effect of randomly distributed infills on seismic base shear for rc buildings with soft ground floor...

EFFECT OF RANDOMLY DISTRIBUTED INFILLS ON SEISMIC

BASE SHEAR FOR RC BUILDINGS WITH SOFT GROUND FLOOR

Submitted by

Jahid Hasnain

Submitted to the

DEPARTMENT OF CIVIL ENGINEERING

BANGLADESH UNIVERSITY OF ENGINEERING AND TECHNOLOGY

In partial fulfillment of requirements for the degree of

BACHELOR OF SCIENCE IN CIVIL ENGINEERING

2009

DECLARATION

This is hereby declared that the studies contained in this thesis is the result of

investigation carried out by the author except for the contents where specific

references have been made to the investigation of others.

The whole thesis is done under the supervision of Professor Dr. Khan Mahmud

Amanat (Department of Civil Engineering, BUET) and no part of this thesis has been

submitted concurrently for any degree or other qualification to any other institution.

Signature of author

(Jahid Hasnain)

ACKNOWLEDGEMENT

My profound gratitude to almighty Allah for his unlimited kindness and blessings for

what this effort has been successfully carried out.

I wish to express my deepest thanks to Dr. Khan Mahmud Amanat, Professor,

Department of Civil Engineering, BUET for his encouraging supervision al through

the study. His systematic and invaluable guidance with affectionate persuasion have

helped me greatly during the study.

My special gratitude to my parents, the source of inspiration for all my efforts and

achievements.

ABSTRACT

The common design practice of RC framed building now-a-days is to keep provision

for parking facilities. To do so the whole structural system gets the characteristics of

soft story and that’s vulnerable to seismic load. Regular design practice (According to

BNBC, 1993) of such RC frame is carried out without considering the structural effect

of masonry infill and thus the design becomes really unsafe under lateral load. Now-a-

days in Bangladesh an extensive urbanization process is going on and apartment

buildings with such unsafe design may face disastrous phenomena under medium

strength earthquake.

The equivalent static force method (ESFM) we use to find the base shear can’t

consider the structural effect of masonry infill and the base shear value is

underestimated irrespective of the amount of infill application or not. This study will

be confined to analyze the effect of random applied structural infill and observe the

variation in base shear value for the uncertain infill location for different parameters.

To sort out the actual behavior of masonry infill as structural component of RC frame

system a numerical study has been carried out using response spectrum method

(RSM). The study was involved to find the base shear modification due to the

application of random infill with soft ground floor and to get safe design value for

such structurally modified building system

It’s investigated that random application of infill makes the structure behave

differently and the base shear value varies in a certain range for same percentage of

infill. It makes the building frame stiffer at some locations and modifies the natural

period for the random location of infill at structure in presence of soft floor. The

structural sway characteristic also changes tremendously. As a result the base shear

value increases than that we find by ESFM and the ground floor sway gets high

enough to cause failure of the structure. For design simplicity and safety, a

modification factor for such soft floor system is sorted. Thus a suitable modification

factor is expected to be suggested for the safe design of MI-RC framed structure

against seismic vulnerability.

CONTENTS

DECLARATION ii

ACKNOWLEDGMENT iii

ABSTRACT iv

LIST OF FIGURES vii

LIST OF TABLES xi

BBREVIATIONS xii

Chapter 1: INTRODUCTION

1.1 GENERAL 1

1.2 BEHAVIOR OF MI-RC FRAME UNDER EARTHQUAKE LOAD 2

1.3 OBJECTIVE AND SCOPE OF THE STUDY 4

1.4 ASSUMPTIONS FOR MODELING SIMPLICITY 4

1.5 ORGANIZATION OF THE THESIS 5

Chapter 2: LITERATURE REVIEW

2.1 INTRODUCTION 6

2.2 BEHAVIOR OF MASONRY INFILLED RC FRAME UNDER LATERAL LOAD 7

2.3 COMPUTATIONAL MODELLING AND ANALYSIS OF INFILLED FRAME 11

2.3.1 Equivalent Diagonal Strut Method 12

2.3.2 Coupled Boundary Method 14

2.3.3 Plasticity Model 15

2.3.4 Approximate Method 15

2.4 CHOICE OF MODEL 17

2.5 MODELING FOR EQUIVALENT DIAGONAL STRUT APROACH 17

2.5.1Beam and Column Moment Capacity 18

2.5.2Determination of Equivalent Strut Stiffness 19

2.6 EFFECT OF EARTHQUAKE ON BUILDING FRAME WITH SOFT STORY 23

2.7 CONSIDERATION OF SOFT STORY IN DIFFERENT BUILDING CODES 25

2.7.1 Without Considering Soft Story Phenomenon 25

2.7.2 Considering Soft Story Phenomenon 27

Chapter 3: FINITE ELEMENT MODELING OF INFILL FRAME

3.1 INTRODUCTION 28

3.2 SOFTWARE FOR FINITE ELEMENT ANALYSIS 28

3.3 ASSUMPTIONS FOR MODELING SIMPLIFICATION 28

3.4 CHARACTERIZATION OF STRUCTURAL COMPONENTS IN MODEL 29

3.4.1 BEAM4 (3-D Elastic Beam) for Beam and Column 29

3.4.2 Shell63 (Elastic Shell) for Slab 31

3.4.3 MASS21 (Structural Mass) for load application 33

3.4.4 LINK8 (3-D Spar or Truss) for load application 34

3.4.5 Support Condition 35

3.4.6 Load application 35

3.5 SEISMIC LOAD CALCULATION 36

3.5.1 Static Analysis (Equivalent static Force Method) 37

3.5.2 Modal Analysis 37

3.6 MODEL CHARACTERISTICS FOR ANALYSIS 46

CHAPTER 4: ANALYSIS OF RESULTS AND DISCUSSION

4.1 INTRODUCTION 47

4.2 SCOPE OF STUDY 47

4.3 VARIATION IN BASE SHEAR FOR RANDOM APPLICATION OF INFILL 47

4.3.1 Range of variation in base shear value 48

4.3.2 Modification factor for different parameters 48

CHAPTER 5: CONCLUSION AND RECOMMENDATION

5.1 GENERAL 74

5.2 FINDINGS OF THE INVESTIGATION 74

5.3 RECOMMENDATION FOR FUTURE STUDY 75

REFERENCE 76

APPENDIX: ANSYS SCRIPT USED IN THE ANALYSIS 79

LIST OF FIGURES

Figure Caption Page No.

1.1 Soft story collapse (Golcuk, Tuskey 1999) 3

1.2 Soft story collapse of ground floor (Loma-Prieta-1999) 3

1.3 Soft story collapse (Hanwang hospital 1999) 3

1.4 Failure due to ground cracks (Tungshih,1999) 3

2.1a Multistoried apartment building with open ground floor for parking 6

2.1b Soft story mechanism 7

2.2 Change in lateral load transfer mechanism due to masonry infills 8

(Murty and Jain 2000)

2.3 Interactive behavior of frame and infill 9

2.4 Analogous braced frame 9

2.5 Modes of infill failure 10

2.6 Modes of frame failure 10

2.7 Material modeling of masonry infill as diagonal strut 12

2.8 (a) Masonry infilled frame sub-assemblage in masonry infill panel frame 12

2.8 (b) Masonry infill panel in frame structure 13

2.8 (c) Constitutive model for infill panel by Madanl et. Al. (1997) 13

2.8 (d) Strength envelope for infill panel by Madanl et al. (1997) 14

2.9 Proposed composite yield criterion with iso-shear stress lines 16

2.10 Frame forces equilibrium 19

2.11 Open ground story building

(a) actual building 24

(b) building being assumed in current design practice 24

2.12 Effects of masonry infills on the first mode shape of a typical frame of a

ten story RC building , Displacement profile

(a) fully infilled frame 24

(b) open ground floor frame 24

3.1 BEAM4 Geometry 29

3.2 SHELL63 Geometry 31

3.3 MASS21 Geometry 33

3.4 Fig. 3.4 LINK8 Geometry 34

3.5 Finite Element modeling of total structure 36

3.6 Normalized response spectra for 5% Damping ratio 38

3.7 Different patterns of random infill application (6 storied building) 39




3.7 (a) First mode shape 44

3.7 (b) third mode shape 44

3.7 (c) Sixth mode shape 45

3.7 (d) Seventh mode shape 45

3.7 (e) 10th mode shape 45

3.7 (f) 15th mode shape 45

4.1 Variation in base shear value (RSM) of 6 storied building for random 49

infill pattern (no infill on Ground floor and 20% infill on upper floors)








infill pattern (20% infill on Ground floor and 20% infill on upper floors)







4.9 Base shear variation of 8 storied building for random application of Infill 53

(20% on upper floors) with no infill on ground floor








(20% infill on ground floor and 20% infill on upper floors)








(20% infill on upper floors) with no infill on ground floor































4.33 Base shear comparison between ESFM and RSM 65

(20% infill on upper floors with no infill on ground floor)








(20% infill on upper floors with 20% infill on ground floor)







4.41 Modification factor for no infill on GF and 20% infill on upper floors 70




4.45 Modification factor for 20% infill on GF and 20% infill on upper floors 71




4.49 Modification factor for different number of spans for a 6 storied building 73

with 40% infill on upper stories and no infill on GF

LIST OF TABLES

Table Caption Page No.

3.1 Values and dimensions for the parameters and structural components 46

4.1 Base shear variation of 6 storied building for random application 49

of Infill (in different percentage) with no infill on ground floor


of Infill (in different percentage) with 20% infill on ground floor


of Infill (in different percentage) with no infill on ground floor

4.4 Base shear variation of 8 storied building for random 55

application of Infill (in different percentage) with 20% infill on ground floor


application of Infill (in different percentage) with no infill on ground floor




application of Infill (in different percentage) with no infill on ground floor



4.9 Modification factor for different no. of spans for 69

a 6 storied building with 40% infill on upper stories and no infill on GF

ABBREVIATIONS

ESFM - Equivalent Static Force Method.

RSM - Response Spectrum Method.

BNBC - Bangladesh National Building Code

σy - Vertical Compressive stress

τxy - Shear stress

E - Young’s Modulus of elasticity

K - Stiffness of the structure

fm´ - masonry prism strength

Vm - maximum lateral force

um - Displacement corresponding to the lateral force

Ad - Area of equivalent diagonal strut

Ld - Length of equivalent diagonal strut

Mn - nominal moment

As - Steel area

fy - yield strength of steel

fc’ - strength of concrete

ρ - Density

σ - Poisson’s ratio

V - Design base shear

Z - Seismic zone coefficient

I - Coefficient of structural importance

C - Numerical coefficient

R - Response modification factor for structural system

W - Total seismic Dead load

T - time period of natural vibration

S - Seismic zone coefficient

DL - Dead Load

LL - Live load

PW - Partition wall

MI - Masonry Infill

CHAPTER 1

INTRODUCTION

1.1 GENERAL

Earthquake vulnerability of building has been a major concern for structural

engineers. A proper way of increasing seismic resistance mechanism has always been

a prime concern to ensure a safe structural system. The modern concept shows that

the capability of withstanding earthquake depends on the ability of absorbing seismic

energy coming on structure as shear. Suitable stiffness proportion for whole structural

system can control the base shear effect on building.

Primary objectives of infill application are to functioning as partition wall, exterior

wall for internal privacy, around stairs and service shafts. With the primary functions

the masonry infill also acts as structurally active component. The structural infills

brace the frame laterally and increase the stiffness of the surrounding frame units. For

simplicity of structural design the lateral strength and stiffness modification effect of

infill is not taken into consideration and the building system is not being designed as

proper seismic resistant structure. The effect of earthquake is more serious under the

soft ground floor form of structure. The floor system (normally ground floor) without

any partition wall (either masonry or RC wall) between columns is called soft floor

system. This system is introduced to provide parking facilities in high-rise apartment

buildings but the process makes the upper floors stiffer than the soft ground floor.

The horizontal bracing act of infill modifies the vibration behavior of the building

frame. The natural period of building is modified due to the mass contribution on total

weight and due to the increase of inplane rigidity on upper floors. Conventional

analysis techniques don’t consider infill as structural component and the structural

behavior of building frame is different under seismic load than predicted. Presence if

masonry infill on upper floors making them stiffer causes rigid body movement under

seismic vibration. Thus the columns at open ground floor not being strong enough get

damaged permanently under horizontal vibration. The structural collapse of soft floor

system is a serious issue as this is the most common practiced commercial system of

RC building frame now-a-days. So the structural effect of masonry infill is to be

recognized and the proper modification on RC frame design procedure should be

adopted.

1.2 BEHAVIOR OF MI-RC FRAME UNDER EARTHQUAKE

LOAD

The challenge of a structural engineer is to design the building frame in such a way so

that the damage during earthquake can be controlled under acceptable limit without

causing risk of life. The design of most of the building frame is done considering base

shear less than elastic base shear corresponding to the strongest vibration due to

earthquake at that site. The dynamic analysis is not applied in most cases. As a result,

many structures have failed or severely damaged during earthquake. Extensive studies

have been carried out to find the options of seismic vulnerability and their remedy.

