seismic performance of an irregular structure with …

SEISMIC PERFORMANCE OF AN IRREGULAR STRUCTURE WITH

AND WITH OUT SETBACKS USING E-TABS

A.Janardhan [1], Vuppu Karthik Kumar[2], Srija Nataraj[3]

1. Assistant Professor, Dept. of Civil Engineering, SIIET, Hyderabad, Telangana. 2. Assistant Professor, Dept. of Civil Engineering, SIIET, Hyderabad, Telangana. 2 M.Tech Student, Dept. of Structural Engineering, SDES, Sheriguda, Hyderabad, Telangana 3 [email protected], 9441010096, 2 [email protected],9441360577, 3 [email protected] , 9666644848

ABSTRACT

A common type of vertical geometrical irregularity in building structures arises from abrupt reduction of

the lateral dimension of the building at specific levels of the elevation. This type of building is known as

the setback building. Earthquake is an important aspect to be considered while designing structures.

Many researchers have worked to study the effect of structures with irregular plan. This paper presents

effects of plan and shape configuration on irregular shaped structures. Buildings with irregular geometry

respond differently against seismic action. The parameter that decides the performance against different

loading conditions is Plan Geometry. The effect of irregularity(plan) on structure have been carried out

using structural analysis software E-TABS for different types of soil. There are several factors which

affect the behaviour of building from which storey drift and lateral displacement play an important role in

understanding the behaviour of structure. Results are expressed in form of graphs and bar charts. Based

on these, conclusions have been presented.

Key words: Set back, Earthquake, E-TABS (software for structural analysis).

1. INTRODUCTION:

Earthquakes are the most unpredictable and devastating of all natural disasters, which are very difficult to save over

engineering properties and life, against it. Hence in order to overcome these issues we need to identify the seismic

performance of the built environment through the development of various analytical procedures, which ensure the

structures to withstand during frequent minor earthquakes and produce enough caution whenever subjected to major

earthquake events so that it can save as many lives as possible. The analysis procedure quantifying the earthquake

forces and its demand depending on the importance and cost, the method of analysing the structure varies from linear

to non linear. The behaviour of a building during an earthquake depends on several factors, stiffness, and adequate

lateral strength, and ductility, simple and regular configurations. The buildings with regular geometry and uniformly

distributed mass and stiffness in plan as well as in elevation suffer much less damage compared to irregular

configurations. But nowadays need and demand of the latest generation and growing population has made the

architects or engineers inevitable towards planning of irregular configurations.

International Journal of Research

Volume VIII, Issue I, January/2019

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1.1 GLOBAL DEFICIENCIES:

Global deficiencies can broadly be classified as plan irregularities and vertical irregularities, as per the Code.

Some of the observed irregularities are as follows:

Plan Irregularities:

Torsional irregularity due to plan symmetry and eccentric mass from water tank.

Frequent re-entrant corners.

Diaphragm discontinuity due to large openings or staggered floors, along with the absence of collector

elements.

Out-of-plane offset for columns along perimeter.

Nonparallel lateral load resisting systems (not observed in the building studied).

Vertical Irregularities:

Stiffness irregularity, soft storey due to open ground storey.

Mass irregularity (not observed in the building studied).

Vertical geometric irregularity from set-back towers.

In-plane discontinuity for columns along the perimeter of the building.

Weak storey due to open ground storey.

Fig 1.1 Plan Irregularity Fig 1.2 Vertical Irregularity



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2. METHOD OF ANALYSIS:

2.1 METHODOLOGIES USED IN THE PRESENT STUDY:

Linear Dynamic analysis – Response Spectrum analysis as per IS 1893:2002

Non-linear Dynamic analysis – Time History analysis

2.1.1 Response Spectrum Method (Linear Dynamic Analysis)

This method is applicable for those structures where modes other than the fundamental one affect

significantly the response of the structure. In this method, the response of Multi-Degree-of-Freedom (MDOF)

system is expressed as the superposition of modal response, each modal response being determined from the spectral

analysis of single-degree-of-freedom (SDOF) system, which are then combined to compute the total response.

Modal analysis leads to the response history of the structure to a specified ground motion; however, the method is

usually used in conjunction with a response spectrum.

