seismic vulnerability of rc frames with re-entrant corners

DISSERTATION On

SEISMIC VULNERABILITY OF RC FRAMES WITH RE-ENTRANT CORNERS Submitted to Visvesvaraya Technological University, Belagavi

In partial fulfilment of the requirement for the award of the degree of Master of Technology In Structural Engineering Submitted by

Shreyasvi C (USN: 1DA13CSE16) Under the guidance of Dr. B. Shivakumara swamy Professor and Head Department of Civil Engineering Dr. Ambedkar institute of technology Bengaluru 2014 - 2015

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ACKNOWLEDGEMENT The euphoria of success in completing a project would be incomplete without mentioning the names of this people who have sincerely helped me to achieve this milestone. I take this opportunity to express my deepest gratitude and appreciation to all those who have helped me directly or indirectly towards the successful completion of this project. I would like to express my profound sense of gratitude to our institution “Dr. AMBEDKAR INSTITUTE OF TECHNOLOGY”, Bengaluru, which has provided me an opportunity in fulfilling my dream. I am extremely grateful to my guide Dr. B.SHIVAKUMARASWAMY, Professor and Head, Department of Civil Engineering, Dr.AIT, Bengaluru, for its constant support, encouragement and valuable guidance throughout this project work. He has been of immense support, guidance and suggestions throughout the study. I am extremely thankful to Dr. C.NANJUNDASWAMY, Principal, Dr. AIT, Bengaluru, for the facilities made available at the college for carrying out this dissertation work successfully. I also thank Dr. S. RAGHUNATH, Professor, BMSCE, Bengaluru, for his guidance and valuable suggestions in conducting the parametric study. I would like to express my heartfelt gratitude to my family members for their constant support in completion of this dissertation work successfully. Last but not the least, I wish to thank all the technical, non-technical and administrative staff of Civil Engineering Department, Dr. AIT, Bengaluru and my friends who have directly or indirectly helped me during this project work. SHREYASVI C 1DA13CSE16

ABSTRACT Seismic vulnerability of India states that there are about 11 million seismically vulnerable houses in zone V and 50 million in zone IV. There about 80 million houses overall which are vulnerable to seismic activity. Past earthquake experiences demonstrate the fact that buildings with rectangular plan or box type buildings perform well than buildings with irregular shaped plans. During Bhuj (2001) earthquake majority of the buildings damages were not designed for seismic loading and most of the buildings were not engineered. It also implicates that irregular buildings are undesirable as they do not possess sufficient seismic resistance. Hence, it is necessary that all buildings be designed for seismic loading and irregular configuration must be avoided. However, irregular buildings are inevitable in few circumstances and hence, more attention has to be given in understanding their behaviour. In this study re-entrant corners have been evaluated by performing linear and non linear dynamic analysis (as per the recommendation of IS1893:2002). Models with 1 way asymmetry, 2 ways asymmetry in plan and vertical asymmetry were chosen. Linear dynamic analysis has been carried out for all the seismic zones and medium and hard soil site conditions. Non linear direct integration time history analysis has been carried out by using the real ground motion data of El Centro (1940) and Bhuj (2001). The performance of these irregular models has been compared with a model of rectangular plan configuration also known as control building. Vulnerability of these building models has been quantified from the results obtained after performing pushover analysis.

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CONTENTS Declaration

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Acknowledgement

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Abstract

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Contents

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List Of Tables

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List Of Figures

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Chapter 1 - Introduction 1.1 Preamble

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1.2 Structural Irregularities

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1.3 Necessity For Study

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1.4 Objective Of Study

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1.5 Scope Of Study

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1.6 Scheme Of Thesis Presentation

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Chapter 2 – Literature Review 2.1 General

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2.2 Literature Review

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2.3 Summary

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Chapter 3 – Structural Modelling 3.1 General

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3.2 Analysis Using Etabs

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3.3 Modelling Of Members

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3.4 Building Description

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3.5 Design Data

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3.6 Load Combinations

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Chapter 4 – Methods Of Analysis 4.1 Overview

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4.2 Seismic Design Philosophy

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4.3 Assumptions

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4.4 Methods To Determine The Design Lateral Force

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4.5 Seismic Evaluation / Performance Based Evaluation

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4.6 Vulnerability Index

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Chapter 5 – Results And Discussion 5.1 Over View

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5.2 Results From Response Spectrum Analysis

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5.3 Results From Non Linear Time History Analysis

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5.4 Results From Pushover Analysis

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Chapter 6 - A Case Study 6.1 Introduction

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6.2 Structural Modelling Details

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6.3 Results And Discussion

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Chapter 7 - Conclusion 7.1 General

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7.2 Conclusion

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7.3 Scope Of Future Work

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References

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List Of Publications

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LIST OF TABLES

1.1 Classifications Of Re-Entrant Corners Based On A/L Ratio

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3.1 Details Of Modelling

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4.1 Zone Factor For Various Seismic Zones

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4.2 Seismic Coefficient Ca And Cv For MCE

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4.3 Seismic Coefficient Ca And Cv For DBE

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4.4 Details Of The Earthquake Used In This Study

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4.5 Building Performance Levels (FEMA 356)

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4.6 Earthquake Hazard Levels (FEMA 356)

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4.7 Selection Of Performance Objectives

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4.8 Weightage Factor For Various Performance Ranges Of Hinges

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5.1 Torsion In Re-Entrant Columns

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6.1 Structural Details Of The Model

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LIST OF FIGURES 1.1 Arrival Of Seismic Waves At The Site.