The elementary cause of seismic failure is the detachment of exterior cladding of

parapets and various non structural elements of the building. Such detachment may

cause progressive collapse of structure in absence of alternative load paths. An

obvious characteristic of lateral load resisting system is to be capable of providing

continuous load path to the foundation so that the inertial loads developed due to

acceleration of individual elements are transferred to floor diaphragm then to vertical

element then to foundation and finally to the ground. Inadequate toughness and

strength of individual elements and failure to tie them as combined body the

individual elements or whole structure can be collapsed. Sudden change in stiffness,

mass or strength creates discontinuity in structural load path and results lateral load

distribution and deformation differently from anticipated. Such discontinuity of load

paths happens due to change in structural system in vertical direction, change in story

height and material, unanticipated participation of non structural elements etc. Such

discontinuity tend to cause the inelastic deformation be concentrated at the

discontinuity. Now-a-days the most common form of vertical discontinuity is the

application of infill on upper floors keeping the ground floor open. The discontinuity

of stiffness and strength of the structure with upper floors to the ground causes huge

deformation at ground level and causes failure to structures.

Fig-1.2 Soft story collapse of ground floor of a

building at San-Francisco

(Loma-Prieta-1999)

Fig-1.1 Soft story collapse due to

excessive deformation of ground

floor (Golcuk, Tuskey 1999)

Fig-1.4 Failure due to ground

cracks (Tungshih,1999)

Fig-1.3 Soft story collapse

(Hanwang hospital 1999)

1.3 OBJECTIVE AND SCOPE OF THE STUDY

The objective of the present study is to sort out the base shear modification under the

action of earthquake load on masonry infilled RC frame having open ground floor.

The elementary goal is to feature on the consideration of combined structural effect of

infill with soft ground floor compared to bare frame. The specific objectives of the

investigation can be summarized as follows;

To develop a 3D finite element model of building with infill on upper floors

and soft ground floor.

Modeling of infill as diagonal struts and applied in different percentage

randomly on frame system.

To analyze the building system (featuring certain variables) by both

Equivalent Static Force Method (ESFM) and dynamic Response Spectrum

Method (RSM) following Bangladesh National Building Code (BNBC, 1993).

Comparison of base shear values by the two methods for certain structural

variables.

To analyze the variation in base shear for same percentage of randomly

applied infill in different patterns.

To obtain some modification factor for base shear respective to the traditional

design value by ESFM.

To study the change in modification factor with change of span no. and length.

There are a number of factors and variables on which the study can be carried but

here, the base shear value for earthquake load on infilled structure will be focused and

analyzed. Buildings with regular and symmetric geometry will be considered only.

1.4 ASSUMPTIONS FOR MODELING SIMPLICITY

The investigation is based on the following assumptions;

Material is linearly elastic and isotropic

All dead and live loads are taken as vertical while only earthquake load is

taken as lateral

Infill is modeled as diagonal strut with same homogeneous material properties

of concrete

Dead load including infill (partition wall) mass contribution is modeled as

mass element with vertical acceleration only

1.5 ORGANIZATION OF THE THESIS

The whole thesis is organized into five chapters. Chapter 1 introduces the present

study while Chapter 2 focuses on the review of relevant theories, methods of analysis

and behavior of RC frame with infill. Chapter 3 illustrates the methodology of finite

element modeling by suitable program package. Chapter 4 is organized with analysis

and discussion on output results based on various parameters. Chapter 5 is for the

summary of findings from current study and concluding recommendations for future

investigation and extension of this work.

CHAPTER 2

LITERATURE REVIEW

2.1 INTRODUCTION

To accommodate shelter for urban population a huge volume of multistoried building

has been being constructed from last few years. Normal trend is to provide parking

facilities by keeping open story at ground level or basement while there are brick

masonry infill wall panels at the upper floors. This building procedure makes the

upper floors stiffer and a soft story on ground floor.

Irregularities of lateral stiffness in vertical direction are occurred due to the

application of random infill on different floor levels with open ground floor. As a

result a soft story mechanism is developed. According to the Bangladesh National

Building Code (BNBC, 1993) a soft story is defined as one that has lateral stiffness

less than 70% of the story above or below. Modification in stiffness and response

characteristics of building frame under lateral load is greatly influenced due to the

soft floor phenomenon. That’s why negative effects like stress concentration on upper

floor levels, great deflection at ground floor columns are causing failure of ground

Fig-2.1a Typical multistoried apartment building with open ground floor for parking

facility

floor columns under lateral loads. From the structural point of view the soft floor

mechanism (fig-2.1 b) under lateral load (mainly the earthquake) has been a major

concern for structural engineers. The research results under different structural

combinations tend to conclude with controversial outcomes. So, assessing the

characteristics of seismic behavior of such masonry infilled Reinforced Concrete

structure are sill causing difficulties in design application. This analytical research

will help to analyze the range of variation of structural behavior of such type of RC

frame system with random application of masonry infill.

In reality the design is done assuming no infill contribution in most of the cases

because of the absence of adaptable ideal procedures to count the effect of infill on

frame structure.

The significance of strength contribution and modification of masonry infill in RC

frame under lateral load is recognized from few decades and some practical

application of some research outputs is trying to be established under regular

simplified form. Here the application features and limitations of these approaches will

be highlighted and an acceptable conclusion for effect of random infill application

will be attempted to formulate.

2.2 BEHAVIOR OF MASONRY INFILLED RC FRAME UNDER

LATERAL LOAD

The masonry infill is used to fulfill some functional requirements of the building

structure like partitioning, providing building envelope, temperature & sound barrier

Fig-2.1b Soft story mechanism

etc. The structural contribution of masonry infill under seismic load is not considered

correctly due to the lack of analytical knowledge.

Researchers (Klingner and Bertero in 1978, Bertero and Brokkenc in 1983, Mehrabi

et al. in 1996) have concluded that the proper and careful use of infill can

significantly increase the strength and stiffness of structure subjected to seismic

excitations. To ensure the adequate safety of building the selection of infill location

must be such that the torsional and soft story effect is minimized under architectural

restrictions.

In 3D RC frame system the confined masonry infill walls contribute a vital part on

resisting lateral seismic loads on building. To develop a logical approach of designing

such RC frames the behavior of masonry infill is closely investigated (Moghaddam

and Dowling in 1987, Smith and Coul in 1991, Murty and Jain in 2000). It was also

investigated experimentally that the masonry infill walls have a very high lateral

stiffness and low deformability. So, the application of masonry infill in RC frames

changes the lateral load transfer mechanism from predominant frame action to

predominant truss action as shown in fig-2.2.

Under the effect of high in plane rigidity of the masonry wall the relatively flexible

frame is stiffened significantly. The relatively stiff bracing system is contributed

partly by its in plane shear resistance (Fig. 2.3) and by the behavior as diagonal

bracing strut.

(a) Predominant frame action (b) Predominant truss action

Fig. 2.2 Change in lateral load transfer mechanism due to masonry infills

(Murty and Jain 2000)

Under horizontal loading the frame is deformed with double-curvature bending of the

columns and beams. The translation of the upper part of the column in each story and

the shortening of the loading diagonal of the frame causes the column to learn against

the wall as well as to compress the wall along its diagonal. It’s roughly analogous to a

diagonal braced frame (Fig. 2.4).

Fig. 2.3 Interactive behavior of frame and infill

Fig. 2.4 Analogous braced frame

The potential modes of failure of masonry infilled frame structure are occurred due to

the interaction of infill walls with frame.

The failure modes are given below (Fig. 2.5 and 2.6):

Tension failure of tensioning column due to overturning moments.

Flexure or shear failure of the columns.

Compression failure of the diagonal strut.

Diagonal tension cracking of the panel and

Sliding shear failure of the masonry along horizontal mortar beds.

Fig. 2.5 Modes of infill failure

Fig. 2.6 Modes of frame failure

The perpendicular tensile stresses are caused by the divergence of the compressive

stress trajectories on the opposite sides of the leading diagonal as they approach the

mid region of the infill. The shear failure of wall steps down through the joints of

masonry and participated by the horizontal shear stresses in the bed joints. The

diagonal cracking of the wall is through the masonry along a line or line parallel to

the loading diagonal and caused by tensile stresses perpendicular to the loading

diagonal. The perpendicular tensile stresses caused by the divergence of the

compressive stress trajectories on opposite sides of the loading diagonal as they

approach the middle region of the infill. The diagonal cracking is initiated and

spreads from the middle of the infill while the tensile stresses are at maximum

tending to stop near the compression corners, where the tension is suppressed.

The nature of the forces in the frame can be understood by referring to the analogous

braced frame shown in (fig. 2.4). The windward column or the column facing the

seismic load first is in tension and the leeward column or the other side of the

building facing seismic load last is in compression. Since the infill bears on the frame

not as exactly a concentrated force at the corners, but over the short lengths of the

beam and column adjacent to each compression corner, the frame members are

subjected also to transverse shear and a small amount of bending. Consequently the

frame members or their connections are liable to fail by axial force or shear and

especially by tension at the base of the windward column.

2.3 COMPUTATIONAL MODELLING AND ANALYSIS OF

INFILLED FRAME

Different types of modeling approach were attempted for featuring infill

characteristics in RC frame. Holmes (1961) replaced the infill by an equivalent pin-

jointed diagonal strut. Smith (1962) conducted a series of tests on laterally loaded

square mild steel frame models infilled with micro-concrete. From the model

deformation results he concluded that the wall could be replaced by an equivalent

diagonal strut connecting the loaded corners. As the elastic methods were not able to

fully feature the actual characteristics of infilled frames, attention was paid to the

theories of plasticity. Wood (1958) extended the limit analysis of plasticity with the

assumption of perfect plasticity. Recently a method was developed by Saneinejad

(1995) that allows for interface shear forces and both the elastic and plastic behavior

of material. The stiffness of structural system is determined with variations in

geometrical and mechanical characteristics. The analysis is carried out utilizing the

boundary element method (BEM) for the infill and dividing the frame into finite

elements, so as to transform the mutual interactions of the two subsystems into

stresses distributed along the boundary for the infill and into nodal actions for the

frame. Some of the methods of analyzing the infilled frames are discussed in

following sections.

2.3.1 Equivalent Diagonal Strut Method

The first published research on modeling of infill panel as an equivalent diagonal

strut method was applied by Holmesh (1961). He assumed that the infill wall acts as

diagonal compression strut as shown in (fig-2.7) of the same thickness and elastic

modulus as the infill with a width equal to one-third the diagonal length. He also

concluded that at the infill failure, the lateral deflection of the infilled frame is small

compared to the deflection of the corresponding bare frame.

Fig. 2.7 Material modeling of masonry infill as diagonal strut

Fig. 2.8 (a) Masonry infilled frame sub-assemblage in masonry infill panel frame

Saneinejad and Hobbs (1995) developed a method based on the equivalent diagonal

strut approach for the analysis and design of steel or concrete frames with concrete or

masonry infill walls subjected to in-plane forces. The method takes into count the

elasto-plastic behavior of infilled frames considering the limited ductility of infilled

materials. Governing factors like infill aspect ratio, shear stresses at the infill-frame

interface, relative beam and column strength are taken into account for this

development.

The analytical assumptions are the contribution of the masonry infill panel (fig-2.8 a)

to the response of the infilled frame can be modeled by replacing the panel by a

system of two diagonal masonry compression struts (fig-2.8 b). The stress-strain

relationship for masonry in compression (fig-2.8 c) used to determine the strength

envelope of the equivalent strut, can be idealized by a polynomial function. Since the

tensile strength of masonry is negligible, the individual masonry struts are considered

Fig. 2.8 (b) Masonry infill panel in frame structure

Fig. 2.8 (c) Constitutive model for masonry infill panel by Madan et al. (1997)

to be ineffective in tension. However, the combination of both diagonal struts provide

a lateral resisting mechanism for the opposite lateral directions of loading. The lateral

force-deformation relationship for the structural masonry infill panel is assumed to be

a smooth curve bounded by a bilinear strength envelope with an initial elastic

stiffness until the yield force Vy and there on a post yield degraded stiffness until the

maximum force Vm is reached (fig-2.8 d). The corresponding lateral displacement

values are denoted as uy and um respectively.

The analytical formulations for the strength envelope parameters were developed on

the basis of the available “Equivalent strut model” for infilled masonry frames.

2.3.2 Coupled Boundary Method

Papia (1998) developed a method to analyze infill in which the behavior of infilled

frames subjected to horizontal loads by an iterative procedure. The stiffness of the

structural system is determined with variations in geometrical and mechanical

characteristics. The stiffness contribution by brickwork or concrete panels in

reinforced concrete or steel frames can provide to be decisive in relation to structural

safety. The analysis is carried out using boundary element method (BEM) for the

Fig. 2.8 (d) Strength envelope for masonry infill panel by Madan et al. (1997)

infill and opportunely dividing the frame into finite elements, so as to transform the

mutual interactions of the two systems into stresses distributed along the boundary for

the infill and nodal actions for the frame. This makes it possible to take into account

the separation arising between the two substructures when mutual tensile stresses are

involved.

At first, infill without opening are considered, using BEM with constant elements for

two dimensional problems in elasticity. Then the result is compared with those

obtained using the simplified equivalent pin-jointed strut model.

2.3.3 Plasticity Model

A method of analyzing of infill based on plasticity theory which is adopted to

describe the inelastic behavior utilizes modern algorithmic concepts, including an

implicit Euler background return mapping scheme, a local Newton-Raphson and a

consistent tangential stiffness matrix. It features tensile fracture energy and

compressive fracture energy. The framework of plasticity theory is generally

adequate to apply to both isotropic and anisotropic behavior. In anisotropic plasticity

models the hardening behavior has been simulated with the fraction model. An

accurate analysis of anisotropic materials requires a description for all stress states.

