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EFFECTS OF PLANS CONFIGURATION ON

SEISMIC VULNERABILITY OF RC BUILDING

A dissertation submitted to

Visvesvaraya Technological University, BelgaumFor the partial fulfillment of

Master of Technology

in

Structural Engineering

By

KHAMRULISLAM.M.NALBAND

(USN: 5XG11CSE07)

Under the guidance of

Prof. SIDDALINGAPPA.S

GOVERNMENT OF KARNATAKA

DEPARTMENT OF TECHNICAL EDUCATION

GOVERNMENT ENGINEERING COLLEGE

DEVAGIRI, HAVERI- 581 110 2012-2013



GOVERNMENT OF KARNATAKA

DEPARTMENT OF TECHNICAL EDUCATION

GOVERNMENT ENGINEERING COLLEGE

DEVAGIRI, HAVERI - 581 110DEPARTMENT OF CIVIL ENGINEERING

Certificate

Certified that the project work entitled “Effects of Plans Configuration on Seismic

Vulnerability of RC Building” carried out by Mr. Khamrulislam.M.Nalband

(USN: 5XG11CSE07), a bonafide student of Government Engineering College, Haveri

in partial fulfillment for the award of Master of Technology in Structural Engineering

of the Visvesvaraya Technological University, Belgaum during the year 2012-2013. It iscertified that, all the corrections / suggestions indicated for internal assessment have been

incorporated in the report deposited in the department library. The project report has been

approved as it satisfies the academic requirements in respect of project work prescribed

for the said Degree.

External Viva

Name of the examiners Signature with date

1.

2.

…………………………………..

Signature of the Guide

Prof. Siddalingappa.S

………………………………

Signature of the HODDr. Jagadish G. Kori

……………………………..

Signature of the Principal

Dr. K.B. Prakash



CANDIDATE‟S DECLARATION

This is for the firm assertion of the concerned authorities that the dissertation work

entitled “Effects of Plans Configuration on Seismic Vulnerability of RC Building”

has been completed by the undersigned strictly on an individual basis for the partial

fulfillment of the requirements for the award of “Master of Technology” in

“Structural Engineering”, under Visvesvaraya Technological University, Belgaum

during the year 2012-13.

The investigation report and results presented in the dissertation work has not been

submitted to any University (or) Institution for the award of any Degree (or) Diploma.

Place: Haveri KHAMRULISLAM.M.NALBAND

Date: M. Tech. (Structural Engg)

(USN: 5XG11CSE07)



i

ACKNOWLEDGEMENT

The satisfaction that accompanies the successful completion of any task would be

incomplete without the mention of the people who make it possible whose constant

guidance and encouragement crown all the efforts with success.First and foremost I would like to place on record my heartiest gratitude to my guide,

Prof. Siddalingappa.S Civil Engineering department, Government Engineering College,

Haveri, for having taken me under his guidance and helped me with his invaluable

suggestions and excellent guidance.

Though it may appear that the following exposition is a monotonous boat of an unusual

acknowledgement assert beyond the confines of the simple sense of the owned gratitude

to pass on my deep felt thanks on our beloved Dr. Jagadish G. Kori, Head of the

department, Civil Engineering department, Government Engineering College, Haveri, on

their excellent guidance.

I express my deep gratitude to my institute, Government Engineering College, Haveri,

which provide an opportunity and platform for fulfilling my dreams, and desire to reach

my goal.

I sincerely thank my respected Dr. K. B. Prakash, Principal, Government Engineering

College, Haveri, who is the constant source of inspiration, throughout the academics.

I am grateful to my Parents and Friends who have been great support throughout the

development of my project. Last but not the least I would like to extend my thanks to the

teaching and non-teaching staff of our department and well-wishers for their timely help

either directly or indirectly for the completion of my project.

KHAMRULISLAM.M.NALBAND



ii

ABSTRACT

Many buildings in the present scenario have irregular configurations both in plan and

elevation. This in future may subject to devastating earthquakes. In model, it is necessary

to identify the performance of the structures to withstand against disaster for buildingstructures. In Oder to identify the most vulnerable building among the models considered,

the various analytical approaches are performed to identify the seismic demands in both

linear and nonlinear way. It is also examined the effect of different lateral load patterns on

the performance of various irregular buildings in pushover analysis. This study creates

awareness about seismic vulnerability concept on practicing engineers. Nonlinear static

analysis has been adopted for a project work, this is an iterative procedure so it is difficult

to solve by hand calculation and that‘s why software is required to do nonlinear static

analysis. ETABS 9.7 have features to perform nonlinear static analysis. This project is an

approach to do nonlinear static analysis in simplify and effective manner. An analysis has

been performed to study the lateral forces and base shear of a Multi-storeyed (10-story)

building for ten different models. 1st model is when the shape is regular/rectangular

configuration, 2nd model is of L-shape, 3rd model is of T-shape, 4th model is of Plus-

shape, 5th model is C-shape, 6th

model is H-shape, 7th

model is S-shape, 8th

model is

Diaphragm Discontinuity, 9th

model is Staggered(Z1) shape and 10th

model is

Staggered(Z2) type . Building is subjected to earthquake load in accordance with

equivalent static force method as per IS 1893(Part 1): 2002. To perform analysis by

equivalent static force method ETABS V9.7 is used and also all models have been

validated in MS Excel tool for comfort manual calculations. Equivalent static force

method produces same Magnitude of earthquake. However, when the buildings are

subjected to Pushover analysis method, significant increase in lateral forces as well as

total base shear has been observed.



iii

CONTENTS

Page No.

Acknowledgment i

Abstract ii

Contents iii

List of tables vi

List of Figures vii

1. Introduction 1

1.1 General 1

1.2 Architectural Features 4

1.3 Origin of Earthquake 5

1.3.1 Historical Background 5

1.3.2 Earthquake sources 5

1.3.3 Plate Tectonics 6

1.3.4 Elastic Rebound Theory 6

1.3.5 Earthquake waves 7

1.3.6 Earthquake Magnitude 7

1.3.7Earthquake Intensity 8

1.4 Aims and Objectives

2. Literature review 9

3. Structural Behavior during ground motion 19

3.1 General 19

3.2 Terminology 20

3.2.1 Closely Spaced Modes 20

3.2.2 Critical Damping 20

3.2.3 Damping 20

3.2.4 Design acceleration spectrum 21

3.2.5 Design Basis Earthquake 21

3.2.6 Design Horizontal acceleration coefficient (Ah) 21

3.2.7 Design Lateral Force 21

3.2.8 Ductility 21

3.2.9 Epicenter 21

3.2.10 Effective peak ground acceleration 21

3.2.11 Floor Response Spectra 21



iv

3.2.12 Focus 22

3.2.13 Importance Factor 22

3.2.14 Intensity of Earthquake 22

3.2.15 Liquefaction 22

3.2.16 Litho logical Features 22

3.2.17 Magnitude of Earthquake 22

3.2.18 Maximum considered earthquake 23

3.2.19 Modal Mass 23

3.2.20 Modal Participation Factor 23

3.2.21 Mode Shape Coefficient 23

3.2.22 Natural Period 23

3.2.22.1 Fundamental Natural Period 23

3.2.22.2 Modal Natural Period 23

3.2.23 Normal Mode 24

3.2.24 Response reduction factor 24

3.2.25 Response Spectrum 24

3.2.26 Seismic Mass 24

3.2.27 Seismic Weight 24

3.2.28 Structural Response Factor 24

3.2.29 Time History Analysis 24

3.2.30 Zone Factor 24

3.2.31 Zero period acceleration 24

4. Structural Configurations for Effective Earthquake Resistance 25

4.1 Structural Configurations 25

4.1.1 Plan Regularity 31

5. Evaluation of seismic performance of building 365.1 General 36

5.1.1 Performance objectives 37

5.1.2 Performance Levels 37

5.2 Earthquake ground motions 39

5.3 Basic Safety Objective 40

5.4 Retrofit strategy and Retrofit system 41

5.5 Methods of Analysis for evaluation of seismic performance of building 42

5.5.1 Elastic Method of Analysis 42



v

5.5.1.1 Seismic Coefficient Method 42

5.5.1.2 Linear elastic dynamic analysis 42

5.5.2 Inelastic Method of Analysis 42

5.5.2.1 Inelastic Time History Analysis 43

5.5.2.2 Inelastic Static analysis or Pushover Analysis 43

5.5.2.2.1 Capacity Spectrum Method 45

6. Analysis and Results 49

6.1 Analysis and Validation of different models 49

6.1.1 Description of model 49

6.2 Analysis and Validation of 3D Frame 55

6.3 Analysis and Validation of 3D Frame of proposed models 57

6.3.1 Elastic Method- EQSM 57

6.3.1.1 Validation of proposed models 59

6.3.2 Inelastic Static Analysis 70

7. Discussions and Conclusions 75

7.1 Discussions 75

7.2 Conclusions 76

8. Scope for further studies 77

References 78

APPENDICES 82



vi

LIST OF TABLES

Page No.

Table 4.1 Attributes and benefits of optimal structural configuration 29

Table 5.1 Description of structural performance levels 37

Table 5.2 Description of non-structural performance levels 38

Table 5.3 Building Performance Levels 39

Table 5.4 Earthquake Hazard Levels (ATC-40) 39

Table 5.5 Earthquake Hazard Levels (FEMA-273) 40

Table 5.6 Configuration Deficiencies in a building 41

Table 6.1 Manual results (spreadsheet) for rectangular model for soil type-I 59

Table 6.2 Base shear values for considered models of soil type-I 61

Table 6.3 Displacement values for considered models of soil type-I 62

Table 6.4 Drift values for considered models for soil type-I 63

Table 6.5 Base shear values for considered models of soil type-II 65

Table 6.6 Displacement values for considered models of soil type-II 66

Table 6.7 Drift values for considered models for soil type-II 67

Table 6.8 Base shear values for considered models of soil type-III 67

Table 6.9 Displacement values for considered models of soil type-III 68

Table 6.10 Drift values for considered models for soil type-III 68

Table 6.11 Comparison of base shear with MS Excel and Etabs for

10-Storey building model for all type of soils 69

Table 6.12 Summary of member level performances of all building models

in soil type-I 70

Table 6.13 Summary of member level performances of all building models

in soil type-II 71Table 6.14 Summary of member level performances of all building models

in soil type-III 72



vii

LIST OF FIGURES

Page No.

Fig. 1.1 Simple plan shape buildings perform well during earthquake 5

Fig. 1.2 Showing the phenomena of elastic rebound theory 6Fig. 1.3 Different type of earthquake waves 7

Fig. 3.1 Inertia force and relative motion within a building 20

Fig. 4.1 Different plan irregularities 31

Fig. 4.2 Typical limits for plan irregularities 34

Fig. 4.3 Irregularities due to plan discontinuity for lateral resisting systems 35

Fig. 4.4 Plan Irregularities due to unfavorable core location 35

Fig. 5.1 Backbone curve for actual hysteretic behavior 45

Fig. 5.2 Demand Curve 46

Fig. 5.3 Capacity Curve 46

Fig. 5.4 Hysterious behavior of structure from capacity curve 47

Fig. 5.6 Pushover curve in F-D Format 48

Fig. 6.1 Regular Configuration- Rectangular model 50

Fig. 6.2 Irregular Configuration- H model 50

Fig. 6.3 Irregular Configuration- C model 51

Fig. 6.4 Irregular Configuration- L model 51

Fig. 6.5 Irregular Configuration- T model 52

Fig. 6.6 Irregular Configuration- Plus model 52

Fig. 6.7 Irregular Configuration- S model 53

Fig. 6.8 Irregular Configuration- Diaphragm model 53

Fig. 6.9 Irregular Configuration- Z1 model 54

Fig. 6.10 Irregular Configuration- Z2 model 54

Fig. 6.11 Model- L1 55

Fig. 6.12 Storey Shear Diagram 60

Fig. 6.13 Comparison of base shear for 10-storey building model- Soil I 61

Fig. 6.14 Comparison of displacements for 10-storey building model- Soil I 62

Fig. 6.15 Comparison of storey drifts for 10-storey building model- Soil I 63

Fig. 6.16 Comparison of base shear for 10-storey building model- Soil II 64

Fig. 6.17 Comparison of displacements for 10-storey building model- Soil II 65

Fig. 6.18 Comparison of storey drifts for 10-storey building model- Soil II 66

Fig. 6.19 Comparison of base shear for 10-storey building model- Soil III 67



viii

Fig. 6.20 Comparison of point displacements for 10-storey building model-

Soil III 68

Fig. 6.21 Comparison of storey drifts for 10-storey building model- Soil III 68

Fig. 6.22 Comparison of base shear with MS Excel and Etabs for

10-storey building models for all type of soils 69

Fig. 6.23 Comparison of base shear for 10-storey building models

for all type of soils 70

Fig. 6.24 Comparison of pushover curve for all building models in

push-x and push-y for soil-I 71


push-x and push-y for soil-II 72


push-x and push-y for soil-III 73

Fig. 6.27 Member Level performances of 10-story diaphragm model 74

Fig. 7.1 Percentage increment in drift in all soils-I, II, III 76

Fig. 7.2 Percentage increment in displacements in all soils-I, II, III 76

Fig. 7.3 Comparison of Displacements in different models. 77

Fig. 7.4 Comparison of Storey Drifts in different models. 77



Effects of Plans Configuration on Seismic Vulnerability of RC building

M.Tech in Structural Engineering, G E C, Haveri Page 1

Chapter 1

INTRODUCTION

1.1GeneralAlthough there are so many studies about earthquakes but however it has not been

possible to predict when and where earthquake will happen. It has been learned how to

pinpoint the locations of earthquakes, how to accurately measure their sizes, and how to

build flexible structures that can withstand the strong shaking produced by earthquakes

and protect our loved ones. Occurrence of recent earthquakes in India and in different

parts of the world resulted losses, especially human lives. It has highlighted the structural

inadequacy of buildings to carry seismic loads. There is an urgent need for assessment of

existing buildings in terms of seismic resistance. In view of this various organizations in

the earthquake threatened countries have come up with documents, which serve as

guidelines for the assessment of the strength expected performance and safety of existing

buildings so that they will carrying out the necessary rehabilitation, if required. The Code

of Practice on Earthquake Resistant Design of Buildings and Structures is in existence

since 1962, it is being followed only by few government organizations, as a result non

compliant buildings are being constructed in the country especially in private sector. Onlyrecently, the codal provisions on Earthquake Resistant Design are made mandatory in few

States and its implementation is yet to take full momentum. As a result, existing

earthquake unsafe buildings are still glowing to an alarming proportion. Like other

earthquakes in the past, the recent earthquakes of KilIari 1993, Bhuj 2001, Kashmir 2005

and Haiti 2010 have exposed the seismic vulnerability of construction practices being

followed in the country. It has clearly demonstrated that not only non-engineered rural

houses are vulnerable to earthquakes but also engineered multistoried buildings in big

cities are also mostly vulnerable due to faulty design and construction. Considering the

large number of people, high fatality in RC buildings and volume of economic activities,

the social risk involved in cities is also very high so the seismic retrofitting of the existing

buildings has to be undertaken to make these unsafe houses safe to resist future

earthquakes, thereby reducing the number of casualties significantly. The problem of

seismic retrofitting of large stock of unsafe buildings is so big that any government action

is just not feasible and therefore individual house owner/builder has to undertake the

retrofitting measures. However, government can take up retrofitting of its own buildings





and some public utility buildings which are of post earthquake importance. The

deficiencies in buildings and structures against earthquake may arise at (i) Planning stage

with faulty configuration and irregularities, (ii) design stage due to inadequate strength

and ductility, and (iii) construction stage due to faulty construction practices. Revision of

design codes is a continuing process all over world and usually results in up-gradation of

seismic hazard and increase in design forces. In India also several regions have been

upgraded in terms of seismic ones thereby rendering buildings unsafe according to new

code. All these factors make the retrofitting of existing structures necessary. The

retrofitting may also be required if change in usage of a building takes place or there is a

major alteration/extension of building. The level of retrofitting of a building depends on

the seismic zone in which building is situated and the level of performance desired fromthe building. Important buildings are desired to have a higher performance level during

future earthquakes. The seismic zone governs the design earthquake forces and the

performance level governs the permissible damage or the permissible values of members‘

actions due to earthquake forces. Not only member forces and strength are important, the

nonlinear deformations and ductile capacity of members are also important for seismic

safety of building and need to be evaluated and examined. Much literature on retrofitting

of building is already available including the Bureau of Indian Standards (BIS). The

techniques have been presented for the type of construction prevailing in India. Emphasis

has been on detailing the techniques with illustrations, so that these may be easily

understood and applied by common engineers, architects and builders. A need has been

felt to provide adequate information about seismic retrofit design of masonry and RC

buildings which can be easily understood and implemented. The Guidelines deal with

important aspects of seismic hazard estimation, systematic inspection of existing

buildings, tests for estimation of in-situ strength and extent of damage and, deterioration

in masonry and RC buildings, mathematical modeling of frames, frame-tubes, shear walls

and frames with infill, and various methods of analysis for earthquake forces for seismic

evaluation which requires knowledge of structural behavior, materials of construction,

principles of seismic intervention and behavior of modified structure, and various

retrofitting materials. This includes performance levels of various types of buildings. The

definition of these performance levels has been taken from Federal Emergency

Management Agency (FEMA) and Applied Technology Council (ATC).





