On the other
I' II
~.
~ I
.A
(
,,
( ! I
/',
hand, for T < 1.5 sees, the inelastic displacements are considerably larger than the --.
elastic displacement (Figure 5.34), and the required yielding strength is larger than the
232
) \
v
,..-.,
required linear elastic strength divided by 1-t (Figure 5.32). Thus, for the SCT type of
EQGM, the validity of the approximate methods to estimate nonlinear response from the
linear response is perhaps limited toT larger than 3.0 sees.
It can be concluded that the linear response of the building subjected to the SCT-EW
ground motion can not always be used to estimate its nonlinear response accurately with
traditional approximate methods.
The above discussion shows the particular nature of the SCT-EW ground motion, which
is believed to be representative of EQGMs induced on deep soft clays by earthquakes
at large epicentral distances. It needs to be emphasized that the SCT-EW ground motion
was selected to carry out the various analyses of the building because it was considered
to be the most demanding for the linear and nonlinear behavior for the building to be
designed (i.e., the 30-story building).
5.7 RELIABILITY OF RESULTS OBTAINED FROM 20 NONLINEAR ANALYSIS
Before discussing the performance of the 30-story building, it is necesary to assess the
reliability of the results obtained from nonlinear analysis. On one hand, it should be
considered that the results obtained from the nonlinear analysis are not 100% reliable. I I '· · Some reasons why a 2D model of a 3D building can not capture the real behavior of the
··'-'
building have been discussed in section 5.3. Note that the results given in section 5.3
show why the 2D model (like the one used in the analyses with DRAIN 2DX) is not able
to reproduce exactly the behavior of a 3D model analyzed with input in one direction and
neglecting torsional effects (3D model shown in Figure 5.1 ). In other words, the 2D model
is not even capable of reproducing the behavior of the building when the building is
subjected to a motion that is parallel to the direction of the plane in which the 2D model
, ""· is contained, i.e., the 2D model can not predict the 2D response of the building. As
mentioned in section 5.3, the 2D model is not able to predict correctly the sequence on
/' which plastic hinges form through height, and would likely underestimate the strength and
deformation demands on the beams located on the upper stories.
233
From the above discussion it can be concluded that a 20 model can not provide an
exact estimate of the 20 response of the building. Questions that naturally arise are: how
significant are the responses of the elements located perpendicular to the plane in which '~- ·
the 20 analysis is conducted? How important are the torsional effects in the overall
response of the building? Figures 4.8 to 4.1 0 summarize the results obtained from an ,-,
elastic 30 THA for service limit state (motion was input in the direction shown in Figure
4.1 and er + eacc were accounted for in the analysis). As shown in Figures 4.8 and 4.9,
there is a significant response in the two main axes of the building (EW parallel to plane
that contains 20 models used for nonlinear analyses). Figure 4.1 0 shows that nonlinear
behavior is expected in the two directions for the service ground motion. By scaling the
story shears in Figure 4.1 0 by 0.30/0.07, the story shears for safety limit state can be
obtained, and from these shears it can be concluded that significant nonlinear behavior
is expected in the NS and EW direction. A 20 model parallel to the EW direction can not
estimate exactly the behavior of the building. Also, as shown in Figure 5.35, for elastic
30 THA for safety the elastic torsional response of the building is very large. Tendencies
regarding elastic torsional response similar to those discussed in section 3.5.3 for the
results of an elastic RSA (accounting for er + eacJ can be seen in the results of the elastic
THA: there is a large amplification of ·the elastic torsional response of the building
because of the coupling of the translational and rotational OOF. The effects of torsion in
Figure 5.35 can not only be seen because the displacements in the end frames in the EW
and NS are considerably larger than those corresponding to the center of mass in those
directions, but also because the ratio of the displacement in the NS direction to that in the
EW direction is about 0.60 for the displacements at the center of mass and about 0.80
for the displacements at the end frames. The large elastic torsional response can not be
captured by the 20 model. Finally, at this stage is impossible to assess the nonlinear
torsio!lal response of the building and a 30 nonlinear THA needs to be carried out.
It needs to be considered that the 30-story building was designed using earthquake
input simultaneously in two perpendicular directions, 100% of the earthquake input in one
direction plus 30% in the perpendicular direction. The elastic 30 THA results suggest that
234
, ........
( I
' .'
'\ \
• ,<:;.. ' l \
'"" I .
this way of accounting for the bidirectional earthquake input is not conservative when the
effect of eacc needs to be accounted for in the analysis. The effects of the earthquake
input in two directions are more important in the columns than in the beams, because not
only there are moments in two directions, but there is an important increase (in absolute
value) in the axial load induced by the lateral loads in the columns. It can be concluded
that, in general, a 20 analysis of the building will not predict accurately the behavior of
the beams and particularly that of the columns, because these important effects due to
bidirectional ground motion are not accounted for.
It is difficult to assess from the results of the 20 nonlinear analysis what percentage
of the concentration of deformation in the lower stories is due to modelling limitations and
what percentage is due to the following design errors: not accounting for the contribution
of the slab when the beams were sized and their reinforcement computed, and the fact
that the lower story was overdesigned compared to the rest of the beams (as discussed
in section 5.4).
Nevertheless, the results obtained from the nonlinear analysis are used to characterize
the behavior of the 30-story building. As shown in Figures 4.34, 4.35, 4.44 and 4.45, the
nonlinear analysis of an elasto-perfectly plastic SDOFS model of the building agrees
reasonably well with those obtained for the global response of the 30-story building.
Although the exact behavior of the building can not be reproduced, a reasonable estimate
of the global behavior can be obtained.
5.8 SEISMIC PERFORMANCE OF THE 30-STORY BUILDING
Although the results of the THA presented in section 4.3.4 and 4.3.5 need to be
consi~ered carefully, they provide enough information to assess the seismic performance
of the building. The deformation demands predicted by the 20 analysis in the lower
stories are thought to be overestimated, while those in the upper levels are thought to be
,.:::, underestimated.
235
From the results obtained in sections 4.3.4, it can be concluded that the 30-story
building performs inadequately for service. Nonstructural damage and moderate structural
damage are expected under the chosen service ground motion. The largest 101 computed
is around 0.008, while about 20 stories have an 101 of 0.005 or larger (Figure 4.35}. The
inadequacy of the 30-story building for drift control is evident when the drift limit set by
UBC (equal to 0.0035 at first significant yielding) is considered. From a strength point of
view, it can be seen in Figures 4.37 to 4.41 that moderate nonlinear behavior is expected
in the majority of the beams of the structure. Figure 4.41 summarizes all of this nonlinear
behavior of the beams by means of a damage index. Given the above performance of the
building, every time the building is subjected to a ground motion similar to that defined
in this report as the service ground motion (SCT-EW scaled to a PGA of 0.07g}, the cost
for repairing the structural and nonstructural damage to the building will be high.
As shown in Figure 5.34 for aT of 2.5 sees, if a system remains elastic, its maximum
displacement would be larger than that obtained when the system develops l.l of 2, 3 and
4. For the structure to perform adequately at service limit state, it should remain elastic,
and thus it is necessary to increase its strength. But if the building remains elastic, a large
increase in the displacement is expected, and thus a large increase in its stiffness needs
to be considered if the building is to satisfy drift requirements. Thus, UBC underestimates
considerably the required strength and stiffness for the structure to perform satisfactorily
under service limit state. The main reason for the inadequate performance lies in the
large value of Rw (equal to 12} used to obtain the reduced spectra for which the building
has to be designed. The large reduction in forces has the following two consequences in
the design of the building.
• Reduced Stiffness. The 101 at allowable stress state has to be satisfied for the reduced
forces, and thus the stiffness of the structure to meet UBC 101 requirements does not
need to be large (if larger forces were used, the structure would have to be stiffer to
satisfy 101 requirements).
• Low First Significant Yield Strength. Because the reduced forces are used to perform
an elastic analysis of the building, the strength for first significant yield would be low.
236
I
/ \
('
~ .. ;
-..,,r
I
It can be argued, sometimes correctly, that the probable large overstrength of the
constructed structure would allow it to perform satisfactorily for a safety type of ground
motion. Nevertheless, a large overstrength would not help the structure for drift control,
because in its elastic range of behavior (service), drift control is a matter of stiffness and
not of strength. Also, a large overstrength would not prevent some elements of the
structure from undergoing inelastic behavior if the design forces are low. So, although the
large reduction of elastic forces may be justified from a safety strength point of view, it
can not be justified by drift control and strength requirements for service. It is necessary
to establish the service earthquake ground motion or the service site spectra for strength
and displacement, so that it will be possible to estimate the minimum stiffness (maximum
period) of the structure required to ensure that the IDI will not exceed an acceptable
value, and to ensure that all elements of the structure remain elastic.
From the results obtained in section 4.3.5, it can be concluded that the 30-story building
has an inadequate performance for safety. The largest IDI computed is 0.025 (Figure
4.45), which, although it can be considered acceptable from the point of view of
preventing the failure of the structure (since the maximum local plastic rotation is 0.0262,
which is smaller than the supplied rotational capacity as shown in Figure 5.36) it results
in excessive nonstructural damage (and perhaps even unacceptable damage to the
contents of the building). Figures 4.48 to 4.53 show the nonlinear behavior of the building
when subjected to the safety ground motion. Figure 4.53 summarizes the nonlinear
behavior of the elements by means of a damage index. As shown in Figure 4.53, the
damage index in all beams of several floors is larger than 1 (maximum damage index of
1 .35), which, according to Park and Ang, would imply the failure of all those beams, and
thus the probable collapse of the building. It needs to be noted that, as shown in Figure
5.36, the maximum rotations in the beams are smaller than the supplied rotational
capacity in them. Nevertheless, several beams are expected to fail. This fact can only be
explained by considering the hysteretic behavior of the beams, i.e., it is necessary to
consider the large values of cumulative plastic rotations (and other parameters that can
characterize the hysteretic behavior such as cumulative ductility, ~a; number of yield
237
reversals, NYR; and number of equivalent yielding cycles at maximum f..t, NEVCflmaJ.
Although from an RC member failure point of view the drift control for safety is
acceptable, the drifts are too large to control damage to nonstructural elements and to
the contents of the structure. From an energy dissipation capacity point of view, the
structure performed unsatisfactorily because several members of the building are
expected to fail, as suggested by the maximum value of damage index of 1.35. This
means that the structure was underdesigned for strength, because its members are not
able to dissipate energy in a controlled way (i.e., the hysteretic behavior of the members
is inadequate). To illustrate this point, several SDOFS were analyzed and their results
summarized in Table 5.3. The purpose of analyzing the SDOFS was to estimate the local
damage in the building by applying the Park and Ang expression to the results obtained
from them. It should be noticed that because the global ductility and local ductility
demands and capacities of a system are not linearly related, in some cases the use of
a DMI computed from a SDOFS can not reflect the local damage to a structure. As
shown in Table 5.3, the value of damage index computed from the SDOFS does not
match well that obtained for the local damage of the 30-story building. Nevertheless, to
estimate value of local damage index from the results of SDOFS, the following expression
was used:
local DMI = [ local DMI real 30-story building (1.35) l DMI SDOFS DMI SDOFS rsprsssntingrsal30-story building (2.19}
Although the use of the above expression is not correct, it is thought to yield a reasonable
estimate of how the local damage index in the 30-story building changes as the strength
of its RC members is increased. As suggested by the values in Table 5.3, the members
of the 30-story building should have an increase in their strength of about 50% to reduce
local damage index to 1 (the increase in strength needs to be achieved carefully, because
increasing the strength of aRC member by merely increasing its longitudinal steel ratio
and/or shear span ratio can reduce drastically its deformation capacity). Also, it should
{·
\ J
I ·,
r-
I I,
be considered that an improvement in the confinement of the ends of the beams will f
238
enhance their ultimate rotational capacity and thus reduce the value of the damage index.
Thus, an increase in the strength of the members of the structure and/or an improvement
~ f in their confinement detailing could prevent the structure from collapsing (but not from
serious damage to nonstructural components and contents of the structure).
.~.
I I It is somewhat surprising that although the elastic site spectra for safety were reduced
by 1.4/12 (load factor for earthquake!Rw), that is, were reduced 8.6 times, the damage
index is close to one (even for a ground motion as severe as the SCT-EW ground motion
scaled up to a PGA of 0.3g). Some insight into this fact can be found in Figure 5.29,
where it can be seen that for SCT-EW the reduction in the reponse for a 1-l of 4 and aT
of 2.5 is about 8. Although it should be noted that Figure 5.30 was obtained for SCT-EW
and the analysis of the building was carried out for SCT-EW accelerations scaled up by
1.76 (0.30g/0.17g), Figure 5.30 shows that for a quasiharmonic motion the nonlinear
response is reduced significantly compared with the elastic response. Because of this
significant reduction, even if the structure is designed for small strength, the demanded
f 1-l is not very large, as shown in Table 5.1 for a SDOFS. Nevertheless, as discussed by
Uang and Bertero [Ref. 12], the demands of strength and maximum global ductility ratio
_f -~-
( i
,!'' .....
are not enough to characterize the damage induced to a system when it is subjected to
the SCT-EW ground motion. Although the strength demands are low, nonlinear demands
(such as those corresponding· to large number of load cycles, large demand of
accumulated ductility, large demand for hysteretic energy dissipation, etc.) on the
members of the structures are very large. The large cumulative plastic demands can lead,
as they do for the 30-story building, to the failure of several of the building's members.
It can be concluded that the performance of the 30-story building designed according
to UBC requirements is unsatisfactory from the point of view of both drift control and
energy dissipation capacity (which can be related to insufficient strength of the members
as shown for a SDOFS}, although the underdesign for strength is not as large as was
anticipated from the large values of Rw used in the design.
239
BEAM IN THIRD BAY OF FRAME B Neglecting Axial Accounting for Axial
STORY Deformation in Columns Deformation in Columns Exact VL/2 Exact VL/2
1 37.69 37.83 41.12 41.15
5 32.68 32.78 41.13 41.04
10 29.98 30.04 43.09 42.87 15 25.50 25.58 40.84 40.57
TABLE 5.1 COMPARISON BETWEEN THE EXACT MOMENTS AND THOSE ESTIMATED ACCORDING TO FIGURE 5.19 AT LEFT END OF BEAM LOCATED IN THE THIRD BAY OF FRAME B.
BEAM IN THIRD BAY OF FRAME B
Neglecting axial Accounting for Axial Deformation in Columns
SHEAR DUE TO: STORY deformation in
columns Axial forces in columns Shear in perpendicular beams
Shear (1) Shear (2) (2)/(1) Shear (3) [(3)+(2)]/(1) ratio ratio
1 16.63 16.55 0.995 1.53 1.087 5 14.09 14.70 1.043 2.94 1.252
10 12.92 14.30 1.107 4.15 1.428 15 11.00 12.94 1.176 4.48 1.584
TABLE 5.2 EFFECT OF ACCOUNTING FOR THE AXIAL DEFORMATIONS OF
r
I
\ I
;' .....
THE COLUMNS IN THE MOMENT AT THE LEFT END OF THE : ; BEAM LOCATED IN THE THIRD BAY OF FRAME B.