The yield criterion proposed for this study combines the advantages of modern

plasticity concepts with a powerful representation of anisotropic material behavior,

which includes different hardening/softening behavior along each material axis. For

modeling orthotropic material behavior, a Hill-type criterion for compression and

Rankine-type criterion for tension are proposed (fig). The model is formulated in such

a way that each internal parameter is related to two independent fracture energies

along each material axis.

2.3.4 Approximate Method

An approximate method has been suggested by Smith and Coull (1985). It may be

classified as elastic approach except for the criterion used to predict the infill

crushing. A plastic type masonry infill is assumed. Stresses in the infill relating to

shear failure of the infill is related to the combination of of shear and normal stresses

included at points in the infill when the frame bears on it as the structure is subjected

to the external lateral shear.

An extensive series of plane stress membrane finite-element analysis has shown that

the critical values of this combination of stresses occur at the centre of the infill and

that they can be expressed empirically by,

Shear stress, τxy=Lt

Q43.1 2.1

Vertical Compression stress, 𝛔y= Lt

QLh )2.0/8.0( 2.2

Stresses in the infill relating to diagonal tension failure are related to the maximum

value of diagonal tensile stress in the infill. This occurs at the centre of the infill and

based on the result of the analysis it may be expressed empirically as

Diagonal Tensile stress, 𝛔d= Lt

Q58.0 2.3

Where,

Q is the horizontal shear load applied by the frame to the infill of length L, height h and

thickness t.

These stresses are governed mainly by the proportion of the infill. They are little

influenced the stiffness properties of the frame because they occur at the centre of the

infill away from the region of contact with the frame.

Fig. 2.9 Proposed composite yield criterion with iso-shear stress lines

2.4 CHOICE OF MODEL

Among the computational models discussed previously the approximate method is

primarily intended for preliminary through manual calculation. Plasticity and

Boundary Element Method are based on continuum plasticity approach in which the

infill is modeled as an assemblage of several plane stress elements via special

interface element. Such model is suitable for detailed or micro level study of the

stress, strain, damage, cracks, failure at various locations of primary interest of the

infill panels. Such model is not suitable for investigating overall structural behavior

of building where infill is only a structural component. In that case equivalent strut

model is more suitable. The equivalent diagonal strut model using time rate

independent constitutive features can be used for a static non linear analysis as well as

time history analysis. The same model can be featured with hysteretic formulation for

static monotonic analysis and quasi-static cyclic analysis. The equivalent diagonal

strut model considers the entire infill panel as a single unit and takes into account

only the equivalent global behavior. As a result the approach does not permit study of

local effect such as frame iteration within the individual infilled frame sub-

assemblage. Plasticity and Boundary Element approach are used to capture the spatial

and temporal variations of local conditions within the infill. However the equivalent

strut model allows for adequate equivalence of the nonlinear force deformation

response of the structure and individual components under lateral load. Thus the

macro model is better suited for representing the behavior of infill in nonlinear time-

history analysis of large or complex structures with multiple components. Therefore,

the equivalent diagonal strut model is selected for modeling and analyzing the

characteristics of infilled frames.

2.5 MODELING FOR EQUIVALENT DIAGONAL STRUT

APROACH

For the infilled masonry frame shown in fig, the maximum lateral force Vm and

corresponding displacement um in the infill masonry panel (Saneinejad et al. 1995)

are

Vm± = Ad f´m cosθ ≤

cos)tan45.01(

lvt≤

cos

83.0 lt 2.4

um± =

cos

dm L 2.5

where, t = thickness of the panel

l´ = lateral dimension of infill panel

f´m = masonry prism strength

ε´m = corresponding strain

θ = inclination of diagonal strut

v = basic shear strength of masonry

Ad and ld = area and length of the equivalent diagonal struts respectively

calculated as,

Ad =

cos

)1(c

bb

c

ccc

ftl

fth

≤ 0.5cos

c

a

f

fht

2.6

Ld = ])1[( 222 lhc 2.7

The quantities αc, αb, 𝛔c, τb, fa and fc depend on the geometric and material properties

of the frame and infill panel. These can be estimated using the formulations of the

‘Equivalent Strut Model’ proposed by Saneinejad et al. (1995). The lateral yield force

Vy and displacement of the infill panel may be calculated from geometry

Vy± =

α)(1

uαK-Vm m0

2.8

um±

= )1(

uK-Vm m0

2.9

The initial stiffness K0 of the infill masonry panel may be estimated using the

following formula (Manad et al. 1997)

K0 = 2(Vm/um) 2.10

The parameters Vm, Vy, um, uy, K0 are shown in figure 2.8.

2.5.1 Beam and Column Moment Capacity

To find out the stiffness of equivalent strut (K0) it requires to determine the following

properties of beam, column and joint,

Mpc = Plastic resisting moment of column

Mpb = Plastic resisting moment of beam

Mpj = Plastic resisting moment of joint

To determine the Mpc and Mpb it requires to provide reinforcement in beams and

columns. These moments can be calculated on the basis of the following formulae,

Mn = Asfy(d-2

a) 2.11

And a = bf85.0

fA

c

ys

2.12

2.5.2 Determination of Equivalent Strut Stiffness

The equivalent strut model proposed by Saneinejad and Hobbs (1995) and later

modified by Madan et al. (1997) is discussed here in details.

Mathematical derivation of equivalent strut model

It begins with the idealized free body diagram of an infill panel and the surrounding

frame as shown in figure 2.10

From figure 2.10, r = l

h< 1 2.13

Where, r = aspect ratio of the frame

h= centre to centre height of the beam

l = centre to centre height of column

Fig. 2.10 Frame forces equilibrium

r´ = l

h

< 1 2.14

Where, h’= height of infill

l’ = length of infill

tanθ = l

h 2.15

tanθ = l

h

2.16

Where, θ = inclination of diagonal strut

fc = 0.6𝜙 f´m 2.17

𝜙 = constant valuing 0.65

f´m= compressive strength of masonry

αch ≤ 0.4h 2.18

αbl ≤ 0.4l 2.19

Where, α = normalized length of contact

c,b = subscripts designated for columns and beams respectively

The length of the proposed stress blocks (figure 2.10) may not exceed 0.4 times the

length corresponding infill dimensions.

Fc = μr2Cc 2.20

Fb = μCb 2.21

Where, C,F = frame-infill contact normal and shear force (figure 2.10)

μ = coefficient of friction of the frame-infill interface

MA = MC =Mpj 2.22

Where, MA and MC = bending moment at loaded corners (points A and C in

figure 2.10),

Mpj = least of the beam, the column and their connection plastic resisting moment

called the joint plastic moment.

MD = MB = Mj < Mpj 2.23

Mc = βcMpc 2.24

Mb = βbMpb 2.25

Where, MB and MD = bending moments at the unloaded corners (figure 2.10)

Mj =either of these values.

Mc and Mb = maximum intermediate elastic moment of column and beam.

βc ≤ βb = 0.2 2.26

βb ≤ β0 = 0.2 2.27

Where, β0 = nominal or rather upper bounded value of the reduction factor

Let, h´ = h and l´ = l

Frame forces equilibrium requires the following;

V = H tanθ 2.28

H = Cc + Fb + 2S 2.29

V = Cb + Fc + 2N 2.30

Where, H and V= horizontal and vertical components of the external forces.

S and N = Shear and axial forces respectively over the uncontacted length of

the column.

𝛔 and τ = proposed uniform frame-infill contact normal and shear forces.

θ = angle of the infill diagonal.

Rotational equilibrium of the infill requires the following;

Cc(22

hhc ) – Fc ×

2

l – Cb(

22

llb ) + Fb ×

2

h = 0 2.31

Where, Cc = 𝛔ctαch

Cb = 𝛔btαbl

Fc = τctαcl

Fb = τbtαbl

Taking the static moment of the forces acting on the column and beam about point A,

S = - 0.5𝛔ctαc2h+

h

MM jpj 2.32

N = - 0.5𝛔btαb2l+

l

MM jpj 2.33

Substituting for contact forces, Cc and Fb and also column shear force, S into 2.29

leads the collapse load as follows;

H = 𝛔ct(1-αc)αch+τbtαbl+2h

MM jpj )( 2.34

At peak load the infill is subjected to failure resulting from combined normal and

shear stress acting on the contact surfaces in the loaded corners. The well known

Tresca hexagonal yield criterion described by Chen (1982) is mathematically

convenient for this combination and is given by

𝛔2+3τ

2 = fc

2 2.35

Where, fc = effective compressive strength of the infill.

Assuming rectangular stress block as shown in figure 2.12 can be written also in

terms of the contact stresses as follows;

τc = μr2𝛔c 2.36

τb = μ𝛔b 2.37

This relation would be satisfied only with the real contact stresses as follows

If Ac > Ab, then, 𝛔b = 𝛔c and 𝛔c = 𝛔c0 (Ab/Ac) 2.38

If Ac < Ab, then, 𝛔c = 𝛔c0 and 𝛔b = 𝛔b0 (Ac/Ab) 2.39

Where, Ac = r2 𝛔c0αc(1- αc – μr) 2.40

Ab = 𝛔b0αb(1- αb - μr) 2.41

The actual compressive strength of masonry infill depends on the direction of stresses

and it can be found by;

fa = fc[1-(Ld/40t)2] 2.42

The effective length of diagonal strut;

Ld = ])1[( 222 lhc 2.43

Where, Ld is not greater than 40t and fc is effective compressive strength of

masonry.

Ad =

cos

)1(c

bb

c

ccc

ftl

fth

≤ 0.5cos

c

a

f

fht

2.44

Where, Ad =the cross-sectional area of the diagonal strut for effective

compressive strength, fc

Vm±

≤ Adf´mcos ≤

cos)tan45.01(

lvt≤

0.83

cos

lt

2.45

um± =

cos

dml 2.46

The initial stiffness, K0 of the infill masonry panel may be estimated using the

following formula (Madan ey al. 1997);

K0 = 2(Vm/um) 2.47

2.6 EFFECT OF EARTHQUAKE ON BUILDING FRAME WITH

SOFT STORY

Open ground floor or soft story mechanism forms a poor framing system because of

sudden drop in stiffness and strength in ground floor. In practice, stiff masonry infill

walls (fig- 2.11 a) are neglected and only bare frames (fig- 2.11 b) are considered for

design consideration. The mode shapes vary based on the location and quantity of

infill on upper floor levels with soft floor on ground level.

In case of fully infilled frame, lateral displacements are uniformly distributed along

the height as shown in Fig-2.12 (a). But in case of open ground floor , the major

portion of the lateral displacement is accumulated on the ground floor level because

of its flexible behavior due to lack of infill in Fig-2.12 (b). Similarly, in case of

seismic loading the shear force and bending moment are concentrated on soft ground

floor level instead of being distributed uniformly.

Total seismic loading experienced by a building during earthquake depends on its

natural period. The seismic force distribution and energy dissipation is dependent on

the distribution of stiffness and mass of the structure along its height. The upper

stories being very stiff undergoes less inter-floor lateral drift while the soft ground

floor being less stiff undergoes very high lateral drift and the soft story columns

(a) (b)

Fig. 2.11 Open ground story building (a) actual building (b) building being assumed

in current design practice

Fig. 2.12 Effects of masonry infills on the first mode shape of a typical frame of a ten

story RC building , Displacement profile (a) fully infilled frame (b) open ground

floor frame

dissipate most of the seismic energy in the process of plastic hinges. Thus the

possibility and risk of collapse is very high in case of soft story under lateral loads.

The feature of soft story mechanism is not considered in the present method of

analysis for earthquake load. In static method we only consider the first mode of

vibration (that’s suitable for regular bare frames) while the behavior of infilled and

irregular frames are far more complicated and uncertain. That’s why the dynamic

analysis is helpful to account for the other modes of vibration and consider the

irregularity of stiffness features in building frame caused by random distribution of

infill on upper floors. If we can consider the true dynamic features of the frame

system then the design will be safer and adequate.

2.7 CONSIDERATION OF SOFT STORY IN DIFFERENT

BUILDING CODES

Building codes specify the design and construction requirements ensuring public

safety from structural failure and loss of life and wealth. Because of the differences in

magnitude of earthquake, geological formations, construction types, economical

development and other features the seismic design aspects are different in different

building codes. The national building codes of different countries can be classified in

two broad categories for our discussion. First are those Codes do not consider the

features of Masonry Infill walls while designing RC frames and the others are those

consider the features of Masonry Infill walls while designing RC frames.

Modification factor = static

RSM

V

V

Where, RSMV = Base shear by RSM

STATICV = Base shear by static analysis

2.7.1 Without Considering Soft Story Phenomenon

There are some advantageous features of masonry infill walls like high initial lateral

stiffness, cost effectiveness, ease in construction etc. Proper location and distribution

of infill application can increase the defense tremendously against seismic action.

These codes want to ensure the safety through proper layout and quality control

instead of considering the soft story features directly. In most cases the codes state

that the regular geometry of structures perform better against earthquake loads while

unsymmetrical application of MI walls introduce irregularities in structure. In case of

low rise buildings and low risk zone for seismic danger the codes normally

recommend static analysis while for high rise structures dynamic analysis is

recommended for adequate modeling and to obtain actual seismic design force.

Natural period of vibration is an important factor for seismic force design. Normally

the natural period is higher in case of bare frames than masonry infilled RC frames.