Two checklists have been given for systematic inspection of masonry and RC frames.

These checklists are useful in preliminary evaluation and identification of major

deficiencies in existing buildings. These Guidelines cover retrofitting of non-engineered,

engineered and earthquake damaged buildings. These also cover non-engineered rural and

semi-urban houses, these buildings are constructed in mud, stone or brick masonry,

without any consideration to strength and ductility of the structure. 'The retrofitting

techniques for such buildings are based on failure mode identification and behavior of

such buildings in past earthquakes. The techniques have been tested in laboratories and

field, and known to provide adequate safety intended for such buildings. Retrofitting of

RC buildings is much more systematic and rational process than that of non-engineered

load bearing wall buildings. The different techniques available for retrofitting of RC buildings have been described. The principles of retrofitting of RC buildings are:-

(i) Removal of irregularities and asymmetry,

(ii) Increasing the strength and stiffness of structure,

(iii) Enhancement of deformation capacity (or ductility), and

(iv). Earthquake demand reduction by Base-isolation (or Supplemental Energy

Dissipation.)

Different techniques based on these principles have been illustrated. The emphasis on

reinforcement detailing, bond of old and new concrete, and anchorage of new

reinforcement is highlighted. Outline and principle of advanced techniques (e.g. Base-

Isolation and Supplemental Damping) has also been provided. However, a detailed

description and mathematical formulation of these advanced techniques are beyond the

scope of these guidelines and references have been provided for further reference.

Evaluation and retrofitting of damaged structures is an urgent task after an earthquake, as

safe shelter is under pressing demand after a damaging earthquake. This requires some

quick evaluation and retrofitting techniques. The techniques for quick evaluation of need

and viability of retrofitting, temporary emergency support of the damaged structures, and

repair and retrofitting of structures are also covered. Retrofitting and strengthening of

existing structures require use of special materials. Bonding of old and new concrete and

shrinkage are the main governing factors in selection of material. A description of

materials available for this purpose, including a range from ordinary cement-sand grout,

concrete to polymers and epoxy, use of Fibre Reinforced Polymers/Plastics (FRP) in

strengthening and retrofitting has also been described with the points of caution.





Specialized machinery and preparations required for use of different retrofitting materials

are also outlined.

Many buildings in the present scenario have irregular configurations both in plan and

elevation. The behavior of a building during earthquakes depends critically on its overall

shape, size and geometry, in addition to how the earthquake forces are carried to the

ground. Hence, at the planning stage itself, architects and structural engineers must work

together to ensure that the unfavorable features are avoided and a good building

configuration is chosen. The importance of the configuration of a building as been

summarized: ―If we have a poor configuration to start with, all the engineer can do is to

provide a band-aid - improve a basically poor solution as best as he can. Conversely, if

we start-off with a good configuration and reasonable framing system, even a poorengineer cannot harm its ultimate performance too much.‖

1.2 Architectural Features

A desire to create an aesthetic and functionally efficient structure drives architects to

conceive wonderful and imaginative structures. Sometimes the shape of the building

catches the eye of the visitor, sometimes the structural system appeals, and in other

occasions both shape and structural system work together to make the structure a marvel.However, each of these choices of shapes and structure has significant bearing on the

performance of the building during strong earthquakes. The wide range of structural

damages observed during past earthquakes across the world is very educative in

identifying structural configurations that are desirable versus those which must be

avoided (Fig 1.1).





Fig 1.1: Simple Plan Shape Buildings Perform well during Earthquakes

1.3 ORIGIN OF EARTHQUAKE

Earthquakes are one of the most devastating forces in nature. Earthquakes disasters have

been known since ancient times. Earthquakes have been instrumental in changing the

course of history. Some of the most significant disasters in the last hundred years have

been caused by Earthquakes.

1.3.1 HISTORICAL BACKGROUND

Records of every major earthquake in China during the last 3000 years. Records of major

earthquakes in India up to last 2500 years. Records of major earthquakes over 2000 years

in Middle-East. Legends about earthquakes in India and several other ancient

civilizations.

1.3.2 EARTHQUAKES SOURCESMost Earthquakes are concentrated along boundaries of earth‘s plates. Some Earthquakes

also occur away from plate boundaries. Earthquakes in many parts are also associated

with volcanic activities. In recent times, earthquakes may have been triggered by human

structures and activities (dams, mining etc.)

1.3.3. PLATE TECTONICS





Motion of earth‘s plates explained using Plate Tectonics According to Plate Tectonics

earth‘s land-mass were earlier joined together. The land-mass have broken up and have

drifted apart. Relative motion is still continuing, relative motion at plate boundaries cause

earthquakes. Considerable evidence now exists to support Plate Tectonics. Types of

evidences are Geological and geomorphologic – similar rock formations,

Anthropological – similar vegetation and animal life, Geomagnetic – magnetic anomalies

support drifting away of land and Mass from Atlantic ridge and other places.

1.3.4 ELASTIC REBOUND THEORY

Elastic rebound theory is used to explain occurrence of earthquakes (Fig 1.2). Earth‘s

crust is under tremendous strain at the plate boundaries. Relative motion across a fault

line will eventually lead to rupture. Fault rupture suddenly releases energy, causing an

earthquake

Figure 1.2: Showing the phenomena of elastic rebound theory

1.3.5 EARTHQUAKE WAVES

Elastic rebound produces waves from the point of rupture. The rupture may be localized

at a point, along a slip line or a slip surface. Earthquake waves have clearly identifiable





components. They are Primary wave (refractory), Secondary or shear wave (transverse),

Raleigh wave (refractory) and Love wave (transverse).Figure of these waves are given in

figure 3.

Figure 1.3: Different type of earthquake waves

1.3.6 EARTHQUAKE MAGNITUDE

Earthquake magnitude is most commonly defined in Richter magnitude. It is logarithm of

the maximum displacement (in μm) recorded on a particular type of seismograph 100 km

from the epicentre. Richter magnitude is open-ended and has no maximum value.

Scientifically more useful measure is based on seismic moment and measures the total





energy that is released. Both magnitudes give similar value for moderate earthquakes

(M5.0 – M7.5)

1.3.7 EARTHQUAKE INTENSITY

Earthquake intensity is a measure of its consequence. Most popular intensity scales are

primarily based on structure damage.MMI (Define 12 intensities) based only on

performance of buildings. MSK (Defines Intensities) base on building performance,

geotechnical effects as human perception. Most countries use MSK intensity scale or its

modifications to suit local conditions.

1.4 AIMS AND OBJECTIVES

In the present study optimum configuration of ten different cases of a hypothetical

building of different configurations for 10 storey building have been analyzed as a

lumped modal mass system using Equivalent static method and Non-Linear static

(pushover) method.

The objectives of the study are as follows:-

To identify the most vulnerable building among the models considered, the

various analytical approaches are performed to identify the seismic demands in

both linear and nonlinear way.

To examined the effect of lateral load patterns on the performance of various

irregular buildings in pushover analysis.

To identify the performance levels of the structure through pushover curves.

To study various patterns of hinge formations.

To identify the seismic forces with different soil parameters.





Chapter 2

LITERATURE REVIEW

K Rama Raju, A Cinitha and Nagesh R Iyer (2012) [1]

In their paper entitled ―Seismic performance evaluation of existing RC

buildings designed as per past codes of practice‖ have discussed about Assessing the

capacity of existing building as per the present codes of practice is an important task in

performance-based evaluation. In order to enhance the performance of existing buildings

to the present level of ductile design prescribed by present codes and find the retrofit or

design a rehabilitation system, there is an urgent need to assess accurately the actual

lateral load resistance and the potential failure modes. In this paper, a typical 6-storey

reinforced concrete (RC) building frame is designed for four design cases as per the

provisions in three revisions of IS: 1893 and IS: 456 and it is analysed using user-defined

(UD) nonlinear hinge properties or default-hinge (DF) properties, given in SAP 2000

based on the FEMA-356 and ATC-40 guidelines. An analytical procedure is developed to

evaluate the yield, plastic and ultimate rotation capacities of RC elements of the framed

buildings and these details are used to define user-defined inelastic effect of hinge for

columns as P-M-M and for beams as M3 curves. A simplified three parameter model is

used to find the stress – strain curves of RC elements beyond the post yield region of

confined concrete. Building performance of structural components in terms of target

building performance levels are studied with the nonlinear static analysis. The possible

differences in the results of pushover analysis due to default- and user-defined nonlinear

component properties at different performance levels of the building are studied.

Shaikh Mohammed Rizwan, Yogendra Singh (2012) [2]

In their paper entitled “Effect of Strength Eccentricity on Torsional

Behaviour of RC Frame Building” have discussed about attempts to understand the

inelastic seismic behaviour of asymmetric multi-storey RC Buildings using non-linear

dynamic time history analysis. Both inherently asymmetric and artificially generated

eccentric building models were considered. Two categories of artificially generated

models were considered. In first category, groups of mass asymmetric systems (MSS)

having strength, stiffness and both strength and stiffness eccentries were considered. In





the second category of models, mass eccentricity was introduced in otherwise symmetric

models. Building systems were modelled as 3D Space frame with lumped plasticity. The

response is evaluated using the peak rotational ductility demand of beams of the different

frames as measures of their inelastic response. Investigations of first category of

artificially generated MSS showed that the response can be better co-related with the

strength eccentricity. The results from second category of systems not designed for

torsion indicated that there is significant variation in the beam ductility demands of

different frames, whereas systems designed for torsion indicated a shift in the centre of

strength towards the centre of mass and exhibited almost uniform ductility demand in

beams of various frames for smaller eccentricities.

Reyes Indira Herrera, Juan Carlos Vielma, Ronald Ugel, Yolsanie Martínez,

Alex Barbat (2012) [3]

In their paper entitled “Optimal design and earthquake resistant design evaluation of

low rise framed RC Building” have discussed about seismic response of an existing two

stories RC building using nonlinear analysis. The original model was resized and there

were obtained two buildings designed under two different methodologies to fulfil the

Venezuelan codes requirements for a high seismic hazard. An elastic analysis was applied

to the original building in order to verify interstory drifts; the resizing building it was

designed under requirements of strong column- weak beam condition. A third building

was modelled according to the seismic displacement design procedure.

It were performed nonlinear static analysis and 2D and 3D dynamic analyses, obtaining

capacity curves, structural ductility, structural performance point, global and inter story

drifts for each building. Torsional effects for the resizing building were also computed

from 3D analysis. In the original building it was obtained a weak seismic behaviour,

while resized buildings presented good seismic performance under the Limits States

evaluated in this study.

Ravikumar C M, Babu Narayan K.S, Sujith B V, Venkat Reddy D (2012)

[4]

In their paper entitled “Effect of Irregular Configurations on Seismic Vulnerability of

RC Buildings” has discussed about the behaviour of building during earthquake and it





depends critically on its overall shape, size and geometry. Building with simple geometry

in plan have performed well during strong past earthquake but building with u, v, H & +

shaped in plan have sustained significant damage. Their work is focused on the study of

Seismic demands of different irregular R.C buildings using various analytical techniques

for the seismic zone V (hard rock) of India. The configuration involves plan irregularities

such as diaphragm discontinuity, re-entrant corners and vertical irregularities such as

geometrical irregularity, buildings resting on sloping ground. The performance was

studied in terms of time period, base shear, lateral displacements, storey drifts and

eccentricity in linear analysis using a code – IS1893 (Part 1):2002 .Whereas the

performance point and hinge status in Non linear analysis using ATC40. Also an attempt

was made in pushover analysis to identify the correct lateral load pattern when differentirregular buildings were considered. The entire modelling, analysis and design was

carried out by using ETABS 6.0 nonlinear version software.

T. Mahdia and V. Soltan Gharaieb (2011) [5]

In their paper entitled “Plan Irregular RC Frames: Comparison of Pushover with

Nonlinear Dynamic Analysis” have discussed about the seismic behaviour of three

intermediate moment-resisting concrete space frames with unsymmetrical plan in five,seven and ten stories are evaluated by using pushover analysis. In each of these frames,

both projections of the structure beyond a re-entrant corner are greater than 33 percent of

the plan dimension of the structure in the given direction. The performance of these

buildings has been investigated using the pushover analysis. Results have been compared

with those obtained from non-linear dynamic analysis.

Pacific Earthquake Engineering Research Centre (PEER) – Report No. 05/2010

[6]

This report entitled “Guidelines for Performance-Based Seismic Design of Tall

Buildings” These Guidelines for Performance-Based Seismic Design of Tall Buildings

present a recommended alternative to the prescriptive procedures for seismic design of

buildings contained in standards such as ASCE 7 and the International Building Code

(IBC). They are intended primarily for use by structural engineers and building officials

engaged in the seismic design and review of individual tall buildings. Properly executed,the Guidelines are intended to result in buildings that are capable of achieving the seismic





performance objectives for Occupancy Category II buildings intended by ASCE 7 .

Alternatively, individual users may adapt and modify these Guidelines to serve as the

basis for designs intended to achieve higher seismic performance objectives.

The organization of the Guidelines is as follows. The first three chapters

introduce the Scope, target performance objectives, and intended proper use of the

procedures Contained in the Guidelines. Chapter 4 describes documentation that normally

should accompany a design conducted according to the Guidelines. Chapter 5 describes

seismic input to be considered for the building design. Chapters 6 through 8 present

detailed guidance for preliminary design, design for serviceability, and design for

maximum considered earthquake effects. Chapters 9 and 10 outline recommended

procedures for presentation of design results and project review, including use of aseismic structural peer review panel.

Pacific Earthquake Engineering Research Centre (PEER) – Report No.

111/2010 [7]

This report entitled “Modeling and Acceptance Criteria for Seismic Design and

Analysis of Tall Buildings” this report is the result of further work under the PEER Tall

Buildings Initiative to develop modeling recommendations and acceptance criteria fordesign and analysis of tall buildings. It is intended to serve as a resource document for the

Guidelines for Seismic Design of Tall Buildings, published as a companion report by

PEER (2010) and report is also published as ATC-72-1.