240
,- '
I I
I J
. '
SCT-EW SCALED TO P G A= 0.30 G
DISPLACEMENT DUCTILITY DAMAGE INDEX ULTIMATE DEMANDS BASE SHEAR
NORMAL CUMULATIVE from SDOFS LOCAL (~-t) (~-tJ
0.11 w 4.59 38.35 2.19 1.35 (real)
0.12W 4.55 34.06 2.05 1.26 0.13 w 4.44 30.48 1.91 1.18 0.15W 4.12 24.84 1.66 1.02
TABLE 5.3 EFFECT OF AN INCREASE OF STRENGTH IN THE DAMAGE INDEX (FROM SDOFS THA)
241
•• • •• •• ••
.. -• "' "' • •• ••
.. .. •• •• ."' "' • ®
d~ct' are 10
.. ········-···-·--·
"' n of ®
loading • • - • • • - • @)
• • • • • g:ird - •• ay
® first second
• bay bay •• ·······················@
l- 4.8 m -+- 4.11 m -t- 5.3 m -1- 5.3 m -+- 4.8 m -+- 4.8 m --1
1 DOF per story
FIGURE 5.1 MODEL USED FOR SIMPLIFIED ANALYSIS OF 30-STORY BUILDING
242
I 1
I 1
I l
- .
I i
-"~,
I J
-
,-
Envelope of End Moments in Beams Frame B
Story First Bay 30
25
20
15
10
5
Story
30
25
20
15
10
5
Story
30
25
20
15
10
5
I ' I
' '
second Bay
Third Bay
'· \\ \ \
'·,,
\
left End left End Right End - - - -Right End ---·-·····
Moment (ton-m)
\ \ \
\ l
20 Moment (ton-m)
FIGURE 5.2 BEAM MOMENT ENVELOPES FOR ANALYSIS NEGLECTING AXIAL DEFORMATION OF THE COLUMNS
243
Envelope of End Moments for Beams Frame B
Story First Bay 30
25
20
15
10
5
Story
30
25
20
15
10
5
Story
30
25
20
15
10
5
I I
). ·~,
/ '·, ',, / '
I \ I
Second Bay
I I
I I
I
20
Third Bay
Left End left End Right End Right End ···-··-·····
Moment (ton-m)
Moment (ton-m)
FIGURE 5.3 BEAM MOMENT ENVELOPES FOR ANALYSIS ACCOUNTING FOR AXIAL DEFORMATION OF THE COLUMNS
244
r 1
\ '
_/'\ __
I ,
! I
I
Gravity End Moments in Beams Frame B Story First Bay
30
25
20
15
10
5
-15 -10
30
25
20
15
10
5
Story
30
25
20
15
10
5
Second Bay
Third Bay
10 15
L.eftEnd -Right End ·······
Moment (ton-rn)
10 15 Moment (ton-m)
FIGURE 5.4 BEAM GRAVITY MOMENTS FOR ANALYSIS NEGLECTING AXIAL DEFORMATION OF THE COLUMNS
245
Gravity End Moments in Beams Frame B
Story First Bay 30
25
10
5
30
25
20
15
10
5
30
25
20
15
10
5
Second Bay
Third Bay
10 15
L.sftEnd -Right End -------
Moment (ton-m)
10 15 Moment (ton-m)
FIGURE 5.5 BEAM GRAVITY MOMENTS FOR ANALYSIS ACCOUNTING FOR AXIAL DEFORMATION OF THE COLUMNS
246
,, \
FRAME B Axis of symmetry
J undeformed configuration
, .................................................. , ...................................................•..... ~---···············································'
i i i : deformed configuration
1st column 2nd column 3rd column +-- 4.8 m 4.8 m --+--
MOMENTS:
4th column 5.3m --+
First Bay Second Bay Third Bay
FIGURE 5.6 MOMENTS IN BEAMS DUE TO DIFFERENTIAL AXIAL DEFORMATION IN NEIGHBORING COLUMNS
247
Earthquake End Moments in Beams Frame B Story First Bay
30j
L.aft End 25 Right End ·······
20
15
10
5
Moment (ton-m)
Story Second Bay 30
25
20
15
10
5
20
Story Moment (ton-m)
Third Bay 30
25
20
15
10
5
Moment (ton-m)
FIGURE 5.7 BEAM MOMENTS DUE TO LATERAL LOADS FOR ANALYSIS NEGLECTING AXIAL DEFORMATION OF THE COLUMNS
248
I \
~··
\ I
'• :
I
I
Earthquake End Moments in Beams Frame B Story First Bay
30 I Lsft End
25 Right End ·······
20
15
10
5
Moment (IDn-m)
Story Second Bay 30
25
20
15
10
5
Story Moment (ton-m)
Third Bay 30
25
20 ..
15
10
5
Moment (ton-m)
FIGURE 5.8 BEAM MOMENTS DUE TO LATERAL LOADS FOR ANALYSIS ACCOUNTING AXIAL DEFORMATION OF THE COLUMNS
249
Story 30
25
20
15
10
5
Axial Forces in Columns Frame B Elastic Analysis without Axial deformation
\ I I \ \ \
\
' .\ '·
- Fourth Column
-- Third Column
----··· Second Column
- ·- F'nt Column
Axial Force (ton)
FIGURE 5.9 AXIAL FORCES IN COLUMNS DUE TO LATERAL LOADS FOR ANALYSIS NEGLECTING AXIAL DEFORMATION OF THE COLUMNS
Story 30
25
20
15
10
Axial Forces in Columns Frame B Elastic Analysis with Axial deformation
- FOUI1h Column
- - Third Column
....... Second Column
- ·- F'rrst Column
Axial Force (ton)
FIGURE 5.10 AXIAL FORCES IN COLUMNS DUE TO LATERAL LOADS FOR ANALYSIS ACCOUNTING AXIAL DEFORMATION OF THE COLUMNS
250
I I
' 1
' ·'
' I
' I
i )
368.38 -24.87 -83.88
~ . 41 0.00 .J 0.00 .791 0.00
___ 15_.43 ___ ~1-~~-1_1 ___ ·-1) 37.69
I r 19.481 22.13
0.00 0.00
381.09
I 'r 25.42
35.98 0.00
-67.29
16.63
FIGURE 5.11 FREE BODY OF FIRST FLOOR OBTAINED FROM ANALYSIS NEGLECTING AXIAL DEFORMATION OF THE COLUMNS
293.41 -20.44 -50.38
~. ,0.00 1 .J 0.00 .7210.00
.r--15_.95 _______ 29_.92 ___ -""711~·1) 32.88
l ~ 16~:;54 )
o.oo 1 o.oo 368.39
--29.90 r31.75 -21.71
I 'r 27.80
29.40 0.00
-53.58
14.09
FIGURE 5.12 FREE BODY OF FIFTH FLOOR OBTAINED FROM ANALYSIS NEGLECTING AXIAL DEFORMATION OF THE COLUMNS
251
204.53 -14.58 -34.93
~-I 0.00 rl I 0.00 10.00
.58 .47 14.39 26.89 I) 29.98
12.92
I 0.00 r 18~~i771 r 27.59 I 0.00
r: 25.58 29.90 27.75
0.00
221.52 ·15.70 -37.08
FIGURE 5.13 FREE BODY OF TENTH FLOOR OBTAINED FROM ANALYSIS NEGLECTING AXIAL DEFORMATION OF THE COLUMNS
-9.46 -21.41
rl .Jo.oo 22.57
I r 12.60 I r 23.60 I r: 21.87 14.04 25.60 23.95
0.00 0.00 0.00
141.28 ·1o.42 ·23.93
FIGURE 5.14 FREE BODY OF FIFTEENTH FLOOR OBTAINED FROM ANALYSIS NEGLECTING AXIAL DEFORMATION OF THE COLUMNS
252
' I
' I
I I
I I
( I
2.W.48 80.90 -7.74
~ :'241 0.12 rk J 0.18 rk _j 0.21
4'ri.oo ~(, ~~) 41.12
I /1r 18.99 I /1y 26.43 I /1~ 26.09
18
.
09
19.89 37.04 38.24 0.44 0.28 1.32
. . 270.42 79.82 -11.07
FIGURE 5.15 FREE BODY OF FIRST FLOOR OBTAINED FROM ANALYSIS ACCOUNTING FOR AXIAL DEFORMATION OF THE COLUMNS
188.04 73.97 3.47
~ . I 0.34 rk _l 0.73 rk .J 0.74
~.. . ~n ~I) .1.13
I /1r 14.31 I /1y28.12 I /1~=· 17
... 13.58 28.94 32.35
0.90 0.80 3.05 . .
201.12 76.01 1.05
FIGURE 5.16 FREE BODY OF FIFTH FLOOR OBTAINED FROM ANALYSIS ACCOUNTING FOR AXIAL DEFORMATION OF THE COLUMNS
253
119.84 58.90 11.88
~ .6710.81 rk .l1.31 rk J 1.33
~78 *'" ¢-;'1) 43m
I /lr 11.32 I /lr 24.64 I /lr 30.82 18.44
11.94 26.22 32.DS 1.29 1.44 4.87 . . .
131.73 10.70
FIGURE 5.17 FREE BODY OF TENTH FLOOR OBTAINED FROM ANALYSIS ACCOUNTING FOR AXIAL DEFORMATION OF THE COLUMNS
40.29
I -- 8.84 I --20 05
1.43 r 9.51 1.84 r21.;0
77.24 44.15
I r 30.19 27.90
5.41
14.12
FIGURE 5.18 FREE BODY OF FIFTEENTH FLOOR OBTAINED FROM ANALYSIS ACCOUNTING FOR AXIAL DEFORMATION OF THE COLUMNS
254
, I
L v
FIGURE 5.19 APPROXIMATE METHOD TO ESTIMATE THE MOMENT AT THE LEFT END OF THE BEAM LOCATED ON THE THIRD BAY
beam perpendicular toFrameB
\ deformed axial extension . \ n iguration .
\£ ool~:~~ ................................................................................... ..
column in
Frame A
column in
Frame B
column in
FrameC
FIGURE 5.20 EFFECT OF PERPENDICULAR BEAMS
255
d~ loading
I- 4.8 m -+- 4.8 m -l- 5.3 m ~ 5.3 m -+- 4.8 m -+- 4.8
• • 1 OOF per story
®
®
®
rigid diaphragm
FIGURE 5.21 SECOND MODEL USED FOR SIMPLIFIED ANALYSIS OF 30-STORY BUILDING
256
Story
30
25
20
15
10
5
5 10
Effect of 20 Modelling Frame B, Bay 3
·· ....
··. · ..
3D model
15 20 25 30 35 40 45 Moment (ton-m)
FIGURE 5.22 EFFECT OF 2D MODELLING ON MAGNITUDE OF THE MOMENT AT THE LEFT END OF THE BEAMS LOCATED IN
THE THIRD BAY
257
Story
30
25
20
15
10
5
Effect of 20 Modelling Moment Ratios on Frame B, Bay 3
1 r-----~------~------~------~----~ 0.75 0.8 0. 5 0.9 0.95 1
20 model/"30 modeln
FIGURE 5.23 REDUCTION OF MOMENT DUE TO 2D MODELLING
258
·a
Story 30
25
20 design moment (elastic 30 analysis)
15
10
5
1
Left End
10 20 30 40 50 60 70 80 90 1 Moment (ton-m)
FIGURE 5.24 EVOLUTION OF THE MOMENT AT THE LEFT END OF THE BEAMS LOCATED IN THE THIRD BAY ACCORDING TO PUSHOVER ANALYSIS
259
Story 30
25
20
15
10
5
Pushover Inelastic Analysis Frame 8, Third Bay ......... ............
. .. '· ........
Left End ............. ........ .....
............
moment at ~ - 0.225 m
design moment (elastic 3d analysis)
moment at A1 = 0.225 m
supplied yield strength
......... .. '1
,.... .... .. .. " .. .. :.
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Moment Ratio
FIGURE 5.25 REDUCTION OF THE MOMENT AT THE LEFT END OF THE BEAMS LOCATED IN THE THIRD BAY ACCORDING TO PUSHOVER ANALYSIS
260
Story 30
25
20
15
10
5
1
Pushover Inelastic Analysis Frame B, Third Bay
Right End
4 1•0.225 m
design moment (elastic 30 analysis)
-130 -120 -110 -100 - -10 Moment (ton-m)
FIGURE 5.26 EVOLUTION OF THE MOMENT AT THE RIGHT END OF THE BEAMS LOCATED IN THE THIRD BAY ACCORDING TO PUSHOVER ANALYSIS
261
Story 30
25
20
15
10
5
Pushover Inelastic Analysis Frame 8, Third Bay
.............. ........ ............
Right End .............
······:
moment at ~ - 0.225 m
design moment (elastic 3d analysis)
moment at A, = 0.225 m
supplied yield strength
'······· .... \ .. .. .. . \\ ... ~.\ ..
.. .• ..
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Moment Ratio
FIGURE 5.27 REDUCTION OF THE MOMENT AT THE RIGHT END OF THE BEAMS LOCATED IN THE THIRD BAY ACCORDING TO PUSHOVER ANALYSIS
262
4000~--------~----------------------------~
3000 ··································································· ·· - without P-A ·········· with P-A ·
2000 ·························· ........... ······· ........... ·····;············ ... ··'········ .......... ············ . '
c g 1000 ························ ··········· ········ ......................... ········ ···.···· . ..... ~ Q) .c C/) Q) ~ -1000 .......................................................................... ········ co
-2000 ························,·········'(····· ..................... ············ ................................... .
-3000 ................................................................. V ...•.. : •........................•........................................
-4000+---~----~----~--~----~----~--~--~ 0 1 0 20 30 40 50 60 70 80
Time (sees) FIGURE 5.28 EFFECT OF P-~ ON TIME HISTORY OF BASE SHEAR FOR
SAFETY
1.2.,-----------------------------------,
1 ····································································!!····· -- without P-A ·········· with P-A ., ., '·
0.8 ···············-·······················-··· ············· --~--) ·,.-~j---~;-·-f..············r···············--·-··--·····-··················· . i :: ! 1 !: n J: ... n
: ! j j: :: J. :~ I: 1•\ I' ;1 ~ :1 ~ 0 6 ----------------------····················· -- ... 11 •••• -· ••• - .. -~.:--~-~-~.t--!~--!-l-----U·-~-t..::.. .. ?t •••• A ... !i .. J£ ... ~L--~---······· ._ . n ; I~: 1! !: ::II :: r\ :: H :'! !: :: ;~ :~ +-' ' i ! 1
1 I : I i! l :, : \ l : : :1 ,'\ ~ : { : ! :, : : :' \ I
C 04 , .. : : ::•, ;. '' 'r ;I., :r ;. :, :.(\' Q) • ········-·························--······· • • ·· • • · · • ·• ~- · -. ~, :; ~--·: i··: t··, ~·t·t--:-~--: }-~·-'r·• ·t·~--- · ··.'
E ! 0 ol,,:l I 'I of 1 1\ I I ff ,,,,, I'
: I : : i I i ' U1 ~ ~ I i I I ' I : I ' I I I I I I : ' : Q) .·: : :; ·;'::vv: ::\::::·~:::~:: ~i (.) o.2 ............................................ : ...... · ... -; ~· ...... ' .. ; ·.: ::.~ ·-· \-) ~. ... :.v ..... v ctS 1 I I • " I , I I 1 • , , t 1 1
: u ! ~ ·,. ~ i: •:J \: ·tl} :: \j \{ \; Q. 0 ° I ,: l ~ j
1 1,; ~: \1 ~ \•' en . . . . .. . . . . . . . .. .. . . ........ , ......... :· . . . . . . . . ·~; . .. ~ -· .. ~ .. - ·- .. ~ .... . i:5 I :
Q. I ' i= -0.2 ..................................... ........ : .......... ::.: . ! . .. ......... .. -· . --· ·- .................. ..
v i 11 ! -0.4 .......................... ...... ...... ... .. ..................... ..... . . .. . ................ .. .......................................... .