That’s why the design force for MI RC frames is higher than bare frames. There are

some suggestions in different codes about the natural period in case of MI-RC frames.

The following empirical formula in Eqn 2.7.1 is given by IS-1893 (2002), NBC-105

(1995), NSR-98 (1998) Egyptian code (1988), Venezuelan code (1988), Algerian

code (1988), ESCP-1 (1983);

Ta = d

h09.0 2.7.1

Where, h is the height of building in meter and d is the base dimension of building in

meter at the plinth level along the considered direction of the lateral force.

French code (AFPS-90, 1990) recommends the following Eqn 2.7.2 for masonry

infilled buildings;

T = 0.06hd

h

d

h

2 2.7.2

Amanat and Hoque (2006) studied the fundamental periods of vibration of a series of

regular RC framed buildings using 3-D FE modeling and modal eigenvalue analysis

including the effects of infill. The time period determined from eigenvalue analysis

was remarkably close to those predicted by the code formulas. It’s also observed that

the randomness of infill application does not cause much variation of the period if the

total amount of infill panel is same. Based on the findings of the study some practical

guidelines are suggested for determining the fundamental period of RC frames using

rational approaches like modal analysis.

2.7.2 Considering Soft Story Phenomenon

Vertical irregularities are introduced in MI-RC frames due to the reduction or absence

of MI in particular stories compared to other adjacent stories. This matter creates

irregularities in mass, stiffness, strength along the height of the structure. As a result

the design of the beam and column is needed to be modified according to

modification of base shear value under lateral load due to formation of irregularities

for random MI application. There are some building codes where instruction for

design modification for soft story phenomenon is given.

The Indian seismic code (IS-1893 2002) requires members of the soft story (story

stiffness less than 70% of that in the story above or less than 80% of the average

lateral stiffness of the three stories above) to be designed for 2.5 times the seismic

story shears and moments obtained without considering the effects of MI in any story.

The factor of 2.5 is specified for all the buildings with soft stories irrespective of the

extent of irregularities. The other option is to provide symmetric RC shear walls

designed for 1.5 times the design story shear force in both directions of the building

as far away from the center of the building as feasible.

Costa Rican code (1986) requires that all structural resisting system must be

continuous from the foundation to the top of the building and stiffness of a story must

not be less than 50% of that of the story below.

Mezzi (2004) illustrated soft story to be very dangerous from seismic viewpoint as

the lateral response of these buildings is characterized by a large rotation ductility

demand concentrated at the extreme sections of the columns of the ground floors,

while the superstructure behaves like a quasi-rigid body. A solution was proposed for

the preservation of a particular architectonic double soft story configuration.

CHAPTER 3

FINITE ELEMENT MODELING OF INFILL FRAME

3.1 INTRODUCTION

In this chapter the full structural modeling of 3D MI-RC frame is made including

individual modeling like beam, column, slab, infill, load etc. with proper support

condition. To model the masonry infill, link element is taken as diagonal strut and for

load application, mass element is chosen accordingly. For the analysis both

equivalent static force method (according to BNBC) and RSM is considered. The

comparison of effect of infill between ESFM and RSM is done to asses the real

structural characteristics of soft story.

3.2 SOFTWARE FOR FINITE ELEMENT ANALYSIS

A good number of software packages are available for finite element analysis in civil

engineering field. Some of those are designed for specialized structural analysis and

specific behavioral characteristics. Among them ANSYS program package has more

advantageous features for the analysis performed in this research. So, the ANSYS

10.0 package has been selected for its vastness, flexibility and ease in use as finite

element analysis tool.

3.3 ASSUMPTIONS FOR MODELING SIMPLIFICATION

We assumed linearly elastic homogeneous material for the RC frame that is always

steel reinforced in reality. According to ACI recommendation, the analysis results for

RC frame are accurate enough for this simplification only if appropriate properties of

concrete are considered. The structural property of masonry infill is modeled as

compressive diagonal strut assuming negligible tensile strength of masonry. This

simplification is fare enough to resist the lateral load by compression only.

3.4 CHARACTERIZATION OF STRUCTURAL COMPONENTS

IN MODEL

3.4.1 BEAM4 (3-D Elastic Beam) for Beam and Column

Element Description

BEAM4 is a uniaxial element with tension, compression, torsion, and bending

capabilities. The element has six degrees of freedom at each node: translations in the

nodal x, y, and z directions and rotations about the nodal x, y, and z axes. The

geometry, node locations, and coordinate systems for this element are shown in fig

3.1 The element is defined by two or three nodes, the cross-sectional area, two area

moments of inertia (IZZ and IYY), the torsional moment of inertia (IXX) and the

material properties.

Fig. 3.1 BEAM4 Geometry

Input Summary

Element Type - BEAM4

Nodes - I, J, K (K orientation node is optional)

Degrees of Freedom - UX, UY, UZ, ROTX, ROTY, ROTZ

Real Constants - AREA, IZZ, IYY, HEIGHT, WIDTH, IXX

Material Properties - EX, PRXY, DENS

Output Data

The solution output associated with the element is in two forms:

Nodal displacements included in the overall nodal solution

Additional element output

Assumptions and limitations

The beam must not have a zero length or area. The moments of inertia,

however, may be zero if large deflections are not used.

The beam can have any cross-sectional shape for which the moments of

inertia can be computed. The stresses, however, will be determined as if the

distance between the neutral axis and the extreme fiber is one-half of the

corresponding thickness.

The element thicknesses are used only in the bending and thermal stress

calculations.

The applied thermal gradients are assumed to be linear across the thickness in

both directions and along the length of the element.

If you use the consistent tangent stiffness matrix (KEYOPT(2) = 1), take care

to use realistic (that is, “to scale”) element real constants. This precaution is

necessary because the consistent stress-stiffening matrix is based on the

calculated stresses in the element. If you use artificially large or small cross-

sectional properties, the calculated stresses will become inaccurate, and the

stress-stiffening matrix will suffer corresponding inaccuracies. (Certain

components of the stress-stiffening matrix could even overshoot to infinity.)

Similar difficulties could arise if unrealistic real constants are used in a linear

prestressed or linear buckling analysis.

Eigenvalues calculated in a gyroscopic modal analysis can be very sensitive to

changes in the initial shift value, leading to potential error in either the real or

imaginary (or both) parts of the eigenvalues.

3.4.2 Shell63 (Elastic Shell) for Slab

Element Description

SHELL63 has both bending and membrane capabilities. Both in-plane and normal

loads are permitted. The element has six degrees of freedom at each node: translations

in the nodal x, y, and z directions and rotations about the nodal x, y, and z-axes.

Stress stiffening and large deflection capabilities are included. A consistent tangent

stiffness matrix option is available for use in large deflection (finite rotation)

analyses.

Input Summary

Element Type - SHELL63

Nodes - I, J, K, L


Real Constants - TK(I), TK(J), TK(K), TK(L)


Fig. 3.2 SHELL63 Geometry

Output Data




Assumptions and Restrictions

Zero area elements are not allowed. This occurs most often whenever the

elements are not numbered properly.

Zero thickness elements or elements tapering down to a zero thickness at any

corner are not allowed.

The applied transverse thermal gradient is assumed to vary linearly through

the thickness and vary bilinearly over the shell surface.

An assemblage of flat shell elements can produce a good approximation of a

curved shell surface provided that each flat element does not extend over more

than a 15° arc. If an elastic foundation stiffness is input, one-fourth of the total

is applied at each node. Shear deflection is not included in this thin-shell

element.

A triangular element may be formed by defining duplicate K and L node

numbers. The extra shapes are automatically deleted for triangular elements so

that the membrane stiffness reduces to a constant strain formulation. For large

deflection analyses, if KEYOPT(1) = 1 (membrane stiffness only), the

element must be triangular.

For KEYOPT(1) = 0 or 2, the four nodes defining the element should lie as

close as possible to a flat plane (for maximum accuracy), but a moderate

amount of warping is permitted. For KEYOPT(1) = 1, the warping limit is

very restrictive. In either case, an excessively warped element may produce a

warning or error message. In the case of warping errors, triangular elements

should be used.

If the lumped mass matrix formulation is specified, the effect of the implied

offsets on the mass matrix is ignored for warped SHELL63 elements.

3.4.3 MASS21 (Structural Mass) for load application

Element Description

MASS21 is a point element having up to six degrees of freedom: translations in the

nodal x, y, and z directions and rotations about the nodal x, y, and z axes. A different

mass and rotary inertia may be assigned to each coordinate direction.

Input Summary

Element Type - MASS21

Nodes - I


Real Constants - MASSX, MASSY, MASSZ

Material Properties - DENS

Output Data

Nodal displacements are included in the overall displacement solution. There is no

printed or post element data output for the MASS21 element.


2-D elements are assumed to be in a global Cartesian Z = constant plane.

If you specify KEYOPT(2) = 1, the element operates in the nodal coordinate

system

The mass element has no effect on the static analysis solution unless

acceleration or rotation is present, or inertial relief is selected

Fig. 3.3 MASS21 Geometry

The standard mass summary printout is based on the average of MASSX,

MASSY, and MASSZ if (KEYOPT(3) = 0).

In an inertial relief analysis, the full matrix is used. All terms are used during

the analysis.

3.4.4 LINK8 (3-D Spar or Truss) for diagonal strut

Element Description

LINK8 is a spar which may be used in a variety of engineering applications. This

element can be used to model trusses, sagging cables, links, springs, etc. The 3-D spar

element is a uniaxial tension-compression element with three degrees of freedom at

each node: translations in the nodal x, y, and z directions. As in a pin-jointed

structure, no bending of the element is considered. Plasticity, creep, swelling, stress

stiffening, and large deflection capabilities are included.

Input Summary

Element Type - LINK8

Nodes - I, J

Degrees of Freedom - UX, UY, UZ

Real Constants - AREA


Fig. 3.4 LINK8 Geometry

Output Data





The spar element assumes a straight bar, axially loaded at its ends, and of

uniform properties from end to end.

The length of the spar must be greater than zero, so nodes I and J must not be

coincident.

The area must be greater than zero.

The temperature is assumed to vary linearly along the length of the spar.

The displacement shape function implies a uniform stress in the spar.

The initial strain is also used in calculating the stress stiffness matrix, if any,

for the first cumulative iteration.

3.4.5 Support Condition

At foundation level all column ends are considered to act under fixed support

condition with all degrees of freedom of the support being restrained.

3.4.6 Load application

The x-z plane is acting as the horizontal plane in global co-ordinate system. The load

cases considered according to BNBC, 1993.

The considered load can be categorized to vertical and lateral directions.

Vertical load

Dead Load: Weight of permanent structural and nonstructural component of the

structure is considered as dead load. The structural self weight is already taken with

the modeling and the rest nonstructural vertical load is applied as mass for floor finish

(1.437 2310

mmN ) and partition wall (Infill) on nodes as uniformly distributed

load.

Live Load: The temporary load acting on structure as occupancy load is called live

load and considered as uniformly distributed surface load (valuing 2.395

2310

mmN ) in vertical direction.

Lateral Load

Earthquake Load: The earthquake load acts at lateral direction. Here, this seismic

load is considered for both static and modal analysis according to BNBC, 1993.

3.5 SEISMIC LOAD CALCULATION

Two methods are used to compare the results of seismic load.

Static analysis (Equivalent static Force Method)

Modal analysis

Fig. 3.5 Finite Element modeling of total structure

3.5.1 Static Analysis (Equivalent static Force Method)

According to BNBC, 1993 empirical equations are given in this method is applied for

calculation of seismic base shear based on vibration period of whole structure. No

consideration for structural nonlinearity and stiffness is made here and the considered

period is for first mode of vibration only.

Design Base Shear, WR

ZICV 3.1

Where,

Z = Seismic zone co-efficient

I = Structural importance coefficient

W = Total seismic dead load

R = Response modification factor for structural system

C = 3

2

25.1

T

S 3.2

S = Sight co-efficient for soil characteristics

T = Fundamental period of vibration

= 43

n )h(073.0 3.3

hn = Height of structure above base (in meter)

3.5.2 Modal Analysis

Modal analysis is helpful to determine the critical vibration characteristics of

structure. The natural frequency and mode shape is important to determine the design

forces of structure under dynamic loading condition and modal analysis is used to do

that.

Response Spectrum Method (RSM)

In this method of dynamic analysis the multiple modes of response of a structure are

taken into account. It’s a plot of the peak or the steady-state response of a series of

frequencies that are forced to oscillate under same base vibration. From the resulting

plot we can asses the pick of the natural frequency for a particular mass of the linear

structure. To get the actual dynamic impact all significant modes should be

considered. The no. of mode considered should be at least the no. of floors. A value

for damping is needed to input otherwise the response will be infinite. RSM can also

be performed for multiple degree of freedom systems but it’s accurate only for a low

value for damping. Modal analysis is performed only to identify the mode shape

while the response for the particular mode can be assessed from the response

spectrum. The peak response is then combined to get the resultant response. The

combination of dynamic response must be done under specified established procedure

like SRSS (square root of sum of squares), CQC (Complete Quadratic Combination)

etc.

Random distribution of infill:

The position of infill is very important to the contribution on structural modification.

In current 3D analysis the random infill position is featured for each cases.

Fig. 3.6 Normalized response spectra for 5% Damping ratio

Fig- 3.7 Different patterns of 20% random infill application (6 storied building)

Methods of modal combination:

SRSS meaning Square root of the Sum of the Squares is a very common approach of

modal combination. It’s done on the maximum modal values in order to estimate the

values of displacement or forces. The SRSS rule for modal combination was

developed by E. Rosenblueth’s in his PhD thesis (1951).