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1.2 The Newyorker Hotel, New York

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1.3 Aerial View Of Manhattan City With Irregular Buildings

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1.4 Flow Chart Representing Various Structural Irregularities In A Building

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1.5 Plan Shapes Showing Re-Entrant Corners

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1.6 Structural Action Of Re-Entrant Corner

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1.7 Damages Caused At The Re-Entrant Corner Of West Anchorage High School, Alaska, During 1964 Earthquake 1.8 Damages In Between The Openings In The Wall And At The Top Due To ReEntrant Corner

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1.9 Damages In The Column In The Upper Storey Due To Re-Entrant Corners

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1.10 Re-Entrant Corners Showing Computation Of A/L Ratio

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1.11 Damages During 2010 Haiti Earthquake

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3.1 Details Of The Finite Element Package Used For The Study

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3.2 Flowchart Of The Steps Involved In Modelling Using Etabs

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3.3 Plan Of The Control Building

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3.4 Plan Of The Type A Building

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3.5 Plan Of The Type B Building

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3.6 Plan Of The Type C Building

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3.7 Building Model Of Type D Plan Configuration

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3.8 3d View Of The Control Building With Shear Walls At All The Four Corners

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3.9 3d View Of Type A Building With Shear Wall At Both The Re-Entrant Corners

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3.10 3d View Of Type B Building With Shear Wall At The Re-Entrant Corners

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3.11 3d View Of Type C Building With Shear Wall At The Re-Entrant Corners

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4.1 Flowchart Representing Classification Of Analysis Methods

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4.2 Flowchart Depicting Various Methods Of Analysis

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4.3 Map Representing Seismic Zoning In India

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4.4 Design Spectra For Rock And Soil Sites For 5% Damping.

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4.5 Design Spectrum For Various Zones Corresponding To Medium Soil Site

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Condition 4.6 Design Spectrum For Various Zones Corresponding To Rock Site Condition

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4.7 Idealized Pushover Curve

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4.8 Static Approximations In The Pushover Analysis

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4.9 Determination Of Performance Point

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4.10 Pictorial Representation Of The Non Linear Time History Analysis

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4.11 Geographical Location Of El Centro Epicentre

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4.12 Displaced Rail Tracks

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4.13 Accelerogram Of El Centro Earthquake

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4.14 Geographical Location Of Bhuj Earthquake

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4.15 Condition Of Bachau In Kutch District After Bhuj Earthquake

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4.16 Accelerogram Of Bhuj Earthquake

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4.17 Flowchart Representing The Steps Involved In Performing NLTHA

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4.18 Performance Based Analysis Procedure

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4.19 Performance Levels

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5.1 Modal Periods

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5.2 Mode Shapes Of Building Models

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5.3 Storey Displacement Corresponding To Zone II And Medium Soil

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5.4 Storey Displacement Corresponding To Zone III And Medium Soil

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5.5 Storey Displacement Corresponding To Zone IV And Medium Soil

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5.6 Storey Displacement Corresponding To Zone V And Medium Soil

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5.7 Storey Displacement Corresponding To Zone II And Hard Soil

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5.8 Storey Displacement Corresponding To Zone III And Hard Soil

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5.9 Storey Displacement Corresponding To Zone IV And Hard Soil

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5.10 Storey Displacement Corresponding To Zone V And Hard Soil

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5.11 Comparison Of Storey Displacement Of Control Building In Medium And Hard Soil For Zone V. 5.12 Comparison Of Storey Displacement Of Type A In Medium And Hard Soil For Zone V. 5.13 Comparison Of Storey Displacement Of Type B In Medium And Hard Soil For Zone V. 5.14 Comparison Of Storey Displacement Of Type C In Medium And Hard Soil

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For Zone V. 5.15 Comparison Of Storey Displacement Of Type D In Medium And Hard Soil For Zone V.

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5.16 Storey Drift Of Building Models For Seismic Zone II And Medium Soil

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5.17 Storey Drift Of Building Models For Seismic Zone III And Medium Soil

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5.18 Storey Drift Of Building Models For Seismic Zone IV And Medium Soil

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5.19 Storey Drift Of Building Models For Seismic Zone V And Medium Soil

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5.20 Storey Drift Of Building Models For Seismic Zone II And Hard Soil

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5.21 Storey Drift Of Building Models For Seismic Zone III And Hard Soil

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5.22 Storey Drift Of Building Models For Seismic Zone IV And Hard Soil

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5.23 Storey Drift Of Building Models For Seismic Zone V And Hard Soil

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5.24 Comparison Of Storey Drift Of Control Building For Medium And Hard Soil For Seismic Zone V. 5.25 Comparison Of Storey Drift Of Type A For Medium And Hard Soil For Seismic Zone V. 5.26 Comparison Of Storey Drift Of Type B For Medium And Hard Soil For Seismic Zone V 5.27 Comparison Of Storey Drift Of Type C For Medium And Hard Soil For Seismic Zone V 5.28 Comparison Of Storey Drift Of Type D For Medium And Hard Soil For Seismic Zone V 5.29 Comparison Of Storey Drift Of Control Building With And Without Shear Wall For Seismic Zone V And Medium Soil 5.30 Comparison Of Storey Drift Of Type A With And Without Shear Wall For Seismic Zone V And Medium Soil 5.31 Comparison Of Storey Drift Of Type B With And Without Shear Wall For Seismic Zone V And Medium Soil 5.32 Comparison Of Storey Drift Of Type C With And Without Shear Wall For Seismic Zone V And Medium Soil