Serhan Guner and Frank J. Vecchio (2010) [8]

In their paper entitled “Pushover Analysis of Shear-Critical Frames: Verification and

Application” have discussed an analytical procedure was recently developed for thenonlinear analysis of reinforced concrete frame structures consisting of beams, columns,

and shear walls under monotonic and pushover loading. The advantage of the procedure

lies in its inherent and accurate consideration of shear effects and significant second order

mechanisms within a simple modeling process suitable for use in practice. Herein, the

application of the procedure to 33 previously tested specimens, two-thirds of which were

shear-critical, is presented to verify the algorithms developed. Important considerations in

nonlinear modeling are also discussed to provide guidelines for general modeling

applications. The procedure is found to simulate the experimental behaviors of the





specimens examined with a high level of accuracy. Experimental strengths, stiffness‘s,

ductility‘s, and failure modes were all calculated accurately. Computed parameters such

as crack widths, reinforcement strains, and member deformations were also represented

successfully. The procedure exhibits excellent convergence and numerical stability,

requiring little computational time.

Yong Lua, Xiaoming Gub, Jianwu Weib (2009) [9]

In their paper entitled “Prediction of seismic drifts in multi-storey frames with a new

storey capacity factor” has discussed about standard procedures exist for the estimation

of the total (or roof) displacement of a structure for seismic, based on the response spectra

of single degree of freedom (SDOF) systems. However for a more realistic prediction of

the seismic demands, especially in context of the performance based design, an

appropriate estimation of the storey drift distribution is necessary. A few general

approaches are available in the literature, and these often require certain structural

modeling analysis. The present paper aims to provide a simple alternative method for the

prediction of the storey drift distribution and the critical drift concentration in a RC

Frame. A new storey capacity factor is introduced, to represent the combined effect of the

storey strength and stiffness on the distribution of storey drift along the frame height,

while the storey strength and stiffness are evaluated, taking into account different possible

plastic mechanisms. The structural regularity is subsequently evaluated based on the

storey capacity factor. Nonlinear pushover and dynamic response history analysis are

performed on several representative multi storey frames, to verify the correlation between

the storey capacity factor profile and the distribution of the of the actual storey drifts.

Results indicate that the inverse of the storey capacity factor correlates well with the

storey drift distributions. An empirical relationship between the critical drift

concentration factor and the overall regularity index is derived based on the dynamic

analysis results.

Mehdi P, Faramarz K, Moghadamb.A.S (2009) [10]

In their paper entitled “A consecutive modal pushover procedure for estimating the

seismic demands of tall buildings” have discussed about the nonlinear static procedure

(NSP), based on pushover analysis, has become a favorite tool for use in practical





applications for building evaluation and design verification. The NSP is however,

restricted to single mode response. It is therefore valid for low-rise buildings where the

behavior is dominated by the fundamental vibration mode. It is well recognized that the

seismic demands derived from the conventional NSP are greatly underestimated in the

upper storeys of all tall buildings, in which higher-mode contributions to the responses

are important. This paper presents a new pushover procedure which can take into account

higher-mode effects. The procedure, which has been named the consecutive modal

pushover (CMP) procedure, utilizes multi-stage and single-stage pushover analysis. The

final structural responses are determined by enveloping the results of multi-stage and

single-stage pushover analyses. The procedure is applied to four special steel moment-

resisting frames with different heights. A comparison between estimates from the CMP procedure and the exact values obtained by nonlinear response history analysis (NL-

RHA), as well as predictions from modal pushover analysis (MPA), has been carried out.

It is demonstrated that the CMP procedure is able to effectively overcome the limitations

of traditional pushover analysis, and to accurately predict the seismic demands of tall

buildings

Raul Gonzalez Herrera1 and Consuelo Gomez Soberon (2008) [11]

In their paper entitled “Influence of Plan Irregularity of Buildings” have discussed

about an analytical description of the damages caused by different plan irregularities,

during seismic events of different magnitudes. Although these effects of architectonic

and/or structural configuration have been identified like not adapted in previous damages,

have come maintaining their presence in constructions anywhere in the world. The effects

of commented irregularities were studied with qualitative analyses of important and

recent investigations, as much in Mexico as abroad. The work describes to the geometric

forms that are repeated more in the urban areas in México (squared, rectangular, section

U, section L and section T), as well as its variations from plants observed with extracted

aerial photography of Google Earth. These architectonic plants were modeled in

SAP2000 considering one, two and four levels to determine the effect of the geometric

form in the seismic behavior of structures with elastic analyses. Also, effects of the

extension in rectangular plants and the inclusion of projections in sections with

architectonic plans U, L and T were studied. In all the studied systems, effects of different





irregularities are analyzed based on the variation of displacements, with respect to regular

systems.

C.V.R.Murthy (2008) [12]

In his paper entitled “Seismic strengthening of RC Frame buildings: The formal

quantitative approaches” has discussed about 2001 Bhuj earthquake and this has

confirmed that the Indian multi-storey reinforced concrete buildings with open ground

storey are highly vulnerable to strong seismic ground motions. Urgent measures of

seismic strengthening are required to seismically upgrade the large stock of such existing

buildings. A number of prescriptive techniques for retrofitting these buildings are being

suggested by various interest groups. But, a formal quantitative approach is necessary to

this effort of seismic retrofitting. This paper outlines the available methods for

quantifying the effectiveness of proposed measures. These methods have been arrived at

from a conceptual standpoint and applied in practice to real projects. The prevalent

professional environment of the country urgently needs to seek this formal approach fo r

seismic retrofit of most existing RC buildings.

Barbara Borzia, Rui Pinhob, Helen Crowleya (2008) [13]

In their paper entitled “Simplified pushover-based vulnerability analysis for large

scale assessment of RC buildings” have discussed about analytical methods for large

scale assessment of the seismic vulnerability of RC buildings have only recently become

feasible due to a combination of advancements in the field of seismic hazard assessment

and structural response analysis. In many of the original procedures to define analytical

vulnerability curves, non linear time-history analysis of prototype structures with

randomly varying structural characteristics were carried out for a set of representative

earthquakes. However, running nonlinear dynamic analysis for a large number of

structures is extremely time consuming and alternative methods have thus been sought.

The method presented in this paper defines the nonlinear behavior of a random population

of buildings through a simplified pushover and displacement-based procedure.

Displacement capacity limits are identified on the pushover curve and these limits are

compared with the displacement demand from a response spectrum for each building in

the random population, thus leading to the generation of vulnerability curves.





Sekhar Chandra Dutta (2008) [14]

In his paper entitled “Assessing the additional seismic vulnerability in post-elastic

range due to P-Δ effect” have discussed that the earthquake damage surveys have

reflected the vulnerability of high rise constructions, because of lateral drift under the

effect of ground acceleration. Though several reasons may be attributed to such failure,

the present paper attempts to investigate the contribution of one of the agents responsible

for aggravating such a failure, which is namely the P-Δ effect. It has been shown

elsewhere that the impact of P-Δ effect is expected to be rather marginal within the elastic

range of seismic behavior because of less lateral drift. Presently accepted seismic design

philosophy known as ‗Dual Design Philosophy‘ speaks in favour of allowing the structur e

to respond with stipulated and limited inelasticity to strike a balance between economy

and safety. In this context, for successful implementation of the philosophy particularly

for saving life in the event of severe earthquake, it becomes important to investigate the

seismic behavior of the structure in the inelastic range where eventually P-Δ effect may

be substantially influential. The so called P-Δ effect occurs in structures which are

subjected to significant lateral in presence of gravity loading. However, the extent may

vary. Due to the lateral deflection of the vertical elements in a structure, centroid` of the

mass and hence the time of action due to gravity is shifted away from the line of action of

the resultants of the reaction force. As a result an additional overturning moment of a

magnitude equal to the product of the gravity for ce (P) and the lateral deflection (Δ) is

developed in the structure. Such P-Δ effect on a structure as a whole may be accounted

through the second order analysis incorporating the effect of such large lateral deflection

Δ considering the deformed geometry adequately in the stiffness matrix. The effect may

be adequately incorporated as an increase in the overturning moment additionally causeddue to the large displacement of the centre of mass of the structure. However, once

material yielding starts, the lateral displacements increases very rapidly. Such increase in

lateral displacement makes the increment in overturning moment due to P-Δ effect quite

significant. When this effect once becomes significant, keeps on progressively increasing

the lateral drift, due to gradual increase in such overturning moment in the drift. Thus, for

civil engineering structures, the material nonlinearity triggers the P-Δ effect in a

significant manner and introduces geometrically nonlinear behaviour. In this context the

present study makes a limited attempt to investigate the significance of P-Δ effect on





inelastic seismic behaviour of low rise multi-storeyed buildings. An effort of

symmetrically representing the effect of the same through using yield point spectra has

been very recently made (2). P-Δ effects on single degree freedom system (SDOF)

structures in earthquake are reported in the study (3). Another study (4) was made on

dynamic P-Δ effects in flexible inelastic MDOF system. However further intensive efforts

are required to evolve guidelines for successful implementation of seismic dual design

philosophy which clearly points out the needs as well as significance of the study taken

up in this paper. There has been a tendency among practicing engineers to neglect P-Δ

effect, in design practice from the notion that its contribution for causing damage is

significant when compared to the damage caused due to shear failure, overturning due to

lateral joists, torsion and other primary visual effects under seismic forces. Only certaindesign codes grossly restricts excessive lateral drift from the perspective of pounding

damage between buildings and also to restrict discomfort to the inhabitants due to

excessive sway at the higher storey levels. On the other hand, restriction avoids collapse

due to P-Δ effect. But in general the significance of seismic induced P-Δ effects in

aggravating failure needs also to be critically explored and the same is investigated in this

paper for multi-storeyed building structures.

Petti.L, De Iuliis.M (2008) [15]

In their paper entitled “Torsional seismic response control of asymmetric-plan

systems by using viscous dampers” have discussed about a new approach to locating

viscous dampers optimally is herein presented in order to control the torsional seismic

response of asymmetric-plan buildings. Firstly, the efforts of the plan-wise distribution of

supplemental damping on torsionally dynamic behaviour have been investigated by using

modal analysis techniques in the state space representation in order to highlight the main

physical aspects of the problem. Optimal design criteria have been carried out by

evaluating the H∞ and H₂ norms of transfer function relating the maximum edge

displacement to the input seismic excitation. The3se norms represent suitable

performance indexes to investigate the optimal plan-wise distribution of extra structural

dampers by means of parametrical analysis on varying the dynamic characteristics of

asymmetric-plan system. The numerical constraints on the mechanical parameters related

to the practical application of the proposed control strategy are taken into account. Simple





design formulae to model the results for the H₂ norm are proposed and positively verified

through broad numerical experimentation which compared the seismic response of

asymmetric systems to synthetic and real excitations for different design strategies in a

plan-wise arrangement of supplemental damping.

Applied Technology Council (ATC-40) (1996), [16], prepared a report on Seismic

evaluation and retrofit of concrete buildings sponsored by California Safety Commission.

Although the procedures recommended in this document are for concrete buildings, they

are applicable to most building types. This document provides a practical guide to the

entire evaluation and different retrofit process using performance-based objectives.

Although it is not intended for the design of new buildings, the analytical procedures

described in this document are certainly applicable. The seismic performance of a

structure is dependent upon the performance characteristics of its critical components.

The critical components are those that are necessary for vertical stability and those that

comprise the seismic load path. It is expected that this document will be used by both

retrofit design professionals performing seismic evaluations and retrofit designs and

government agency personnel and policy makers charged with implementing retrofit

programs.

Federal emergency management agency (FEMA 356), Nov 2000, [17], is a report on

prestandard and commentary for the seismic rehabilitation of buildings prepared by

American society of civil engineers. This Prestandard for the Seismic Rehabilitation of

buildings, specifies nationally applicable provisions for the rehabilitation of buildings to

improve seismic performance. The procedures contained in this standard are specifically

applicable to the rehabilitation of existing buildings and are, in general, more appropriate

for that purpose than are new building codes.

Federal Emergency Management Agency (FEMA 273) NEHRP GUIDLINES (1997),

[18], developed a set of technically sound, nationally applicable guidelines (with

commentary) for the seismic rehabilitation of buildings. The guidelines documents

produced as a result of this project are expected to serve as a primary resource on the

seismic rehabilitation of buildings for the use of design professionals, educators, model

code and standards organizations, and state and local building regulatory personnel.





Assess the technical adequacy of the Guidelines design and analysis procedures. It

compares the acceptance criteria of the Guidelines with the prevailing seismic design

requirements for new buildings in the building location to determine whether

requirements for achieving the ―basic safety objective‖ are equivalent to or more or less

stringent than those expected of new buildings.





Chapter 3

STRUCTURAL BEHAVIOUR DURING GROUND

MOTION

3.1 General

When a structure is subjected to ground motions in an earthquake, it responds by

vibrating. The random motion of the ground caused by an earthquake can be resolved in

any three mutually perpendicular directions: the two horizontal directions (x and y) and

the vertical direction (z). This motion causes the structure to vibrate or shake in all three

directions; the predominant direction of shaking is horizontal. All the structures are

primarily designed for gravity loads — force equal to mass times gravity in the vertical

direction. Because of the inherent factor of safety used in the design specifications, most

structures tend to be adequately protected against vertical shaking. Generally, however,

the inertia forces generated by the horizontal components of ground motion require

greater consideration in seismic design. Earthquake generated vertical inertia force must

be considered in the design unless checked and proved to be in significant, In general,

buildings are not particularly susceptible to vertical ground motion, but its effect should

be borne in mind in the design of RCC columns, steel column connections, and

prestressed beams. Vertical acceleration should also be considered in structures with large

spans, those in which stability is a criterion for design, or for overall stability analysis of

structures with large spans. Structures designed only for vertical shaking, in general, may

not be able to safely sustain the effect of horizontal shaking. Hence, it is necessary to

ensure that the structure is adequately resistant to horizontal earthquake shaking too. As

the ground on which a building rest is displaced, the base of the building moves suddenly

with it, but the roof has a tendency to stay in its original position. The tendency to

continue to remain in its original position is known as inertia. So the upper part of the

structure will not respond instantaneously but will lag because of inertial resistance and

flexibility of structure. Since the roofs and foundations are connected with the walls and

columns, the roofs are dragged along with the walls/columns. The building is thrown

backwards and the roof experiences a force called the inertia force (fig 3.1). The

maximum inertia force acting on a simple structure during an earthquake may be obtained

by multiplying the roof mass m by the acceleration a. When designing a building





according to the codes, the lateral force is considered in each of the two orthogonal

horizontal directions of the structure. For structures having lateral force-resisting

elements (e.g. frames, shear walls) in both directions, the design lateral force is

considered along one direction at a time, and not in both the directions simultaneously.

Figure 3.1: Inertia force and relative motion within a building

3.2 TERMINOLOGY

For the purpose of standard, the following definitions shall apply which are applicable

generally to all structures as per IS 1893 (Part 1): 2002

3.2.1 CLOSELY-SPACED MODES

Closely-spaced modes of a structure are those of its natural modes of vibration whose

natural frequencies differ from each other by 10 percent or less of the lower frequency.

3.2.2 CRITICAL DAMPING

The damping beyond which the free vibration motion will not be oscillatory.

3.2.3 DAMPING

The effect of internal friction, imperfect elasticity of material, slipping, sliding, etc in

reducing the amplitude of vibration and is expressed as a percentage of critical damping.





3.2.4 DESIGN ACCELERATION SPECTRUM

Design acceleration spectrum refers to an average smoothened plot of maximum

acceleration as a function of frequency or time period of vibration for a specified damping

ratio for earthquake excitations at the base of a single degree of freedom system.

3.2.5 DESIGN BASIS EARTHQUAKE (DBE)

It is the earthquake which can reasonably be expected to occur at least once during the

design life of the structure.

3.2.6 DESIGN HORIZONTAL ACCELERATION COEFFICIENT (Ah)

It is a horizontal acceleration coefficient that shall be used for design of structures.

3.2.7 DESIGN LATERAL FORCE

It is the horizontal seismic force prescribed by this standard that shall be used to design a

structure.

3.2.8 DUCTILITY

Ductility of a structure, or its members, is the capacity to undergo-large inelastic

deformations without significant-loss of strength or stiffness.