)(1

2

00

N

n

nrr 3.4

The peak response in each mode is squared, the squared modal peaks are summed and

the square root of the sum provides an estimation of the peak total response.

This modal combination rule provides excellent response estimates for structures with

well separated natural frequencies. This limitation has not always been recognized in

applying this rule to practical problems and at times it has been misapplied to systems

with closely spaced natural frequencies such as piping systems in nuclear power

plants and multistory buildings with unsymmetric plan. For three dimensional

structures, in which a large number of frequencies are almost identical, this

assumption is not justified.

Another method is CQC meaning Complete Quadratic Combination for modal

combination. It’s a more modern method over SRSS as it has overcome the limitation

of SRSS. This method was first applied by Wilson, Kiureghian and Bayo, 1981 is

applicable to a wider class of structures. It’s based on random vibration theories with

wide acceptance to most engineers and has been incorporated as an option in most

modern computer programs for seismic analysis. The peak value of a typical force

can now be estimated, from the maximum modal values by the CQC method with the

application of the following double summation equation.

21

1 1

000 )(

N

i

N

n

niin rrr 3.5

Each of the N 2 terms on the right side of this equation is the product of the peak

responses in the i th and the n th modes and the correlation coefficient ρin for these

two modes ; ρin varies between 0 and 1 and ρin=1 for i=n. Hence the eqn 3.5 becomes

21

1

00

1 1

2

00 )(

N

n

niin

ni

N

i

N

n

n rrrr

3.6

In this study the CQC method of modal combination is used for its useful features for

closely spaced modes of complex 3-D structures.

Different mode shapes:

In case of modal analysis different mode shapes for probable vibration pattern are

encountered. Different mode shapes have different frequencies of vibration. Some of

the modes are closely spaced showing similar pattern of vibration. Here some well

distinguished mode shapes are featured to give some ideas about the different modes

of vibration in dynamic analysis.

(2) Elevation (2) Top view

Fig. 3.7 (a) First mode shape


Fig. 3.7 (b) third mode shape

Fig. 3.7 (f) 15th mode shape

Fig. 3.7 (c) Sixth mode shape Fig. 3.7 (d) Seventh mode shape


Fig. 3.7 (e) 10th mode shape

3.6 MODEL CHARACTERISTICS FOR ANALYSIS

In the present study the main objective is to study the variation range in seismic effect

in multistoried building for random application of infill with soft story. For the study

6, 8, 10 and 12 story buildings having 4 span × 4 bay has been analyzed by ANSYS

package. A reference structure is shown in fig.- 3.5. The dimensions of structural

components were assumed relatively and the material parameters were taken

accordingly for normal concrete.

Table 3.1: Values and dimensions for the parameters and structural components

Parameter Value/Dimension

Span length 4000 mm

Bay width 3000 mm

Floor height 3000 mm

Slab thickness 120 mm

Floor finish 1.437×10-3

N/mm2

Live load 2.395×10-3

N/mm2

Beam 450 mm×250 mm

Corner column 350 mm×350 mm

Exterior column 400 mm×400 mm

Interior column 500 mm×500 mm

Gravitational acceleration 9810 mm/sec2

Concrete properties

Modulus of elasticity 20000 N/mm2

Poisson’s ratio 0.13

Density 2.4×10-9

Ton/mm3

Unit weight 2.36×10-5

N/mm3

CHAPTER 4

ANALYSIS OF RESULTS AND DISCUSSION

4.1 INTRODUCTION

Seismic characteristics of masonry infilled RC frame with soft ground story effect

have been examined in this study considering variable parameters. The parameters

taken based on practical values and dimensions so that the actual building behavior

under natural seismic load is reflected accordingly. The variation of base shear value

under dynamic analysis for the random application of infill is tried to investigate. The

lateral drift for soft story mechanism and effect of no. of span is also tried to be

searched to facilitate the design modification for the current study.

Firstly the random effect of infill on upper floors has been studied for 6,8,10 and 12

storied building with open ground floor and 20% infill on ground floor. The effect of

no. of span on modification factor has been investigated for similar building systems.

4.2 SCOPE OF STUDY

The current study is actually involved with a large number of variables but our

concentration will be limited to the effect of random distribution of infill and

variation in base shear for variable no. of span. The other parameters and variables

are beyond the scope of this study.

4.3VARIATION IN BASE SHEAR FOR RANDOM APPLICATION

OF INFILL

The findings of the parametric study are discussed according to the results. The study

is done for 6, 8, 10 and 12 storied building having different percentage of infill on

upper floors with soft ground story.

4.3.1 Range of variation in base shear value

The results obtained from the analysis of finite element model of MI-RC frame are

tabulated sequentially and shown graphically.

From the results obtained (table-4.1 to table-4.12 and fig-4.1 to fig-4.32) we find that

for a particular frame the effect of randomly applied infill is not the same on base

shear value. Under each parameter the RSM analysis is done for 10 times and the

variation in result is observed. The bar charts show that for infill percentage less than

50% (20% and 40%) the base shear value has a wider range of variation while for

infill percentage greater than 50% (60% and 80%) the range of variation is narrower.

This is because for less % of infill the opportunity of variation in infill location and

pattern is far higher while for high % of infill the opportunity of variation in infill

location and pattern is less.

It is observed that for higher % of infill application the standard deviation of base

shear value by RSM is not of large value. So we can use individual value of base

shear for random effect with certain reliability. But in case of infill % less than 50%

we must take an average of close values neglecting the highly deviated ones.

4.3.2 Modification factor for different parameters

To find the modification factor for randomly applied infill at different percentage, the

average values have been used. Here two sets of ground floor condition with different

% of infill on upper floors for 6, 8, 10 and 12 storied buildings have been analyzed.

From the previous results we have some correlations for modification factor for

application of different percentage of infill. The factor increases with increase of no.

of floors.

Table 4.1: Base shear variation of 6 storied building for random application of Infill

(in different percentage) with no infill on ground floor Upper floor infill

percentage 20% 40% 60% 80%

Base shear values by RSM

for different patterns of

infill application

(KN)

602 686 826 935

590 722 847 935

606 724 834 937

606 718 830 936

581 719 827 938

610 719 831 938

591 687 843 933

602 723 828 935

595 723 830 922

603 721 829 935

Average Base shear by

RSM (KN) 599 714 833 934

Standard deviation 9.04 14.73 7.01 4.62

Base shear by ESFM (KN) 543 595 648 700

Modification Factor 1.10 1.2 1.29 1.33

Fig-4.1: Variation in base shear value (RSM) of 6 storied building for random infill

pattern (no infill on Ground floor and 20% infill on upper floors)

565

570

575

580

585

590

595

600

605

610

615

1 2 3 4 5 6 7 8 9 10

Bas

e S

he

ar in

RSM

(K

N)

Fig-4.2 : Variation in base shear value (RSM) of 6 storied building for random infill






500

550

600

650

700

750

1 2 3 4 5 6 7 8 9 10

Bas

e s

he

ar in

RSM

(K

N)

500

550

600

650

700

750

800

850

900

1 2 3 4 5 6 7 8 9 10

Bas

e s

he

ar in

RSM

(K

N)

500

600

700

800

900

1000

1 2 3 4 5 6 7 8 9 10

Bas

e s

he

ar in

RSM

(K

N)

Table 4.2: Base shear variation of 6 storied building for random application of

Infill (in different percentage) with 20% infill on ground floor Upper floor infill

percentage 20% 40% 60% 80%



infill application

(KN)

526 631 802 901

578 678 819 888

582 641 791 906

582 668 807 867

526 642 765 874

578 646 777 877

582 596 798 871

555 644 809 885

578 656 773 896

582 653 813 898


RSM (KN) 567 646 795 886





pattern (20% infill on Ground floor and 20% infill on upper floors)

500

510

520

530

540

550

560

570

580

590

1 2 3 4 5 6 7 8 9 10

Bas

e s

he

ar in

RSM

(K

N)







500

520

540

560

580

600

620

640

660

680

700

1 2 3 4 5 6 7 8 9 10

Bas

e s

he

ar in

RSM

(K

N)

500

550

600

650

700

750

800

850

1 2 3 4 5 6 7 8 9 10

Bas

e s

he

ar in

RSM

(K

N)

500

550

600

650

700

750

800

850

900

950

1 2 3 4 5 6 7 8 9 10

Bas

e s

he

ar in

RSM

(K

N)


Infill (in different percentage) with no infill on ground floor Upper floor infill

percentage 20% 40% 60% 80%


for different patterns of infill

application

(KN)

839 1033 1215 1391

854 1018 1197 1395

810 1026 1213 1396

842 972 1213 1388

806 1033 1210 1393

785 1028 1214 1401

829 1034 1207 1390

841 1028 1197 1402

840 934 1210 1391

821 1029 1216 1387

Average Base shear by RSM

(KN) 826.7 1013.5 1209.2 1393.4






700

720

740

760

780

800

820

840

860

880

1 2 3 4 5 6 7 8 9 10

Bas

e s

he

ar in

RSM

(K

N)







700

750

800

850

900

950

1000

1050

1100

1 2 3 4 5 6 7 8 9 10

Bas

e s

he

ar in

RSM

(K

N)

700

800

900

1000

1100

1200

1300

1 2 3 4 5 6 7 8 9 10

Bas

e s

he

ar in

RSM

(K

N)

700

800

900

1000

1100

1200

1300

1400

1500

1 2 3 4 5 6 7 8 9 10

Bas

e s

he

ar in

RSM

(K

N)

Table 4.4: Base shear variation of 8 storied building for random application

of Infill (in different percentage) with 20% infill on ground floor Upper floor infill

percentage 20% 40% 60% 80%



infill application

(KN)

811 989 1167 1297

773 986 1113 1351

783 978 1104 1320

803 948 1118 1333

754 946 1091 1324

800 930 1116 1312

786 938 1122 1318

757 929 1135 1301

776 952 1128 1344

725 925 1113 1325


RSM (KN) 777 952 1121 1323




Fig-4.13: Base shear variation of 8 storied building for random application of Infill


700

720

740

760

780

800

820

1 2 3 4 5 6 7 8 9 10

Bas

e s

he

ar in

RSM

(K

N)







700

750

800

850

900

950

1000

1050

1 2 3 4 5 6 7 8 9 10

Bas

e s

he

ar in

RSM

(K

N)

700

750

800

850

900

950

1000

1050

1100

1150

1200

1 2 3 4 5 6 7 8 9 10

Bas

e s

he

ar in

RSM

(K

N)

700

800

900

1000

1100

1200

1300

1400

1 2 3 4 5 6 7 8 9 10

Bas

e s

he

ar in

RSM

(K

N)



percentage 20% 40% 60% 80%

Base shear values by RSM for

different patterns of infill

application

(KN)

982 1400 1640 1891

1068 1390 1631 1886

1056 1368 1615 1886

1027 1318 1628 1892

1003 1363 1637 1860

1013 1378 1654 1890

994 1397 1656 1890

1037 1385 1669 1892

1081 1325 1664 1884

1045 1409 1632 1897


(KN) 1031 1373 1643 1887






900

920

940

960

980

1000

1020

1040

1060

1080

1100

1 2 3 4 5 6 7 8 9 10

Bas

e s

he

ar in

RSM

(K

N)







900

1000

1100

1200

1300

1400

1500

1 2 3 4 5 6 7 8 9 10

Bas

e s

he

ar in

RSM

(K

N)

900

1000

1100

1200

1300

1400

1500

1600

1700

1800

1 2 3 4 5 6 7 8 9 10

Bas

e s

he

ar in

RSM

(K

N)

900

1100

1300

1500

1700

1900

2100

1 2 3 4 5 6 7 8 9 10

Bas

e s

he

ar in

RSM

(K

N)


Infill (in different percentage) with 20% infill on ground floor Upper floor infill

percentage 20% 40% 60% 80%



infill application

(KN)

1052 1289 1584 1807

1114 1310 1556 1829

1092 1279 1570 1814

1080 1309 1566 1783

1044 1311 1567 1795

1071 1327 1567 1801

1064 1306 1533 1808

1070 1256 1584 1806

1066 1308 1545 1810

1085 1347 1581 1793


(KN) 1074 1304 1566 1805






900

950

1000

1050

1100

1150

1 2 3 4 5 6 7 8 9 10

Bas

e s

he

ar in

RSM

(K

N)







900

1000

1100

1200

1300

1400

1 2 3 4 5 6 7 8 9 10

Bas

e s

he

ar in

RSM

(K

N)

900

1000

1100

1200

1300

1400

1500

1600

1700

1 2 3 4 5 6 7 8 9 10

Bas

e s

he

ar in

RSM

(K

N)

900

1000

1100

1200

1300

1400

1500

1600

1700

1800

1900

1 2 3 4 5 6 7 8 9 10

Bas

e s

he

ar in

RSM

(K

N)



percentage 20% 40% 60% 80%



application

(KN)

1156 1550 1880 2135

1182 1587 1873 2139

1165 1593 1868 2142

1166 1589 1866 2126

1160 1581 1867 2132

1213 1562 1868 2136

1199 1525 1856 2148

1131 1514 1856 2129

1155 1583 1872 2153

1203 1605 1819 2130


(KN) 1173 1569 1863 2137






1100

1120

1140

1160

1180

1200

1220

1 2 3 4 5 6 7 8 9 10

Bas

e s

he

ar in

RSM

(K

N)







1100

1200

1300

1400

1500

1600

1700

1 2 3 4 5 6 7 8 9 10

.