-0.6 ....................................................................... .. .. ................................................................ .
-0.8+----r------.----~---~-~-----.-----.-------l 0 1 0 20 30 40 50 60 70 80
Time (sees)
FIGURE 5.29 EFFECT OF P-~ ON TIME HISTORY OF TIP DISPLACEMENT FOR SAFETY
263
Story 30
25
20
15
10
5
Nonlinear THA Effect of P-a
-1 000 1000 2000 3000 4000 Shear( ton)
FIGURE 5.30 EFFECT OF P-d ON STORY SHEARS FOR SAFETY
264
· Story
30
25
20
15
10
Time History Inelastic Analysis Safety Envelope of I Dl
without P-A
IDI
FIGURE 5.31 EFFECT OF P-~ ON 101 FOR SAFETY
265
with P-A
Sa/g 1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0 0 0.5
SCT-EW Ground Motion Acceleration Spectra
1.0 1.5 2.0 2.5 3.0 T (sec)
FIGURE 5.32 ACCELERATION SPECTRA OBTAINED FOR SCT-EW (; = 0.05)
266
Strength Ratio 12
11
SCT-EW Ground Motion Elastic 1 inelastic strength ratio
. .. 10 :~ .. . . . . g _,............... .-"", : ~ , .... ' : .
: \ J,L=4 •• \ 8 ' ' ,........ . : . '- ............ , .. · ~
7 . .: ............. ··\,_ - \ ' u-3 l~~~ • / : •••·• r- ~ ::o
: :)/ \j --..JV \
4 --------------------------------------------:~---!----- --- ---- -
3 ···················································································:<(/:~:':" ..... ·····························--·~ ----2···················· ..... . .. ~ ... · 2 .... ~ ......... .
1
o~~~~~~~~~~~~~~~~~~~
0 0.5 1.0 1.5 2.0 2.5 3.0 T (sec)
FIGURE 5.33 REDUCTION OF ACCELERATION FOR INELASTIC RESPONSE ON SDOFS SUBJECTED TO SCT·EW (; = 0.05)
267
Disp. Ratio 5
4.5
4 . ~',~ 4
3.5
0
. . . . . .
SCT-EW Ground Motion Inelastic I elastic displacement ratio
0.5 1.0 1.5 2.0 2.5 3.0 T (sec)
FIGURE 5.34 INELASTIC/ELASTIC DISPLACEMENT RATIOS FOR SDOFS SUBJECTED TO SCT-EW (; = 0.05)
268
I
Floor 30 '
' ' ' '
25
20
15 -W
3D ELASTIC THA Real + Accidental Eccentricities
. . . . . . . . . . . I . .
I I I I . .
I I I I .
II"
I I I .
. I . . . .
I . . . . . . . . . . • . . . . . . .
• . . N-S
E-W end frame
center of mass
I . . I I end frame
10
N-S center of mass
5
-3 -2 -1 1 4 Displacement (m)
FIGURE 5.35 TORSIONAL EFFECTS ON STORY DISPLACEMENTS OBTAINED FROM ELASTIC 3D THA
269
Story
30
25
20
15
10
5
Nonlinear THA for Safety Maximum Rotations in Beams
~ bound of rotational :.. .. 1
capacity of beams
:. . ..
I ······1
f .............. --.. i ....... i
'· .. 1 ~~--~--~~--~~--~--~~--'~--~~
0.005 0.01 0.015 0.02 0. 25 0.03 0.035 0.04 0.045 0.05 0.055 0.06 9max
FIGURE 5.36 COMPARISON OF MAXIMUM ROTATIONS OBTAINED FOR THA FOR SAFETY VS. SUPPLIED ROTATIONAL CAPACITY
270
6 FINAL REMARKS AND CONCLUSIONS
6.1 COMPARISON OF THE SEISMIC PERFORMANCE OF THE 30-STORY BUILDING
DESIGNED ACCORDING TO DIFFERENT DESIGN PHILOSOPHIES
In this section, the seismic performance of the 30-story building designed according to UBC
is assessed by comparing its performance with that of two other designs (Japanese and
Conceptual designs) of buildings with identical configurations. Some of the figures shown in this
section have been previously shown in Chapters 4 and 5 of this report: they are repeated to
allow a fluent reading of the material presented in this chapter.
6.1.1 INTRODUCTORY REMARKS
As mentioned in Chapter 1, several modern high-rise buildings are being constructed
on soft soil. Unfortunately, the significant advances that have been made in the
technology of construction of tall buildings have not been followed by studies that aim at
understanding their behavior and interaction with the soil on which they are built,
particularly when subjected to intense ground motions. There are several issues that need
to be addressed to obtain a rational and sound design of tall buildings in seismic zones,
among which the following can be mentioned: first, current seismic code regulations pay
very little attention to specific problems encountered in the design of tall buildings
subjected to intense ground motion; and second, given their high slenderness ratios, tall
buildings tend to have long periods that in several cases come close to the fundamental
period of soft soils, and thus large amplification of their static response, particularly in the
elastic range, can be expected due to engineering resonance.
The 30-story building designed according to 1991 UBC in this report has the same
configuration, structural system and structural layout as those of a building that has been
designed and built in Japan [Ref. 6]. This building was redesigned by Bertero and Bertero
using a Conceptual Design Methodology [Ref.S].
This section summarizes some of the most important results of a series of studies
271
[Refs. 5 and 6] carried out to assess the performance of two 30-story buildings designed
according to Japanese practice and Conceptual design guidelines. Also, some of the most
important characteristics of the 30-story building designed according to 1991 UBC are
summarized. The main objective of this section is to assess the adequacy of UBC
methodology and the new proposed Conceptual design methodology [Ref. 5] for
Earthquake-Resistant Design (EQRD) of tall buildings on soft soil. To assess the
adequacy of the designs, the properties and seismic performance of the Japanese,
Conceptual and UBC designed buildings are compared.
6.1.2 SOFT SOIL SPECTRA
Before attempting to discuss the behavior of the 30-story building designed according
to different design practices, it is necessary to review the characteristics of earthquake
ground motions (EQGMs) recorded on soft soil sites. Once these characteristics are
defined in a qualitative way, the response of the different designs can be discussed.
Figure 6.1 shows a qualitative schematic representation of the strength and
displacement spectra for soft soil sites. The following observations can be made regarding
these spectra.
Strength: an increase in strength will almost always result on a reduction in the ductility
demands. As shown in Figure 6.1 a, there is a large elastic strength demand for single
degree-of-freedom systems (SDOFS) with a fundamental period of vibration (T) similar
to the predominant period of the soil (T9). A large reduction in the response can be
observed in SDOFSs with T ... T9 which are allowed to yield, i.e., the nonlinear strength
demand on these SDFSs is considerably smaller than the linear strength demand.
For a SDOFS with T smaller than T9
, an increase in strength will result in less
displacement: as the strength increases, the ductility demands are expected to decrease,
and, as shown in Figure 6.1 b, the displacement (~) of a system decreases when it
develops a smaller 1-1· For aT around T9 an increase in strength does not always lead to
a decrease in displacement. As shown in Figure 6.1 b for this region ofT, ll corresponding
272
to 1-l of 1 (linear elastic) is larger than that corresponding to larger values of f..l, and thus
a decrease in the value of 1-l is not necessarily reflected in a decrease in the displacement
(as expected for SDOFS with T smaller than T J. Say a system has a strength such that
a 1-l equal to or larger than two is expected according to the spectra shown in Figure
6.1.a: assume that the strength of the system is increased in such a way that a linear
elastic response is now expected according to the same spectra, then, according to the
spectra shown in Figure 6.1 b, an increase in the displacement of the system is expected.
For T greater than T9
, the displacement of the structure converges on one value,
independently of the value of 1-l of the SDOFS, and thus of its strength.
• Stiffness: It has been usually accepted that an increase in the stiffness of the system
(decrease in its T) will lead to a decrease in the displacement of the system (unless the
T of the system is very large). Contrasting with this notion, the spectra for soft soil show
that an increase in stiffness is only effective in controlling the elastic displacement of the
SDOFS when T is smaller than T9
(Figure 6.2a}; note that for T larger than T9
, an
increase in stiffness could be reflected in larger elastic displacements, as shown in Figure
6.2b. For 1-l larger than 1, an increase in stiffness usually results in a smaller
displacement, as shown in Figure 6.2c.
• Damping: Soft soil EQGMs in general tend to have narrow-band frequency content,
that is, the energy of the ground motion tends to accumulate on frequencies that are
similar to that corresponding to T9• The narrower the band of frequencies, the closer the
ground motion resembles a harmonic type of motion. The effect of viscous damping in
the reduction of the elastic response of SDOFS subjected to harmonic loads is well
known, and thus viscous damping can play a very important role in reducing the response
of systems subjected to quasiharmonic EQGMs (recorded on soft soils). In this case, an
increase in viscous damping can produce a significant decrease in the strength demands
and displacement. A SDOFS with T around T9
will benefit the most from the effects of
higher damping, as shown in Figure 6.3.
Hysteretic Energy Dissipation: In soft soils, the reduction of the response of a
SDOFS due to inelastic behavior is generally considerably larger than that observed for
SDOFS subjected to EQGMs recorded in firm soil. Usually, for a SDOFS with T close to
273
T9, the reduction in strength demands is larger than CJJ.A., where Ce is the elastic strength
demand, as shown in Figure 6.1a. However, for systems with T < T9
, the hysteretic
energy dissipation can increase with an increase in ll·
From the above observations, it can be concluded that the behavior of a SDOFS
subjected to an EQGM recorded on soft soil depends considerably on how its value of
T compares to that of T9• EQGMs recorded on soft soil sites show large variation in the
value of T9, because this dynamic property usually depends on parameters such as the
shear wave velocity and the depth of the soft soil at the site. For a given EQGM, T9
can
be defined as the T associated with the maximum spectral velocity [Ref. 28] (essentially
the same T9 can be obtained from the Fourier amplitude spectrum or the energy input
spectrum, because of the relationship between these three spectra). Figure 6.4 shows the
T9
for several ground motions recorded on soft soils. In the figure, the largest T9
corresponds to the SCT-EW ground motion recorded in the lake zone of Mexico City
during the 1985 events. In these Mexican events, another EQGM (Central de Abastos},
which was recorded in the lake zone, has a T9 between 3 and 4. Thus, it can be
concluded that the T9s of EQGMs recorded on soft soils range approximately from 1 to
3.5. It should be considered that the soil properties are strain-dependent and that,
depending on the intensity of the EQGM, T9 can show small variations. Another aspect
to be considered is the fact that the peak ground acceleration (PGA) is limited by the
shear resistance of the soft soil, that is, to estimate a .reasonable upper bound of the
value of PGA it is necessary to consider the shear strength of the soft soil at the site.
Three important characteristics of the behavior· of SDOFS subjected to EQGMs
recorded in soft soils should be noted: first, as shown in Figure 6.1, large elastic strength
and displacement demands are expected for SDOFS with T - T 9
, and thus a small
variation in T can result in a large change of the elastic response of the system; second,
the nonlinear strength and displacement demands on SDOFS with T - T9 are
considerably smaller than their ·elastic counterparts; and third, it should be noted that to
achieve a reduction in the elastic displacement of a SDOFS with aT larger than T9, the
274 I
period of the structure needs to be diminished in such a way that Tis smaller than Tg [in
some cases this can demand a considerable increase in the stiffness of the system (see
Figure 6.2b)].
The values of T associated with the different designs of the 30-story building are as
follows: 1.67 sees for Japanese design [Ref. 6], 1.70 sees for Conceptual design [~ef. 5]
and 2.53 sees for UBC design. A more detailed discussion about the dynamic properties
of the different designs is left to section 6.1.3.3. The values of T for Japanese and
Conceptual designs show practically no difference, while the T of UBC design is about
50% larger. The advantages or disadvantages corresponding to the response of a
SDOFS with T of 1.7 sees as compared with that of a SDOFS with T of 2.53 strongly
depend on the Tg value of the EQGM. Many cases can be discussed, but they can be
summarized in three cases, as shown in Figure 6.5: case 1 corresponds to Tg less than
1.7, case 2 to Tg between 1.7 and 2.53 and case 3 to Tg larger than 2.53.
For case 1, the strength demands will be smaller for T of 2.53 sees (considerably
smaller in the case of elastic response). The reduction in the response due to nonlinear
behavior, i.e., ~' (as well due to viscous damping) will be considerably larger for the
SDOFS with T of 1.7 sees. The displacements of the two systems would be similar, with
the elastic displacement larger for the SDOFS with T of 1.7 sees and the nonlinear
displacement larger for ~he SDOFS with T of 2.53 sees.
For case 2, while the strength demand will usually be smaller for the SDOFS with T of
2.53 sees, its displacement (linear elastic or nonlinear) will usually be larger. Assuming
that the elastic displacement of the SDOFS with T of 2.53 sees would be larger than
acceptable for adequate performance, the period of this SDOFS would need to be
reduced considerably to obtain a reduction in its elastic displacement (see Figure 6.2b).
Note that this is not the case for the· SDOFS with T of 1. 7 sees, as shown in Figure 6.2a.
For case 3, the strength and displacement demands are considerably smaller in the
275
SDOFS with T of 1. 7 sees.
The vast majority of ground motions recorded on soft soil have T9 ranging from 1 to 2,
and thus cases 1 and 2 would be likely observed. That means that, in general, the
SDOFS with T of 1. 7 sees will have larger strength demands, while the SDOFS with T
of 2.53 will have larger displacements.
Sometimes the strength and displacement demands are not enough to assess the
performance of a building. Other parameters that can be related to the nonlinear behavior
of the structure are useful to assess the damage induced by an EQGM to a system. Such
parameters include number of yield reversals (NYR), cumulative ductility (~-tJ and
dissipated hysteretic energy (EH). There is a need to carry out a statistical study of
spectra corresponding to these parameters for EQGMs recorded in soft soil, in such a
way that it will be possible to establish schematic spectra such as those shown for
strength and displacement in Figure 6.1.
6.1.3 CHARACTERISTICS OF THE THREE DESIGNS OF THE 30-STORY BUILDING
To establish the comparison of the performance of the different 30-story buildings, it
is first necessary to compare their strength, stiffness, mass (weight), and energy
dissipation capability (viscous damping and hysteretic energy). Obviously, these
properties are not independent of each other, and to achieye a good design it is not
sufficient to consider the way in which each one relates to one another, but also the way
these properties are affected by the interaction of the building and the soft soil at the
construction site.
An accepted philosophy of design of earthquake-resistant structures considers the
behavior and performance of the structure subjected to the following three types of
EQGMs.
· 1. Resist minor levels of EQGM, which can occur frequently, without damage.
276
2. Resist moderate-level of EQGM, which can occasionally occur, without structural
damage, but possibly experience some nonstructural damage.
3. Resist major levels of EQGM, whose probability of occurrence is very small, without
collapse or serious damage that can jeopardize life, but possibly with some structural as
well as nonstructural damage.