3.2.9 EPICENTRE

The geographical point on the surface of earth vertically above the focus of the

earthquake.

3.2.10 EFFECTIVE PEAK GROUND ACCELERATION (EPGA)

It is a 0.4 times the 5 percent damped average spectral acceleration between period 0.1 to

0.3 s. This shall be taken as Zero Period Acceleration (ZPA).

3.2.11 FLOOR RESPONSE SPECTRA

A floor response spectrum is the response spectra for a time history motion of a floor.

This floor motion time history is obtained by an analysis of multi-story building for





appropriate material damping values subjected to a specified earthquake motion at the

base of structure.

3.2.12 FOCUS

The originating earthquake source of the elastic waves inside the earth which cause

shaking of ground due to earthquake.

3.2.13 IMPORTANCE FACTOR (I)

It is a factor used to obtain the design seismic force depending on the functional use of

the structure, characterized by hazardous consequence of its failure, its post-earthquake

functional need, historic value, or economic importance.

3.2.14 INTENSITY OF EARTHQUAKE

The intensity of an earthquake at a place is a measure of the strength of shaking during

the earthquake, and is indicated by a number according to the modified Mercalli Scale of

M.S.K. Scale of seismic intensities.

3.2.15 LIQUEFACTION

Liquefaction is a state in saturated cohesion less soil where the effective shear strength is

reduced to negligible value for all engineering purpose due to pore pressure caused by

vibrations during an earthquake when they approach the total confining pressure. In this

condition the soil tends to behave like a fluid mass.

3.2.16 LITHOLOGICAL FEATURES

The nature of the geological formation of the earths‘ crust above bed rock on the basis of

such characteristics as colour, structure, mineralogical composition and grain size.

3.2.17 MAGNITUDE OF EARTHQUAKE (RICHTER‟S -

MAGNITUDE)

The magnitude of earthquake is a number, which is a measure of energy released in an

earthquake. It is defined as logarithm to the base 10 of the maximum trace amplitude,

expressed in microns, which the standard short-period torsion seismometer (with a period





of 0.8 s, magnification 2800 and damping nearly critical) would register due to the

earthquake at an epicenter distance of 100 km.

3.2.18 MAXIMUM CONSIDERED EARTHQUAKE (MCE)

The most severe earthquake effects considered by this standard.

3.2.19 MODAL MASS (MK)

Modal mass of a structure subjected to horizontal or vertical, as the case may be, ground

motion is a part of the total seismic mass of the structure that is effective in mode k of

vibration. The modal mass for a given mode has a unique value irrespective of scaling of

the mode shape.

3.2.20 MODAL PARTICIPATION FACTOR (PK)

Modal participation factor of mode k of vibration is the amount by which mode k

contribution to the overall vibration of the structure under horizontal and vertical

earthquake ground motion. Since the amplitudes of 95 percent mode shapes can be scaled

arbitrarily, the value of this factor depends on the scaling used for mode shapes.

3.2.21 MODE SHAPE COEFFICIENT (фik)

When a system is vibrating in normal mode k, at any particular instant of time, the

amplitude of mass I expressed as a ratio of the amplitude of one of the masses of the

system, is known as mode shape coefficient (фik).

3.2.22 NATURAL PERIOD (T)

Natural period of structure is its time period of undamped free vibration.

3.2.22.1 FUNDAMENTAL NATURAL PERIOD (Tl)

It is the first (longest) modal time period of vibration.

3.2.22.2 MODAL NATURAL PERIOD (Tk)

The modal natural period of mode k is the time period of vibration in mode k.





3.2.23 NORMAL MODE

A system is said to be vibrating in a normal mode when all its masses attain maximum

values of displacements and rotations simultaneously, and pass through equilibrium

positions simultaneously.

3.2.24 RESPONSE REDUCTION FACTOR (R)

It is the factor by which the actual base shear force, that would be generated if the

structure were to remain elastic during its response to the Design Basis Earthquake (DBE)

shaking, shall be reduced to obtain the design lateral force.

3.2.25 RESPONSE SPECTRUM

The representation of the maximum response of idealized single degree freedom systems

having certain period and damping, during earthquake ground motion. The maximum

response is plotted against the undamped natural period and for various damping values,

and can be expressed in terms of maximum absolute acceleration, maximum relative

velocity, or maximum relative displacement.

3.2.26 SEISMIC MASS

It is the seismic weight divided by acceleration due to gravity.

3.2.27 SEISMIC WEIGHT (W)

It is the total dead load plus appropriate amounts of specified imposed load.

3.2.28 STRUCTURAL RESPONSE FACTOR (Sa/g)

It is a factor denoting the acceleration response spectrum of the structure subjected to

earthquake ground vibrations, and depends on natural period of vibration and damping of

the structure.

3.2.29 TIME HISTORY ANALYSIS

It is an analysis of the dynamic response of the structure at each increment of time, when

its base is subjected to a specific ground motion time history.





3.2.31 ZONE FACTOR (Z)

It is a factor to obtain the design spectrum depending on the perceived maximum seismic

risk characterized by Maximum Considered Earthquake (MCE) in the zone in which the

structure is located. The basic zone factor include in this standard are responsible estimate

of effective peak ground acceleration.

3.2.32 ZERO PERIOD ACCELERATION (ZPA)

It is a value of acceleration response spectrum for period below 0.03 s (frequencies above

33 Hz





Chapter 4

STRUCTURAL CONFIGURATIONS FOR

EFFECTIVE EARTHQUAKE RESISTANCE

4.1Structural Configurations

Configuration plays an important role in the seismic performance of structures subjected

to earthquake actions. Post - earthquake reconnaissance has pointed towards the

observation that buildings with irregular configurations are more vulnerable than their

regular counterparts. There are several reasons for this observed poor structural

performance of irregular structures. Concentrations of inelastic demand are likely to occur

in zones of geometrical discontinuities and/or mass and stiffness irregularities. If the

available ductility is limited, failure is initiated, thus possibly leading to collapse.

Unexpected load paths and overstress of components can cause significant adverse

effects. To prevent unfavourable failure modes, adequate ‗conceptual design‘ is required

at an early stage. In addition, thorough assessment of the structural configuration is vital

to achieve adequate seismic performance. Structural configuration has two fundamental

aspects: the overall form and the type of lateral resisting system employed. The impact of

structural configuration, in plan and elevation, on seismic performance depends upon:

(i) Size: as the absolute size of the structure increases, the range of cost - efficient

configurations and systems is reduced. For example, while standardized simple and

symmetrical shapes are generally used for high - rise buildings, more options are

available for low - to medium – rise structures. The same is also true in bridge

engineering where very long spans (> 600 – 800 m) impose the use of suspension cables.

Size may also dictate the choice of specific materials of construction. For example, high -

rise structures may require high - strength concrete (e.g. Laogan and Elnashai, 1999 ;

Aoyama, 2001 , among others).

(ii) Proportion: earthquake response of a structure depends on its relative proportions

rather than absolute size. Low slenderness in plan and elevation is beneficial. Reduced

elevation slenderness minimizes overturning effects. For buildings, the ratio of the height

( H ) to the smallest depth ( B) should not exceed 4 – 5 (Dowrick, 1987). This figure is

exceeded by far in modern tall buildings worldwide, which exhibit H / B of 10 – 15

(CTBUH, 1995). Multi - storey structures may also employ narrow shapes. In this case,





the slenderness ratio is critical. Large aspect ratios in plan render torsional effects more

likely to occur. Asynchronous motions at the foundation of building structures may also

be caused by high width - to - depth ratios.

(iii) Distribution and concentration: vertical and plan distribution of stiffness and mass is

important to achieve adequate seismic performance. In tall and slender buildings, lateral

deformability reduces the earthquake - induced forces. Problems related to deflection

control may arise, however, in earthquake and wind response of high - rise structures.

Low - rise buildings should be flexible to reduce the shear forces due to ground motions.

Tall buildings should be stiff to control the lateral deformations. Seismic motions are

multi - dimensional, thus structures need to be able to resist the imposed loads and

deformations in any direction. Adequate distributions of structural systems to resist loads(vertical and lateral) can prevent concentrations of inelastic demands. Structural elements

can be arranged in orthogonal directions to ensure similar stiffness and resistance

characteristics in both main directions, i.e. they should possess bidirectional resistance

and stiffness.

(iv) Perimeter resistance: torsional motion tends to stress lateral resisting systems non -

uniformly.

High earthquake - induced torsional moments can be withstood by lateral resisting

components located along the perimeter of the structure. Perimeter columns and walls

create, for instance, structural configurations with high rigidity and strength (also referred

to as ‗torsional stiffness and resistance‘). The location in plan of systems for earthquake

resistance significantly influences the dynamic response. The higher the radius of

gyration of the plan layout of the structure, the higher the lever arm to resist overturning

moments. In framed systems, the bending stiffness is significantly affected by the layout

of columns in plan and elevation. Frames employing perimeter columns possess high

bending stiffness and resistance; this is also true for frame - wall systems. The importance

of structural configuration in earthquake response has been recognized and implemented

by codes of practice and design guidance documents worldwide. To achieve adequate

performance, these standards and guidelines provide basic principles for ‗conceptual

design‘, which are summarized below:

(i) Simplicity: consists of clear and direct paths for vertical and horizontal forces due to

the combination of gravity and earthquake loading. Its fulfillment gives rise to reliable

predictions of seismic behaviour. Compact, convex and closed shapes perform better than





complex, concave and open sections. In addition, dimensioning, detailing and

construction of simple structures are often more cost - effective than for complex

structural systems.

(ii) Uniformity: implies even distribution of structural elements in plan and elevation,

allowing for smooth and direct transmission of the inertial forces generated by the masses

of structural and non - structural components height - wise. Concentrations of stresses or

large ductility demands cause premature collapse. It may be necessary to subdivide the

entire building into independent units by using seismic joints. Uniform distributions of

mass, strength and stiffness eliminate large eccentricities between the centre of mass and

that of stiffness. Torsion generates undesirable effects in the earthquake response of

structures.(iii) Symmetry: symmetrical or quasi - symmetrical structural layouts, well distributed in

- plan, are available solution for the achievement of uniformity. Structural symmetry

means that the centre of mass and centre of resistance are located at, or close to, the same

point. Eccentricity produces torsion and stress concentrations. Symmetry is important in

both directions in plan and elevations. The use of evenly distributed structural elements

allows more favourable redistribution of action effects within the entire structure.

Symmetry combined with simplicity is beneficial for earthquake response but

architectural constraints sometimes make this difficult to achieve. Symmetrical shapes,

which employ offset cores, cause undesirable torsional effects. Shapes with re - entrant

corners can be symmetrical, but lack compactness.

(iv) Redundancy: this is a measure of the degree of indeterminacy and reliability of

structural systems. Redundancy primarily arises from the capacity of structures to provide

an alternative loading path after any component failure. The quantification of this system

property in framed structures can be carried out through the ‗redundancy index‘ (Bertero

and Bertero, 1999). This index is defined as the number of critical (or inelastic) regions of

the structural systems that dissipate significant amounts of hysteretic energy (or

dissipative regions). In frames, adequate redundancy is achieved by ensuring that the

number of beam plastic hinges is high, e.g. at all beam ends. Redundancy can be

significantly affected by the configuration of the structure; it also depends on the

connection behaviour. For example, for buildings under biaxial and torsional motions,

redundant framed systems employing ductile connections exhibit adequate seismic

performance (Wen and Song, 2003).





(v) Bidirectional resistance and stiffness: lateral resisting elements and systems arranged

in an orthogonal in - plan pattern provide similar resistance and stiffness characteristics in

the principal directions of the structure. High horizontal stiffness is effective in limiting

excessive displacements that may lead to instabilities (e.g. due to P - Δ effects) or to

extensive structural and non - structural damage.

(vi) Torsional resistance and stiffness: adequate torsional stiffness and resistance is

necessary to reduce torsional motions which tend to stress the structural elements non -

uniformly. In this respect, arrangements in which the main elements resisting the seismic

actions are distributed close to the periphery of the building present clear advantages.

Structures with compact and convex layouts exhibit high torsional stiffness and

resistance. Inelastic demands on joints due to torsion are high. These structuralcomponents are generally weak - links in the load path for gravity and earthquake loads

they should possess adequate stiffness, strength and ductility.

Table 4.1 Attributes and benefits of optimal structural configurations.

Attributes Benefits

Low width - to - depth ratio Low torsional effects

Low height - to - base ratio Low overturning effects

Similar storey heights Elimination of weak/soft storeys Short spans Low unit stress and deformation

Symmetrical plan shape Elimination/reduction of torsion

Uniform plan/elevation stiffness Elimination of stress

Uniform plan/elevation resistance Elimination of stress

Uniform plan/elevation ductility High energy dissipation

Perimeter lateral resisting systems High torsional resistance potential

Redundancy High plastic redistribution

(vii) Diaphragm behaviour at storey level: floor and roof systems act as horizontal

diaphragms in building structures. These collect and transmit inertia forces to the vertical

elements of lateral resistant systems, i.e. columns and structural walls. They also ensure

that vertical components act together under gravity and seismic loads. Diaphragm action

is especially relevant in cases of complex and non - uniform layouts of vertical structural

systems, or where systems with different horizontal deformation characteristics are used





together (as in dual or mixed systems). High in - plane stiffness and resistance is required

to ensure adequate seismic response of storey diaphragms.

(viii) Adequate foundation: stiff and resistant foundations and their connections with the

superstructure ensure that the whole structure is subjected to uniform seismic excitation.

Rigid, box – type or cellular foundations, containing a foundation slab and a cover slab

are adequate for structures composed of a discrete number of structural walls, which

differ in width and stiffness. Buildings with isolated foundation elements – footings or

piles – should utilize a foundation slab or tie beams between these elements in both main

directions. Ideal structural configurations for earthquake - resistant design should possess

the attributes listed in Table 4.1. Major benefits that can be achieved are also given in the

table. Features in Table 4.1 can be utilized to classify structural configurations as ‗ regular‘ or ‗ irregular ‘ Regular structures are those employing the attributes in Table 4.1 . These

systems generally show adequate seismic performance; regularity is thus necessary but

not sufficient under earthquake loading. Detailing is as important as regularity. Although

expressed in a qualitative rather than quantitative manner, Table 4.1 provides simple

guidelines that can be used in conceptual structural seismic design. The physical

significance of structural regularity is intuitive but its quantitative definition is often very

difficult. Structures may have plan irregularities as illustrated in Figure 4.1; these depend

on geometry, lateral stiffness and strength distributions, mass ratios along the height,

mass - resistance eccentricity and discontinuity in diaphragm stiffness. Regular structures

are likely to exhibit uniform energy distribution, hence uniform damage distribution

under earthquake actions. Irregularities are commonly associated with geometrical

properties, such as size and shape. However, buildings with irregular plans and elevations

may employ regular structural systems to resist vertical and lateral loads. Criteria to

identify irregularities exist and it is often possible to estimate them (e.g. Arnold and

Reitherman, 1982). Torsion increases as a function of the eccentricity between centres of

mass C M and rigidity C R. The distance between C M and C R can be used to quantify

torsional effects. Criteria for regular structures are outlined hereafter for plan and

elevationrespectively.





Figure 4.1 Different Plan Irregularities (Elensai)

4.1.1 Plan Regularity

Structures with regular plan configurations are compact, i.e. described by polygonal

convex lines. Square, rectangular and circular shapes are compact. Square or rectangular

configurations with minor re - entrant corners can still be considered regular. Large re -

entrant corners creating crucifix forms give rise to irregular configurations (Figure 4.1).