1100

1200

1300

1400

1500

1600

1700

1800

1900

2000

1 2 3 4 5 6 7 8 9 10

Bas

e s

he

ar in

RSM

(K

N)

1100

1300

1500

1700

1900

2100

2300

1 2 3 4 5 6 7 8 9 10

Bas

e s

he

ar in

RSM

(K

N)


Infill (in different percentage) with 20% infill on ground floor

F

i

g

-

4

.

2

9

:

B

a

s

e

s

h



Upper floor infill

percentage 20% 40% 60% 80%



application

(KN)

1135 1573 1921 2207

1251 1569 1917 2140

1214 1499 1917 2181

1241 1480 1872 2213

1184 1593 1920 2204

1109 1515 1831 2210

1168 1595 1872 2209

1106 1581 1856 2168

1239 1593 1916 2211

1219 1601 1873 2178


(KN) 1187 1560 1890 2192



Modification Factor 1.52 1.81 2 2.13

1000

1050

1100

1150

1200

1250

1300

1 2 3 4 5 6 7 8 9 10

Bas

e s

he

ar in

RSM

(K

N)







1100

1200

1300

1400

1500

1600

1700

1 2 3 4 5 6 7 8 9 10

Bas

e s

he

ar in

RSM

(K

N)

1100

1200

1300

1400

1500

1600

1700

1800

1900

2000

1 2 3 4 5 6 7 8 9 10

Bas

e s

he

ar in

RSM

(K

N)

1100

1300

1500

1700

1900

2100

2300

1 2 3 4 5 6 7 8 9 10

Bas

e s

he

ar in

RSM

(K

N)

Fig-4.33: Base shear comparison between ESFM and RSM (20% infill on upper floors

with no infill on ground floor)



0

200

400

600

800

1000

1200

1400

6 8 10 12

Bas

e s

he

ar (

KN

)

No. of story

Base shear by ESFM Base shear by RSM

0

200

400

600

800

1000

1200

1400

1600

1800

6 8 10 12

Bas

e s

he

ar (

KN

)

No. of story

Base shear in ESFM Base shear in RSM





0

200

400

600

800

1000

1200

1400

1600

1800

2000

6 8 10 12

Bas

e s

he

ar (

KN

)

No. of story


0

500

1000

1500

2000

2500

6 8 10 12

Bas

e s

he

ar (

KN

)

No. of story



with 20% infill on ground floor)



0

200

400

600

800

1000

1200

1400

6 8 10 12

Bas

e s

he

ar (

KN

)

No. of floors


0

200

400

600

800

1000

1200

1400

1600

1800

6 8 10 12

Bas

e s

he

ar (

KN

)

No. of floors






0

200

400

600

800

1000

1200

1400

1600

1800

2000

6 8 10 12

Bas

e s

he

ar (

KN

)

No. of floors


0

500

1000

1500

2000

2500

6 8 10 12

Bas

e s

he

ar (

KN

)

No. of floors


No infill on ground floor with various % of infill on upper floors

For 6 story building the recommended base shear modification factor for safe design

are 1.1, 1.2, 1.3 and 1.4 respectively for 20%, 40%, 60% and 80% infill on upper

floors.



floors.



floors.



floors.

20% infill on ground floor with various % of infill on upper floors



floors.



floors.



floors.



floors.

The results show that the factor is less (for any % of infill on upper floors) in case of

20% infill than no infill on ground floor.

From graphs (Fig-4.37 to Fig- 4.44) plotted for modification factor against no. of

floors show that the factor increases with the increase of floors. A logarithmic

equation is developed for each case for further use by extrapolation. An upper

rounded (0.1) value found from each equation is fair enough to use for 15 story

building. The recommended modification factors for 15 story building with soft

ground floor are 1.7, 2.1, 2.3 and 2.5 respectively for 20%, 40%, 60% and 80% infill

on upper floors.

Fig- 4.41 Modification factor for no infill on GF and 20% infill on upper floors


Modification factor=VRSM / VESFM



Fig- 4.45 Modification factor for 20% infill on GF and 20% infill on upper floors

Variation with number of span

Analysis shows that (Table-4.9 and fig-4.45) the modification factor remains almost

constant for 0% on ground floor with any % of infill on upper floors for various no.

of spans. So it’s obvious that there is no such effect of no. of span on seismic base

shear modification for soft story.

Table 4.9: Modification factor for different no. of spans for a 6 storied building

with 40% infill on upper stories and no infill on GF No. of span Span length (mm) 2000mm 4000mm 6000mm 8000mm

2

EQ (static) 88 192 343 539

RSM 97 226 561 954

Modification factor 1.1 1.18 1.64 1.77

4

EQ (static) 309 704 1281 2041

RSM 355 889 2202 3732


6

EQ (static) 666 1536 2817 4510

RSM 764 1894 4724 8294


Fig-4.49 Modification factor for different number of spans for a 6 storied building with

40% infill on upper stories and no infill on GF

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

2 4 6

Mo

dif

icat

ion

Fac

tor

No. of span

CHAPTER 5

CONCLUSION AND RECOMMENDATION

5.1 GENERAL

In the present study computational investigation has been performed on reinforced

concrete frame structure having various percentage of masonry infill on upper floors

with no infill and 20% infill on ground floor. The application of infill has been done

randomly and the effect of seismic load has been investigated. The analysis was

carried for 6, 8, 10 and 12 storied buildings for 20%, 40%, 60% and 80% infill on

upper floors. For each individual case at least 10 runs have been made to study the

variation on base shear for randomly applied infill. The analysis is done both by

ESFM and RSM so that a comparison can be made on the actual MI-RC soft story

behavior with the current design practice. Based on the investigation some

modification factor has been recommended on various cases of infill application.

5.2 FINDINGS OF THE INVESTIGATION

The general output of the investigation indicates a different characteristic behavior of

infilled RC frame than from bare frames. The summary of the findings can be

tabulated as follows;

The presence of structurally active infill on upper floors causes increase in

base shear value of the building.

The random location of infill shows a range of variable base shear value for

same framing system. To use base shear modification factor for infill % less

than 50% (on upper floors), it must be considered with the average of closely

valued cases. For infill % higher than 50% (on upper floors), the variation is

not significantly large to go for several runs.

20% infill application on ground floor normally cause an insignificant

reduction on base shear value than open ground floor but for 12 story building

and 80% infill on upper floors, the base shear increases a little with 20% infill

on ground floor. It can be said that the base shear value doesn’t change much

for 20% infill on ground floor.

A safe base shear modification factor can be recommended as 1.5, 1.8, 2.0 and

2.3 for 6, 8, 10 and 12 storied building respectively. With some logical

judgment and graphical extrapolation we can recommend a factor of 2.5 for

15 storied building.

5.3 RECOMMENDATION FOR FUTURE STUDY

The current study on infill behavior with soft floor has been carried under limited

scope. The results are not sufficient to apply as so many other factors and variables

have not been studied so far. Advancement of current study can be done combining

some other variables together. The following fields related to this study can be

considered for further analysis;

The model was considered to be linearly elastic. To be more realistic with the

results a finite element analysis with non linear material properties can be

performed.

The investigation can be carried for high-rise structures with floor number

more than 20.

Rather than equivalent strut model for infill, other methods of infill modeling

can be tried to verify the results.

The asymmetric building frames can be studied under the variables considered

for symmetric frames.

Other economical ways for the remedy of infilled RC frame with soft story

mechanism should be studied as the current recommendation of considering

higher base shear value can increase the cost of construction.

REFERENCES

AFPS(1990) “Recommendations for the reaction of rules Relative to the Structures

and Installation Built in Regions Prone to Earthquakes”, French Association of

Earthquake Engineering, Paris, France.

Algerian Seismic Code (1988) “Algerian Earthquake Resistant Regulations”,

Ministry of town Planning and Construction, Algiers, Algeria.

Amanat, K. M. and Hoque, E. (2006) “A Rationale for Determining the natural

period of RC Building FramesHaving Infill” Engineering Structures, Vol.28, pp. 495-

502.

Bertero V. and Brokken S. (1983) “Infills in Seismic Resistant Building”, Journal of

the Structural Engineering, ASCE, Vol.109, No.6, June, pp.1337-1361

BNBC, (1993) Housing and Building Research Institute and Bangladesh Standards

and Testing Institution, Bangladesh National Building Code

Cost Rican Seismic Code (1986) “Seismic Code of Costa Rica”, Federal College of

Engineers and Architects of Costa Rica, San Jose, Costa Rica.

Egyptian Seismic Code (1988) “Regulations for earthquake resistant design of

buildings in Egypt”, Egyptian Society for Earthquake Engineering, Cairo, Egypt.

ESCP-1, (1983) “Code of practice for loading, Ethiopia”, Ministry of Urban

development and Housing, Addis Ababa, Ethiopia.

Holmes M. (1961) “Steel Frame with Brickwork and Concrete infilling”, Proceedings

of the Institution of Civil Engineers, Vol.-19, pp.473-478.

IS-1893 (2002) Bureau of Indian Standards, Indian Standard Criteria for Earthquake

Resistant Design of Structures-Part-1: General Provisions and Buildings (Fifth

revision), New Delhi, India

Klingner, R. E. and Bertero, V. V. (1978) “Earthquake Resistance of Infilled

Frames”, Journal of the Structural Engineering, ASCE, Vol.104, No.ST6, June,

pp.973-989

Madan A., Reinhorn A. M., Mander J. B. and Valles R. E. (1997) “Modeling of

Masonry Infill Panels for Structural Analysis”, ASCE Journal of Structural

Engineering, Vol.123, No.10, October, pp..1295-1297

Mehrabi, A. B. Shing P. B., Schuller, M. P. and Noland J. N. (1996) “Experimental

Evaluation of Masonry Infilled RC Frames”, Journal of the Structural Engineering,

ASCE, Vol.122, No.3, March, pp.228-237

Mezzi, M. (2004) “Architectural and Structural Configurations of Buildings with

Innovative seismic Systems”, 13th

World Conference on Earthquake Engineering,

August, (Paper No. 1318), Vancouver, B.C., Canada.

Mogaddam H. A., Dowling P. J. (1987) “The State of the Art in infilled Frames”,

Imperial College of Science and Technology, Civil Engineering Dept., London, UK,

ESEE Report no.87-2

Murty C. V. R.and Jain S. K. (2000) “Beneficial influence of Masonry Infills on

seismic performance of RC frame buildings”, Proceedings, 12th

World Conference on

Earthquake Engineering, New Zealand, Paper No. 1790

NBC-105, (1995) “Nepal National Building Code for For Seismic Design of

Buildings in Nepal”, Ministry of Housing and Physical Planning, Department of

Buildings, Kathmandu, Nepal.

NSR-98 (1998) “Colombian Standard for Seismic Resistant Design and

Construction”, Bogota, Columbia.

Papia M. (1998), “Analysis of Infilled Frames Using Coupled Finite Element and

Boundary Element Solution Scheme”, Int. J. Num. Meth. Eng., Vol.26, pp. 731-742

Rosenblueth, E. (1951) “A basis for Seismic Design”, Ph.D. Thesis, University of

Illinois, Urbana, Ill.

Saneinjad A. and Hobbs B. (1995) “Inelastic Design of Infilled Frames”, ASCE

Journal of Structural Engineers,Vol -121, No.4,April, pp.634-643

Smith B. S. (1962) “Lateral Stiffness of Infilled Frames”, ASCE Journal of Structural

Division,Vol-88,ST6,pp.183-199

Smith B. S. and Coull (1991) “A infilled-Frame structure, Tall building structures

analysis and design”, John Wiley & Sons, inc. 168-174

Venezuelan Seismic Code (1988) “Regulations for Earthquake Resistant Buildings”,

Commission De Normas Industriales, Covenin, Caracas, Venezuela.

Wilson, E. L. (2002) “Three dimensional static and dynamic analysis of Structures, A

physical approach with emphasis on Earthquake Engineering”, Third edition,

Computers and Structures, Inc. Berkeley, California, USA, ISBN 0-923907-00-9

Wood R. H.(1958),”The Stability of Tall Buildings.Proceedings of the Institution of

Civil Engineers”, Vol.-11, pp.69-102

APPENDIX: ANSYS SCRIPT USED IN THE ANALYSIS

FINISH

/CLEAR

!!!!!!!!DATA INPUT FOR BEAM,COLUMN AND SLAB!!!!!!

!!!!!!!! mm , N !!!!!!!

NSPAN=4 !!no of span!!

NFLOOR=6 !!no of floor!!

NBAY=NSPAN

SPANL=4000 !!span length!!

BAYW=3000

FLOORH=3000 !!floor height!!

BASE=1500 !!depth under GF to base!!

slabTh=120 !!5inch!!

unitwt=2.36e-5 !!!150pcf!!!

BDIV=4

LDIV=3

FFLOOR=1 !!!parameter for infill

generation!!!

SPMR=0 ! 1.0 FOR

FINDING SPMULT

tinfl=40 !!!total structural infill!!!

tinflf=0 !!ground floor infill %!!