In the performance of a building, three levels of earthquake ground motion can be
considered. The first one is associated with minor levels of EQGM, and the performance
of the structure is considered adequate only if the structure does not suffer damage
(structural and nonstructural). The second level of EQGM is associated with a moderate
level of earthquake ground motion, and the performance of the structure is considered
acceptable if the structure has no structural damage (in some cases, some nonstructural
damage is considered acceptable, while in others it is unacceptable). Finally the third
level of EQGM is associated with very intense earthquake ground motions, and the
performance of the structure is considered satisfactory if, in spite of structural as well as
nonstructural damage, the structure can resist the ground motion without collapse or
serious damage that can jeopardize the life of the occupants or that of the people in the
surrounding properties.
Although the ideal design would be the one considering the above three levels of or
EQGMs, it has been considered that in the majority of cases a two-level design is enough
to obtain adequate overall designs of EO-resistant structures. The following are
summaries of three different design philosophies.
Conceptual Design. The Conceptual design has been carried out considering two limit
states or design levels [Ref. 5] as follows:
-Service Limit State. EQGMs with return periods of 10 years which can have a PGA
of 70 gals are considered. This limit state is controlled by the first significant yielding of
the members of the building. The performance of the structure is considered satisfactory
if there is no structural damage to the members of the structure (undamaged: elastic),
277
and there is no nonstructural damage (interstory drift index, 101, < 0.003). A viscous
damping coefficient (;) of 0.02 is considered.
- Safety Limit State. EQGMs with return periods of 450 years which can have a PGA
of 300 gals are considered. This limit state is controlled by the collapse of the building.
The performance of the building is considered acceptable if the_ structural damage could
be controlled .in such a way as to prevent collapse (damage index, DMI, < 0.8) and the
nonstructural damage could be controlled (101 < 0.0125}. A; of 0.05 is considered for this
limit state.
• Japanese Design. The Japanese design has been carried out considering two levels
[Ref. 6] as follows.
- First Design. The first structural calculation is based on allowable stresses of
members, i.e., the stresses in all members should be less than the allowable stresses
prescribed by AIJ. An EQGM with a maximum acceleration of 250 gals needs to be
considered. 101 must be less than 0.005. A; of 0.03 is considered for the first vibration
mode.
- Second Design. The second structural calculation is based on ultimate strength of
members. The structure can suffer damage but it should not collapse. EQGMs with
maximum acceleration of 400 gals should be considered. The intended story shear should
be 1.5 times that of .the First Design. IDI must be less than 0.01. A ; of 0.03 is
considered for the first vibration mode.
UBC Design. The UBC design of the 30-story building has been carried out as follows:
- Drift Requirements. IDI of the building should be limited to 0.0025 at allowable
stress level. To satisfy drift limit, an allowable stress spectrum, obtained by reducing 12
times the ordinates of an elastic site spectrum developed for EQGMs having a 1 0%
probability of being exceeded in 50 years, i.e., a return period of 485 years. A PGA of 300
gals (the same as that corresponding to a return period of 450 years) and a; of 0.05
were considered to obtain the elastic site spectra.
278
- Strength Requirements. The elastic strength of the RC elements should be
computed carrying out a response spectra analysis (RSA) using a spectrum obtained by
scaling up 1.4 times the UBC allowable stress spectrum (as defined above). UBC requires
the base shear, deflections, member forces and moments, obtained from the RSA, to be
scaled up (or down) by a factor equal to K V5r/ VoYN• where K is equal to 0.90 for regt,Jiar
buildings and 1 .0 for irregular buildings, V sr is the static base shear computed according
to section 2334 of UBC, and V0YN is the base shear obtained from the RSA. The forces
used in the design of the RC members correspond to their first significant yielding.
6.1.3.1 WEIGHTS
The weights reported for the three buildings are significantly different [Refs. 5, 6]. Table
6.1 summarizes these weights. The weight of beams and columns of the Japanese
design is about 13880 tons, while that for the Conceptual design is 14270 tons. As can
be seen, these two weights are very similar, while that for UBC design is 9425 tons
(9425/13880 = 0.68). The weights of these members plus the weight of the slab is 24050
tons for the Japanese design, 22400 ton for Conceptual design (22400/24050 = 0.93) and
17555 (17555/24050 = 0.73) for UBC design. Finally, the Conceptual design total weight
is 26150/29711 = 0.88 that of the Japanese design, while UBC design total weight is
22635/29711 = 0. 76 that of the Japanese design.
6.1.3.2 STIFFNESS
Figures 6.6 and 6. 7 show the variation over height of the gross moment of inertia (I~
of beams and columns. Figure 6.6 shows the moment of inertia of the beams that are
located in the exterior and interior frames of the Conceptual, UBC and Japanese designs.
In the Conceptual and UBC designs, there are only two different types of beams at each
story. One corresponds to all internal frames, and the other to all external frames (lg of
the beams located in the internal frames is larger than that corresponding to the beams
located in the external frames). The Japanese design shows a more complicated pattern
of beam sizes in plan and height. The values of inertia shown for the Japanese design
correspond to typical interior and exterior beams within a story (again, lg internal beam
279
is larger than 19 external beam). As shown in Figure 6.6, the interior beams of the
Conceptual design have 19 distribution similar to that corresponding to the interior beams
of the Japanese design, except in stories 27 to 30. In general, the 19
of the interior beams
corresponding to UBC design is about 50% that of the beams of the Japanese design.
The 19
of the exterior beams corresponding to the Conceptual design is larger than that
of the Japanese design, which in turn is larger than that corresponding to UBC design.
Figure 6. 7 shows the 19
of columns for the three designs. The Conceptual and UBC
design have only one size of column at every story. The Japanese design has 2 or 3
different column sizes per story. In the figure, the largest and smallest 19
for the columns
in the Japanese design are shown. As shown, the 19
of Conceptual design columns is
significantly larger than that of the Japanese design, which in turn is considerably larger
than the 19
of UBC design. Note that the sizes of columns were maintained constant over
height for the Conceptual design.
The concrete strength ranges from 240 to 420 kg/cm2 in Japanese design, 21 0 to 420
in the Conceptual design, and from 240 to 420 in UBC design. For all designs, the
. modulus of elasticity of the concrete is about 15000 v'f~ for concrete of normal weight (f~
in kg/em~.
6.1.3.3 DYNAMIC PROPERTIES
The dynamic properties of the 30-story buildings were estimated analytically. Table 6.2
summarizes the values obtained for the periods in sees of the three first translational
modes of vibration. The dynamic properties of the Japanese design were determined from
a 20 analysis [Ref. 6], and thus no information regarding its rotational modes was found.
To estimate the above dynamic properties, the models of the building corresponding
to the Conceptual and the UBC designs were established by considering the masses
shown in Table 6.1, the effective moment of inertia for beams to account for cracking, and
19
for columns.
280
6.1.3.4 VISCOUS DAMPING
Table 6.3 summarizes the different values of viscous damping used in the analysis and ' design of the different 30-story buildings. Note that for the Japanese and UBC designs,
the value of ; is the same for both EQGM levels (; equals 0.03 for Japanese and 0.05
for UBC); while for the Conceptual design, the value of; is different for the different levels
of EQGM. The reason for this is that the building designed according to Japanese
practice is supposed to remain elastic for both EQGM levels; the building designed
according to UBC shows significant nonlinear behavior for both levels of EQGM (as
discussed in section 4.3.4 and 4.3.5); and finally, the building designed according to
Conceptual design is supposed to remain elastic for service EQGM and to exhibit
significant nonlinear behavior for the safety EQGM.
6.1.3.5 STRENGTH AND DEFORMABILITY CAPACITY
To obtain an estimate of these properties, pushover analyses were carried out on the
three designs. Unfortunately, not enough information could be gathered regarding the
nonlinear behavior of the Japanese design subjected to statically increasing loads.
Table 6.4 summarizes the ultimate strength of the three designs. It should be noticed
that the ultimate strength of the Japanese building was obtained from Figure 6.8 [Ref. 6].
It can be seen in the figure that the ultimate strength at the first story is about 7000 tons.
It is not known if this is the ultimate shear capacity of the structure or if the structure was
just pushed until the base shear reached this value.
The base shear vs. tip displacement curves of the UBC and Conceptual designs can
be seen in Figure 6.9, where it can be seen that P-~ effects on the UBC design are very
large, while they are not significant for the Conceptual design. Tables 6.5 and 6.6
summarize the most important points of the base shear vs. tip displacement curves
obtained from the pushover analysis of the Conceptual and UBC designs. Figure 6.8 [Ref.
6] shows the story shear vs. interstory displacement curves obtained from a pushover
analysis carried out on the Japanese design. Figures 6.1 0 and 6.11 show the distribution
281
over height of I 01 obtained from the pushover analyses of the different designs. As shown
for all designs, when the structure remains elastic the 101 tends to be about constant from , stories 5 to 25 (approximately}, and then reduces considerably from story 5 to 1 and from
story 25 to 30. As shown for Conceptual and UBC design, once some members of the
structure have yielded, the deformation of the building starts concentrating at a few
stories. This concentration is not excessive for the Conceptual design, but the
concentration in the UBC design is excessive. Some of the causes for this inadequate
concentration of deformation in the UBC design were: not accounting for the contribution
of the slab to the strength of the beam when designing the longitudinal steel of the beam;
and excessive P-A effects. At this stage, it is difficult to assess the real causes that
produce this concentration of deformation, given that the 20 analytical model of the
structure can not capture adequately the behavior of the 30 30-story building, as
discussed in Chapter 5 of this report. It should be noted that the pushover test neglects
any upper-mode effect, and thus the 101 of the upper stories is likely to be smaller than
those obtained from a time-history analysis (see section 4.2).
6.1.4 SEISMIC PERFORMANCE OF DIFFERENT DESIGNS OF 30-STORY BUILDING
The comparison of the seismic performances of the three buildings can not be carried
out on a rational basis by using the available information [Refs. 5,6]. Some of the reasons
why a detailed comparison can not be established between the three designs follow.
Performance Criteria. The 30-story building was designed according to different
criteria. One of the facts that is very difficult to reconcile in order to compare the three
designs is the fact that Japanese design is oriented to obtaining a structure that should
remain elastic (should not reach first significant yielding}, while the Conceptual and UBC
designs were oriented to obtain, for ultimate limit state, a building that is supposed to
dissipate large amounts of energy through hysteretic behavior.
Ground Motions Selected to Analyze the Performance of the Building. The ground
motions used to study the seismic performance of the buildings have very different
dynamic characteristics. The results of time-history analysis (THA) of the 3 designs can
be found in Refs. 5 and 6 and in Chapter 4 of this report. In them, it can be seen that for
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the study of the performance of the Conceptual and UBC designs, the SCT EQGM was
used in such a way that its EW component has a PGA of 0.07g for service limit state and
0.30g for ultimate limit state. Meanwhile, for the Japanese design, the THA were carried
out using El Centro NS, Taft EW, Tokyo NS, and Sendai (Miyagi-Ken-Oki) EW; all of
them scaled up to a maximum acceleration of 250 gals for a severe EQGM and to 400
gals for the worst EQGM. As discussed later, it appears that of all the four EQGMs used
for the THA of the Japanese design, the Sendai EW produces the most critical response.
By comparing Figures 6.12 and 6.13, the large difference in the characteristics of the
EQGMs used to compare the performance of the UBC and Conceptual designs vs. that
of the Japanese design can be appreciated. Figure 6.12 shows in ~olid lines the response
of SDOFS with a~ of 0.05 to the SCT-EW EQGM scaled up to a PGA of 0.3g, while the
discontinuous lines represent the response to the SCT-EW EQGM without scaling. Figure
6.13 shows in solid lines the response of SDOFS with a ~ of 0.03 to the Sendai EW
EQGM scaled up to a maximum acceleration of 0.4g, while the discontinuous lines
represent the response to the Sendai EW EQGM without scaling. The spectra shown in
Figures 6.12 and 6.13 were obtained using a few values of T, and thus are rough,
especially in the short period range.
By comparing the spectra shown in Figures 6.12 and 6.13, it is clear that for a building
with a T of 1.67 sees (Japanese design) the SCT-EW EQGM is considerably more
demanding (for strength as well as displacement) than the Sendai EW EQGM.
Figures 6.14 to 6.16 summarize the response of the Japanese design to several
EQGMs scaled up to a maximum acceleration of 400 gals [Ref. 6]. As shown, the Sendai
EW ground motion produces the most critical response of the building, mainly in the lower
stories. The results shown in Figures 6.14 and 6. 16 are discussed in Ref. 6.
6.1.4.1 SEISMIC PERFORMANCE AT SERVICE LIMIT STATE OF CONCEPTUAL AND
UBC DESIGNS
To compare the reliability of these designs at service limit state, the following
283
performance criteria are used:
• Structural Damage. This limit state is limited by the first significant yielding of the
members of the building.
Nonstructural Damage. The performance of the structure is considered satisfactory 1 if there is no nonstructural damage (101 < 0.003).
In Ref. 5 and Chapter 4 of this report, the results of several response spectra analyses
(RSA) and THA are reported. The elastic analyses on both series of results were carried
out using the ETABS program [Ref. 13], while the nonlinear analyses were carried out
using the DRAIN 2DX program [Ref. 18]. The following is a summary of those results:
Conceptual. First, an elastic RSA was carried out using the design spectra developed
for the site using several EQGMs recorded on soft soils, scaled to a PGA of 0.07g and
using a ; of 0.02. Bidirectional input was considered using 1 00% of the input in one
direction and 30% in the perpendicular direction. Figures 6.17 to 6.19 summarize the
results of the RSA. As shown in Figures 6.17 and 6.18, the floor displacements and IDI
at the end frame are significantly increased when the accidental eccentricity (eaJ is
accounted for in the RSA. A detailed discussion of this issue can be found in section
3.5.3 of this report. It should be noted these two figures are obtained by computing the
total displacement in a floor, that is, the displacements are obtained by adding vectorially
those corresponding to X and Y directions. As shown in Figure 6.18, when eacc is not
considered in the analysis, the IDI are slightly larger than the limit of 0.003, and thus the
performance of the Conceptual design can be considered satisfactory. When eacc is
accounted for in the RSA, the IDI in stories 1 0 to 28 are larger than 0.003: nevertheless
they are acceptable. Figure 6.19 shows that the maximum stress ratios for all the beams
and columns of the building are less than 1 (greater than 1 implies yielding). Thus, from
a strength point of view, the design is satisfactory.
Later, an elastic THA was carried out on the building. For this purpose, the SCT-EW
ground motion was scaled to 0.07g PGA and applied in the X direction. Simultaneously,
30% of this input was applied in the Y direction. Only real eccentricities (er) and a ; of
284
I
0.02 were considered in the analysis. Results similar to those obtained from the RSA
analysis were obtained.
UBC. First, elastic RSA and THA analyses were carried out on the building. For the
RSA, the same design spectra used for the elastic RSA of the conceptual design was
used, while for the THA, the SCT-EW component was used. Input was considered using
100% of the input in one direction (EW direction) only, in such a way that the results of
these analyses could be compared directly with those obtained from the nonlinear
analyses carried out on the building (20 nonlinear analyses were carried out due to the
lack of an appropriate analytical tool to carry out a full 30 analysis of the building).
Figures 6.20 to 6.23 summarize the results of these analyses. As shown in Figures 6.20
to 6.22, the response obtained from the elastic THA is larger than that obtained from the
RSA. As shown in Figure 6.21, the 101 (up to 0.009) are considerably larger than 0.003,
and thus the performance of the UBC design is inadequate. Figure 6.22 shows that
elastically computed story shears obtained from the analysis exceed considerably those '
used in the design of the building for first significant yield. Figure 6.23 shows that
considerable yielding can be expected in the beams and columns of the building. Thus,
from a strength point of view as well, the design is unsatisfactory.