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5.33 Base Shear Response Of Type A Building Model

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5.34 Base Shear Response Of Type B Building Model

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5.35 Base Shear Response Of Type C Building Model

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5.36 Base Shear Response Of Type D Building Model

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5.37 Floor Response Spectra Of Control Building

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5.38 Floor Response Spectra Of Type A Model

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5.39 Floor Response Spectra Of Type B Model

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5.40 Floor Response Spectra Of Type C Model

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5.41 Floor Response Spectra Of Type D Model

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5.42 Moment Envelope Along The Height Of The Control Building.

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5.43 Moment Envelope Along The Height Of The Type A Building.

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5.44 Moment Envelope Along The Height Of The Type B Building.

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5.45 Moment Envelope Along The Height Of The Type C Building.

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5.46 Moment Envelope Along The Height Of The Type D Building.

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5.47 Performance Point Of Control Building Without Shear Wall.

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5.48 Performance Point Of Control Building With Shear Wall.

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5.49 Performances Point Of Type A Model Without Shear Wall.

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5.50 Performances Point Of Type A Model With Shear Wall.

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5.51 Performance Point Of Type B Model Without Shear Wall.

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5.52 Performance Point Of Type B Model With Shear Wall.

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5.53 Performance Point Of Type C Model Without Shear Wall.

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5.54 Performance Point Of Type C Model With Shear Wall.

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5.55 Performance Point Of Type D Model Without Shear Wall.

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5.56 Pushover Curves Of Control Building Without And With Shear Wall.

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5.57 Pushover Curves Of Type A Model Without And With Shear Wall.

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5.58 Pushover Curves Of Type B Model Without And With Shear Wall.

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5.59 Pushover Curves Of Type C Model Without And With Shear Wall.

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5.60 Pushover Curve Of Type D Model

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5.61 Formation Of Hinges In Control Building

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5.62 Formation Of Hinges In Control Building With Shear Wall

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5.63 Formation Of Hinges In Type A Model

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5.64 Formation Of Hinges In Type A Model With Shear Wall

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5.65 Formation Of Hinges In Type B Model

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5.66 Formation Of Hinges In Type B Model With Shear Wall

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5.67 Formation Of Hinges In Type C Model

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5.68 Formation Of Hinges In Type C Model With Shear Wall

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5.69 Formation Of Hinges In Type D Model

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5.70 Comparison Of Vulnerability Index Of Models With And Without Shear Wall

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6.1 Plan And 3d Model Of The Re-Entrant Building

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6.2 Plan And 3d Model Of The Regular Building

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6.3 Joint Displacement With 42.85% Re - Entrant Corner

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6.4 Joint Displacement With 23.2% Re - Entrant Corner

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6.5 Joint Displacement With 50% Re - Entrant Corner

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6.6 Maximum Storey Displacement For Re-Entrant Building.

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6.7 Storey Drift For Re-Entrant Building

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6.8 Column Forces

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6.9 Comparison Of Storey Drift Between Regular And Re-Entrant Building

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6.10 Modal Periods

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6.11 Joint Displacement From Time History Analysis.

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6.12 Column Forces In Re-Entrant Columns From Time History Analysis.

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6.13 Floor Response Spectra Of Re-Entrant Building

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6.14 Floor Response Spectra Of Regular Building

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6.15 Base Shear Response Of Re-Entrant Building

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6.16 Base Shear Response Of Regular Building

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6.17 Formation Of Plastic Hinges In The Re-Entrant Building

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6.18 Formation Of Plastic Hinges In The Regular Building

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Seismic Vulnerability of RC Frames with Re– Entrant Corners 2015

CHAPTER 1: INTRODUCTION 1.1 PREAMBLE: Earthquakes are natural phenomena which occur due to the release of accumulated stress in the form of waves during rupture of rock along a fault plane. The complexity in understanding their behaviour is because of many factors such as source effect, variations in the path also known as path effect and local site effects where the structures are located. The dynamic load acting on a structure during an earthquake is due to the action of the shock waves which causes movement of the supporting structure such as foundation leading to the displacement of the structure (fig 1.1). Earthquakes are highly unpredictable in nature and they can last for few seconds but still be devastating. There are about 11 million seismically vulnerable houses in seismic zone 5 and 50 million in seismic zone 4. Overall 80 million building units are vulnerable to seismic activity [2]. Seismic ground motions are hazardous causing loss of life and incurring economic losses as well. These losses are encountered due to damage of the buildings and in the worst case scenario due to collapse of the building. These ground motions are measured using seismograms which are installed at predetermined locations. Structures located near to epicentre are more affected than the ones far away from it. An earthquake is measured in two ways. One of the ways is to study the impact of the earthquake on the structure and life which is termed as intensity and another way is to quantify the seismic waves in terms of magnitude. Intensity and magnitude have no inter relationship as an earthquake of larger magnitude can be of very low intensity if it takes place in a deserted or uninhabited area. Earthquakes not only cause ground shaking, there are many other side effects from it such as landslides, floods, tsunami, fire breakouts etc which can result in damage to structure and injury to life. The damage in a structure begins from a point of weakness. These weaknesses further trigger the damage. Usually such weak spots are present in the structure due to irregularity in mass and stiffness distribution. Structural irregularities are such weak spots in a structure from where the damage initiates and are explained in detail in the subsequent sections. Irregular buildings are preferred due to their aesthetically pleasing appearance and optimized functionality. However, past earthquakes have demonstrated their poor seismic performance. Figure 1.2 and 1.3 shows real examples of irregular buildings.