Methods of Analysis

Linear Non - Linear

Non-LinearDynamic Non – linear Static Dynamic Static

Seismic

Coefficient

Time History

Analysis

Push over

Analysis

Response

Spectrum

method



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2.1.1.1 Calculation of the Method

The maximum modal displacement, for a structural modal, can now be calculated for a typical mode n with

period Tn and corresponding spectrum responses value S(ωn). The maximum modal response associated with period

Tn is given by

Y(Tn)MAX = S(ωn) / ω2n

The maximum modal displacement response of the structural modal is calculated from

Un = Y(Tn)MAXφn

The corresponding internal modal forces are calculated from standard matrix structural analysis using the

same equations as required in static analysis.

2.1.2 Non-Linear Time History Analysis

In nonlinear dynamic procedure the building model is similar to the one used in non-linear static

procedures incorporating directly the inelastic material response using in general finite elements. The main

difference is that seismic input is modelled using a time history analysis, which involves time-step-by-time-step

evaluation of the building response.

Whenever structure is subjected to strong earthquake excitation, it may not remain in linear range. The

main advantage of non-linear time history analysis is stiffness of the structure is updated each and every time

step.The governing equation for an elastic system is:

Mü + ců + fs(u,ů) = -müg(t)

3. NUMERICAL STUDIES:

Example Buildings Studied

The plan layout, elevation and 3D view of the reinforced concrete moment resisting frame building of 15

storied building for a symmetrical building with and without set back and an asymmetrical building with and

without set back. In this study, the plan layout is deliberately kept similar for the buildings under study. The each

storey height is kept 3 m for all the 4 building models. The buildings are considered to be located in the seismic

zone-2 and intended for commercial (Hotel) use. In the seismic weight calculations only 25% of the floor live load

is considered. The input data given for all the different buildings is detailed below.

Design Data



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Material Properties

Model 1:

Young’s modulus of (M30) concrete, E = 27.386x106 KN/m²

Young’s modulus of (M25) concrete, E = 25x106 KN/m²

Density of Reinforced Concrete = 25KN/m³

Assumed Dead load intensities

Floor finishes = 1.5KN/m²

Live load (Rooms) = 3 KN/ m²

Member properties

Thickness of Slab = 0.125m

Column size for all floors = (0.6mx0.6m),(0.3mx0.60m)

Beam size = (0.23m x 0.575m)

Earthquake Live Load on Slab as per clause 7.3.1 and 7.3.2 of IS 1893 (Part-I) - 2002 is calculated as:

IS: 1893-2002 Equivalent Static method

Design Spectrum

Zone – II

Zone factor, Z (Table2) – 0.10

Importance factor, I (Table 6) – 1.0

Response reduction factor, R (Table 7) – 5.00

Vertical Distribution of Lateral Load,

n

jjj hw

iiBi

hwVf

12

2

IS: 1893-2002 Response Spectrum Method: Spectrum is applied from fig.2 of the code corresponding to medium

soil sites. The spectrum is applied in the longitudinal and transverse directions.



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4. CALCULATIONS:

Natural periods and average response acceleration coefficients:

For Eight – Storied building with Setback:

Fundamental Natural period, Ta= 0.075*h0.75 (For Bay Frame)

= 0.075*50.40.75

= 1.4186sec

For medium soil sites, Sa/g = �.��

� (Because 0.55 ≤ T ≤ 4.00)

= �.��

�.�� = 0.9586

Design horizontal seismic coefficient, g

Sax

R

Ix

ZAh

2

Ah = �.��

��

�

� � 0.9586 = 0.00956

Design Seismic Base Shear for Model 1 = VB = -------- KN

4.1 PERFORMED ANALYSIS IN ETABS:

The analysis and design of the building is carried out using ETABS computer program. The following

topics describe some of the important areas in the modelling. The innovative and revolutionary new ETABS is the

ultimate integrated software package for the structural analysis and design of buildings. Incorporating 40 years of

continuous research and development, this latest ETABS offers unmatched 3D object based modelling and

visualization tools, blazingly fast linear and nonlinear analytical power, sophisticated and comprehensive design

capabilities for a wide-range of materials, and insightful graphic displays, reports, and schematic drawings that

allow users to quickly and easily decipher and understand analysis and design results.

Defining of the slab sections

Equivalent Static Analysis

Response Spectrum Analysis



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4.2 STEPS BY STEP PROCEDURE FOR RESPONSE SPECTRUM METHOD:

Step-1

Depending on the location of the building site, identify the seismic zone and assign Zone factor (Z) (Use

Table 2 along with Seismic zones map or Annex of IS-1893 (2002).