Later, a nonlinear 20 THA was carried out. The SCT-EW EQGM scaled up to 0.07g
and a; of 0.05 were used for this purpose. The results from this analysis are summarized
in Figures 6.22 and 6.24 to 6.27. As shown in Figures 6.24 and 6.25, the displacement
and 101 obtained from the nonlinear THA are considerably smaller than those predicted
from the elastic THA analysis (Figures 6.20 and 6.21). Thus, it can be concluded that the
nonlinear response of a tall building on soft soil can be overestimated considerably from
the linear response of the system. Further discussion of this issue can be found in section
5.6 of this report. As shown in Figure 6.1, when the system's T is close to Tg, the elastic
response is considerably larger than the nonlinear response. As shown in Figures 6.26
and 6.27, the nonlinear demands on the beams are small, and thus the structural damage
to them is not significant. A damage index (DM I) was used to characterize the damage
to the beams. A maximum value of 0.18 was obtained. From this value it was estimated
285
· that the damage on the beams would be repairable. Although the nonlinear response is
smaller than the linear one, the performance· of the UBC design should be considered
inadequate, given the fact that nonlinear response can be observed in several members
and a maximum 101 of 0.0079 was obtained in the nonlinear THA. Note in Figure 6.25
that a large concentration of deformation occurs at stories 3 to 1 0.
Finally a 30 elastic THA was carried out on the building to assess the adequacy of a
20 model to study the behavior of the building. For this purpose, the SCT EQGM was
used. Because the analysis program did not allow the use of two independent
components of an EQGM (in two perpendicular directions), the following was done: the
SCT-EW and SCT-NS components were added vectorially until the direction of the ground
acceleration principal direction (that in which the ground acceleration is the largest) was
established as that having a counterclockwise rotation of 28 degrees with respect to the
EW direction; then, the SCT-EW component of the SCT EQGM motion was applied in the
acceleration principal direction, and scaled up in such a way that its component in the EW -
direction had a PGA of 0.07g. A ~ of 0.05 and er plus eacc were considered in the
analysis. Figures 6.28 to 6.30 summarize the results from this analysis. Figure 6.28
shows the displacements at the end frames for EW and NS direction, while Figure 6.29
shows the 101 corresponding to these displacements. By comparing Figures 6.20 and
6.28, and Figures 6.21 and 6.29, it can be seen that the displacements and 101 obtained
from the elastic 30 THA at the end frame are larger in the EW direction than those
obtained from elastic THA analysis considering input only in the EW direction.
Nevertheless, the most important effect can be seen in the NS directions, where the
displacements and 101 are very large. Figure 6.30, which shows the story shears obtained
from the elastic 30 THA, also shows that the story shears in the EW and NS directions
are larger than those used for design at first significant yield, and that the distribution of
story shears obtained from a 20 nonlinear analysis (where moderate plastic rotations
were demanded from the RC members of the building) is similar to the elastic story shear
distribution obtained for the N-S direction: thus, nonlinear behavior is expected in the two
directions. Also, it can be seen that the story shears in the NS direction are about 55 to
286
60 those in the EW direction. Thus, it can be concluded that a 20 analysis of the building
can not estimate correctly the real behavior of the building.
Finally, it was checked how closely a generalized elasto-perfectly plastic single degree
of freedom system (SOOFS) estimated the response of the building. A good coincidence
was considered important, because the only way to compare the performance of the three
designs was by comparing the response of generalized SOOFS. As shown in Figure 6.24,
the response of the SDOFS matches reasonably well that obtained in the analysis of the
30-story building (see sections 4.3.4 and 4.3.5 of this report).
6.1.4.2 SAFETY LIMIT STATE
To compare the reliability of the UBC and Conceptual designs at safety limit state, the
following performance criteria are used:
Structural Damage. The structural damage can be controlled in such a way that failure
of any member is avoided.
Nonstructural Damage. The performance of the structure is considered satisfactory
if non-structural damage can be limited (101 < 0.0125).
In Ref. 5 and Chapter 4 of this report, the results of several 20 nonlinear THA are
reported. The nonlinear analyses were carried out using the DRAIN 2DX program [Ref.
18]. The following is a summary of those results.
Conceptual. A 20 nonlinear THA was carried out using the SCT-EW EQGM scaled up
to a PGA of 0.30 g and a; of 0.05. Figures 6.31 to 6.34 summarize the results obtained.
As shown in Figure 6.32, a maximum 101 of 0.012 is obtained, which is smaller than the
limit established for satisfactory performance. In the same figure it can be observed that \
there is a slight concentration of deformation at stories 5 to 1 0. Figures 6.33 and 6.34
show the plastic rotations on the members of the building. As shown, there are large
hinge rotations (maximum plastic rotation, SmaJ in the beams and columns of the lower
stories. In fact, the hinge rotations of the beams in the four lower stories practically
coincide with the cumulative plastic rotations (SacJ in the beams. A detailed discussion
287
of the reasons for the observed behavior can be found in Ref. 5. Mainly, the large value
of hinge rotations in the lower stories is due to the formation of hinges in the end columns
of these stories. Because of the hinging of the columns, the hinges on the beams are not
able to rotate in the opposite direction when there is a reversal in load direction, i.e., the
rotation keeps accumulating in one direction independently if the EQGM excitation causes
the building to move in two opposite directions. The largest hinge and cumulative plastic
rotations in the beams were 0.0458 rad and 0.1129, respectively. The largest hinge and
cumulative plastic rotations in the columns were 0.0529 rad and 0.0529 respectively. The
maximum damage was concentrated in the external beams of the first four stories. A OMI
of 0.90 was estimated in these beams {a DMI of 1 can be interpreted as failure in the
member [Ref. 5]). Although the performance of the structure can be considered
satisfactory from stiffness and strength point of view, it is necessary to consider the
potential effects of the component of the ground motion in the perpendicular direction {as
shown in Figures 6.28 to 6.30, these effects can be significant). In the conceptual design,
the columns suffered large hinge rotations (0.0529), and thus heavy damage can be
expected on them (DMI is very difficult to estimate in columns given the fact that the
earthquake-induced axial forces in them vary throughout the analysis: nevertheless, the
extent of the damage can be judged if the maximum rotation capacity of the column, 0.06
rad, for an axial load of 0 is considered). Again, the extent of the damage to the columns
due to perpendicular motion still needs to be assessed, but an increase in damage can
be expected.
Due to the large strength of the beams of the building, the design of the columns
becomes very difficult from a practical point of view, given the very large axial forces
induced in the columns when the building is subjected to an EQGM. The hinging of I
several end columns in the lower story lead in this case to large hinge rotations in some
beams. Thus, it is very important to consider carefully the design of the columns in the
lower stories.
UBC. A 20 nonlinear THA was carried out using the SCT -EW EQGM scaled to a PGA
288
of 0.30g and a; of 0.05. Figures 6.31 to 6.34 summarize the results obtained. Figure
6.31 clearly shows that, unlike the Conceptual design, the UBC design does not vibrate
around its undeformed configuration, i.e., the buildings tends to deform in one direction.
As shown in Figure 6.32, a maximum IDI of 0.025 is obtained, which is significantly larger
than the limit established for satisfactory performance (and that obtained for the
Conceptual design). Furthermore, in considering the significance of the IDI value of 0.025
it has to be kept in mind that this value was not computed considering the effects of
torsion and bidirectional EQGMs. In the same figure it can be observed that there is a
large concentration of deformation at stories 4 to 1 0. Some studies have been carried out
to explain this concentration of deformation in a few stories. Some factors contributing to
it are: neglecting the strength of the slab in the· design of the longitudinal steel of the
beams (which create a larger OVS on the top beams relative to the bottom beams),
excessive P-A effects due to the flexibility of the building (which is larger in the bottom
stories). Nevertheless, at this stage it is difficult to assess the exact causes of this
behavior given that a 20 analysis can not predict accurately the real behavior of the
building (see Chapter 5 of this report for a detailed discussion).
Figures 6.33 and 6.34 show the plastic rotations on the members of the building. As
shown, there are large hinge rotations (maximum plastic rotations) in the beams and
columns of the lower stories. The largest hinge and cumulative plastic rotation in the
beams were 0.0262 rad (which is significantly less than the 0.0458, value corresponding
to the larger plastic hinge rotation on the Conceptual design) and 0.1265 (similar to
0.1129 obtained in Conceptual design), respectively. The largest hinge and cumulative
plastic rotations in columns were 0.0040 rad and 0.0131 (which are significantly smaller
than 0.0529 and 0.0529 obtained in Conceptual design), respectively. The maximum
damage was concentrated in the beams of stories 4 to 10. A DMI of 1.35 was estimated
in these beams (recall that a DMI of 1 can be interpreted as failure in the member). Thus,
it can be concluded that sever~l beams in stories 4 to 10 are likely to fail, which will
probably be reflected. in the collapse of the building. It can be concluded that the UBC
design is inadequate from a drift control and energy dissipation capacity point of view.
289
It should be noted that the inelastic rotations in the columns are much smaller than
those of the beams. Usually for this to happen, two things have to be combined: first, the
columns of the building should be overdesigned in comparison with the beams, in such
a way that no hinging occurs in the columns; and second, the columns are flexible in such
a way that their lateral elastic deformation, once hinges appear on the beams, are large.
Figure 6.35 summarizes these considerations. It is necessary to consider the potential
effects of the component of the ground motion in the perpendicular direction (as shown
in Figures 6.28 to 6.30, these effects ·can be significant).
Finally, it was checked how closely a generalized elasto-perfectly plastic SDOF model
representing the building estimated the response of the building. Figure 6.35 shows that
the results obtained in the SDOFS match reasonably well those obtained in the analysis
of the 30-story building.
By comparing the response of the Conceptual Design to the UBC design, the following
observations can be made:
The difference between the DMI of both designs, 1.35 vs. 0.90, is considerably smaller
than the difference in their strengths, 0.11 W vs. 0.30 W. Damage was controlled to an
acceptable value in the Conceptual design, as opposed to that in the UBC design.
Nevertheless, the value on the beams of the UBC design is not as large as it would be
expected considering its large underdesign for strength. As mentioned in section 4.3, a
small increase in the strength of a system usually results in a reduction in the DMI. Also,
by enhancing the confinement of the beams, a reduction in the value of DMI is obtained.
The maximum rotations of beams and columns are considerably larger in the
Conceptual design. The reason for this is the extensive hinging of the end columns due
to the large axial forces acting on them. In the Conceptual design, the damage in the
beams with larger DMI is due to a large values of maximum rotation; while in those of the
UBC design, damage is associated mainly to the hysteretic behavior of the member. To
illustrate this point, the value of DMI is computed for two beam~, one corresponding to
the UBC design and the other to the Conceptual design:
290
UBC design, DMI= 0·0262 +0.15°·1247 +0·1169 =0.55+0.76=1.31 0.~ 0.~
Conceptual design, DMI= 0·0458 +0.15°·0458+0 =0.76+0.12=0.88 0.06 0.06
Note that in the Conceptual design, the larger value of DMI was associated to beams
where the maximum rotation was large (and equal to the accumulated rotation).
Previously, the reason for the large value of maximum rotation in the Conceptual design
was discussed. To achieve a true comparison of the above values of DMI, the following
should be noticed:
• The ultimate rotational capacity, eu, of the Conceptual design beam is considerably
larger than that of the UBC design (0.06 vs 0.048). If the beam on the UBC design had
a value of eu equal to 0.06, then its DMI would be equal to 1.05. Thus, if the beams in the
Conceptual and UBC designs have similar detailing and amount of transverse
reinforcement, they would have very similar DMI.
For the UBC design, the magnitude of damage suggested by the above value of DMI
(1.31) can be associated with practically all the beams located in floors 6 to 8 (see Figure
4.53). Nevertheless, for the Conceptual design, the magnitude of damage suggested by
the value of DMI = 0.88 can only be associated with a few locations: the external ends
of the external beams on the third and fourth stories (see Ref. 5). Thus, not only the
maximum value of DMI needs to be considered to assess damage to the building; the
distribution of DMI values among the members of the building is important to assess how
extensive was the damage.
6.1.4.3 COMPARISON OF PERFORMANCE OF 3 DESIGNS BY THE STUDY OF THE
BEHAVIOR OF SDOFS
The three designs were modelled with elasto-perfectly plastic SDOFS with the following
291
properties:
Conceptual. T = 1. 7 sees (first translational mode), V = 0.30 W.
Japanese. T = 1 .67 sees (first translational mode), V = 0.24 W.
UBC. T = 2.53 sees (first translational mode), V = 0.11 W.
Several models were added to assess the consequence of increasing the strength of
the UBC SDOFS:
UBC2. T = 2.53 sees (first translational mode), V = 0.30 W.
UBC3. T = 2.53 sees (first translational mode), V = 0.12 W.
UBC4. T = 2.53 sees (first translational mode), V = 0.13 W.
uses. T = 2.53 sees (first translational mode), V = 0.15 W.
The EQGMs used in the analyses of the SDOFS are summarized in Table 6. 7 and
shown in Figures 6.12, 6.13, 6.36 and 6.37. The SCT-EW EQGM was recorded in the
lake zone of Mexico City (soft silty clay) during the 1985 Mexican earthquakes, the
Emeryville and Foster City EQGMs were recorded in the San Francisco Bay Area (bay
mud) during the Lorna Prieta earthquake, and the Sendai-EW EQGM was recorded in .
Sendai City (alluvium) during the 1978 Miyagi-Ken-Oki earthquake. The SCT-EW record
was chosen because it was considered as the critical EQGM for the UBC and Conceptual
designs, the Emeryville and Foster City EQGMs were considered because they were
recorded in the San Francisco Bay Area, while the Sendai-EW record was chosen
because it was the one that produced the largest response of all the EQGMs used to
analyze the Japanese design.
As remarked before, the SDOFS provide a reasonable estimate of the global behavior
of the 30-story building. In this paper, an attempt to obtain a reasonable estimate of the
local damage produced to the 30-story building was carried out by estimating the DMI of
the SDOFS. It should be noticed that because the global ductility and local ductility
demands and capacities of a system are not linearly related, in some cases the use of
a DMI computed from a SDOFS can not reflect the local damage to a structure. Values
of OMI were computed from the SDOFS using the formulas given by Park and Ang [Ref.
292
5]. Table 6. 7 summarizes the response of the different SDOFS. In it I.A. represents the
-'1 displacement ductility ratio, fla (= l:laccllly) represents the cumulative plastic displacement
ductility ratio, DMI the damage index and Dl the drift index computed from the results
obtained from nonlinear THA of the SDOFSs.
To compute the DMI in the SDOFS, it was assumed that the ultimate deformation
capacity of the system was equal to 6 times the yield deformation (which does not
necessarily coincide with the ultimate localfl of the members of the structure). Note that
in Ref. 5 it has been shown that the ultimate displacement is about 6 times the yield
displacement for the 30-story building designed using Conceptual Design Methodology.
Because the Japanese building has similar dynamic properties, detailing and strength, it
is assumed that a ultimate to yield displacement ratio similar to that obtained for the
Conceptual design can be used. As discussed in section 4.3.3 of this report, for the UBC
I building this ratio is around 5. Nevertheless, it should be considered that this ratio is
limited to 5 due to the large concentration of deformation in a few stories, which produced
large deformations on a few beams. It is considered that if such concentration of
deformation can be avoided, the ultimate displacement of the building can easily reach
the value of 6.