Dr. Ambedkar Institute of Technology, Bengaluru.

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Figure 1.1: Arrival of Seismic Waves at the Local Site.

Figure 1.2: The New Yorker hotel, New York (Wikipedia.org)


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Figure 1.3: Aerial view of Manhattan City with irregular buildings

1.2 STRUCTURAL IRREGULARITIES: Any structure is considered as irregular if there is a variation in the distribution of mass or stiffness or both. A regular structure has no such significant variation and hence, their seismic behaviour is more predictable and favourable. However, in case of irregular structure they undergo complex, unacceptable seismic behaviour making the structural response difficult to predict. Hence, there is a need for extensive study in understanding there response to seismic loading. There are two types of structural irregularities, namely: 1. Vertical irregularity. 2. Plan irregularity. Vertical irregularity: The uneven distribution of mass, strength or stiffness along the height of the building results in vertical irregularity. Plan irregularity: This arises due to discontinuity in mass, stiffness or strength along the plan of the building. Hence, it is also termed as horizontal irregularity. Their seismic response is a combination of translation and torsion, which is due to stiffness and mass eccentricity in the structure. IS 1893 (PART 1): 2002 classifies the structural irregularities as depicted in Fig. 1.4.


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STRUCTURAL IRREGULARITIES

VERTICAL IRREGULARITY

PLAN IRREGULARITY

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Stiffness Irregularity

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Torsion Irregularity

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Mass Irregularity

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Re-Entrant Corners

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Vertical Geometric Irregularity

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Diaphragm Discontinuity

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Lateral System Discontinuities

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Out – Of – Plane Offsets

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Weak Storey

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Non – parallel systems

Figure 1.4: Flow chart representing various structural irregularities in a building.

1.2.1. RE–ENTRANT CORNERS: IS 1893 (PART 1): 2002 defines re-entrant corner as a location in a structure where in the projection of the building component beyond that point exceeds 15% of its plan dimension in the given direction. When the building is subjected to ground motion inertial forces are mobilized. These forces travel along different paths known as „load paths‟ through various structural components and finally being transferred to the soil through foundation. In case of buildings with re-entrant corners, the shape of the plan is such that it necessitates indirect load paths which lead to local stress concentration at point where load path bends. Reentrant corners in a building pose two major serious threats. Firstly, they cause differential motions in different wings of the building due to variation in rigidity leading to local stress concentration at the notch of the re-entrant corner. On the other hand, they induce significant torsion in the building. (Fig. 1.6)


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“+” shape

L shape

T shape

H shape

Figure 1.5: Plan shapes showing re-entrant corners Figure 1.6: Structural action of re-entrant corner Previous earthquake experiences have demonstrated that buildings with re-entrant corners suffer significant seismic damages. One such example has been shown in fig. 1.7. This is a school building in Alaska, North America. The upper storey has been fully damaged due to the local stress concentration at the notch. corner

Figure 1.7: Damages Caused At the Re Entrant Corner of West Anchorage High School, Alaska, during 1964 Earthquake. Dr. Ambedkar Institute of Technology, Bengaluru.

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Figure 1.8: Damages In Between the Openings in the Wall and At the Top Due To Re-Entrant Corner.

Figure 1.9: Damages in the Column in the Upper Storey Due To Re-Entrant Corners.


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Figure 1.10: Re-entrant corners showing computation of A/L ratio. Table 1.1 classifications of re- entrant corners based on A/L ratio A/L Ratio

Condition

0.20

Highly deficient

1.3 NECESSITY FOR STUDY: A structure can collapse or suffer severe damage during an earthquake due to various structural weaknesses as mentioned before. The performance of the building during earthquakes due to presence of various structural irregularities has been illustrated in the following sections.

Figure 1.11: Damages during 2010 Haiti earthquake Dr. Ambedkar Institute of Technology, Bengaluru.

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Conventional methods of analysis and design make an attempt to make the structure withstand strong ground motion based on the strength of the individual members constituting the structure. However, making the structure seismic resistant involves huge amount of expenses and uneconomical. In such cases, more attention has to be paid to make use of the ductile nature of the structure by allowing it to undergo inelastic deformation. This has an added advantage of eliminating the possible brittle failure in a structure which is undesirable. Also most of the earthquakes have demonstrated that buildings of regular configuration perform well when compared to buildings of irregular configuration. Sometimes these irregular buildings are inevitable. In such cases we need to minimize the vulnerability of irregular buildings by strengthening the structural weaknesses so that they do not pose threat to the structure. Unfortunately, detailed analysis about structural irregularities using non linear time history analysis is not extensively carried out. Since, earthquakes cannot be controlled the only option left is to monitor the seismic performance of the building. There is a necessity for extensive use of more complex methods such as pushover analysis and non linear direct integration time history analysis in order to understand the seismic behaviour of the buildings and design them accordingly. Also, these engineered structures must be capable of surviving an earthquake and be operational after the event. In this study, one of the plan irregularities has been considered and non linear analysis has been performed to study the performance of the structure subjected to real earthquakes.