*if,tinfl,LE,0,then

tinfl=0

*endif

pinflf=tinflf/2 !!!!percent infill at

ground floor!!!

nfpanl=(nspan*(nbay+1)+(nspan+1)*nbay)

ninflf=nint(nfpanl*pinflf/100)

nnflf=nfpanl*tinflf/100 !!!nnflf=no. of

infill at ground floor!!!

nnodeg=(nbay+1)*nspan*bdiv

pinfl=tinfl/2 !!!!percent infill at

other floors!!

npanel=(nspan*(nbay+1)+(nspan+1)*nbay)*(nfloor-1)

ninflx=nint(npanel*pinfl/100)

ntinfl=npanel*tinfl/100

FF=1.437e-3 !!!weight 30psf!!!

Ar=(BAYW*NBAY)*(SPANL*NSPAN)*(nfloor)

!!!!mass 30 psf!!!

PW=9.567e-4 !!!!minimum 20psf infill

weight!!!

Winfl=(ntinfl*spanl*floorh*2.395e-3)/Ar !!!5"or 127

mm brick wall=2.395e-3 N/mm2!!!

DL=(FF+PW+winfl)

LL=2.395e-3 !!!!weight 50 psf!!!

BEAMH=450

BEAMW=250

BEAMA=BEAMH*BEAMW

BEAMI1=(BEAMW*BEAMH**3)/12

BEAMI2=(BEAMH*BEAMW**3)/12

BEAMI3=BEAMI1+BEAMI2

CORH=350 !!!!corner column!!!!

CORW=350

CORA=CORW*CORH

CORI1=(CORW*CORH**3)/12

CORI2=(CORH*CORW**3)/12

CORI3=CORI1+CORI2

EXH=400 !!!!exterior column!!!!

EXW=400

EXA=EXH*EXW

EXI1=(EXW*EXH**3)/12

EXI2=(EXH*EXW**3)/12

EXI3=EXI1+EXI2

INTH=500 !!!!interior column!!!!

INTW=500

INTA=INTW*INTH

INTI1=(INTW*INTH**3)/12

INTI2=(INTH*INTW**3)/12

INTI3=INTI1+INTI2

g=9810.0

/PREP7

ET,1,BEAM4

MP,EX,1,20000

MP,PRXY,1,0.13

MP,DENS,1,2.4e-9

R,1,BEAMA,BEAMI1,BEAMI2,BEAMW,BEAMH,

RMORE,,BEAMI3

R,2,CORA,CORI1,CORI2,CORH,CORW,

RMORE,,CORI3

R,3,EXA,EXI1,EXI2,EXH,EXW,

RMORE,,EXI3

R,4,INTA,INTI1,INTI2,INTH,INTW,

RMORE,,INTI3

ET,2,SHELL63

R,5,slabth,slabth,slabth,slabth

ET,3,LINK8

MP,EX,2,20000

MP,PRXY,2,0.0

MP,DENS,2,0.0

R,10,75000

K,1,0,0,0

K,2,0,BASE,0

K,3,SPANL,BASE,0

K,4,SPANL,BASE,BAYW

K,5,0,BASE,BAYW

K,6,0,BASE+FLOORH,0

K,7,SPANL,BASE+FLOORH,0

K,8,SPANL,BASE+FLOORH,BAYW

K,9,0,BASE+FLOORH,BAYW

L,2,3

L,3,4

L,4,5

L,5,2

L,2,6

A,6,7,8,9

LSEL,S,LOC,Y,BASE+FLOORH/2,BASE+FLOORH/2

LGEN,NSPAN+1,ALL,,,SPANL

LSEL,S,LOC,Y,BASE+FLOORH/2,BASE+FLOORH/2

LGEN,NBAY+1,ALL,,,,,BAYW

LSEL,S,LOC,X,SPANL/2,SPANL/2

LGEN,NBAY,ALL,,,,,BAYW

LSEL,S,LOC,X,SPANL/2,SPANL/2

LGEN,NSPAN,ALL,,,SPANL

LSEL,S,LOC,Z,BAYW/2,BAYW/2

LGEN,NSPAN,ALL,,,SPANL

LSEL,S,LOC,Z,BAYW/2,BAYW/2

LGEN,NBAY,ALL,,,,,BAYW

LSEL,ALL

LGEN,NFLOOR,ALL,,,,FLOORH

ASEL,S,LOC,X,SPANL/2,SPANL/2

AGEN,NBAY,ALL,,,,,BAYW

ASEL,S,LOC,X,SPANL/2,SPANL/2

AGEN,NSPAN,ALL,,,SPANL

ASEL,ALL

AGEN,NFLOOR,ALL,,,,FLOORH

L,1,2

LSEL,S,LOC,Y,BASE/2,BASE/2

LGEN,NSPAN+1,ALL,,,SPANL

LSEL,S,LOC,Y,BASE/2,BASE/2

LGEN,NBAY+1,ALL,,,,,BAYW

NUMMRG,ALL

GPLOT

!MESHING

TYPE,1

!!!!!BEAM!!!!

REAL,1

*DO,VAR,1,NSPAN,1

LSEL,S,LOC,X,SPANL*(VAR-0.5),SPANL*(VAR-0.5)

LESIZE,ALL,,,BDIV,,1

LMESH,ALL

*ENDDO

*DO,VAR,1,NBAY,1

LSEL,S,LOC,Z,BAYW*(VAR-0.5),BAYW*(VAR-0.5)


LMESH,ALL

*ENDDO

!!!!!CORNER COLUMN!!!!!

REAL,2

*DO,VAR,1,NFLOOR,1

LSEL,S,LOC,Y,BASE+FLOORH*(VAR-0.5),BASE+FLOORH*(VAR-0.5)

LSEL,A,LOC,Y,BASE*(VAR+1-VAR)*0.5,BASE*(VAR+1-VAR)*0.5

LSEL,R,LOC,X,0,0

LSEL,R,LOC,Z,0,0

LESIZE,ALL,,,LDIV,,1

LMESH,ALL

*ENDDO

*DO,VAR,1,NFLOOR,1



LSEL,R,LOC,X,SPANL*NSPAN,SPANL*NSPAN

LSEL,R,LOC,Z,0,0


LMESH,ALL

*ENDDO

*DO,VAR,1,NFLOOR,1



LSEL,R,LOC,X,0,0

LSEL,R,LOC,Z,BAYW*NBAY,BAYW*NBAY


LMESH,ALL

*ENDDO

*DO,VAR,1,NFLOOR,1






LMESH,ALL

*ENDDO

!!!!!EXTERIOR COLUMN!!!!

*if,nspan,gt,1,then

REAL,3

*DO,VAR,1,NFLOOR,1



LSEL,R,LOC,X,(0.5*SPANL),(NSPAN-0.5)*SPANL

LSEL,R,LOC,Z,0,0


LMESH,ALL

*ENDDO

*DO,VAR,1,NFLOOR,1



LSEL,R,LOC,Z,(0.5*BAYW),(NBAY-0.5)*BAYW

LSEL,R,LOC,X,0,0


LMESH,ALL

*ENDDO

*DO,VAR,1,NFLOOR,1






LMESH,ALL

*ENDDO

*DO,VAR,1,NFLOOR,1






LMESH,ALL

*ENDDO

!!!!INTERIOR COLUMN!!!!

REAL,4

*DO,VAR,1,NFLOOR,1

LSEL,A,LOC,Y,BASE+FLOORH*(VAR-0.5),BASE+FLOORH*(VAR-0.5)





LMESH,ALL

*ENDDO

*endif

!!!!SLAB!!!!

TYPE,2

REAL,5

*DO,VAR,1,NSPAN,1

ASEL,S,LOC,X,SPANL*(VAR-0.5),SPANL*(VAR-0.5)


AMESH,ALL

*ENDDO

ALLSEL,ALL

/VIEW,1,1,1,1

GPLOT

!!!!DEAD LOAD SLAB CONTRIBUTION!!!!

MASSpF=DL*(BAYW*NBAY)*(SPANL*NSPAN)/g !!!MASS PER

FLOOR!!!

FLOORA=(SPANL*NSPAN)*(NBAY*BAYW)

MASSpA=MASSpF/FLOORA

X1=SPANL/BDIV

Z1=BAYW/BDIV

contA=(X1*Z1) !!!contributing

area!!!!

MSSpNI=(MASSpA)*contA !!!MASS PER internal

NODE !!!

MSSpNE=0.5*(MASSpA)*contA !!!MASS PER

external NODE !!!

MSSpNC=0.25*(MASSpA)*contA !!!MASS PER corner NODE

!!!

winflf=(nnflf*floorh*bayw*127*1.88e-5) !!!ground floor

infill contribution 120pcf!!!

winflg=winflf/nnodeg

msflgf=winflg/g

massgf=msflgf/2

ALLSEL,ALL

ET,4,MASS21

MP,DENS,3,2.4e-9

R,7,MSSpNI,MSSpNI,MSSpNI !!!MASS ELEMENT

GENERATION!!!

R,8,MSSpNE,MSSpNE,MSSpNE

R,9,MSSpNC,MSSpNC,MSSpNC

R,11,-MSSpNE,-MSSpNE,-MSSpNE

R,12,massgf,massgf,massgf

ALLSEL,ALL

TYPE,4

REAL,12

YY=BASE

DELGX=SPANL/BDIV

NpSPAN=(BDIV*NSPAN+1)

*DO,G1,1,NpSPAN,1

XX=(G1-1)*DELGX

*DO,G2,1,NBAY+1,1

ZZ=(G2-1)*BAYW

E,NODE(XX,YY,ZZ)

*ENDDO

*ENDDO

ALLSEL,ALL

TYPE,4

REAL,12

YY=BASE

DELGZ=BAYW/BDIV

NpBAY=(BDIV*NBAY+1)

*DO,G3,1,NSPAN+1,1

XX=(G3-1)*SPANL

*DO,G4,1,NPBAY,1

ZZ=(G4-1)*DELGZ

E,NODE(XX,YY,ZZ)

*ENDDO

*ENDDO

ALLSEL,ALL

TYPE,4

REAL,7

*DO,ME,1,NFLOOR,1 !!!ME- MASS ELEMENT!!!

YY=BASE+ME*FLOORH

DELX=SPANL/BDIV


*DO,N1,2,NpSPAN-1,1

XX=(N1-1)*DELX

DELZ=BAYW/BDIV

NpBAY=(BDIV*NBAY+1)

*DO,N2,2,NpBAY-1,1

ZZ=(N2-1)*DELZ

E,NODE(XX,YY,ZZ)

*ENDDO

*ENDDO

*ENDDO

ALLSEL,ALL

TYPE,4

REAL,8


YY=BASE+ME*FLOORH

DELX=SPANL/BDIV


*DO,N3,1,NpSPAN,1

XX=(N3-1)*DELX

DELZ=BAYW/BDIV

NpBAY=(BDIV*NBAY+1)

*DO,N4,1,NpBAY,NpBAY-1

ZZ=(N4-1)*DELZ

E,NODE(XX,YY,ZZ)

*ENDDO

*ENDDO

*ENDDO

ALLSEL,ALL

TYPE,4

REAL,8


YY=BASE+ME*FLOORH

DELX=SPANL/BDIV


*DO,N5,1,NpSPAN,NpSPAN-1

XX=(N5-1)*DELX

DELZ=BAYW/BDIV

NpBAY=(BDIV*NBAY+1)

*DO,N6,1,NpBAY,1

ZZ=(N6-1)*DELZ

E,NODE(XX,YY,ZZ)

*ENDDO

*ENDDO

*ENDDO

ALLSEL,ALL

TYPE,4

REAL,11


YY=BASE+ME*FLOORH

DELX=SPANL/BDIV



XX=(N20-1)*DELX

DELZ=BAYW/BDIV

NpBAY=(BDIV*NBAY+1)


ZZ=(N21-1)*DELZ

E,NODE(XX,YY,ZZ)

*ENDDO

*ENDDO

*ENDDO

ALLSEL,ALL

TYPE,4

REAL,9


YY=BASE+ME*FLOORH

DELX=SPANL/BDIV



XX=(N7-1)*DELX

DELZ=BAYW/BDIV

NpBAY=(BDIV*NBAY+1)


ZZ=(N8-1)*DELZ

E,NODE(XX,YY,ZZ)

*ENDDO

*ENDDO

*ENDDO

ALLSEL,ALL

!!!!infill data input!!!!