The comparison of the DMI computed from the SDOFS and the 30-story building shows
that the DMI of the SDOFS tends to overestimate the local damage. As shown in Table
6. 7, this is very noticeable for UBC design (0.36 vs. 0.18 at service limit state and 1. 72
vs. 1.35 at ultimate limit state); while for the Conceptual design the difference is small
(0.96 vs. 0.90 for safety limit state). Although it can not be said that the DMI from the
SDOFS give an accurate estimate of the local damage of the 30-story building, it shows
reasonable well the tendency that the building has to suffer certain type of damage. Thus,
DMI of SDOFS is used to compare, in a qualitative way, the performance of the different
designs. The first thing that should be considered is that the Conceptual and japanese
design have practically the same T (1.67 vs. 1.7 sees.). For all EQGMs, the DMI
corresponding to the Japanese SDOFS is larger than that for the Conceptual SDOFS.
293
It can be seen that the larger strength of the Conceptual SOOFS (0.30 W) is reflected in
a smaller 1-t and a smaller I-ta• which lead to a smaller value of OMI.
It can be seen from Table 6. 7 and Figure 6.13 that the Japanese SOOFS remains
elastic for the Sendai EW EQGM scaled to a maximum acceleration of 0.4g. This result
coincides with what has been reported for the Japanese design [Ref. 6]. Nevertheless,
if the Japanese SOOFS is subjected to SCT -EW the following can be observed: for a
PGA of 0.07g, it remains elastic; for PGA of 0.17g, a OM of 0.58 is obtained, which can
be interpreted as non-reparable damage to the building; and, for a PGA of 0.30g, a OM
of 1.34 can be obtained, which can be interpreted as very heavy damage. The
performance of the Japanese building, which can be considered adequate for some
EQGMs (such as those used in the THA analysis of the model of the Japanese building)
can be clearly inadequate for other EQGMs (recorded in soft soils).
From the results obtained for the Emeryville EQGM, it can be seen that ~.t. I-ta• and OMI
for the Conceptual and Japanese SDOFS are larger than those corresponding to the UBC
SOOFS (Figure 6.36 shows that the Emeryville EQGM is considerably more demanding
for a SOOFS with T of 1. 7 sees than for one with T of 2.5 sees). The Emeryville EQGM
demands moderate nonlinear behavior from the Japanese SDOFS. For the Foster City
EQGM, the Conceptual, Japanese and UBC SDOFS show nonlinear behavior. In this
case the Conceptual SOOFS show small inelastic demands while the Japanese and UBC
SOOFS show moderate demands (Figure 6.37 shows that the Foster City EQGM is more
demanding for a SDOFS with T of 1 . 7 sees than for one with T of 2.5 sees, although the
difference is not as large as that corresponding to the Emeryville EQGM shown in Figure
6.36)
Some researchers consider the Lorna Prieta earthquake (during this event, the
Emeryville and Foster City EQGMs were recorded) as a damageability limit state type of
EQGM. It should be noticed that for the Japanese SDOFS subjected to the Emeryville and
Foster City EQGMs, the 1-t demands are 1.60 and 1.59, respectively, which would very likely
294
I
translate into reparable structural damage. The Japanese SDOFS does not perform well
according to the Japanese philosophy of design when subjected to damageability EQGMs
recorded in bay mud. The Conceptual SDOFS show very small 1-t demands and thus,
damage is smaller than in the Japanese SDOFS. The UBC SDOFS show moderate 1-t
demand for Foster City EQGM while it shows very small 1-t demand for the Emeryville
EQGM.
In the above discussion, it is necessary to consider other sources of overstrength
besides that provide by the structural members (such as contributions from nonstructural '
} elements). Thus, the nonlinear demands on a real building are probably slightly smaller
\ I
I
than those obtained in the SDOFS. Other issue that has not been considered is the effect
of accounting for the interaction between the soil and the structure (although for SCT -EW
EQGM, analytical studies show that this interaction can be detrimental [Ref. 29]).
The UBC2 SDOFS was defined to study the performance of the UBC SDOFS in case
it had a similar strength/unit weight than that corresponding to the Conceptual SDOFS.
As shown, the nonlinear demands on the UBC2 SDOFS are, in general, smaller than
those on the Conceptual SDOFS. Thus in general, for a constant strength, a SDOFS with
a T of 1. 7 sees will have larger nonlinear demands that a SDOFS with a T of 2;53 sees.
The UBC3, UBC4 and UBC5 SDOFSs were defined to show the influence of small and
moderate increase in the strength of the structure in the value of DMI. Although no
definite conclusions can be obtained given the fact that the SDOFS overestimates the
value of DMI as compared to that computed from local damage in the 30-story building,
a tendency is easily noticed: an increase in the strength of the SDOFS produces an
important decrease in the values of 1-t and I-ta• and thus on the value of DMI.
One of the bigger problems that arises when a tall building is designed in a soft soil (T9
usually varies from 1 to 2 sees) can be noted by considering simultaneously the values
of DMI and Dl from Table 6. 7. With the exception of the Emeryville and Sendai EQGMs,
the Dl corresponding to the UBC SDOFS is clearly too large. Contrasting with this, the
295
Dl for the Conceptual and Japanese SDOFS are appropriate for drift control. Although
from a strength and damage point of view it would appear attractive to use a large T, this
would lead in most cases to excessive drifts. Note that for SCT-EW, PGA of 0.3g, an
increase in strength results in smaller DMI. Nevertheless, it results in larger Dl. Thus, a
problem that commonly arises in the design of a tall building on soft soil is that to control
drift under the safety EQGM (and the elastic drift under the service EQGM), the structure
has to have a large stiffness which can lead to a T that is close to T 9
(for 30-story
building, it seems it is the case). With this T, a large amplification in the linear response
can be expected in this zone of the spectra, as shown in Figure 6.1 , as well as a large
reduction in the strength and displacement demands when the building shows nonlinear
behavior. In spite of these attractive characteristics of the nonlinear behavior (large
reduction of strength and displacement), the energy input to the structure has to be
dissipated somehow. In some cases, this leads to large NYR and cumulative plastic
displacement demands, which usually leads to difficulty in controlling damage (a good
example of this tendencies is the SCT-EW EQGM [Ref. 12]). Thus, the only way that an
acceptable design can be obtained from the point of view of damage and drift control is
to have a system with very large stiffness (as compared to American practice and
probably similar to that typical of Japanese buildings) and large strength.
The behavior of the Conceptual, Japanese and UBC SDOFS subjected to the Emeryville
EQGM needs to be discussed separately. In spite of the efforts devoted to obtaining better
designs, it can be seen from the resuijs on Table 6.7 that in all probability damage would
be larger and drift control poorer in the Conceptual and Japanese SDOFS as compared with
those corresponding to the UBC design. The reasons for these unexpected resuijs can be
seen in Figure 6.36, where the strength and displacement spectra are plotted for the
Emeryville EQGM. As shown, the strength and displacement demands are considerably
larger for a SDOFS with T of 1. 7 sees than for one with T of 2.53 sees.
6.1.5 CONCLUSIONS
Uncertainty about the value of T9
corresponding to a given site with soft soil, together
296
\ I
{
\
\
with the difficulty of estimating the true value of T of a building, make it difficult to attain
an efficient design. Nevertheless, as shown by the results of Table 6. 7, a rational design
approach will lead to a system that performs considerably better than a system designed
according to current American practice (although the very important exception given by
the response of the SDOFSs to the Emeryville EQGM should be remarked). The
Japanese SDOFS seem~ to have a problem of damageability, as shown by its nonlinear
behavior when subjected to EQGMs recorded in bay mud.
For tall buildings designed in soft soils with T close to Tg, the large elastic response and
the large reduction in the response when the system undergoes inelastic behavior (in
strength and displacement) leads to the necessity of using at least a two-limit-state
approach: service and safety limit state. Because the system is supposed to remain
elastic for the service limit state, a large amplification of the EQGM can be expected for
strength as well as displacement as shown in Figure 6.1. Nevertheless, for safety limit
state, where nonlinear behavior is expected, a large reduction in the strength and
displacement demands (with respect to the elastic demands) can be observed. Thus,
although the PGA of the service EQGM can be smaller than that corresponding to the
safety EQGM (which does not necessarily have the same dynamic characteristics as the
service EQGM), the different amplification of both EQGMs can lead to comparable drifts
and strength for service and safety. Thus, drift and strength requirements should be
defined and satisfied for both limit states.
The performance of the Conceptual design of the 30-story building can be qualified as
satisfactory from the results obtained from THA of SDOFS and those reported in Ref. 5.
The stiffness and strength of the system are adequate to limit drift as well as structural
and nonstructural damage to acceptable values for service and safety limit states.
UBC design leads to a extremely flexible structure which does not provide adequate
drift control at any limit state and thus can not prevent extensive nonstructural damage
even for service limit state. The strength of the building is not enough to keep the RC
297
members from yielding at service limit state, as shown in the results of Table 6. 7 and
those reported in Chapter 4 of this report. Considering that the DMI obtained from
SDOFS overestimates the local DMI for .the 30-story building, and by analyzing
simultaneously the results reported in Chapter 5 of this report and those in Table 6.7, it
would appear that although the strength is too small to prevent damage to occur at the
service limit state, the strength for safety does not need to be much larger for damage
control in the safety limit state (DMI < 1). It also should be considered that by confining
the ends of the beams by providing closely spaced stirrups, the value of DMI can be
decreased. In the unsatisfactory performance of the UBC design, the need to use a two
limit-state approach for the design of the structure is emphasized. ·
Although some qualitative aspects of the performance of the 30-story building designed
according to different design practices have been established, nonlinear 30 THA
accounting for the effect of the soil-foundation system flexibility and including the effects
of soil damping and radiation damping need to be carried out to attain a better
comparison of the seismic performance of the three designs.
6.2 FINAL CONCLUSIONS AND DESIGN RECOMMENDATIONS
From the results and the discussion of the results obtained in this report, the following
can be concluded regarding the design of tall buildings on soft soil.
6.2.1. UBC DESIGN SPECIFICATIONS
UBC EQRD criteria and procedure. One problem with the UBC approach is the fact
that the design of the structure is not carried out to assure adequate performance of the
building using a multi-level EQRD approach (i.e., considering at least service,
damageability and safety limit states). As discussed in Refs. 2 and 5 and in section 6.1
of this report, in general it is necessary to consider several limit states in order to achieve
an adequate EQRD of any building. This requirement is of utmost importance in the case
of EQRD of tall buildings to be built on deep soft soils. The fact that the building performs
adequately for one limit state does not guarantee its adequate performance for other limit
298
I
',/
f '
I ,
'··
states.
' • The Rw factor (Lateral forces) In UBC design. Another problem with the UBC
approach lies in the fact that the elastic spectra obtained for the site should be reduced
by large values of f\ to obtain the allowab~e stress design spectra. Although the resulting
spectra usually lead to small design lateral forces, it is argued that due to the required
detailing for ductility and to the large overstrength (OVS) of buildings designed and
constructed according to present American practice, these buildings are expected to
perform adequately when subjected to the EQGMs expected at the service and safety
levels. At service limit state, it should be kept in mind that the OVS of the building that
can be obtained due to the supplied ductility does not help it to perform adequately, ,
because the building is supposed to remain elastic. As discussed in section 5.8, the
small design lateral forces used in the design lead to a very flexible building with not
enough elastic strength to prevent yielding in some of its elements. For safety limit state,
the use of Rw to obtain reduced design forces also leads to unconservative design,
because, as shown by the OVS value obtained for the 30-story building designed
according to UBC, the OVS in the building can be significantly lower than that assumed
by using the prescribed Rw. As discussed by Krawinkler and Osteraas [Ref. 30), taller
buildings tend to have smaller OVS values than short and medium-rise buildings, and
thus careful assessment of the expected OVS should be carried out. A constant Rw to
obtain design forces by reducing the linear elastic design response spectra should not be
used in the design of buildings on soft soil for the following reasons.
• As discussed in Chapter 5, the commonly used approach of estimating nonlinear
behavior from linear behavior does not work adequately for EQGM recorded on soft soils,
i.e., the nonlinear response of the system has to be determined from nonlinear response
spectra and not from the use of a reduced linear response spectra. The reduction of the
nonlinear response with respect to the linear response is strongly dependent of the ratio
T /T g (as shown in Figure 6.1), and thus Rw can not be constant.
• The OVS of a building depends on factors such as its height, internal redundancy of
each story and the structural system used (i.e., n, as well as on the procedure used in
299
. its design (elastic design, such as those based on allowable stress, first yielding strength,
ultimate strength, limit design based on plastic redistribution, or elastic design). Thus, Rw
should be a function ofT, the structural system, story redundancy and the design procedure.
The use of constant Rw in general does not allow for efficient design, and can lead to ..
unconservative design, partuicularly in the case of long period structures). A more rational
' .. approach needs to be considered.
·-.. ....._____ _____ --· ----~ ·-- - -~----- -~--~ Accidental torsion In UBC design. There is a need to come up with rational and
consistent procedures to account for accidental torsion in UBC specifications. The current
specifications are difficult to interpret and results that are difficult to justify can be obtained
when eacc is accounted for ih the dynamic analysis of the building. The dynamic
amplification of the elastic torsional effects and its consequences in the design procedure
need to be considered in the specifications of the code. There is need for further research
to understand this elastic dynamic amplification of torsion on multi-degree-of-freedom
systems, and to obtain adequate values of eacc (which should be a function of the number
of stories in a building, i.e., eacc should diminish with increasing number of stories to
account for the smaller probability of having the same value of eacc in many floors) that
are able to reflect real conditions found in American buildings. The effects of torsion in
the inelastic range of buildings needs to be investigated more thoroughly.
Bidirectional Input In UBC design. The results of elastic 3D THA analysis suggest
that significant yielding in the members of the structure can be expected simultaneously
in both directions. In some cases, designing the structure accounting for 1 00% of the
EQGM input in one direction and 30% in the perpendicular direction could lead to
unconservative designs (mainly of the columns) . .A parameterthat considerably influences
the 3D behavior of the structure is the value eacc· For large values of this eccentricity, the
coupling of all three DOFS in the story lead to significant responses in the two
perpendicular directions that define the geometric axes of the plan of the building. Thus
it is very important to estimate a reasonable value of eacc; and once this value is
300
I '
-··"'
I I
I I
established, there is a need to study the response of systems to all three translational
components of EQGM before attempting to establish smoothed design response spectra
(elastic or inelastic) and simplified recommendations on how to account for bidirectional
effects.
UBC code. UBC code has become a collection of very detailed and complex
specifications which the structural engineer must follow to obtain a sound design.
Unfortunately, UBC specifications would yield inadequate design of a tall building located
on soft soil. The rationality of the design process has been buried within such
specifications in such a way that it is very difficult to make adequate design decisions
when the structure to be designed does not conform to the assumptions and limitations
under which the specifications were developed. Under these circumstances, the structural
engineer lacks the background to avoid any possible loophole in the code to result in an
inadequate design.
As more and more specifications, some of which are extremely-diffiqult to interpret (or
allow several interpretations),' are added to the code, the code becomes difficult to use
and departs further from rationality. Although several of these guidelines try to reduce the
uncertainties in the design process, they just hide the·~ from the users of the code: When
.using the UBC code, the basic principles of design· need to be ·stressed, including the . .