1.4 OBJECTIVE OF STUDY: Following are the major objectives of the this study  To study the seismic performance of RC frames with re-entrant corner in different seismic zones for varying soil site conditions.  To investigate the methods for strengthening the re-entrant corners in a building so that they do not pose a serious threat to the structure.  To compare the difference in behaviour of the models before and after strengthening in terms of capacity and performance.  To take up a case study in this regard and link the parametric study to it.


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1.5 SCOPE OF STUDY: In the present study, an attempt has been made to study the vulnerability of re-entrant corners in a building. Variety of cases of re-entrant corners has been considered for the parametric study. In this regard dynamic analysis has been performed which includes both linear and non linear methods. Response spectrum analysis has been performed for all the seismic zones and two types of soil site conditions. Non linear direct integration time history analysis has been performed by considering the ground motion data of two real earthquakes which are El Centro (1940) and Bhuj (2001). In order to quantify the vulnerability of these chosen building models pushover analysis was performed and by making use of the available hinge results obtained from the non linear static analysis quantification was done. Also an attempt has been made to counteract the vulnerability by strengthening this irregularity. The difference in the performance before and after strengthening is represented in terms of capacity curves and performance point of the structure. Taking a step forward a case study was considered to validate the results of parametric study and similar analysis procedure has been adopted.

1.6 SCHEME OF THESIS PRESENTATION: This dissertation has been divided into seven chapters. 

The first chapter gives a brief introduction about the nature of earthquakes and building‟s seismic performance. Also, a brief description about the types of structural irregularities as been discussed. Explanation about Re-entrant corners and their performance in previous earthquakes has been illustrated.

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The second chapter gives a review about the various literatures available with respect to this topic. Literature has been extensively reviewed on plan irregularities and their seismic performance, pushover analysis, time history analysis and quantification of vulnerability.

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The third chapter discusses about the software package chosen to carry out this study and the way in which different components of the structure are modelled. There is a brief description about modelling the non linearity in material behaviour. The models chosen for the parametric study are illustrated in this chapter.


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Seismic Vulnerability of RC Frames with Re– Entrant Corners 2015 

The fourth chapter explicitly explains various methods of analysis used in the study. Also, the seismic assessment methodology adopted for carrying out this research has been explained. Vulnerability index determination has been described in this chapter.



The fifth chapter entitled results and discussion consists of results of various building models of different methods of analysis in graphical and tabular format. The comparison of seismic performance of different building models in different seismic zones for varying soil condition has been discussed.

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The sixth chapter deals with case study which is considered for validating the parametric study and also to provide better understanding of the structural irregularity. The analysis results will be compared and irregularity will be quantified.

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The seventh chapter provides conclusion that has been reached after conducting extensive study on re-entrant corners. This includes estimating the performance of the structure in various aspects and relating that to a practical scenario. Also the scope for future study has been discussed.


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CHAPTER 2: LITERATURE REVIEW 2.1 General: This chapter will focus on recent progress made in the research area related to seismic vulnerability assessment of irregular buildings which includes the latest analysis methods available in this regard. The main aim is to understand the recent developments in this area of research and focus on those topics which have not been extensively studied. Many research articles were studied to understand the types of structural irregularity, seismic behaviour of buildings with irregularity and the variation in their response due to change in seismic zones or soil conditions. Also, the methods which are available for analyzing a structure and their merits and demerits over the other were studied. In the first stage of the review process, impact of different types of irregularity on the structure‟s seismic performance was studied in order to choose the type of irregularity for further investigation. After surveying various papers plan irregularity was chosen in which re-entrant corner has been focussed. It was observed that there is need for extensive study on re-entrant corners. In the next stage, the method of analysis which has been adopted for studying various irregularities was reviewed. Many literatures related to non linear methods of analysis which is currently trending were found and also stated that plan irregular buildings must be analysed dynamically as per the codal provisions. In this regard, dynamic analysis was chosen which included both linear and non linear methods. In this study response spectrum analysis and non linear time history analysis has been focussed to understand their procedure and execution. Also, suitable finite element software had to be selected to carry out this analysis and many literatures suggested ETABS and SAP. However, ETABS software has been used in this study. In the final stage of literature survey methods to quantify seismic vulnerability and also to link the results of the above conducted analysis to the irregularity was studied. It was observed that pushover analysis has to be performed to quantify the vulnerability in the structure. As a result non linear static analysis was performed and vulnerability was quantified. Also these results were compared among different configurations of plans and locations of re-entrant corners as learnt from the detailed study of the available literatures. In this study many codes other than Indian code were studied such as American Technical Council (ATC) 40, Federal Emergency Management Agency (FEMA) 356, and FEMA 440.