*IF,SPMR,NE,1,THEN

TYPE,3

REAL,10

*if,ninflx,gt,0,then

count=0

*dim,store1,array,nspan+5,nfloor+5,nbay+5

rmainx=ninflx

*dowhile,rmainx

/gopr

Xa=nint(rand(1,nspan))

ya=nint(rand(1,nfloor-1))

za=nint(rand(1,nbay+1))

*if,store1(xa,(ya+1),za),eq,0,then

E,NODE((xa-1)*spanl,base+FLOORH+ya*FLOORH,(za-

1)*bayw),NODE(xa*spanl,(base+floorh+(ya-1)*floorh),(za-

1)*bayw)

store1(xa,(ya+1),za)=1

count=count+1

rmainx=ninflx-count

*else

count=count

rmainx=ninflx-count

*endif

*enddo

*endif

TYPE,3

REAL,10

*if,ninflx,gt,0,then

count=0

*dim,store2,array,nspan+5,nfloor+5,nbay+5

rmainx=ninflx

*dowhile,rmainx

/gopr

Xa=nint(rand(1,nspan+1))

ya=nint(rand(1,nfloor-1))

za=nint(rand(1,nbay))

*if,store2(xa,(ya+1),za),eq,0,then

E,NODE((xa-1)*spanl,base+FLOORH+ya*FLOORH,(za-

1)*bayw),NODE((xa-1)*spanl,(base+floorh+(ya-

1)*floorh),za*bayw)

store2(xa,(ya+1),za)=1

count=count+1

rmainx=ninflx-count

*else

count=count

rmainx=ninflx-count

*endif

*enddo

*endif

TYPE,3

REAL,10

*if,ninflf,gt,0,then

count=0

*dim,storeF,array,nspan+5,FFLOOR,nbay+5

rmainf=ninflf

*dowhile,rmainf

/gopr

Xa=nint(rand(1,nspan))

ya=FFLOOR

za=nint(rand(1,nbay+1))

*if,storeF(xa,ya,za),eq,0,then

E,NODE((xa-

1)*spanl,base+FLOORH,(za)*bayw),NODE(xa*spanl,base,za*bayw)

storeF(xa,ya,za)=1

count=count+1

rmainf=ninflf-count

*else

count=count

rmainf=ninflf-count

*endif

*enddo

*endif

TYPE,3

REAL,10

*if,ninflf,gt,0,then

count=0

*dim,store3,array,nspan+5,FFLOOR,nbay+5

rmainf=ninflf

*dowhile,rmainf

/gopr

Xa=nint(rand(1,nspan+1))

ya=FFLOOR

za=nint(rand(1,nbay))

*if,store3(xa,ya,za),eq,0,then

E,NODE((xa)*spanl,base+FLOORH,(za-

1)*bayw),NODE(xa*spanl,base,za*bayw)

store3(xa,ya,za)=1

count=count+1

rmainf=ninflf-count

*else

count=count

rmainf=ninflf-count

*endif

*enddo

*endif

*ENDIF

ALLSEL,ALL

/ESHAPE,1,0

!!!!SUPPORT CONDITION!!!!

NUMMRG,NODE

/SOLU

NSEL,S,LOC,Y,0,0

D,ALL,ALL,0

Nsel,all

ALLSEL,ALL

!!Single point reponse spectrum analysis!!

!modal analysis

antype,modal

modopt,lanb,nfloor*2

solve

finish

!!spectrum analysis!!

/solu

DMPRAT,0.05

Antype,spectr

spopt,sprs

FREQ, 1/100, 1/10, 1/3.0, 1/2.5, 1/2, 1/1.5, 1/1.0,

1/0.8, 1/0.75

SV,0.05, 0.65, 0.7, 0.75, 0.8, 1.2, 1.5, 2.2,

2.5, 2.5

FREQ, 1/0.5, 1/0.15, 1/0.0001

SV,0.05, 2.5, 2.5, 2.5

SED,1,0,0 !!Defines the excitation

direction for SPRS!!

SVTYP,2,9810*0.15/8

SOLVE

FINISH

!!MODE EXPANSION!!

nsel,all

allsel,all

/SOLU

ANTYPE,MODAL

EXPASS,ON

MXPAND,,,,YES,1.0e-5

SOLVE

FINISH

/SOLU

ANTYPE,SPECTR

CQC,1.0e-5,DISP

SOLVE

FINISH

/POST1

SET,LIST

/INPUT,,MCOM

ALLSEL,ALL

LCWRITE,1

sumfx=0

*do,isuppx,1,nspan+1,1

xx=(isuppx-1)*spanl

*do,isuppz,1,nbay+1,1

zz=(isuppz-1)*bayw

yy=0

nn1=node(xx,yy,zz)

*GET,fxn,NODE,nn1,rf,fx

SUMFX=sumfx+fxn

*ENDDO

*enddo

finish

/SOLU

ANTYPE,static

ALLSEL,ALL

ACEL,0,g,0

ALLSEL,ALL

LSWRITE,1

/solu

FDELE,ALL,ALL

SFEDELE,ALL,ALL,ALL

sfdele,all,all

ALLSEL,ALL

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

/solu !!!LIVE LOAD APPLICATION!!!!

ESEL,S,REAL,,5

SFE,all,1,PRES,1,LL

ACEL,0,0,0

ALLSEL,ALL

LSWRITE,2

/solu

ALLSEL,ALL

FDELE,ALL,ALL

SFEDELE,ALL,ALL,ALL

ALLSEL,ALL

!!!Calculation for seismic dead load!!!

/solu

Wb1=beamh*beamw*spanl*nspan*(nfloor)*(nbay+1)*unitwt

wgb1=beamh*beamw*spanl*nspan*(nbay+1)*unitwt

Wb2=beamh*beamw*bayw*nbay*(nfloor)*(nspan+1)*unitwt

wgb2=beamh*beamw*bayw*nbay*(nspan+1)*unitwt

Wcor=corh*corw*4*(floorh*nfloor)*unitwt

Wcoru=corh*corw*4*(base)*unitwt

Wex=exh*exw*(2*(nspan-1+nbay-1))*(floorh*nfloor)*unitwt

Wexu=exh*exw*(2*(nspan-1+nbay-1))*(base)*unitwt

wint=inth*intw*(nspan-1)*(nbay-1)*(floorh*nfloor)*unitwt

wintu=inth*intw*(nspan-1)*(nbay-1)*(base)*unitwt

Wslab=unitwt*slabTH*nspan*spanl*nbay*bayw*nfloor

Wff=FF*nspan*spanl*nbay*bayw*nfloor

Wpw=PW*nspan*spanl*nbay*bayw*nfloor

Winfll=(ntinfl*spanl*floorh*2.39e-3) !!!5"or

127 mm brick wall=2.39e-3 N/mm2!!!

wu=wgb1+wgb2+wcoru+wexu+wintu+winflf

total=(Wb1+wb2+wcor+wex+wint+wslab+wff+wpw+Winfll)

TSW=total+wu

wpf=total/nfloor

!!!seismic calculations!!!

Ct=0.073

hn=(base+nfloor*floorh)/1000

T=Ct*(hn**(3/4))

S=1.5

C=(1.25*S)/(T**(2/3))

*if,C,gt,2.75,then

C=2.75

*endif

W=TSW

Z=0.15

I=1.00

R=8

V=Z*I*C*W/R

!!!modifier to rsm!!!

spmult=-1.56466

*if,SPMR,EQ,1,then

spmult=-v/sumfx

*endif

Ft=0.0

*if,T,gt,0.7,then

Ft=0.07*T*V

*endif

*if,Ft,gt,(0.25*V),then

Ft=0.25*V

*endif

sumwhi=wu*base

*do,ifl,1,nfloor,1

sumwhi=sumwhi+wpf*(base+(floorh*ifl))

*enddo

*do,hy,base,(base+nfloor*floorh),floorh

*if,hy,eq,base,then

force=(V-Ft)*wu*hy/sumwhi

*endif

*if,hy,gt,base,then

force=(V-Ft)*wpf*hy/sumwhi

*endif

*if,hy,eq,(base+nfloor*floorh),then

force=force+Ft

*endif

*do,hz,0,nbay*bayw,bayw

f,node(0,hy,hz),fx,(force/(nbay+1))

*enddo

*enddo

ALLSEL,ALL

lswrite,3

fdele,all,all

allsel,all

LSSOLVE,1,3,1

*CFOPEN,WS,TXT

*VWRITE,W,V

(/"WEIGHT OF STRUCTURE=",F20.6,"N"//"BASE SHEAR=",F20.6,"N")

*CFCLOS

!!!POST PROCESS!!!

/post1

!!!dead load case!!!

lczero

lcdef,2,1,1

lcoper,add,2

lcwrite,2

!!!live load case!!!

lczero

lcdef,3,2,1

lcoper,add,3

lcwrite,3

!!!static EQ!!!

lczero

lcdef,4,3,1

lcoper,add,4

lcwrite,4

!!!modifying rsm method and saving as loadcase 5!!!

lczero

lcfact,1,spmult

lcoper,add,1

lcwrite,5

!!!REACTION FOR!!!

!!1. DL!!!

!!2. LL!!!

!!3. EQ STATIC!!!

!!4. EQ (response spectrum)!!!

!!!cALCULATION FOR DL!!!

LCFILE,2

LCASE,2

SUMFXD=0

SUMFYD=0

SUMFZD=0


xx=(isuppx-1)*spanl


/gopr

zz=(isuppz-1)*bayw

yy=0

nn1=node(xx,yy,zz)


*GET,fyn,NODE,nn1,rf,fy

*GET,fzn,NODE,nn1,rf,fz

SUMFXD=sumfxd+fxn

SUMFYD=sumfyd+fyn

SUMFZD=sumfzd+fzn

*ENDDO

*enddo

!!!calculation reaction for LL!!

LCFILE,3

LCASE,3

SUMFXL=0

SUMFYL=0

SUMFZL=0


xx=(isuppx-1)*spanl


/gopr

zz=(isuppz-1)*bayw

yy=0

nn1=node(xx,yy,zz)




SUMFXL=sumfxL+fxn

SUMFYL=sumfyL+fyn

SUMFZL=sumfzL+fzn

*ENDDO

*enddo

!!!calculation reaction for eq(static)!!!

LCFILE,4

LCASE,4

SUMFXS=0

SUMFYS=0

SUMFZS=0


xx=(isuppx-1)*spanl


/gopr

zz=(isuppz-1)*bayw

yy=0

nn1=node(xx,yy,zz)




SUMFXS=sumfxS+fxn

SUMFYS=sumfyS+fyn

SUMFZS=sumfzS+fzn

*ENDDO

*enddo

!!! calculate reaction for response spectrum method!!!

lcfile,5

lcase,5

sumfxq=0

sumfyq=0

sumfzq=0


xx=(isuppx-1)*spanl


/gopr

zz=(isuppz-1)*bayw

yy=0

nn1=node(xx,yy,zz)




SUMFXq=sumfxq+fxn

SUMFYq=sumfyq+fyn

SUMFZq=sumfzq+fzn

*ENDDO

*enddo

!!!Write reaction in file!!!

*CFOPEN,reaction,TXT

*VWRITE,SUMFYD,SUMFYL,SUMFXS,SUMFXq

(//"REACTIONS FOR DIFFERENT LOAD CASES : "/"DL

:",F20.6,"N"/"LL :",F20.6,"N"/"EQ(Static)

:",F20.6,"N"/"EQ(rsm) :",F20.6,"N")

*CFCLOS

!!!factored load combinations!!!

!! 1. DL*1.4 loadcase6

!! 2. 1.4*DL+1.7*LL loadcase7

!! 3. 1.05*DL+1.275*LL+1.4*EQ(STATIC) LOADCASE8

!! 4. 1.05*DL+1.275*LL-1.4*EQ(STATIC) LOADCASE9

!! 5. 1.05*DL+1.275*LL+1.4*EQ(RSM) LOADCASE10

!! 6. 1.05*DL+1.275*LL-1.4*EQ(RSM) LOADCASE11

! 1. DL*1.4

lczero

lcfact,2,1.4

lcoper,add,2

lcwrite,6

! 2. 1.4*DL+1.7*LL

lczero

lcfact,2,1.4

lcfact,3,1.7

lcoper,add,2

lcoper,add,3

lcwrite,7

! 3. 1.05*DL+1.275*LL+1.4*EQ(STATIC)

lczero

lcfact,2,1.05

lcfavt,3,1.275

lcfact,4,1.4

lcoper,add,2

lcoper,add,3

lcoper,add,4

lcwrite,8

!! 4. 1.05*DL+1.275*LL-1.4*EQ(STATIC)

lczero

lcfact,2,1.05

lcfavt,3,1.275

lcfact,4,-1.4

lcoper,add,2

lcoper,add,3

lcoper,add,4

lcwrite,9

! 5. 1.05*DL+1.275*LL+1.4*EQ(RSM)

lczero

lcfact,2,1.05

lcfact,3,1.275

lcfact,5,1.4

lcoper,add,2

lcoper,add,3

lcoper,add,5

lcwrite,10

! 6. 1.05*DL+1.275*LL-1.4*EQ(RSM)

lczero

lcfact,2,1.05

lcfact,3,1.275

lcfact,5,-1.4

lcoper,add,2

lcoper,add,3

lcoper,add,5

lcwrite,11

! 7. 1*DL+1*EQ(RSM)

lczero

lcfact,2,1

lcfact,5,1

lcoper,add,2

lcoper,add,5

lcwrite,12

! 8. 1*DL+1*EQ(static)

lczero

lcfact,2,1

lcfact,4,1

lcoper,add,2

lcoper,add,4

lcwrite,13

!!!deflection of different levels due to 1*DL+1*EQ(rsm)

*cfopen,drift-rsm,txt

lcfile,12

lcase,12

*do,n,1,nfloor,1

*get,sway,node,node(0,base+n*floorh,0),u,x

*vwrite,n,sway

(//"Level",F5.0,":sway=",F12.6,"mm")

*enddo

*cfclos

*cfopen,drift-static,txt

lcfile,13

lcase,13

*do,n,1,nfloor,1

*get,sway,node,node(0,base+n*floorh,0),u,x

*vwrite,n,sway

(//"Level",F5.0,":sway=",F12.6,"mm")

*enddo

*cfclos

!!topmost level deflection!!

*cfopen,deflection,txt

*do,ncase,1,11,1

lcfile,ncase

lcase,ncase

*get,sway,node,node(0,base+nfloor*floorh,0),u,x

*vwrite,ncase,sway

(//"case",F5.0,":sway=",F12.6,"mm")

*enddo

*cfclos

effect of randomly distributed infills on seismic base shear for rc buildings with soft ground floor...

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