The dynamic response of the wings (also termed ‗multi - mass structures‘) generally

differs from that of the structure as a whole. Multi - mass structures are highly vulnerable

at connections between wings. Relative displacements cause severe damage at the

intersection of various blocks; torsional effects are likely to occur. Other plan

configurations with geometrical symmetry, e.g. I - and H - shapes, are also irregular

because of the response of the wings. Plan irregularities depend upon the size of setbacks,





i.e. re - entrant corners and edge recesses. Limitations for the setbacks can be expressed

as a function of their geometry. For example, for L - , T - and X - sections, the following

limitation can be used:

A/B> 0.15 ÷ 0.20 .................................................eq-1

Where A and B are the length and the depth of the re - entrance, respectively, as shown in

Figure 4.2.

Equation (1) provides the limitation included in seismic design recommendations in the

USA (e.g.FEMA 450, 2004). Alternatively, regularity in plan may be assumed if, for each

setback, the area between the outline of the floor and a convex polygonal line enveloping

the floor does not exceed 5% of the total area. This criterion is adopted in European

design practice (e.g. Euro code 8, 2004). A building structure may have a symmetricalgeometric shape without re - entrant corners and wings but can still be classified as

irregular in plan, since the distribution of mass or vertical seismic resisting elements may

be asymmetric. Torsional effects due to earthquake motions can occur even when static

centres of mass C M and resistance C R coincide. For example, ground - motion waves

acting at an angle to the building axis also cause torsion, as may crack and yield in a non -

symmetrical fashion. Additionally, these effects can magnify torsion due to eccentricity

between the static centres. Generally speaking, buildings having an eccentricity between

the static centre of mass and the static centre of resistance in excess of 10% of the

building dimension perpendicular to the direction of the seismic force are considered

irregular. Quantitative criteria for torsional effects are often provided in a few modern

international seismic codes.

Structures with symmetric and compact shapes but employing plan discontinuity for

lateral resisting systems are not regular. Typical examples are three - sided buildings that

experience high torsional effects under earthquake loading (Ambrose and Vergun, 1999).

Several failures have been observed in past earthquakes for these structures, which are

utilized mainly, but not exclusively, for low - to medium - rise constructions.

Architectural reasons generally impose arrangements of plan layout with steel or

reinforced concrete (RC) frames and walls located along three sides of the perimeter

(Figure 4.3). In commercial buildings, the necessity for large openings for shop windows

on the facade may lead to the use of three - sided buildings of this type. Continuity in plan

between lateral resisting systems is essential for clear and continuous load paths. Core -

type buildings with the vertical seismic - force - resisting system concentrated near the





centre tend to behave poorly during earthquakes. Better performance has been observed

when vertical components are distributed near the perimeter of the building. This may,

however, cause instability due to torsion. Eccentric locations of rigid cores for external

lifts and stairwells also generate undesirable torsional effects (Figure 4.4). For example,

external access towers, which are meant to be used during seismic events, often fail in

their function because they experienced large rotations or collapse. Diaphragm action is

another requirement for plan regularity. Relative stiffness and strength of floors and

bracing systems are critical for earthquake response. Floor systems with high stiffness

and strength ensure adequate distribution of seismic actions among vertical structural

elements. Where discontinuities in the lateral force resistance path exist, the structure is

no longer regular. Significant differences in stiffness between portions of diaphragmsmay cause a change in the distribution of seismic forces to the vertical components and

create torsional forces. Building structures with large aspect ratios in plan are susceptible

to incoherent earthquake motion (also referred to as ‗out - of - phase effects‘). Different

foundation materials may generate amplification of the dynamic response in different

parts of the building. The higher the aspect ratio, the higher the likelihood of incoherence

effects. These effects depend on whether foundation systems, as well as superstructures,

are continuous or not. The probability of having similar live loads in large structures is

inversely proportional to the size of the structure (Nowak and Collins, 2000).

Therefore, the plan aspect ratio should be not greater than 2 – 3. Alternatively, the

structure may be subdivided into independently responding parts by using seismic joints.

Movement gaps are relatively easy to construct for bridge structures but are often highly

unreliable in buildings. Separation joints should be large enough to accommodate lateral

displacements between adjacent buildings and to avoid pounding. Out - of - phase

movements dictate the size of the gap between adjacent structures. As a rule of thumb, the

separation(s) can be assumed as 1/100 of the maximum height (H) of the adjacent

structures, in metres. Separation joints can help to mitigate unfavourable seismic effects

on multi - mass structures. It should, however, be noted that they can have disastrous

effects because of gas entrapment during post - earthquake fires. Debris from severely

damaged or partially collapsed upper storeys can also fall in separation joints. These

should be sealed, where possible, to prevent such occurrences. Irregularities in plan arise

when vertical elements of the lateral force - resisting system are not parallel to or

symmetric with major orthogonal axes. Shapes with sharp corners are unsuitable for





seismic resistance because of the high probability of torsional forces under earthquake

motions. Wedge – shape plans have large eccentricity between centre of mass and centre

of rigidity. In addition, different relative stiffness‘s between narrower and wider

perimeter sides exacerbate torsional effects. Discontinuities in horizontal and vertical

lateral resistant systems are an additional source of irregularity in plan. Out - of - plane

offsets of vertical elements, for example, may impose significant demands on structural

components of earthquake - resistant structures. Extensive damage may be caused by

these offsets; they should not be employed in seismic areas.

Figure 4.2 Typical limits for plan irregularities (adapted from FEMA 450, 2004)

Figure 4.3 Irregularities due to plan discontinuity for lateral resisting systems (three

- sided bui ldings) Key: C M = centre of mass; C R = centre of rigidity





Figure 4.4 Plan irregularities due to unfavourable core location





Chapter 5

EVALUATION OF SEISMIC PERFORMANCE OF

BUILDINGS

5.1. General

The seismic performance of a building is measured by the state of damage under a certain

level of seismic hazard. The state of damage is quantified by the drift of the roof and the

displacement of the structural elements. Initially, gravity push is carried out using force

control method. It is followed by lateral push with displacement control using ETABS

9.7. For carrying out displacement based pushover analysis, target displacement need to

be defined. Pushover analysis gives an insight into the maximum base shear that the

structure is capable of resisting. A building performance level is a combination of the

performance levels of the structure and the non-structural components. A performance

level describes a limiting damage condition which may be considered satisfactory for a

given building with specific ground motion. Performance based evaluation procedure

provides insight about the actual performance of buildings during earthquake. The steps

to be followed in seismic performance evaluation of structures and rehabilitation of

structures are given below

1. Select the performance objective of the building as required by owner to achieve for

given seismic hazard.

2. Review the existing building conditions by visual inspections, existing drawings, and

tests on structure and perform preliminary evaluation of the building.

3. Formulate a strategy for achieving the desired performance objective for given level of

seismic hazard.

4. Assess the performance of the retrofitted structure with any analysis procedures.

5. Check the performance of the structure with desired performance objective.

6. If performance objective is not achieved, formulate new strategy and assess the

performance of the structure again. Do the above process till desired performanceobjective is achieved.





5.1.1 Performance objectives

Performance objective specifies the desired seismic performance of building. Seismic

performance is described by designating the maximum allowable damage state for an

identified seismic hazard.

5.1.2 Performance levels

Performance level describes a limiting damage condition which may be considered

satisfactory for a given building and a given ground motion. Performance levels are

qualitative statements of damage the structure going to experience in future prescribed

earthquakes. Performance levels are described for structural components and

nonstructural components.ATC 40, 1996 defines 6 levels of structural damage or

performance levels and 5 levels of nonstructural damage. The brief details of structural

and non-structural performance levels are given in table 5.1 and table 5.2

Table 5.1 Description of structural performance levels (ATC 40, 1996)

Structural performance level Damage description

Immediate occupancy(IO) Very limited structural damage and risk to

life is negligible. Vertical and lateral

resisting system retains all pre-earthquakes

characteristics.

Damage control Range with more damage than IO and less

than LS

Life safety (LS) Significant damage to structural elements

with some residual strength. Risk to life

from structural damage is very low.

Limited safety Range with more damage than LS and less

than SS

Structural stability(SS) Building is on verge of partial or total

collapse. Significant degradation in stiffness

and strength of lateral resisting system.

Gravity load resisting remains to carry

gravity demand





There is not considered (NC) option in performance level. This is option for owner

weather to consider structural or nonstructural performance level. FEMA 273, 1997

defines same definitions of performance levels as described in ATC 40, 1996 but instead

of structural stability (SS) FEMA 273, 1997 describes as collapse prevention (CP).

Table 5.2 Description of nonstructural performance levels (ATC 40, 1996)

Nonstructural performance level Damage description

Operational Nonstructural systems are in place and

functional. All equipment and machinery

will be in working condition

Immediate occupancy Minor disruption of nonstructural elements

and functionality is not considered. Seismic

safety status should not be affected

Life safety Considerable damage to nonstructural

elements. Risk to life from nonstructural

damage is very low.

Hazards reduced Extensive damage to nonstructural damage.

Risk to life because of collapse or falling of

large and heavy items should be considered

Building performance level is combination of structural and nonstructural performance

levels. There so many combinations of performance levels for owner to choose based on

requirement. Building performance levels that commonly used are given in table 5.3. The

building performance levels represented on pushover curve and load deformation curve

are shown in figure 5.1





Figure.5.1. Backbone curve from actual hysteretic behaviour.

Table 5.3 Building performance levels (ATC 40, 1996 and FEMA 273, 1997)

Building performance levels Combination of structural and

nonstructural performance level

Operational Immediate occupancy(S)+ Operational

(NS)

Immediate occupancy Immediate occupancy(S)+Immediate

occupancy(NS)

Life safety Life safety (S)+ Life safety(NS)

Structural stability (or) Collapse prevention Structural stability (or) Collapse prevention

(S)+Not considered

5.2 Earthquake ground motion

Earthquake ground motion is combined with a desired building performance level to

perform a performance objective. The earthquake ground motion can be specified as level

of shaking associate with a given probability of occurrence or in terms of maximum

shaking from single event. ATC 40, 1996 defines three levels of earthquake ground

motions as given in table 5.4

Table5.4 Earthquake hazard levels (ATC 40, 1996)

Level of earthquake Definition

Serviceability earthquake (SE) Ground motion with a 50 percent chance of

being exceeded in 50 year period

Design earthquake (DE) Ground motion with a 10 percent chance of


Maximum earthquake (ME) Ground motion with a 5 percent chance of


FEMA 273, 1997 defines two levels of earthquake ground motions as given in table 5.5





Table 5.5 Earthquake hazard levels (FEMA 273, 1997)

Level of earthquake Definition

Basic safety earthquake 1 (BSE~1) Ground motion with a 10 percent chance of


Basic safety earthquake 2 (BSE~2) Ground motion with a 2 percent chance of


5.3 Basic safety objective

As per ATC 40, 1996 Basic performance objective is defined as achieving life safety

performance level for design earthquake (DE) and structural stability performance level

for maximum earthquake (ME). As per FEMA 273,1997 guidelines basic safety objective

is defined as achieving life safety performance level for basic safety earthquake~1

(BSE~1) and collapse prevention performance level for basic safety

earthquake~2(BSE~2). The wide variety of building performance level can be combined

with various levels of ground motion to form many possible performance objectives.

Performance objectives for any building may be assigned using functional, policy,

preservation or cost considerations.

5.4 Retrofit strategy and retrofit system

Retrofit strategy is a basic approach adopted to improve the seismic performance of the

building or otherwise reduce the existing seismic risk to an acceptable level. Both

technical strategies and management strategies can be employed to obtain seismic risk

reduction. Technical strategies include such approaches as increasing building strength,

correcting critical deficiencies, altering stiffness, and reducing demand. Management

strategies include such approaches as change of occupancy, incremental improvement,

and phased construction. Retrofit system is the specific method used to achieve the

selected strategy. If the basic strategy is to increase building strength, then the alternative

systems that may used to accomplish this strategy could include addition of shear walls,

thickening of existing shear walls, and addition of braced frames. It is necessary to select

a specific system in order to complete a design.





Table 5.6 Configuration deficiencies in a building (ATC 40, 1996)

Configuration deficiencies Explanation of deficiencies

Incomplete load path Complete load path is required to transfer

lateral load to foundation. Missing links in the

load path must be identified.

Vertical irregularities Vertical irregularities typically occur in a

story which is significantly weaker, more

flexible or heavier than the stories above or

below.

Horizontal irregularities Horizontal irregularities are typically due to

odd plan shapes, re-entrant corners, diaphragm

openings and discontinuities.

Weak column/Strong beam Optimum seismic performance is gained when

frame members have shear strengths greater

than bending strengths of column are greater

than beams to have controlled failure mode.

Column hinging can lead to story mechanism

creating large deflections and inelastic

rotations.

Detailing concern Non-ductile frame exhibit poor seismic

performance. Quantity, spacing, splicing,

location, size, anchorages of bars are to be

checked.

Beam column joint The lateral stability of the frame is dependent

upon beam column joint capacity. Adequate

stiffness and strength must be provided to

sustain repeated cyclic stress reversals.

Adequate reinforcement should be provided in

joint.

The structural performances levels as per FEMA 356 are; (1) Operational, (2) Immediate

occupancy (IO), (3) Life safety (LS), (4) Structural Stability and (5) Collapse prevention

(CP). Typical values of roof drifts for the three performance levels (FEMA356) are; (i)

Immediate Occupancy: Transient drift is about 1% or negligible permanent drift, (ii) Life





Safety: Transient drift is about 2% or 1% permanent drift, (iii) Collapse Prevention: 4%

transient drift or permanent drift.

5.5 Methods of analysis for evaluation of seismic performance

evaluation of buildings

Basically two methods of analysis are available to predict the seismic performance of

structures. Each method has its own advantages and limitations. The details of the two

methods are given below.

5.5.1 Elastic method of analysis

It is assumed that the structure will remain elastic under probable loads. So the strains

and stress are linear along the depth of section. But to design a building to remain elastic

for earthquake forces is uneconomical.

5.5.1.1 Seismic coefficient method

In seismic coefficient method the maximum base shear is calculated based on the

fundamental time period, importance factor, reduction coefficient. Lateral forces are

distributed proportional to square of height. R factor is used to allow structure to go into

inelastic to dissipate energy through yielding.

5.5.1.2 Linear elastic dynamic analysis

This analysis required for Irregular buildings and Tall buildings. Dynamic Analysis can

be time history analysis or response spectrum analysis. Sufficient number of modes must

be considered in analysis such that total mass participation is at least 90%.Elastic

Methods can predict elastic capacity of structure and indicate where the first yielding will

occur, however they don‘t predict failure mechanism and account for the redistribution of

forces that will take place as the yielding progresses. Moreover, force-based methods

primarily provide life safety but they can‘t provide damage limitation and easy repair.

5.5.2 Inelastic method of analysis

Inelastic method of analysis incorporates material nonlinear behavior and geometric

nonlinearity. Material nonlinearity is modelled using nonlinear stress-strain curve.





Geometric nonlinearity is incorporated in structure by calculating secondary moment for

each time step.

5.5.2.1 Inelastic time history analysis or nonlinear response history

analysis

In NRH analysis the reduced stiffness in nonlinear range is considered and the force

deformation is not single valued function. It depends on direction of motion as well. The

inelastic time history analysis is the most accurate method to predict the force and

deformation demands at various components of the structure. However, the use of

inelastic time history analysis is limited because dynamic response is very sensitive to

modeling and ground motion characteristics. It requires proper modeling of cyclic load

deformation characteristics considering deterioration properties of all important

components. Also, it requires availability of a set of representative ground motion records

that accounts for uncertainties and differences in severity, frequency and duration

characteristics. Moreover, computation time, time required for input preparation and

interpreting voluminous output make the use of inelastic time history analysis impractical

for seismic performance evaluation.