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2.2 Literature Review: 

Amin Alavi, Prof. P.Srinivasa Rao (2013)[2] – During the recent earthquakes, buildings with irregularity have not performed satisfactorily. They have demonstrated that irregular buildings are prone to more seismic damage. Therefore, it is necessary to study the performance of such buildings even in low seismic zones so that the damages caused to these buildings can be minimized. In this study eight different configurations of reentrant corners with 5 storeys has been considered. The entire analysis has been carried out using ETABS 9.7. The irregularities chosen are in accordance with the codal provisions of IS 1893. Also accidental torsion in both X and Y direction has been considered. Results illustrate that buildings with higher percentage of re-entrant corner are susceptible to more seismic damages particularly in high seismic zones. Also, the eccentricity between the centre of mass and stiffness plays a vital role in seismic response of the building.



Divyashree M, Gopi Siddappa (2014)

[7]

– Re-entrant corners pose a serious threat to

building‟s seismic performance causing stress concentration at the notch and torsional problems. In this study L- shaped building of four storey height has been considered. Response spectrum method of analysis and pushover analysis has been performed for this model. In order to understand the performance, this model has been compared with a rectangular building. Also the re-entrant corners have been strengthened using bracings and shear walls using various retrofitting technologies. The change in the behaviour of the structure due to retrofitting has been studied.



T. Mahdi, V. Soltangharaie (2012)[23] – The seismic behaviour of three moment resisting frame of five storey, seven storey and ten storey height has been considered in this study. the plan of all the three models contain re-entrant corners. Non linear static analysis and linear time history analysis has been performed. The storey drifts, displacement, and storey shear of the models have been compared. To check the accuracy of these results non linear time history analysis has been performed. The results of all the analysis have been compared and it was observed that linear time history analysis has given fairly accurate results when compared to pushover analysis.


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Mehmed Causevic , Sasa Mitrovic (2010)[14] – various procedures for performing non linear static and dynamic analysis have been developed in the recent years. This paper gives an overview about these procedures that have been implemented in various codes such as Euro code 8 and FEMA 356. Non linear dynamic time history analysis, improvised capacity spectrum method (CSM) and non linear static procedure has been described in this paper. These methods differ in accuracy, complexity involved in carrying out the analysis, clarity about the theory behind it and transparency. Non linear static analysis was developed to overcome the disadvantages of linear methods yet provide a simple procedure. All the three methods make use of performance based concepts laying more stress on damage control. These methods are illustrated by means of a eight storey RC framed building. The results of non linear static and dynamic analysis have been compared. The top storey displacement corresponding to dynamic analysis using real ground motion record gives about 145% of the target displacement obtained from the non linear static procedure.



Putul Haldar and Yogendra Singh (2009)

[19]

- the present seismic design practices in

India are force based concepts with slight attention towards capacity based design. In this paper more stress has been laid on capacity design. A set of code designed buildings have been considered and this concept has been validated with respect to various codal provisions and the expected performance is estimated in both deterministic and probabilistic method. FEMA – 440 and HAZUS methodologies have been employed in estimating the seismic performance and vulnerability. It has been observed that SMRF buildings are more vulnerable when compared with OMRF due to higher allowable drift. It has also implied that deterministic method of estimation is not sufficient as it does not provide complete insight into the seismic behaviour of the structure. 

A. Cinitha.A, P.K. Umesha , Nagesh R. Iyer (2012)[1] – this literature has focussed on performing non linear static analysis and the results from the analysis have been linked to the vulnerability of the structure using suitable formula. In this study they have considered 2 building models of 4 storeys and 6 storeys. These models are varied as OMRF and SMRF to understand the importance of ductility in earthquake resistant design and also to imply that ductile behaviour is desirable in making the structure seismic resistant. More importance has been given in defining the hinges and plastic hinge length.


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Five typical cases corresponding to varying hinge length and properties have been discussed in this regard. Finally, vulnerability of these building models has been computed using a formula which links the hinge performance in various members to a weightage factor associated with each hinge performance level. It has been shown that SMRF buildings are less vulnerable when compared to OMRF building in terms of vulnerability index. Also, the storey vulnerability index has been calculated to detect weak storey if any in the structure. 

FEMA 356

[9]

– this book consist of standard procedures for rehabilitation of the

buildings having suffered seismic damages. This provides a performance based approach and a methodology for assigning the hinges in a structure. it also describes the hinge characteristics. It provides guidelines for design of structural and non structural components in new and existing building. 

ATC 40[4] - this document provides a sound methodology for seismic evaluation and retrofitting of the existing RC buildings. However, this is not intended for new building design yet has applicability. This is applicable to the overall structure including structural and non structural components. It describes the seismic hazard levels, building performance levels and also the acceptability criteria. Damage occurred in a building is expressed in terms of inelastic deformation in post yield stage for various structural members. It provides a methodology to perform pushover analysis and also its theoretical background.

2.3

Summary: Irregular buildings are more vulnerable to seismic activity and have demonstrated poor performance in the previous earthquakes. Re-entrant corner is one such irregularity which causes stress concentration and torsion in the building. As per the guidelines of Indian code dynamic analysis has to be performed for irregular buildings. Response spectrum analysis is a powerful tool to understand the linear behaviour of the structure. But the building needs to undergo non linear analysis as well for complete understanding of the seismic behaviour. Non linear dynamic analysis incorporates an actual environment under real earthquakes and provides results for every increment in time interval. Hence, dynamic analysis has to be performed for clear understanding of the behaviour and pushover analysis has to be performed to quantify the vulnerability of re-entrant corners.