-undeniable fact that every structure-is a unique system which interacts uniquely with its
surroundings. The uncertainty on the design process as well as the general prirlciples of
design need to be addressed in order to obtain a sound design of a tall building.
6.2.2 DESIGN RECOMMENDATIONS FOR TALL BUILDINGS IN SOFT SOIL SITES
Bound design parameters. The linear (and even the nonlinear) response of systems
subjected to EQGM recorded on soft soil is strongly dependent on the ratio T/T9• Given
the difficulty of establishing exact values forT and T9, it is recommended to bound these
two values in such a way that a bounded response of the building can be used to achieve
a sound design. A deterministic design can lead to unconservative designs.
301
Multiple limit state design procedure. The design procedure should consider at least
two limit states in the design of the building:
• Service. Because the response of the building is usually limited to first significant
yielding for this limit state, it would be enough to obtain reliable smoothed linear elastic
design response spectra (SLEDRS) for strength and displacement. These spectra should
be obtained according to a selected level of failure probability based on the available
information on the seismic activity and the sources of potential seismic hazard at the site.
The design should be based first on stiffness and then on strength, i.e., the minimum
stiffness of the structure (required to limit the displacement of the structure to an
acceptable value) should be estimated based on the maximum T that the structure can
have according to the displacement SLEDRS. Once the T has been determined, the
strength of the structure should be estimated from the strength SLEDRS. A design based
on strength alone can lead to unsatisfactory drift control.
/ • Safety. The design for safety on soft soils should-· be based on structural as well as\
nonstructural damage control. Nonstructural damage can be controlled by establishing
appropriate IDIIimits. Nevertheless, the control of structural damage is very complicated,
and conventional ·approaches to limiting structural damage can lead to unconservative
designs, especially for the case of buildings on soft soils. Usually, damage can be
associated with the nonlinear behavior of the system (i.e., with the ductility demands and '
the hysteretic behavior of the system). /
As discussed in Ref. 12, -in some-cases -th-e--maximum -ductility demands of-a given
EQGM on a system can not give a good estimate of the damage potential of the EQGM
to that system, specially for those EQGMs recorded on soft soil. For instance, for the
SCT-EW EQGM [Ref. 12], the following can be observed: the value of~ demanded from
the system does not appropriately reflect the value of the energy input to it by the EQGM,
i.e., for systems with T around T9
, large nonlinear demands such as cumulative plastic
ductility demands (~J and number of yield reversals (NYR) (and thus, a large demand
302
/'
! '
I
I I '·
-,
for energy to be dissipated t_hrough . the hysteretic behavior of the system) can· be
expected even .for moderate values of f..t (2 and 3). In this context, the duration of the
ground motion becomes important.
I-
It is not enough to establish a design target ductility (~r) based on the maximum . . .
ductility de~ands and t~e ultimate deformation capacity of _the system , under
monotonically increasing loads: the hysteretic behavior. of the structure needs. to be
considered to adopt a value of ~r in such a way that damage can be controlled. Thus,
although it is essential to establish reliable smoothed inelastic design response spectra
(SIDRS) for strength and displacement, this information is not sufficient to accomplish a
sound design.
Once the T of the structure has been established from service as well as safety limit
state IDI requirements, the strength of the structure should be estimated according to the
strength SIDRS and an acceptable value of l-Ata~· Establishing an acceptable value of f..ttar
is not easy. Th~ use of an .energy approa9h to limit damage (i.e., e~ergy demands <
energy supply) is promising. A detailed discussion of this approach ca~ be fOUI')d in ~efs.
12 and,31. The main conpern of the designer should be to provide enough strength to the j structure so that the maximum and curl)ulative ductility demands (including J.t, I-ta and
1 .....___..~ ----.,....~ --T-
NYR) can be limited to acceptable values~such a way that hysteretic energy can be
dissipated adequately in the members of the structure (avoiding low cycle fatigue of such
members). As discussed in section 6.1, it can be concluded from the study of SDOFS
subjected to the SCT -EW ground motion that in general, an increase in strength of the
system is accompanied by a decrease in the values of 1-t and J.t8 , and thus to a decrease
in the damage suffered by the system when dissipating the input energy through
hysteretic behavior. As remarked in Refs. 2 and 5, the design of buildings on soft soil with
aT close to Tg should limit the value of ~r to relatively small values (J.t between 2 and
3).
The reduction in the values of the acceleration due to the overstrength (OVS) of the
303
system should be considered in a rational way. It should be considered that OVS is a
function of parameters such as the height of the structure, the story redundancy, the
structural system used, the design procedure used (i.e., limit design considering plastic
redistribution vs. designing using results from elastic analysis), etc. Once the required (· t
strength (ultimate strength) in the structure has been determined, a design strength can
be obtained by reducing the required ultimate strength by using an appropriate·value of I OVS determined for the structure.
--··--.,..----·_........-·~---· ----- ---.---....-~--,_--...--- -~ ~
Finally, the T of the structure should be used with the displacement SIDRS for IJ.tar to
check that 101 can be limited to acceptable values in the building.
304
I ,
;. .... i
. ! !.
I )
\
COMPONENT Japanese Conceptual UBC COMMENTS Design Design Design
slab 10170 ton 8130 ton 8130 ton (2)
beams 7970 7820 5200 (3)
columns 5910 6450 3625 (4)
non-structural and others 4790 3750 4240 (5)
reactive live load 1770 0 1440 (6)
TOTAL 3061 0(1) ton 26150 ton 22635 ton
COMMENTS:
(1) The total weight of this building was estimated elsewhere as 29711 ton [Ref. 6]. The weights reported in this table were estimated from the structural drawings of the building and the loads per unit area used in Japanese practice [Ref. 14].
(2) slab thickness of 15 em for Japanese design and of 12 em in Conceptual and UBC design.
(3) See Figure 6.6. (4) See Figure 6.7. · (5) The weight of nonstructural and other elements are larger for the Japanese design
than those for the Conceptual design and UBC design. (6) Reactive live load was considered as 60 kg/m2 for Japanese design and 50 kg/m2
for UBC design.
TABLE 6.1 SUMMARY OF WEIGHTS, In tons, OF 30-STORY BUILDINGS
305
DESIGN T, T2 Ta COMMENTS
Japanese 1.67 0.55 0.30 {1)
Conceptual 1.70 0.59 0.34 (2)
UBC 2.53 0.84 0.46 (2)
COMMENTS:
(1) from a two dimensional analysis (2) from a three dimensional analysis accounting for the real eccentricity of the center
of mass.
TABLE 6.2 PERIODS, In sees, OF FIRST THREE TRANSLATIONAL MODES OF 30-STORY BUILDING
DESIGN FIRST LEVEL SECOND LEVEL
Japanese SEVERE EQGM, WORST EQGM, PGA = 250 gal: ; = 0.03 PGA = 400 gal:;= 0.03
Conceptual FIRST YIELDING, WORSTEQGM, PGA = 70 gal: ; = 0.02 PGA = 300 gal: ; = 0.05
UBC ALLOWABLE STRESS, ALLOWABLE STRESS reduced elastic site SPECTRA FACTORED spectra (F\v = 12): UP BY 1.4: ; = 0.05 ; = 0.05
' 1
. I I
I I
I
TABLE 6.3 VISCOUS DAMPING USED FOR DIFFERENT DESIGNS OF 3Q- !\
STORY BUILDING
306 \.l
1 '
Design Ultimate Base Shear Design Base Shear
Japanese· 7000 ton (0.24 W) 0.18 W at ultimate (0.12 at allowable stress)
Conceptual 7850 (0.30 W) 0.25 W at ultimate .r
I \
UBC 2451 (0.11 W) 0.063 W at first significant yielding (0.045
/"' I • at allowable stress)
TABLE 6.4 ULTIMATE AND DESIGN BASE SHEARS OF 30-STORY BUILDINGS
-I I
State of Building Tip Displacement Base Shear IDI
Allowable Stress 0.152 m 1 020 ton (.045 W) .0018
First Yield Design 0.213 m 1428 ton (.063 W) .0025
First significant I I yielding 0.266 m 1785 ton (.079 W) .0030
Maximum Base Shear 1.350 m 2451 ton (.1 08 W) .034
TABLE 6.5 UBC DESIGN, SUMMARY OF PUSHOVER ANALYSIS RESULTS
307
State of Building Tip Displacement Base Shear IDI
First significant yielding 0.29 m 4710 ton (.18 W) .0030
Design Base Shear 0.45 m 6540 ton (.25 W) -----
Maximum Base Shear 2.76 m 7850 ton (.30 W) .036
TABLE 6.6 CONCEPTUAL DESIGN, SUMMARY OF PUSHOVER ANALYSIS RESULTS
308
-r ,
I I
_ .........
. ..,
Ground Motion PGA Design j.l .... ""t._!t.., OMI Dl
SCT-EW 0.07 g Conceptual (0.30W) 0.76 0 0.13 .0028 SERVICE
Japanese (0.24W) 0.87 0 0.15 .0025
UBC (0.11W) 1.64 3.41 0.36 (0.18) .0049
UBC2 (0.30W) 0.90 0 0.15 .0079
SCT-EW 0.17 g Conceptual 1.58 4.86 0.38 .0058 DAMAGEABILITY-ULTIMATE
Japanese 1.98 9.92 0.58 .0056
UBC 3.44 16.85 0.99 .0103
UBC2 1.82 1.96 0.35 .0160
SCT-EW 0.30 g Conceptual (0.30W) 2.40 22.29 0.96 (0.90) .0088 ULTIMATE
-~
I I,
Japanese (0.24W) 2.91 34.20 1.34 .0083
UBC (0.11W) 4.59 38.35 1.72 (1.35) .0137
UBC3 (0.12W) 4.55 34.06 1.61 .0148
UBC4 (0.13W) 4.44 30.48 . 1.50 .0157
UBC5 (0.15W) 4.12 24.84 1.31 .0168
UBC2 (0.30W) 2.15 7.08 0.53 .0189
I Foster City 0.28 g Conceptual 1.14 0.23 0.20 .0042 DAMAGEABILITY
Japanese 1.60 0.73 0.28 .0045
UBC 1.94 2.57 0.38 .0058
UBC2 0.85 0 0.14 .0075
Emeryville 260 0.26 g Conceptual 1.16 0.58 0.21 .0043 DAMAGEABILITY (south station) Japanese 1.59 1.34 0.29 .0045
UBC 1.07 O.D7 0.18 .0032
Sendal EW 0.22 g Conceptual 0.59 0 0.10 .0022 WORST ECGM
Japanese 0.74 0 0.12 .0021
UBC 1.21 7.82 0.40 .0036
TABLE 6.7 RESULTS FROM NONLINEAR THA OF SDOFS
309
Cy
increasing 11
a) strength spectra
elastic A < Inelastic A -!
~=1
elastic A>
~-·-,
b) displacement spectra
T
T
FIGURE 6.1 SCHEMATIC STRENGTH AND DISPLACEMENT DEMAND SPECTRA FOR EQGM RECORDED IN SOFT SOIL
310
I
I
,- -
( '
Tg T
a) raduclion of elastic 4 due to increase in S1iffness
b) increase in elastic 4 due to inaease in stiffness
p>1
T
c) reduction of inelastic 4 due to increase in stiffness
FIGURE 6.2 CHANGE IN DISPLACEMENT DEMAND DUE TO REDUCTION OF T FOR EQGM RECORDED IN SOFT SOIL
311
Sa/g 1.1
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
SCT-EW Ground Motion Effect of Damping on Elastic Strength Demand
••• -•••• ~ = 0.10 .· .... ~· ·· ....
I ·-.... .·· ...... / ~ = 0.20 '·. . . .· ,.-·--·-·--. ·. , ,;• ............. ....._ . .. · ·'· ~., ·,. .. --::.:-·..,., .................. · .
._ .......... ______ .:;..,:::::..·.., ......... ....... -· .. __ ...... . .... -,...:,:..--·--·---·--·
o~~~~~~~~~~~~~~~~~~~~
0.2 0.5 1.0 1.5 2.0 2.5 3.0 T (sees)
FIGURE 6.3 EFFECT OF DAMPING ON LINEAR ELASTIC RESPONSE FOR EQGM RECORDED IN SOFT SOIL
312
, I
I '
I I
: '
-VELOCITY (in/sec) VELOCITY (in/sec) 50
FOSTER CITY 0 25
SF 18 STORY BLDG. 350 T;" 1.15 T8• 1.3
40 20
30 15
'• 20 10 --f-
10 5
0 0
0.0 0.5 1.0 1.5 2.0 2.5 3.0 0.0 0.5 1.0 1.5 2.0 2.5 3.0 PERIOD (sec) PERIOD (sec)
VELOCITY (in/sec) VELOCITY (in/sec) I I 60 70
EMERYVILLE FFS 260
50 T
8a 1.5 60
50 v 40
40 30
30 20
20 ,:=...::::.:_
10 10
0 0 0.0 0.5 1.0 1.5 2.0 2.5 3.0 0.0 0.5 1.0 1.5 2.0 2.5 3.0
PERIOD (sec) PERIOD (sec)
VELOCITY (in/sec) VELOCITY (in/sec) 140
SCT EW 25
COLONIA ROMA NOOW
120 T;" 1.25
20 100
80 15
/'•
60 10
40 5
-"I 20 (
0 0 0.0 0.5 1.0 1.5 2.0 2.5 3.0 0.0 0.5 1.0 1.5 2.0 2.5 3.0
.-.:·,. PERIOD (sec} PERIOD (sec)
-FIGURE 6.4 PREDOMINANT GROUND PERIOD FOR VARIOUS SOFT SOIL
SITES
313
T= 1.7secs T•2.53secs T"' 1.7 sees T • 2.53 sees
a) Case 1
c T•1.7secs T• 2.53secs T•1.7secs T•2.53secs A
b) Case2
T •1.7 sees T • 2.53 sacs T • 1.7 sees T • 2.53 sees A
c) Case3
FIGURE 6.5 COMPARISON OF RESPONSE OF SDOFSs WITH T OF 1.7 AND 2.53 SECS
314
\ I
I '
I '
Story Moment of Inertia of Beams
30
25
20 .. ~
15
10
5
1 0.02 0.03 0.04 0.05 0.06
Inertia m4
I j
FIGURE 6.6 SIZES OF BEAMS
315
Story Moment of Inertia of Columns
30 COnceptual
25 Japanese min
Japanese max
20 UBC
-,.,",
15
10
5
1 0.01 0.02 0.03 0.04 0.05 0.06
Inertia m4
l I
FIGURE 6.7 SIZES OF COLUMNS
316
( I
~-- '
( '
SHEFlR CTCNl 10000
7SOO
sooa
2SCC
o.o !i.O
STORY 1
• STORY SHEAR CAPACITY o AIMED STORY SHEAR CAPACITY (l.SQo) • STORY SHEAR FORCE AT YIELDING LIMIT ~ THE FIRST DESIGN SHEAR FORCE (Qo)
7
e.o 12.0
OEFLECT I ON C:::
FIGURE 6.8 STORY SHEAR VS. STORY DRIFT CURVES OBTAINED FROM PUSHOVER ANALYSIS OF JAPANESE DESIGN
317
0.45
0.4
~ 0.35
= 0.3 .c 0 CD0.25 ~
0.2
0.15
0.1
0.05 ·' .· .·
Pushover Analysis
CONCEPTUAL
• ultimate strength
(first failure on a column)
UBC
.-~:::::::::::·: --- ::::::::::;:::::::~ first failure on a beam •#••-- ultimate strength
... first yielding . o~~~~~~~~~~~~~~~~~~~~~~
0 .2 .4 .60 .80 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 Tip Displacement [m]
FIGURE 6.9 BASE SHEAR VS. TIP DISPLACEMENT CURVES OBTAINED FROM PUSHOVER ANALYSES OF CONCEPTUAL AND UBC DESIGN
318
STORY 30
25
20
15
10
1
1- \~ 1-
\ i\ \
\ \ 1- \
\ ~ l
I I .,
1- I I
1- J I I
I I 1- I I . I . I I I
I
I I I . I
I ' v 1- I
/ / ~ I
/
I I a 2 CM/285CM
accounting for flexural cracking of each member
-------· neglecting flexural cracking of each member
FIGURE 6.10 IDI FOR JAPANESE DESIGN CORRESPONDING TO THE FIRST LEVEL OF DESIGN EARTHQUAKE FORCES
319
I I
i I
30
28
26 24
22
20
~ 18 0
OS 16
14
12
10
8 6
4 2
Story 30
25
20
15
10
5
Pushover Analysis
A •0.29m A •1.44m A •2.78m first yielding
a) Conceptual design
y~ \' , ... \\\ I.,_,,, I ..,"\ elastic I·:,, I,,
. \ :II>
I ifli\ I ''' -..,:, I jl I ··,·,- --
1 (1, \ '- <,··>·-\ \\ ' ---<~:.~.:.--I \ '- ·-1 • • --.• _
I \ '-. " ··-- ·-----1 ... ..., ··-. \ ·,, ........................ ........... ..............