5.5.2.2 Inelastic static analysis or pushover analysis

In pushover analysis the structure is subjected to monotonically increasing lateral loads

until target displacement is reached. A predefined load pattern is applied and increased till

yielding in one member occurs then the structure is modified and lateral loads are

increased further. Seismic demand is the representation of earthquake ground motion and

capacity is a representation of the structure‘s ability to resist the seismic demand. There

are three methods to establish the demand of the building. They are (i) capacity spectrum

method, (ii) equal displacement method and (iii) displacement coefficient method. Out of

these three methods, capacity spectrum method is widely used and it is used in the present

study. Instead of plotting the capacity curve, the base acceleration can be plotted with

respect to the roof displacement. This curve is called the capacity spectrum.

Simultaneously, the acceleration and displacement spectral values as calculated from the

corresponding response spectrum for a certain damping (say 5 percent initially), are

plotted as the ordinate and abscissa, respectively.





The representation of the two curves in one graph is termed as the Acceleration versus

Displacement Response Spectrum (ADRS) format. The locus of the demand points in the

ADRS plot is referred to as the demand spectrum. The performance point is the point

where the capacity spectrum crosses the demand spectrum. If the performance point

exists and the damage state at this point is acceptable, then the building is considered to

be adequate for the design earthquake. It must be emphasized that the pushover analysis

is approximate in nature and is based on a statically applied load. Pushover analysis gives

an estimate of seismic capacity of the structural system and its components based on its

material characteristics and detailing of member dimensions. Moreover, the analysis

cannot predict accurately the higher mode responses of a flexible building. Therefore, it

must be used with caution while interpreting the actual behaviour under seismic load.The pushover analysis provides an insight into the structural aspects, which control the

performance during earthquakes. It also provides data on the strength and ductility of a

building. Decisions made at the planning stage on building configuration are more

important since the wide range of structural damages observed educative past earthquake

across the world is very educative in identifying structural configurations that are

desirable versus those which must be avoided. So the irregular structure needs a more

careful structural analysis to reach a suitable earthquake system. Pushover analysis is one

of the methods available to understand the behaviour of structures subjected to earthquake

forces. As the name implies, it is the process of pushing horizontally with a prescribed

loading pattern incrementally until the structure reaches a limit state [ATC-40

1996][16].The static approximation consists of applying a vertical distribution of lateral

loads to a model which captures the material non - linearity of an existing or previously

designed structure, and monotonically increasing those loads until the peak response of

the structure is obtained on a base shear versus roof displacement plot. The objective of

the Push-Over is to establish the lateral displacements of the structure as the applied base

shear is increased monotonically. The relative distribution of the lateral loads that

compose the base shear is maintained fixed during the analysis. Lateral load distribution

employed usually follow the shape of the fundamental mode of vibration, but may be set

arbitrarily to any type of distribution; inverted triangle, parabolic, and uniform have been

employed, the result being sensitive to a certain extent to the distribution employed.

Backbone relationships are employed in most cases. The properties of interest of such





elements are relationships between the forces and the corresponding inelastic

displacements.

During the procedure, once a point of behaviour change is detected for a particular

element, appropriate changes in stiffness properties are made, and a new stage of the

analysis is performed increasing the base shear until reaching a new point of change of

behaviour in any of the elements. This process is carried out iteratively until critical

strength failure of one or several elements is detected or a collapse mechanism is reached.

Results from the push-over analysis are presented in different forms with a base shear vs.

roof lateral displacement plot being the more popular. The ATC-40 and FEMA-273 and

356 have developed the acceptance criteria for pushover analysis using two different

methods such as Capacity Spectrum Method (CSM) and Displacement CoefficientMethod (DCM) to find out the performance point or target displacement of the structure.

5.5.2.2.1 Capacity Spectrum Method (CSM) - ATC 40

The procedure for the CSM has been developed by ATC-40. In CSM, the design curve

shown in Fig.5.2 is reduced by using spectral reduction factors to intersect the capacity

curve shown in Fig.5.3 to find the performance point. The performance point indicated

the seismic capacity of structure which will be equal to seismic demand imposed instructure by ground motion. In pushover analysis, the performance point or target

displacement is based on the assumption that the fundamental mode or uniform mode of

vibration is the predominant response of the structure and mode shapes remain unchanged

until collapse occurs.





Fig 5.2. DEMAND CURVE Fig 5.3. CAPACITY CURVE

The performance point must satisfy two relationships

a) The point must lie on the capacity spectrum or capacity curve in order to represent a

structure at given displacement.

b) The point lie on the spectral demand curve, reduced from the elastic 5 percent damped

design spectrum.

The structure to satisfy the above two relationships the spectral acceleration of structure

and spectral acceleration of the response spectra should be same and the performance

point requires a trial and error method to satisfy the above condition. ATC-40 proposed

three procedures ‗a‘, ‗b‘, ‗c‘ to determine the performance point. Procedure ‗a‘ and ‗b‘

are analytical and ‗c‘ is graphical procedure. Step-by-step procedure for ‗a‘, ‗b‘ and ‗c‘ is

explained in ATC-40. ATC simulates three categories of structural behaviour A, B and C

to consider the damping modification. ‗A‘ represents reasonably full hysteresis loops, ‗B‘

represents moderate reduction in hysteresis area and ‗C‘ represents poor hysteric

behaviour.

The damping that occurs in the inelastic range of structural behaviour is a combination of

viscous damping associated with hysteresis damping can be represented by (Kumar and

Paul, 2007)

βeff= k*βo+0.05

βo= (1/4π) (ED/Es)





ED is the energy dissipated by damping or area enclosed in a single hysteresis loop of

capacity curve, shown in Fig. 5.4

ED = 4 (Vy*Di - Dy*Vi)

Es is the maximum strain energy = Area of triangle ODiB in Fig. 5.4

Es= ViDi/2

For structures which are not typically ductile, the eq. for βo over estimates the equivalent

viscous damping. Imperfect hysteresis loop are taken care by multiplying the effective

viscous damping using a damping modification factor, k (ATC-40).

Fig 5.4 Hysteresis behavior of structure from capacity curve.

The design spectrum in CSM is reduced using spectral reduction factor which is a

function of effective damping with capacity curve of the structure. Spectral reduction

SRA and SRV as per ATC-40 are given by

SRA = 3.21- 0.68 ln (βeff)/ 2.12

SRV = 2.31- 0.41 ln (βeff)/ 1.65

This reduced demand spectra intersect with capacity spectra gives the co-ordinates of

performance point. The capacity of the structure is represented by a force-displacement

curve, obtained by a nonlinear (static pushover) analysis as shown in fig.5.6 using a

pushover analysis, a characteristic nonlinear force-displacement relationship of the

MDOF system can be determined, so further for a work base-shear and roof(top)-

displacement can be used as representative of force-displacement, resply. This analysis

can be finally performed by computer oriented software ETABS version 9.7.





The analysis in ETABS 9.7 involves the following four steps.

1) Modelling,

2) Static analysis,

3) Designing

4) Pushover analysis.

Steps used in performing a pushover analysis of a simple three-dimensional building.

1. Creating the basic computer model (without the pushover data) in the usual manner.

2. Define properties and acceptance criteria for the pushover hinges. The program

includes several built-in default hinge properties that are based on average values from

ATC-40 for concrete members and average values from FEMA-273 for steel members.These built in properties can be useful for preliminary analyses, but user defined

properties are recommended for final analyses.

3. Locate the pushover hinges on the model by selecting one or more frame members and

assigning them one or more hinge properties and hinge locations.

4. Define the pushover load cases. In ETABS 9.7 more than one pushover load case can

be run in the same analysis. Also a pushover load case can start from the final conditions

of another pushover load case that was previously run in the same analysis. Typically a

gravity load pushover is force controlled and lateral pushovers are displacement

controlled.

5. Run the basic static analysis and, if desired, dynamic analysis. Then run the static

nonlinear pushover analysis.

6. Display the pushover curve fig 5.6 and the table.

7. Review the pushover displaced shape and sequence of hinge

Fig 5.6. Pushover (capacity-demand) Curve in F-D Format





Chapter 6

ANALYSIS AND RESULTS

6.1Analysis and validation of Different Models

6.1.1 Description of Models

In the present work a 10-storied RC Frame with different plan configurations without

infill panels situated in zone V of India is taken for the purpose of study, considering

three different soil site parameters i.e. Type-I (Hard/Rock), Type-II (Medium), Type-III

(Soft).

Loadings

Live Load on floors = 3 KN/m²

Live Load on roof = 0 KN/m²

Floor Finish = 0.75 KN/m²

Geometric Properties

Column Size = 400mm x 400mm

Beam Size = 400mm x 500mm

Slab Thick = 125mm

Material Properties

Grade of concrete = M25

Unit weight of concrete = 25 KN/m³

Plan Configurations

Rectangular

C – Type

L – Type

T – Type

Plus – Type

S – Type

Diaphragm Discontinuity

Zig-Zag Pattern 1





Zig-Zag Pattern 2

The above configuration models are further represented by figures 6.1 to 6.10.

Fig 6.1. Regular Configuration- Rectangular Model

Fig 6.2. Irregular Configuration- „H‟ Model





Fig 6.3. Irregular Configuration- „C‟ Model

Fig 6.4. Irregular Configuration- „L‟ Model





Fig 6.5 Irregular Configuration- „T‟ Model

Fig 6.6. Irregular Configuration- „Plus‟ Model





Fig 6.7. Irregular Configuration- „S‟ Model

Fig 6.8. Irregular Configuration- „Diaphragm Discontinuity‟ Model





Fig 6.9. Irregular Configuration- „Z-1‟ Model

Fig 6.10. Irregular Configuration- „Z-2‟ Model





6.2Analysis and validation of 3D frame (Ravikumar.C.M.

2012) [4]

In their paper work is focused on the study of Seismic demands of different irregular

R.C buildings using various analytical techniques for the seismic zone V (hard rock) of

India. The configuration involves plan irregularities such as diaphragm discontinuity, re-

entrant corners and vertical irregularities such as geometrical irregularity, buildings

resting on sloping ground. The performance was studied in terms of time period, base

shear, lateral displacements, storey drifts and eccentricity in linear analysis using a code

– IS1893 (Part 1):2002 .Whereas the performance point and hinge status in Non linear

analysis using ATC40. Also an attempt was made in pushover analysis to identify the

correct lateral load pattern when different irregular buildings were considered. The

entire modelling, analysis and design was carried out by using ETABS 9.7 nonlinear

version software.

Fig 6.11. MODEL L1

The Layout of plan having 5X4 bays of equal length of 5m Figure 6.11. The buildings

considered are Reinforced concrete ordinary moment resisting frame building of 3-

storeys with different irregular configurations. Here stiffness of the infill is neglected in

order to account the nonlinear behaviour of seismic demands. The storey height is kept

uniform of 3m for all kind of building models which are as below.





Input

Loadings:-

Live Load on floors= 1 KN/m²

25% reduction in live load for floors during earthquake

Geometric Properties:-

Beam Size= 0.25m x 0.45m

Column Size= 0.25m x 0.45m

Slab Thickness= 0.25m

Material Properties:-

Unit weight of concrete = 25KN/m³

Modulus of elasticity = Ec= 5000√fck = 25000 N/mm²

Seismic Zone Properties:-

Seismic Zone = V

Soil type = Hard strata

Fundamental natural period= T= 0.075*h^0.75= 0.38 secs

Output

Result Journal Model L1 Validation model L1

Base Shear (KN) 2691.5 2739.84





6.3Analysis and validation of 3D frame of proposed models

6.3.1 Elastic Method- Seismic Coefficient or Equivalent Static Method

The EQSM analysis of the structure is carried to models which as discussed earlier to

know their storey shears, storey drifts, and displacements. Manual validation of models is

done through an MS Excel tool and compared to the results of ETABS. Analysis has been

performed for different soil site parameters of zone V of India of IS 1893:2002.

The design lateral force due to earthquake is calculated as follows:-

Design Horizontal Seismic Coefficient

The design horizontal seismic coefficient Ah, for a structure shall be determined

by the following expression

Ah = ZISa/2Rg

Where;

Z= Zone Factor

I= Importance Factor depending upon the functional use of the structure

R= Response reduction factor, depending upon the perceived seismic

damage Performance of the structure.

Sa/g= Average response acceleration coefficient for soil sites.

Seismic Weight

The seismic weight of each floor is its full dead load, while computing the seismic

weight of each floor, the weight of columns and walls in a storey shall be equally

distributed to the floors above and below the storey. The seismic weight of the

whole building is the sum of the seismic weights of al the floors

Design Seismic Base Shear

The total design lateral force or seismic base shear (V b) along any principal

direction is determined by the following expression

Vb = Ah*W

Where;

W = the seismic weight of the building





Fundamental natural time period

The approximate fundamental natural time period of vibration (Ts) in seconds of a

moment resisting frame building without brick infill panels may be estimated by

the following empirical expression.

Ts = 0.075h0.75 for RC building

Ts = 0.085h0.75 for Steel frame building

For all other buildings, it is given by;

Tn= 0.09h/√d

Where;

h = Height of building in metre

d = base dimension of the building at the plinth level in metre, along the

considered direction of the lateral force

Distrubution of design force

The design base shear (V b) computed is distributed along the height of the

building as below

Qi = VbWih2/Ʃ Wih

2

Where;

Qi = Design lateral force at each floor level

Wi = Seismic weight of floor, i

h = height of floor, h is measured from the base

Design Lateral force

The design lateral force shall first be computed for the building as a whole the

design lateral force shall then be distributed to various floor levels, the design

seismic force thus obtained at each floor level, shall then be distributed to

individual lateral load resisting elements on the floor diaphragm action.

All the 10 building models with different possible plan irregularities are

analyzed for linear static behaviour using ETABS v 9.7. This results obtained

from the analyses are compared with manual calculations i.e. Spreadsheet

calculation. The results presented here are focussed on Lateral load pattern

suitable for carrying out nonlinear static analyses. The M.S. Excel programs





developed in this project work, for the design of lateral loads as per IS: 1893-

2002.

6.3.1.1 Validation of 3D frame of proposed models

Table 6.1 Manual Results (Spreadsheet) for Rectangular Model: - Soil Type – I

SEISMIC WEIGHT CALCULATION

Total width of the building(m) 20

Total breadth of the building(m) 20

Typical Storey Height 3

No.of.storeys 10

Total height of the building(m) 30

MODEL NO 1

MODEL TYPE Rectanguar

soil type Rocky/Hardsoil Seismic

Analysis

according

to IS

1893:2002

zone 5

str IMP

Table 2 - Z 0.36

Table 6 - I 1

Table 7 - R 5

% Damping 5%

M.Factor 1

Building Type RCC Frame without infill

Tax 0.961395764 Cl.7.6

Sa/g 1.040 Fig-2

Ah 0.037445557 Cl.6.4.2

Vb 886.7107923 Cl.7.5.3





CALCULATION OF WEIGHT OF STRUCTURE

Structural

Components

N

o'

SIZES DEAD Other

Loads

Floors Roof Lumped

Len

Brea

Depth

Den

Wt(

KN/

K

KN/m

K

Floo

Ro

Columns 2

3 0.4 0.4 25 240 Live 3 2

0 0 240 120

Beam

X-dir 1

5 0.4 0.5 25 400 Floor 0.75 2

0.75 2

775 775

Y-dir 1

5 0.4 0.5 25 375 Ceilin

0 0 0 0 450 225

Slab elements 1

5 5 0.125 25 937

WPC 0 0 0 0 937. 937

No.of.floo

9 2162 205

STOREY SHEARStorey

No

hi

(

Wi Wi*hi

^2 P_FA

Qi

(KN)

No.of.Joi

nts

Join

t

Total

Force

Total

B.M.

Total

B.M.

1 3 205

1851

0.002

1.97 1 1.97

1.97315 6 5.9

2 6 240

8649

0.010

9.21 1 9.21

11.1892 34 393 9 240

1946

0.023

20.7

1 20.7

31.9252 96 1354 12 240

3459 0.041

36.8

1 36.8

68.7893 206 342240

5405

0.065 57.6

1 57.6 126.389 379 721240

7784

0.093

82.9

1 82.9

209.334 628 1349240

1059

0.127

112.