Step-2

Compute the seismic weight of the building (W) As per Clause 7.4.2, IS-1893 (2002) Seismic weight of

floors (Wi).

Step-3

Establish mass [M]and stiffness [K]matrices of the building using system of masses lumped at the floor

levels with each mass having one degree of freedom, that of lateral displacement in the direction under

consideration. Accordingly, to develop stiffness matrix effective stiffness of each floor is computed using

the lateral stiffness coefficients of columns and infill walls. Usually floor slab is assumed to be infinitely

stiff.

Step-4

Using [M]and [K]of previous step and employing the principles of dynamics compute the modal

frequencies, (�) and corresponding mode shapes, (Ф).

Step-5

Compute modal mass Mkof mode k using the following relationship with n being number of modes

considered

�� =[∑ ��∅��

�� ]�

� ∑ ��∅��

��

[Clause 7.8.4.5a of IS 1893 (2002)]

Step-6

Compute modal participation factors Pkof mode k using the following relationship with n being number of

modes considered

�� =∑ ��∅��

��

∑ ��∅��

��

[Clause 7.8.4.5b of IS 1893 (2002)]

Step-7

Compute design lateral force (Qik) at each floor in each mode (i.e., for ithfloor in mode k) using the

following relationship,

Qik=AkФikPkWi [Clause 7.8.4.5c of IS 1893 (2002)]

A = Design horizontal acceleration spectrum value as per Clause 6.4.2 of IS 1893 using the natural period

�� =��

�

Step-8

Compute storey shear forces in each mode (Vik) acting in storey iin mode k as given by,

�� = ∑ Q�� ik

Step-9



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Compute storey shear forces due to all modes considered, Vi in storey i, by combining shear forces due to

each mode in accordance with Clause 7.8.4.4 of IS 1893 (2002). i.e., either CQC or SRSS modal

combination methods are used.

Step-10

Finally compute design lateral forces at each storey as,

Froof =Vroof

Fi= Vi– Vi+1

5.1 DATA ANALYSIS

1: ASYMMETRICAL L SHAPED BUILDING WITH SET BACKS:

Model 1:

Young’s modulus of (M30) concrete, E = 27.386x106 KN/m²

Young’s modulus of (M25) concrete, E = 25x106 KN/m²

Density of Reinforced Concrete = 25KN/m³

Assumed Dead load intensities

Floor finishes = 1.5KN/m²

Live load (Rooms) = 3 KN/ m²

Member properties

Thickness of Slab = 0.125m

Column size for all floors = (0.6mx0.6m),(0.3mx0.60m)

Beam size = (0.23m x 0.575m)

Earthquake Live Load on Slab as per clause 7.3.1 and 7.3.2 of IS 1893 (Part-I) - 2002 is calculated as:

IS: 1893-2002 Equivalent Static method

Design Spectrum

Zone – II

Zone factor, Z (Table2) – 0.10

Importance factor, I (Table 6) – 1.0



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Response reduction factor, R (Table 7) – 5.00

Vertical Distribution of Lateral Load,

n

jjj hw

iiBi

hwVf

12

2

IS: 1893-2002 Response Spectrum Method: Spectrum is applied from fig.2 of the code corresponding to medium

soil sites. The spectrum is applied in the longitudinal and transverse directions.

6 .CALCULATIONS:

Natural periods and average response acceleration coefficients:

For Eight – Storied building with Setback:

Fundamental Natural period, Ta= 0.075*h0.75 (For Bay Frame)

= 0.075*50.40.75

= 1.4186sec

For medium soil sites, Sa/g = �.��

� (Because 0.55 ≤ T ≤ 4.00)

= �.��

�.�� = 0.9586

Design horizontal seismic coefficient, g

Sax

R

Ix

ZAh

2

Ah = �.��

��

�

� � 0.9586 = 0.00956

Design Seismic Base Shear for Model 1 = VB = -------- KN



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BASE SHEAR EQX: 604.81KN BASE SHEAR EQY: 606.46KN

BASE SHEAR RESPX: 390.31KN BASE SHEAR RESPY: 294.39KN



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CENTRE OF MASS AND CENTRE OF RIGIDITY: due to EQ-X &EQ-Y direction

Table 6.1 Centre of mass and centre of rigidity

STORY DRIFT:

( A )



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(B)

(C)

Table 6.2 Story drift



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STORY SHEAR: the shear and torsion developed at every floor due to EQ-X:

(A)

Table 6.3 Shear and torsion developed at every floor

SHEAR AT THE BASE: 606.48KN

TORSION MOMENT: 5805.751KN-M

DESIGN MOMENT: 22865.217KN-M



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STORY SHEAR: the shear and torsion developed at every floor due to EQ-Y

(B)

Shear and torsion developed at every floor

SHEAR AT THE BASE: 606.48KN

TORSION MOMENT: 3877.774KN-M

DESIGN MOMENT: 22865.217KN-M

MODAL PARTICIPATING MASS RATIOS:

Table 6.4 Modal participating mass ratios



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7. GRAPHS:

7.1 EQ-X (BASE SHEAR KN)

7.2 EQ-Y (BASE SHEAR KN)

7.3 RESP-X(BASE SHEAR KN)

7.4 RESP-Y (BASE SHEAR KN)

7.5 EQ-X(TORSION MOMENT KN-M)

7.6 EQ-X (DESIGN MOMENT KN-M)



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7. CONCLUSION:

Concluded that the difference in elastic and inelastic story drifts between set-back and regular structures

depends on the level of story.

Critical setback ratio RA=0.25 and RH=6/5 shows the variation in story drift which signifies the jumping

of the forces due to unequal distribution of mass along the plan as well as along the height.

Higher ductility demands for set-back structures than for the regular ones and found this increase to be

more pronounced in the tower portions.

When the mass of one floor increases by 50%, the increase in ductility demand is not greater than 20%.

Reducing the stiffness of the first story by 30%, while keeping the strength constant, increases the first

story drift by 20-40%, depending on the design ductility (μ).

The excessive deformation in vertical members often leads to collapse of the storey.

Regular buildings: Those greater than 40m in height in zones IV and V, and those greater than 90m in

height in zones II and III.

Irregular buildings: All framed buildings higher than 12m in zones IV and V, and those greater than 40m in

height in zones II and III.

Mass and stiffness are evenly distributed with building height, thus giving a regular mode shape.

8. REFERENCE:

1. K. CHOPRA – STRUCTUREAL DYNAMICS

2. S.K. DUGGAL – EARTQUKE ANALYSIS OF STRUCTURE

3. PANKAJ AGRAWAL & MANISH SHRIKHANDE – REPAIR AND RETROFITING OF

STRUCTURE

4. Aranda, H., G. R. (1984). "Ductility demands for R/C frames irregular in elevation."Proc, Eighth World

Conf. on Earthquake Engrg., IV, San Francisco, Calif.,559-566.

5. Arnold, C. (1980)."Building configuration: Characteristics for seismic design."Proc,Seventh World

Conf. on Earthquake Engrg., 4, Istanbul, Turkey, 589-592

6. Arnold, C , and Elsesser, E. (1980)."Building configuration: Problems and solutions." Proc, Seventh

World Conf. on Earthquake Engrg., 4, Istanbul, Turkey, 153-160.

7. Blume, J. A., and Jhaveri, D. P. (1969)."Time-history response of buildings with unusual

configurations." Proc, Fourth World Conf. on Earthquake Engrg., Ill,Session A3, Santiago, Chile, Jan.,

155-170.

8. Clough, R. W., and Penzien, J. (1975). Dynamics of structures. McGraw-Hill, NewYork, N.Y,

9. Gardis, P. G., et al. (1982)."The Central Greece earthquakes of Feb.-March 1981."A Reconnaissance

0and Engrg.Rept., Nat. Academy Press, Washington, D.C.



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1.

A JANARDHAN, M TECH (STRUCTURAL ENGINEERING)

ASST PROFESSOR (2 YEARS)

SRI INDU INSTITUTE OF ENGINEERING AND TECHNOLOGY

2

VUPPU KARTHIK KUMAR, M TECH(TRANSPORTATION ENGINEERING)

ASST PROFESSOR (2 YEARS)

SRI INDU INSTITUTE OF ENGINEERING AND TECHNOLOGY



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3.

SRIJA NATARAJ, M TECH(STRUCTURAL ENGINEERING)

STUDENT

SRI DATTA COLLEGE OF ENGINEERING AND SCIENCE



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seismic performance of an irregular structure with …

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