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CHAPTER 3: STRUCTURAL MODELING 3.1 GENERAL: In order to carry out an analysis, the first step is to form a mathematical model of the structure. This model should represent the exact material properties, member cross sections, loading on various members, mass distribution, strength, stiffness, deformability and non linear properties of the structure being modeled. The various members in the model should be connected in such a way that it represents the actual load flow path. Hence, more importance needs to be given to the joints which connect various members. This chapter provides an overview about the three dimensional modeling of RC frames incorporating non linear properties as well so that both linear and non linear analysis can be carried out.

3.2 ANALYSIS USING ETABS: The modeling and analysis of building models has been carried out using ETABS (Extended Three Dimensional Analysis of Building Systems) nonlinear version 9.7.4. ETABS is a powerful drafting, analysis and design software developed by COMPUTERS and STRUCTURES, Inc, Berkeley, California, USA. It has a straight forward approach incorporating structural element terminology such as beams, columns, shear walls etc., contrary to the other programs that use terms such as nodes for joints and members for beams and columns. It provides many automatic functions for the modeling, analysis and design of structural systems with better efficiency in lesser time. The user can easily create a model, apply various types of loads and using superior capabilities of this software can perform state–of – the art analysis and design. Dynamic analysis properties such has automatic lumping of masses, defining mass source, choosing between Ritz and Eigen vector, number of modes to be considered and its direction for response spectrum analysis can be specified by the user. It is easier to include the diaphragm action in the model. It also offers shear wall design steel design, composite along with concrete frame design. The software also provides ductile detailing for various frame elements and wall/ slab elements. ETABS has a user friendly interface and is directly integrated with other soft ware which mainly concentrates on foundation design. The results of analysis and design are available in graphical as well as tabular form which can be printed to a printer or to another document so that they can be used for other calculations. This chapter summarizes some of the important steps involving various stages of modeling and analysis using ETABS.


Page 15


Figure 3.1: Details of the finite element package used for the study

3.3 MODELING OF MEMBERS: BASIC MODEL OF THE STRUCTURE USING GRIDS DEFINE LOAD PATTERNS

DEFINE GEOMETRIC PROPERTIES

DEFINE LOAD CASES DEFINE MASS SOURCE DEFINE LOAD COMBINATIONS ASSIGN FLOOR LOADS

DEFINE LOADS AND ASSIGN SUPPORTS

DEFINE MATERIAL PROPERTIES DEFINE FRAME SECTIONS DEFINE SLAB AND WALL SECTIONS DEFINE DIAPHRAGMS

ANALYSIS DEFORMATION

ASSIGN SUPPORTS

INTERNAL FORCES RESULT INTERPRETATION

SUPPORT REACTIONS

Figure 3.2 flowchart of the steps involved in modeling using ETABS Dr. Ambedkar Institute of Technology, Bengaluru.

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3.3.1 Modeling of Material Properties: The material property for various structural elements such as beam, column, slab and wall are defined by the user in terms of compressive strength of concrete fck, modulus of elasticity Ec, yield strength of steel fy, modulus of elasticity of steel Es, material damping. Apart from this mass per unit volume, weight per unit volume and Poisson‟s ratio must be defined for each material type. The young‟s modulus of elasticity (Ec) of concrete is calculated using the equation 3.1 [10] Ec = 5000√fck……………. (3.1)

3.3.2 Modeling of Beams and Columns: 

The beams and columns are treated as frame elements in ETABS and modeled by considering their joint as rigid.



For linear static and dynamic analysis, modulus of elasticity of the material being used, cross sectional dimensions of the members as well as their length should be specified by the user.



The reinforcement can be either provided by the user or else the software will design the members by default.



In case of non linear analysis, along with the above mentioned properties non linear behavior of the material has to be modeled. Also, the reinforcement detailing of each member must exist before performing this analysis.

3.3.3 Modeling of Slabs / Walls / Shear walls in a building: 

Conventionally reinforced concrete slabs are not included in modeling for analysis of gravity loads. Instead its equivalent load is applied to the supporting beams in the form of trapezoidal or triangular loads. But while performing seismic analysis the in-plane stiffness of the slabs has to be considered.



Slabs can be modeled in three ways considering their structural behavior as shell type slab, membrane type slab or plate type.



In shell type behavior, the in-plane membrane stiffness and out-of-plane bending stiffness is considered.



However, in membrane type behavior, only in-plane membrane stiffness is considered. When this type of structural action is considered for the slab, diaphragms are assigned which are of two types, namely, rigid diaphragms and semi rigid diaphragms. Rigid


Page 17


diaphragms distribute lateral loads to the vertical lateral load resisting system depending on their stiffness whereas flexible diaphragms transfer the load irrespective of member stiffness. The behavior of semi rigid diaphragms lies between these two. 

In case of plate type behavior, only out of plane bending stiffness is considered.



Shear walls are designed to resist lateral loads and modeled as shell elements. They can resist both gravity loads as well as lateral loads. They also improve the stiffness of the structure.

3.3.4 Defining loads and assigning supports: 

Dead load, Live load, floor finish and roof live load patterns should be defined for gravity analysis.



While doing seismic analysis lateral loads are defined in accordance with IS1893 (PART 1):2002.



The live load has to be effectively reduced as per the above mentioned code and this is referred to as mass source in the software.



Live load, floor finish and roof live load are applied to slab elements.