1 112.

322.23 967 2315240

1383

0.166

147.

1 147.

469.686 1409 3725240

1751

0.210

186.

1 186.

656.31 1969 5693240

2162

0.259

230.

1 230.

886.711 2660 8354Ʃ= 8325

Vb= 886.

KN

Figure 6.12 Storey Shear Diagram





ETABS OUTPUT

Table 6.2 Base Shear Values for considered models for soil type – I, Base

Shear in KN

SOIL TYPE-I

MODELS R T Plus S Z-2 L C H Z-1 Diaphra

gm

BASE

SHEAR

864.

75

877.

65

877.

65

877.

65

890.

55

900.

9

903.

45

903.

45

903.

45

924.97

Figure 6.13 Comparison of base shear for 10-storey building models in EQX

direction





Table 6.3 Displacement Values for considered models for soil type – I in

metre

Dis lacement Soil T e - I

Store P C DD H L R S T Z1 Z210 0.030 0.031 0.028 0.030 0.031 0.031 0.030 0.030 0.028 0.029 0.029 0.030 0.027 0.029 0.030 0.030 0.029 0.029 0.027 0.028 0.027 0.028 0.025 0.027 0.028 0.028 0.027 0.027 0.025 0.027 0.024 0.025 0.023 0.024 0.025 0.025 0.024 0.024 0.022 0.026 0.021 0.021 0.020 0.021 0.022 0.022 0.021 0.021 0.019 0.025 0.018 0.018 0.016 0.018 0.018 0.018 0.018 0.018 0.016 0.014 0.014 0.014 0.013 0.014 0.014 0.014 0.014 0.014 0.013 0.013 0.010 0.010 0.009 0.010 0.010 0.010 0.010 0.010 0.009 0.002 0.006 0.006 0.006 0.006 0.006 0.006 0.006 0.006 0.006 0.0061 0.0028 0.0028 0.0026 0.0027 0.0029 0.0029 0.0028 0.0028 0.0026 0.00

BASE 0 0 0 0 0 0 0 0 0 0

Figure 6.14 Comparison of point displacements for 10-storey building models

in EQX direction





Table 6.4 Storey Drifts for considered models for soil type – I in %

Stor

y

STOREY DRIFT (SOIL TYPE-1)

Plus C Diaphrag

H L R S T Z-1 Z-2

10 0.04

0.05

0.04% 0.04

0.04

0.04

0.04

0.04

0.04

0.03

9 0.07

0.08

0.06% 0.07

0.07

0.07

0.07

0.07

0.06

0.06

8 0.09

0.10

0.08% 0.09

0.09

0.09

0.09

0.09

0.08

0.08

7 0.10

0.11

0.10% 0.11

0.11

0.11

0.10

0.11

0.10

0.09

6 0.12

0.12

0.11% 0.12

0.12

0.12

0.12

0.12

0.11

0.11

5 0.12

0.13

0.12% 0.13

0.13

0.13

0.12

0.13

0.11

0.11

4 0.13

0.13

0.12% 0.13

0.13

0.13

0.13

0.13

0.12

0.12

3 0.13

0.13

0.12% 0.13

0.14

0.14

0.13

0.13

0.12

0.12

2 0.13

0.13

0.12% 0.13

0.13

0.13

0.13

0.13

0.12

0.12

1 0.09

0.09

0.09% 0.09

0.10

0.10

0.09

0.09

0.09

0.09

Figure 6.15 Comparison of storey drifts for 10-storey building models in EQX

direction





Table 6.5 Base Shear Values for considered models for soil type – II, Base

Shear in KN

SOIL TYPE-IIMODELS R T Plus S Z-2 L C H Z-1 Diaphra

BASE SHEA 1176.

1193

1193

1193

1211.

1225.

1228.

1228.

1228.

1257.


direction

Table 6.6 Displacement Values for considered models for soil type – II inmetre

Displacement, Soil Type – II

Storey P C DD H L R S T Z1 Z2

10 0.0413 0.0436 0.0388 0.042 0.0433 0.0433 0.0414 0.0419 0.0382 0.0379

9 0.0397 0.0415 0.0372 0.0402 0.0415 0.0416 0.0398 0.0402 0.0367 0.0366

8 0.037 0.0383 0.0347 0.0374 0.0388 0.0388 0.0371 0.0375 0.0343 0.0342

7 0.0335 0.0344 0.0313 0.0336 0.035 0.035 0.0335 0.0339 0.031 0.031

6 0.0292 0.0298 0.0273 0.0293 0.0306 0.0305 0.0293 0.0295 0.0271 0.0272

5 0.0245 0.0247 0.0229 0.0245 0.0256 0.0256 0.0245 0.0247 0.0227 0.0228

4 0.0195 0.0194 0.0182 0.0194 0.0203 0.0203 0.0195 0.0196 0.0181 0.0182

3 0.0143 0.0142 0.0133 0.0141 0.0148 0.0148 0.0143 0.0143 0.0132 0.0134

2 0.009 0.0089 0.0083 0.0088 0.0093 0.0093 0.009 0.009 0.0083 0.0084

1 0.0038 0.0038 0.0035 0.0037 0.0039 0.0039 0.0038 0.0038 0.0035 0.0036

BASE 0 0 0 0 0 0 0 0 0 0






in EQX direction

Table 6.7 Storey Drifts for considered models for soil type – II in metre

Stor

y


Plus C DD H L R S T Z-1 Z-210 0.000

5

0.000

7

0.000

5

0.000

6

0.000

6

0.000

6

0.000

5

0.000

6

0.000

5

0.000

5

9 0.000

9

0.001

0

0.000

9

0.000

9

0.000

9

0.000

9

0.000

9

0.000

9

0.000

8

0.000

8

8 0.001

2

0.001

3

0.001

1

0.001

2

0.001

2

0.001

3

0.001

2

0.001

2

0.001

1

0.001

1

7 0.001

4

0.001

5

0.001

3

0.001

5

0.001

5

0.001

5

0.001

4

0.001

4

0.001

3

0.001

3

6 0.001

6

0.001

7

0.001

5

0.001

6

0.001

7

0.001

7

0.001

6

0.001

6

0.001

5

0.001

4

5 0.001

7

0.001

8

0.001

6

0.001

7

0.001

8

0.001

8

0.001

7

0.001

7

0.001

6

0.001

5

4 0.001

7

0.001

8

0.001

6

0.001

8

0.001

8

0.001

8

0.001

7

0.001

8

0.001

6

0.001

6

3 0.001

8

0.001

8

0.001

6

0.001

8

0.001

8

0.001

8

0.001

8

0.001

8

0.001

6

0.001

6

2 0.001

7

0.001

7

0.001

6

0.001

7

0.001

8

0.001

8

0.001

7

0.001

7

0.001

6

0.001

6

1 0.001

3

0.001

3

0.001

2

0.001

2

0.001

3

0.001

3

0.001

3

0.001

3

0.001

2

0.001

2

0 0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000





Figure 6.18 Comparison of storey drifts for 10-storey building models in

EQX direction

Table 6.8 Base Shear Values for considered models for soil type – III, Base

Shear in KN

SOIL TYPE-IIIMODELS R T Plus S Z-2 L C H Z-1 Dia hr

BASE 1444.

1465.

1465.

1465.

1487.

150

1508.

1508.

1508.

1544.7


direction





Table 6.9 Displacement Values for considered models for soil type – III in

metre

Displacement, Soil Type - III

Store

P C DD H L R S T Z1 Z2

10 0.050

0.053

0.047

0.051

0.053

0.053

0.050

0.051

0.046

0.046

9 0.048

0.050

0.045

0.049

0.051 0.051

0.048

0.049

0.045

0.044

8 0.045

0.047

0.042

0.045

0.047

0.047

0.045

0.046 0.042

0.042

7 0.041

0.042 0.038

0.041

0.043 0.043 0.041

0.041

0.038

0.038

6 0.035

0.036

0.033

0.036 0.037

0.037

0.035

0.036

0.033

0.033

5 0.030

0.030

0.028

0.03 0.031

0.031

0.030

0.030

0.027

0.028

4 0.023

0.023

0.022

0.023

0.024

0.024

0.023

0.024

0.022

0.022

3 0.017

0.017

0.016

0.017

0.018

0.018

0.017

0.017

0.016

0.016

2 0.011 0.011 0.010

0.010

0.011

0.011

0.011 0.011

0.010

0.010

1 0.004

0.004

0.004

0.004

0.004

0.004

0.004

0.004

0.004

0.004

BAS

0 0 0 0 0 0 0 0 0 0


in EQX direction





Table 6.10 Storey Drifts for considered models for soil type – III in metre

Stor

y


Plus C DD H L R S T Z-1 Z-2

10 0.0007

0.0009

0.0006

0.0007

0.0007

0.0007

0.0007

0.0007

0.0006

0.0006

9 0.001

1

0.001

3

0.001

0

0.001

2

0.001

1

0.001

2

0.001

1

0.001

1

0.001

0

0.001

0

8 0.001

5

0.001

6

0.001

4

0.001

5

0.001

5

0.001

5

0.001

5

0.001

5

0.001

3

0.001

3

7 0.001

7

0.001

9

0.001

6

0.001

8

0.001

8

0.001

8

0.001

7

0.001

8

0.001

6

0.001

6

6 0.001

9

0.002

1

0.001

8

0.002

0

0.002

0

0.002

0

0.001

9

0.002

0

0.001

8

0.001

8

5 0.002

1

0.002

2

0.001

9

0.002

1

0.002

2

0.002

2

0.002

1

0.002

1

0.001

9

0.001

9

4 0.002

1

0.002

2

0.002

0

0.002

2

0.002

2

0.002

2

0.002

1

0.002

2

0.002

0

0.002

0

3 0.002

2

0.002

2

0.002

0

0.002

2

0.002

3

0.002

3

0.002

2

0.002

2

0.002

0

0.002

0

2 0.002

1

0.002

1

0.002

0

0.002

1

0.002

2

0.002

2

0.002

1

0.002

1

0.002

0

0.002

0

1 0.001

6

0.001

5

0.001

4

0.001

5

0.001

6

0.001

6

0.001

6

0.001

6

0.001

4

0.001

5

0 0.000

0

0.000

0

0.000

0

0.000

0

0.000

0

0.000

0

0.000

0

0.000

0

0.000

0

0.000

0

Figure 6.21 Comparison of storey drifts for 10-storey building models in EQXdirection





Table 6.11 Comparison of base shear with MS Excel and ETABS for 10-storey

building models for all type of soils

MODEL BASE SHEAR

Type-I Type-II Type-III

Manually Etabs Manually Etabs Manually Etabs

R 886.71079 864.75 1205.927 1176.06 1480.807 1444.13

T 900.34098 877.65 1224.464 1193.6 1503.569 1465.68

Plus 900.34098 877.65 1224.464 1193.6 1503.569 1465.68

S 900.34098 877.65 1224.464 1193.6 1503.569 1465.68

Z-2 913.97116 890.55 1243.001 1211.15 1526.332 1487.22

L 900.34098 900.9 1224.464 1225.22 1503.569 1504.5

C 927.60134 903.45 1261.538 1228.69 1549.094 1508.76

H 927.60134 903.45 1261.538 1228.69 1549.094 1508.76

Z-1 923.33255 903.45 1255.732 1228.69 1541.965 1508.76

Diaphragm 950.59291 924.97 1292.806 1257.97 1587.49 1544.71

Figure 6.22 Comparison of base shear with MS Excel and ETABS for 10-storey

building models for all type of soils





Figure 6.23 Comparison of base shear for 10-storey building models for all type of

soils





6.3.2 Inelastic static analysis or pushover analysis

Table 6.12 Summary of member level performances of all building models in soil

type -I

Performance Levels

Models Directio

Displace

Base A-

B-IO IO-

LS-

CP-

C

D

>E TOT

RPUSH X 0.3214 3274.58

123

184 84 133 0 0 0 0 1640

PUSH Y -0.3203 3323.84

121

194 86 144 0 0 0 0 1640

PPUSH X 0.3166 3369.71

128

187 90 139 0 0 0 0 1700

PUSH Y -0.3166 3369.71

128

187 90 139 0 0 0 0 1700

TPUSH X 0.3278 3431.40

128

188 91 140 0 0 0 0 1700

PUSH Y -0.3294 3438.04

128

177 86 149 0 0 0 0 1700

CPUSH X 0.3175 3436.18

139

192 92 143 0 0 0 0 1820

PUSH Y -0.3264 3619.04

135

200 92 172 0 0 0 0 1820

L

PUSH X 0.3227 3527.85

124

197 97 120 0 0 0 0 1660

PUSH Y -0.3226 3380.25 124

184 84 146 0 0 0 0 1660

Z2PUSH X 0.3247 3584.17

129

210 97 163 0 0 0 0 1760

PUSH Y -0.3562 3613.68

136

173 82 140 0 0 0 0 1760

HPUSH X 0.3339 3595.36

139

191 95 140 0 0 0 0 1820

PUSH Y -0.36 3895.67

134

212 99 162 0 0 0 0 1820

SPUSH X 0.3491 3602.86

128

188 89 142 0 0 0 0 1700

PUSH Y -0.3107 3311.62

128

188 88 143 0 0 0 0 1700

Diaphra

m

PUSH X 0.3249 4187.16

147

204 80 166 0 0 0 0 1920

PUSH Y -0.3248 4187.16

147

204 80 166 0 0 0 0 1920

Z1PUSH X 0.3291 3954.68

135

197 97 167 0 0 0 0 1820

PUSH Y -0.2365 3006.07

144

187 184 9 0 0 0 0 1820

Figure 6.24 Comparison of pushover curve of all building models in push-x and

push-y direction






type -II

Performance Levels

Models Directi

Displacem

Base A-

B-IO IO-LS LS-

CP-

C

D

>E TOTA

R PUSH 0.3214 3274.58

123

184 84 133 0 0 0 0 1640

PUSH -0.3203 3323.84

121

194 86 144 0 0 0 0 1640

T PUSH 0.3278 3431.40

128

188 91 140 0 0 0 0 1700

PUSH -0.3294 3438.04

128

177 86 149 0 0 0 0 1700

C PUSH 0.3175 3436.18

139

192 92 143 0 0 0 0 1820

PUSH -0.3264 3619.04

135

200 92 172 0 0 0 0 1820

L PUSH 0.3227 3527.85

124

197 97 120 0 0 0 0 1660

PUSH -0.3226 3380.25 124

184 84 146 0 0 0 0 1660

H PUSH 0.3339 3595.36

139

191 95 140 0 0 0 0 1820

PUSH -0.36 3895.67

134

212 99 162 0 0 0 0 1820

S PUSH 0.3491 3602.86

128

188 89 142 0 0 0 0 1700

PUSH -0.3107 3311.62

128

188 88 143 0 0 0 0 1700

P PUSH 0.3324 3919.10

129

182 96 127 0 0 0 0 1700PUSH -0.3324 3919.10

129

182 96 127 0 0 0 0 1700

Z1 PUSH 0.3291 3954.68

135

197 97 167 0 0 0 0 1820

PUSH -0.2365 3006.07

144

187 184 9 0 0 0 0 1820

Diaphra

PUSH 0.3249 4187.16

147

204 80 166 0 0 0 0 1920

PUSH -0.3248 4187.16

147

204 80 166 0 0 0 0 1920

Z2 PUSH 0.3304 4489.47

130

203 119 134 0 0 0 0 1760

PUSH -0.3289 4287.76

136

180 132 84 0 0 0 0 1760

Figure 6.25 Comparison of pushover curve of all building models in push-x and

push-y direction






type -III

Performance Levels

Models Direction Displace

Base A-B B-IO IO-

LS-

CP-

C-

D

>E TOT

R PUSH X 0.3214 3274.582

123

184 84 133 0 0 0 0 1640

PUSH Y -0.3203 3323.843

121

194 86 144 0 0 0 0 1640

P PUSH X 0.3166 3369.717

128

187 90 139 0 0 0 0 1700

PUSH Y -0.3166 3369.717

128

187 90 139 0 0 0 0 1700

T PUSH X 0.3278 3431.403

128

188 91 140 0 0 0 0 1700

PUSH Y -0.3294 3438.042

128

177 86 149 0 0 0 0 1700

C PUSH X 0.3175 3436.182

139

192 92 143 0 0 0 0 1820

PUSH Y -0.3264 3619.044

135

200 92 172 0 0 0 0 1820

L PUSH X 0.3227 3527.853

124

197 97 120 0 0 0 0 1660

PUSH Y -0.3226 3380.25 124

184 84 146 0 0 0 0 1660

Z2 PUSH X 0.3247 3584.171

129

210 97 163 0 0 0 0 1760

PUSH Y -0.3562 3613.689

136

173 82 140 0 0 0 0 1760

H PUSH X 0.3339 3595.366

139

191 95 140 0 0 0 0 1820PUSH Y -0.36 3895.675

134

212 99 162 0 0 0 0 1820

S PUSH X 0.3491 3602.865 128

188 89 142 0 0 0 0 1700

PUSH Y -0.3107 3311.627

128

188 88 143 0 0 0 0 1700

Diaphra

PUSH X 0.3194 3624.833

144

210 98 164 0 0 0 0 1920

PUSH Y -0.3194 3624.833

144

210 98 164 0 0 0 0 1920

Z1 PUSH X 0.3291 3954.684

135

197 97 167 0 0 0 0 1820

PUSH Y -0.2365 3006.072 144

187 184 9 0 0 0 0 1820

Figure 6.26 Comparison of pushover curve of all building models in push-x andpush-y direction