l 3
-..., '\ 60
\.90 m ··; 1.20 m >· ) . m \.45 m ·'· m ~' ___ / ____ _ 1 _/ ...-/ _--- ____ .. -··-- ________ !1
1 = 1.50 m
I .· / -- .-·- ----) .... --<~:·-~·-.:..~.::.:.~- .. -·-- -=--- ------- tip displacement / .. ··-·-- .,,_ .. -
0.01 0. 15 0.02 0. 25 0.03 0. 35 0.04 101
b) UBC design
FIGURE 6.11 IDI FROM PUSHOVER ANALYSES OF CONCEPTUAL AND UBC DESIGN
320
Sa/g 1.8
1.8
1.4
1.2
1
0.8
0.6
0.4
SCT-EW, PGA = 0.3 g ~ "'0.05
· .•... -···-····~
0.2 ··••c;;;;·, ... ,.,,,.;;;;;;:;;;.;;;•;;;;;;;;;;;~;:;;;:;;;;,,=:::::::::::::::::::::::::::::::::::::·:.,:::::::~;:::;::=:;:_~:::·.:.iJ.: ~ o~~~~~~~~~~~~~~~~~~~
Disp (em) 200
175
150
125
100
75
50
25
0.5 1.0 1.5
a) pseudoacceleration
0.5 1.0 1.5
b) displacement
2.0
, ... -. . ....... .. _ ...
2.0
2.5 3.0 T (sees)
IJ.-1
2.5 3.0 T (sees)
FIGURE 6.12 STRENGTH AND DISPLACEMENT SPECTRA FOR SCT-EW EQGM SCALED TO PGA OF 0.3G (; = 0.05)
321
S8/g 1
0.8
0.6
0.4
0.2
0
SENDAI EW, MAXIMUM ACCELERATION 0.4g ~ = 0.03
0.2 0.5 1.0 1.5 2.0 2.5 3.0 T (sec)
a) pseudoacceleration Disp (em)
40
35
30
25
20
15
10
5
0 0.2 0.5 1.0 1.5 2.0 2.5 3.0
T (sec) b) displacement
FIGURE 6.13 STRENGTH AND DISPLACEMENT SPECTRA FOR SENDAI EW E(}GM SCALED TO MAXIMUM ACCELERATION OF 0.4G (; = 0.03)
322
I FLOOR R ~----------~~----~------~~----------~
30 ~----------~!~----+'--------~~!----------~ I : I
I / j/ 25 ~~---------~+-~---/~----~-~~------------~
~ I /, ;' 20~~----~.~~--~~/---+--~;_' __ ~----------~
1 //v/~-15 ~--~'----~,~~/--~'---------+------------~
II 0 / ~ ,~ =- ~~ .b I /~ !< I - 4/ v ~4.J' c I.<..,' v , "
I!-- ,/ ~ / .. 10 ~~.--~,~~~-~~-------------+------------~ I 1/ / ..
I 1/ / .. r , ,.
~ ~~~--------~-------------+------------~ .. -I//
t' 20 40 CiTl
FIGURE 6.14 ENVELOPE OF FLOOR DISPLACEMENTS FROM THA OF JAPANESE DESIGN (MAXIMUM ACCELERATION 0.4G)
323
STORI 30
25
20
15
10
5
1
1- \~ ···~-~
1- ',~ ~ ,,~~-~
', ~
-~1 "·~ 1- ~
'1,\ ' ~· \\ , I,
v I \ \ I I
1-
~~ J
I
I I
1- I \ ! ' ; i _( ( toT
~\ I ~
1- -ar ("') :; >r !; ~\ ~t
I ..... 7 1: I :::i .... I ! c
l I / v (
\ I
r I
1
\ I
~ 1- I I
~!::E2 ..
1-
~ -I I
a 1 • a 2.0 c:n/285 em
FIGURE 6.15 ENVELOPE OF 101 FROM THA OF JAPANESE DESIGN (MAXIMUM ACCELERATION 0.4G)
324
s raR·r
\
\ \
\
\
\ \
\
a 2000 4000
FIGURE 6.16 ENVELOPE OF STORY SHEARS FROM THA OF JAPANESE DESIGN (MAXIMUM ACCELERATION 0.4G)
325
Floor 30
28 26 24
22
20
18 16
14
12
10
8
6
4
2
Conceptual Design Floor Displacement
#;/ # f::} _,..;_0 e .- , .. 'lr
·i§' ... ..:···e .:~-• . e x:r··"'· .. j§i' , . ... , .
.•. ······Exterior Frame ..... ··•
... ·· ...... ·· ... ... .,.. ,. ,. , . ... .. ... .. ,. •. , . ..
. · ... · ... _,..• .• ... .• ·' .•
·' .".!·· ~·
0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 Displacement (m)
FIGURE 6.17 FLOOR DISPLACEMENTS FROM ELASTIC RSA FOR SERVICE (CONCEPTUAL DESIGN)
326
Story 30 28
26
24 22
20
18
18
14 12
10
8 8
4 2
Conceptual Design Exterior Frame IDI
Target Service 101-0.003
/ 0.0035 0.004 0.0045 0.005
FIGURE 6.18 101 FROM ELASTIC RSA FOR SERVICE (CONCEPTUAL DESIGN)
327
Story
30 28
26
24
22
20
18
16
14 12
10
8
6 4
2
Maximum Stress-Ratio Service Response Spectrum
Columns
.........
-~~-~sm stories 28, 29 ,30
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 Stress-Ratio
FIGURE 6.19 STRESS RATIOS FROM ELASTIC RSA FOR SERVICE (CONCEPTUAL DESIGN)
328
Floor 30
25
20
15
10
5
Elastic Analyses for Service Comparison of Floor Displacements
THA
1 ~~--~--~--~--,_--~--~~--~--~ ~ ~ ~ ~ ~ ~ M M M
Displacement (m)
FIGURE 6.20 FLOOR DISPLACEMENTS OBTAINED FROM ELASTIC ANALYSES FOR SERVICE (UBC DESIGN}
329
Story 30
25
20
15
10
5
Elastic Analyses for Service Comparison of IDI
'
' ' ' ' ' '
\
\
' ' \
' I
101
\
RSA \
I
' '
' I
' ' I ' \
'
' I
' . '
THA
FIGURE 6.21101 OBTAINED FROM ELASTIC ANALYSES FOR SERVICE
(UBC DESIGN)
330
storxo
25
20
15
10
Elastic and Nonlinear Analyses for Service Comparison of Story Shears
I
I
~ ', ·· .. ' ·.
\ · .. •,
.. Elastic ._ ..,JHA ''-RSA.\.
\ \
Nonlinear THA
\
' ' '
' '
-1000 1000 2000 3000 4000 5000 Shear{ ton)
FIGURE 6.22 STORY SHEARS OBTAINED FROM ELASTIC ANALYSES FOR
SERVICE (UBC DESIGN)
331
Elastic RSA Analysis for Service story Stress Ratios in Members
columns 30
.. · 25
20
15
10
1 ' 5
) 1 r-~--~---r--~--~--~--~~--~--~
3 4 5 10
Stress Ratio
FIGURE 6.23 STRESS RATIOS OBTAINED FROM ELASTIC ANALYSES FOR SERVICE (UBC DESIGN)
332
Floor 30
25
20
15
10
5
Nonlinear THA for Service Envelope of Floor Displacements
/SDOFS 30-story building
11--------.------r----,----,---+--..---.----,------r-----, -0.5 -0.4 -0.3 -0.2 -0.1 0.1 0.2 0.3 0.4 0.5
Displacement (m)
FIGURE 6.24 ENVELOPE OF FLOOR DISPLACEMENTS FROM 20 NONLINEAR THA FOR SERVICE (UBC DESI_GN)
333
Story 30
25
20
15
10
5
Nonlinear THA for Service Envelope of 101
~ SDOFS drift index
0.008 0.012
101
FIGURE 6.25 ENVELOPE OF 101 FROM 20 NONLINEAR THA FOR SERVICE
(UBC DESIGN)
334
Story 30
25
20
15
10
5
Nonlinear THA for Service Maximum Rotations in Members
no plastic behavior in columns
0. 0. Maximum Rotation
FIGURE 6.26 MAXIMUM PLASTIC ROTATIONS FROM 20 NONLINEAR THA FOR SERVICE (UBC DESIGN)
335
Story
30
25
20
15
10
5
Nonlinear THA for Service Maximum Accumulated Rotations in Members
no plastic behavior in oolumns
0.006 0.008 0. 1 0.012 Maximum accumulated rotation
FIGURE 6.27 CUMULATIVE PLASTIC ROTATIONS FROM 20 NONLINEAR THA FOR SERVICE (USC DESIGN)
336
30 ELASTIC THA for Service Floor Real + Accidental Eccentricities
30 ' ' ' ' '
25 ' N-S :
E-W 20
15
10
5
0 -1 -0.8 -0.6 -0.4 -0.2 0.2 0.4 0.6 0.8 1
Displacement (m)
FIGURE 6.28 ENVELOPE OF FLOOR DISPLACEMENTS FROM 3D ELASTIC THA FOR SERVICE (UBC DESIGN)
337
Sto
30
25
20
15
10
5
,
' ,
' I
' '
3D ELASTIC THA for Service Real + Accidental Eccentricities
/
,'
101
N-S E-W
'
'
0.003 0.006 0.009 0. 12
FIGURE 6.29 ENVELOPE OF IDI FROM 30 ELASTIC THA FOR SERVICE (UBC DESIGN)
338
Sto 30
25
20
15
10
5
' ' '
' '
3D Elastic THA for Service Real + Accidental Eccentricities
Nonlinear THA E-W
N-S---\
\
'
' '
' esign irst Vie d
-1000 1000 2000 3000 Shear(ton)
' .. ' '
' ' '
' '
4000 5000
FIGURE 6.30 ENVELOPE OF STORY SHEARS FROM 30 ELASTIC THA FOR SERVICE (UBC DESIGN)
339
Floor 30
28
26
24
22
20
18
16
14 12 10
8
6 4 2
Nonlinear THA for Safety Envelope of Floor Displacements
UBC
-1.2 -1 -0.8 -0.6 -0.4 -0.2 0.2 0.4 0.6 0.8 1.2 Displacements [m]
FIGURE 6.31 ENVELOPE OF FLOOR DISPLACEMENTS FROM 20 NONLINEAR THA FOR SAFETY (CONCEPTUAL AND UBC DESIGNS)
340
Story 30
28 26
24 22
20
18 18
14 12
10
8 8 101 safety
4 2
-o. 25
Nonlinear THA for Safety Envelope of I Dl
101
······-...
UBC
FIGURE 6.32 ENVELOPE OF IDI FROM 2D NONLINEAR THA FOR SAFETY (CONCEPTUAL AND USC DESIGNS)
341
Story 30 •.
28 '>·· ................
Nonlinear THA for Safety Plastic Rotations in Beams
---·-.......... .,:::· ....
··~··~···-·~····~··········-·~ .. ,.::-:. .. i .......
.....
------- e ace -Conceptual
28
24 22
20 18
18
14 12
10
.. ..... e max- UBC _ ... .:::. ... ·.....---
8 8 4 2
... '"> ~ ... ····..... Leacc-UBC ...... ..... ................ ........ ,
' .......... ·····• e max -Conceptual
-·· -·········---···----......... .--···-----·--······-··· _ _...,
0.075 8ph
0.1 0.125 0.15
FIGURE 6.33 PLASTIC ROTATIONS IN BEAMS FROM 2D NONLINEAR THA FOR SAFETY (CONCEPTUAL AND UBC DESIGNS)
342
I
Story 30 ;
28 ....... 28 ~.7
24 \ 22 .~··
\ 20l 18 16
14 12
10 8
6
Nonlinear THA for Safety Plastic Rotations in Columns
9 ace = 9 max - Conceptual
4 . 9max-UBC
2 i 9acc-UBC
0.02 0.03 0.04 8ph
FIGURE 6.34 PLASTIC ROTATIONS IN COLUMNS FROM 20 NONLINEAR THA FOR SAFETY {CONCEPTUAL AND UBC DESIGNS)
343
• plastic hinge
FIGURE 6.35 ROTATIONS IN BEAMS AND COLUMNS OF UBC DESIGN
344
I
Sa/g 1
0.8
0.6
0.4
Disp (em) 40
35
30
25
20
15
10
5
EMERYVILLE 260, SOUTH STATION ~ = 0.05
0.5 1.0 1.5 2.0 2.5 3.0 - T (sec)
a) pseudoacceleration
0.5 1.0 1.5 2.0 2.5 3.0 T (sec)
b) displacement
FIGURE 6.36 STRENGTH AND DISPLACEMENT SPECTRA FOR EMERYVILLE 260 EQGM, SOUTH STATION(;= 0.05)
345
S8/g 1
0.8
0.6
0.4
0.2
FOSTER CITY ~ = 0.05
o~~~~~~~~~~~~~~~~~ 0.1 0.5 1.0 1.5
a) pseudoacceleration
disp (em) 50
45
40
35
30
25
2.0 2.5 3.0 T (sec)
20 .................. __ _
15 ...... ...- ~ = 3 1 0 ......... -·-········-.... _ ... ----~·:--:"~ ....... - -- . ' ..
...-·-.. _,... ~ ~ ~ - ~ ... ~ .._ :.::.. .. ~---=--~--: # - • • ........ 4 5 /---·=·~~(--·.,_:;::.·::::~~-- ·- ..... ~ =
...-:.v--· 'v·· .,;_.,-
o~~~~~~~~~~~~~~~~~
0.1 0.5 1.0 1.5
b) displacement
2.0 2.5 3.0 T (sec)
FIGURE 6.37 STRENGTH AND DISPLACEMENT SPECTRA FOR FOSTER CITY EQGM (; = 0.05)
346
I
I
I
REFERENCES
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348 I
York, New York, 1975.
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349