Figure 6.27 Member level performances of a 10-Storey diaphragm building model





Chapter 7

DISCUSSIONS AND CONCLUSIONS

7.1 DiscussionsIn our study we have compared three different soil parameters which are situated in zone

V and these same is implemented for all the proposed models. Different irregular in plan

configurations are studied and results are obtained. Two different analytical approaches

are performed to study the performance objective. First approach is equivalent static

analysis and later is followed by pushover analysis. Equivalent static analysis was

performed manually and F.E.based Etabs and to avoid repetitive calculations and errors in

calculations all models are programmed in MS Excel tool from figure 6.21 comparison of

both calculations are highlighted and these results reveals that little differences in base

forces and from figure 6.12, 6.15, and 6.18 the base forces observed for different soil and

from this it is pin pointed that diaphragm model is more vulnerable compared to other

models, model- C,H,Z1 are 2nd vulnerable range, model- Z2 is 3rd in vulnerable range,

while model-T, plus, S are 4th in vulnerable range and regular model is less vulnerable

and from figure 6.13, 6.14, 6.16, 6.17 drift and displacement values are increased 7% and

9% with concerned soil parameters and these are as shown in fig. 7.1 and fig. 7.2 andalso for different models difference in drift and displacements are shown in fig. 7.3 and

fig. 7.4. If we approach 2nd

analytical method performance levels of different models are

gathered and vulnerable range is justified after all this justification is carried out with

related triangular inverted loadings of 1st approach and according to this irregular plan

configurations forms more hinges and from the figures represented shows the valid

vulnerable structure accordingly with more no. of. Hinge formations. According to

performance level, all structures are liable to LS-CP, but according to hinge formations

diaphragm model is more with no. of. Hinge formations and is more vulnerable to

earthquake forces as compared to other models. Shows that plan irregular models can

deform largely for less amount of forces. The re-entrant corner buildings (L & Plus)

decreases the performance point as the offsets increases.





Fig. 7.1 Percentage increment in drift in all soils-I, II, III

Fig. 7.1 Percentage increment in displacements in all soils-I, II, III





Fig.7.3 Comparison of Displacements in different models in %.

Fig.7.3 Comparison of Storey Drift in different models in %.





7.2 Conclusions

The equivalent static method doesn‘t consider the irregular effects in the building

and since it depends only on empirical formula the results obtained will be

abnormal.

In pushover analysis the codal type of vertical distribution of lateral force was

found more detrimental in models.

The performances of all the models lies in between life safety and collapse

prevention except the hinge formation levels in diaphragm model is more

compared to other models .

This shows the building model with more no. of. Hinge formations are more

vulnerable to earthquake forces than rest of the models.

The result also shows that, capacity of the buildings may be significant but the

seismic demand varies with respect to the configurations.

Models R, L, P, T, and C & S gives better seismic performance than that of other

models.





Chapter 8

SCOPE FOR FURTHER STUDIES

Within the limited scope of the present work, the broad conclusions drawn from this work

have been reported. However, further study can be undertaken in the following areas:

In the present study all building models are analyzed using linear static and non-

linear static analysis, further it can be analyzed using dynamic analysis.

In the present study sizes of beams and columns are kept same. Work can be done

to optimize the sizes of beams and columns

Further the study can be extended by considering the stiffness of infill panels andcomparing the analysis results.





REFERENCES

1. K Rama Raju, A Cinitha and Nagesh R Iyer (2012), ― Seismic performance evaluation of

existing RC buildings designed as per past codes of practice‖. Sadhana volume 37, part 2, pp. 281-297.

2.

Shaikh Mohammed Rizwan, Yogendra Singh (2012). ―Effect of Strength Eccentricity on

Torsional Behaviour of RC Frame Building‖. Journal of Institution of Engineers, volume

93, issue 1, pp 15-26.

3.

Reyes Indira Herrera, Juan Carlos Vielma, Ronald Ugel, Yolsanie Martínez, Alex Barbat

(2012). ―Optimal design and earthquake resistant design evaluation of low rise framed

RC Building‖. Natural Science, volume. 4, special issue, pp 1-9.

4.

Ravikumar C M, Babu Narayan K.S, Sujith B V, Venkat Reddy D (2012). ―Effect of

Irregular Configurations on Seismic Vulnerability of RC Buildings‖. Architect Research,

volume 2, issue 3, pp 20-26.

5. T. Mahdia and V. Soltan Gharaieb (2011). ―Plan Irregular RC Frames: Comparison of

Pushover with Nonlinear Dynamic Analysis‖. Asian Journal of Civil Engineering, volume

12, issue 6, pp 679-690.

6.

Pacific Earthquake Engineering Research Centre (PEER) – Report No. 05/2010.

―Guidelines for Performance-Based Seismic Design of Tall Buildings‖ University of

California, Berkeley

7.

Pacific Earthquake Engineering Research Centre (PEER) – Report No. 111/2010.

―Modelling and Acceptance Criteria for Seismic Design and Analysis of Tall Buildings‖.

University of California, Berkeley

8. Serhan Guner and Frank J. Vecchio (2010). ―Pushover Analysis of Shear-Critical Frames:

Verification and Application‖. ACI Structural Journal, volume 107, issue 1, pp 72-81.

9.

Yong Lua, Xiaoming Gub, Jianwu Weib (2009). ―Prediction of seismic drifts in multi-

storey frames with a new storey capacity factor‖. Engineering Structu res, volume 31,

issue 2, pp 345-357.

10. Mehdi P, Faramarz K, Moghadamb.A.S (2009). ―A consecutive modal pushover

procedure for estimating the seismic demands of tall buildings‖. Engineering Structures,

volume 31, issue 2, pp 591-599.

11. Raul Gonzalez Herrera1 and Consuelo Gomez Soberon (2008). ―Influence of Plan

Irregularity of Buildings‖. The 14th World Conference on Earthquake Engineering, pp 1-8





12.

C.V.R.Murthy (2008). ―Seismic strengthening of RC Frame buildings: The formal

quantitative approaches‖. Journal of Structural Engineering, volume 35, issue 2, pp 147-

152.

13.

Barbara Borzia, Rui Pinhob, Helen Crowleya (2008). ―Simplified pushover -based

vulnerability analysis for large scale assessment of RC buildings‖. Engineering

Structures, volume 30, issue *, pp 804-820.

14.

Sekhar Chandra Dutta (2008). ―Assessing the additional seismic vulnerability in post-

elastic range due to P-Δ effect‖. Journal of Structural Engineering, volume 35, issue 2, pp

162-167.

15.

Petti.L, De Iuliis.M (2008). ―Torsional seismic response control of asymmetric -plan

systems by using viscous dampers‖. Engineering Structures, volume 30, issue *, pp 3377-3388.

16.

ATC-40 - ―Seismic Evaluation and Retrofit of Concrete Buildings‖, Applied Technology

Council, November 1996.

17. FEMA-273 - ―NEHRP Guidelines for the Seismic Rehabilitation of Buildings‖, Federal

Emergency Management Agency, October 1997.

18. FEMA-356 – ―Pre standard and commentary for the seismic rehabilitation of buildings‖,

Federal Emergency Management Agency, November 2000.

19. IS: 1893 (Part 1): 2002, Indian Standard Criteria for Earthquake Resistance Design of

Structures, Part 1 General provisions and buildings (Fifth Revision), Bureau of Indian

Standards, New Delhi.

20. IS 456:2000, ―Plain and Reinforced concrete – Code of practice‖, Bureau of Indian

Standards, New Delhi.





APPENDICES

SPREADSHEET SUMMARY

TYPES OF MODELS

ANALYSIS





A Brief Summary of the EXCEL SHEETS designed for Seismic Analysis (i.e. Equivalent Static Analysis) of RC

Frames with or without infill panels.

Worksheet one -Summary: A Brief summary

Worksheet two -Type of models: gives the various model shapes and information on structural elements

Worksheet three- INPUTS CUM ANALYSIS: this is the design/structure engineer needs provide all inputs for the structure to be analysed according to IS

1893:2002 and to know the lateral forces acting on the structure i.e. Base Shear (Vb). The design Inputs have been highlighted in dark red.





o umn aX- r - r

G.F 3 0.4 0.4 5 0.4 0.5 3

G+ 3 0.4 0.4 5 0.4 0.5 0

G.F 3 0.4 0.4 5 0.4 0.5 3

G+ 3 0.4 0.4 5 0.4 0.5 0

G.F 3 0.4 0.4 5 0.4 0.5 3

G+ 3 0.4 0.4 5 0.4 0.5 0

G.F 3 0.4 0.4 5 0.4 0.5 3

G+ 3 0.4 0.4 5 0.4 0.5 0

G.F 3 0.4 0.4 5 0.4 0.5 3

G+ 3 0.4 0.4 5 0.4 0.5 0

G.F 3 0.4 0.4 5 0.4 0.5 3

G+ 3 0.4 0.4 5 0.4 0.5 0

G.F 3 0.4 0.4 5 0.4 0.5 3

G+ 3 0.4 0.4 5 0.4 0.5 0

G.F 3 0.4 0.4 5 0.4 0.5 3

G+ 3 0.4 0.4 5 0.4 0.5 0

G.F 3 0.4 0.4 5 0.4 0.5 3

G+ 3 0.4 0.4 5 0.4 0.5 0

G.F 3 0.4 0.4 5 0.4 0.5 3

G+ 3 0.4 0.4 5 0.4 0.5 0

G.F 3 0.4 0.4 5 0.4 0.5 3

G+ 3 0.4 0.4 5 0.4 0.5 0

G.F 4.8 0.375 0.75 6 0.25 0.5 3

G+ 3.6 0.375 0.75 6 0.25 0.5 1.5

G.F 2 0.3 0.6 4 0.3 0.5 4

G+ 3.6 0.3 0.6 6 0.3 0.6 0

15

16

17

18

19

20

ShapeBeamsruc ura emen s

13 ANY 15 10 12 8 4 6 0.125 R

1

mens on roper esS ore

2 H 23 18 16 12

5 5 0.125Rectangular 20 16 15 12

Co umn Beam S aModel

Type NoModel Type

same as

above

1

R

12

4 L 21 16 16 12

3 C 23 18 16

12

6 PLUS 21 16 16 12

5 T 21 16 16

12

8 DIAPHRAGM 24 18 18 12

7 S 21 16 16

12

10 Z-2 22 15 18 12

9 Z-1 22 16 18

14

12

-

Published By

Prof.Satish36 30 30 25

11 L1 24 18 19

0.125

5 5 0.125

5 5 0.125

5 5 0.125

6 6 0.125

Loads

5 5 0.125

5 5 0.125

5 5 0.125

5 5 0.125

5 5 0.125

5 5 0.125

5 5





0

0

Ground Storey Height 3

3 Length Breadth Depth/Thk Density Wt(KN) Floors Roof

10 G.F 20 3 0.4 0.4 25 240 240 120

30 G+ 20 3 0.4 0.4 25 240 775 775

MODEL NO 1 X-dir 16 5 0.4 0.5 25 400 450 225

MODEL TYPE Rectanguar Y-dir 15 5 0.4 0.5 25 375 937.5 937.5 2402.5

soil type Soft Soil 12 5 5 0.125 25 937.5 0

City/Town Bhuj X-dir 2 0 3 0.25 20 0 21623 2057 .5

zone 5 Y-dir 2 0 3 0.25 20 0

str IMP X-dir 2 0 3 1 1 0

Table 2 - Z 0.36 Y-dir 2 0 3 1 1 0

Table 6 - I 1

Table 7 - R 5

% Damping 5%

M.Factor 1

Building Type RCC Frame without infill 1 1 3.0 2,058 18,518 0.0022 3.3 1 3 3

Tax 0.961395764 Cl.7.6 2 6.0 2,403 86,490 0.0104 15.4 1 15 19

Sa/g 1.737 Fig-2 3 9.0 2,403 1,94,603 0.0234 34.6 1 35 53

Ah0.06253408

Cl.6.4.24 12.0 2,403 3,45,960 0.0416 61.6 1 62 115

Vb 1480.807023 Cl.7.5.3 5 15.0 2,403 5,40,563 0.0650 96.2 1 96 211

6 18.0 2,403 7,78,410 0.0935 138.5 1 139 350

7 21.0 2,403 10,59,503 0.1273 188.5 1 189 538

8 24.0 2,403 13,83,840 0.1663 246.3 1 246 784

9 27.0 2,403 17,51,423 0.2105 311.7 1 312 1,096

10 30.0 2,403 21,62,250 0.2598 384.8 1 385 1,481

- 0 - - - - - - -

- 0 - - - - - - -

- 0 - - - - - - -

- 0 - - - - - - -

- 0 - - - - - - -

- 0 - - - - - - -

- 0 - - - - - - -

- 0 - - - - - - -

- 0 - - - - - - -

- 0 - - - - - - -

- 0 - - - - - - -

- 0 - - - - - - -

- 0 - - - - - - -

- 0 - - - - - - -

- 0 - - - - - - -

- 0 - - - - - - -

- 0 - - - - - - -

- 0 - - - - - - -

- 0 - - - - - - -

- 0 - - - - - - -

- 0 - - - - - - -

- 0 - - - - - - -

- 0 - - - - - - -

- 0 - - - - - - -

- 0 - - - - - - -

Ʃ= 8321558 Vb= 1480.81 KN

Lumped Mass

SEISMIC WEIGHT CALCULATIONCALCULATION OF WEIGHT OF STRUCTURE

Total width of the building(m)

Total breadth of the building(m)

Structural Components No's

SIZES DEAD WEIGHT

Typical Storey Height

No.of.storeys

Total height of the building(m)

Beams

Seismic

Analysis

according to

IS 1893:2002

Qi (KN)

STOREY SHEAR

Storey

No

hi

(Mtr)Wi Wi*hi^2

P_FACTOR

Joint

Force

Total

Force

Cummul

ative

Columns

Slab elements

EXT

Brick

Walls

INT

STOREY SHEAR DIADRAM

INVERTED TRIANGULAR LOADING PATTERN

23680

No.of.Joi

nts

- 200.0 400.0 600.0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

Qi (KN)

Qi (KN)




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