Various load combinations are considered taking into account all the above mentioned loads.



The column ends are assigned with fixed support at the base.

3.3.5 Material Non- Linearity: 

While performing non-linear analysis, the property of the material beyond the elastic limit is to be studied. The linear stress – strain relationship defined for linear analysis will not suffice as the main aim of the analysis is to study the material behavior beyond the yield point. Hence, there is a need to define the non linear property of the material in use.



This is achieved by assigning plastic hinges at any position in every individual member corresponding to that member‟s critical bending moment. These hinges represent the post yield behavior of the member to which it has been assigned.



These hinges play a vital role only in case of non-linear analysis such as pushover analysis and non-linear direct integration time history analysis.



These hinges can be assigned to the structure in two ways,


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Seismic Vulnerability of RC Frames with Re– Entrant Corners 2015  Default hinge property as specified by the software based on the sectional property and stress – strain behavior.  User defined hinges. 

Default hinge properties cannot me modified as it is in built in the software and considers the assigned section properties in assigning the hinge property. These hinges are based on FEMA 356 and ATC 40. This type of hinge has been adopted in the study.



In case of user defined hinges, the moment curvature and the type of hysteresis along with other non linearity material data must be provided as an input to the software. Also it can include geometric non linearity.



There are separate hinge properties for beam and column elements. Beams are assigned with M3 hinges (moment along the major axis), as beams are critical to flexure. Similarly, columns are assigned with P-M2-M3 (axial loads, moment along minor axis and moment along major axis) hinges. For a column all the three components are crucial.



The hinges are assigned at a relative distance of 0 & 1. In other words they are assigned near the joints but not exactly at the joint. The absolute distance i.e., hinge length is calculated using Baker‟s formula. These hinges form at a distance of half the average plastic length, Lp. Lp = 0.5 H………….. (3.2) Where H = depth of the beam or column. The software makes use of this formula and assigns the hinges at corresponding distance when default hinges option is invoked.

3.3.6 Interpretation of Results: 

After the completion of analysis, the results of the building models are obtained in the form of graphs and tables.



Results are available in tabular form under various sections such as displacement, reactions, modal results, structure results, frame results, shell results and hinge results.



Under graphical representation, deformed shape, storey response plot, plot function, response spectrum curve, static pushover curve, stress diagrams.


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3.4 BUILDING DESCRIPTION: In order to understand the seismic behavior of re-entrant corners, a total of five building models with ground and four storeys were studied. They are as follows:  Control building – regular plan configuration of rectangular shape (fig. 3.3)  Type A – irregular plan with re-entrant corner (fig. 3.4)  Type B – one way asymmetrical building plan (fig. 3.5)  Type C – two way asymmetrical building plan (fig 3.6)  Type D – vertical asymmetry i.e., regular building plan till first four storey and irregular plan for the upper storey (fig. 3.7) The plan area and storey stiffness of all the building models are equal in order to facilitate comparison. The same building model provided with shear walls at the re-entrant corner has been studied in order to understand the effect of shear walls in providing sufficient resistance to seismic loading and also to validate the same as a remedy to counteract the ill effects due to reentrant corner. Few critical columns are identified in all the models and the torsional moments developed in them were studied.

CENTRE OF MASS = (6, 7.5) CENTRE OF RIGIDITY = (6, 7.5)

Figure 3.3: Plan of the control building Dr. Ambedkar Institute of Technology, Bengaluru.

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A

A/L = 4/12 = 0.334 B/L = 8/12 = 0.667 CENTRE OF MASS = (6.9, 10.6) CENTRE OF RIGIDITY = (6.96, 10.8)

B

L

Figure 3.4: Plan of Type A building

A

A/L = 4/20 = 0.2 CENTRE OF MASS = (10, 5.3) CENTRE OF RIGIDITY = (10, 5.24)

L

Figure 3.5: Plan of Type B building Dr. Ambedkar Institute of Technology, Bengaluru.

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A/L = 4/16 = 0.25 CENTRE OF MASS = (6.5, 6.4) A

Figure 3.6: Plan of Type C building

CENTRE OF RIGIDITY = (6.56, 6.3)

L

CENTRE OF MASS = (6, 7.5) CENTRE OF RIGIDITY = (6, 7.5)

Figure 3.7: Building model of Type D plan configuration. Dr. Ambedkar Institute of Technology, Bengaluru.

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Re-entrant corners can be strengthened by providing different types of bracings such as single diagonal bracings, inverted V bracings, K bracings and shear walls at the notch. An investigation has been carried out by providing shear walls at the re-entrant corners for the same models as considered above. The performance of these modified building models are compared with that of previous ones to understand the effect of shear walls in making a structure seismic resistant. Three dimensional views of the modified building models have been shown below.

Figure 3.8: 3D View of the Control Building with Shear Walls at all the Four Corners.


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Figure 3.9: 3D view of type A building with shear wall at both the re-entrant corners

Figure 3.10: 3D view of type B building with shear walls at the re-entrant corners. Dr. Ambedkar Institute of Technology, Bengaluru.

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Figure 3.11: 3D view of type C building with shear walls at the re-entrant corners.

3.5 DESIGN DATA: In all these building models the plan area and storey stiffness has been made approximately equal so that comparison of different models can be performed based on the change in their plan shapes. However, the number of columns is not same in all the models. There will be an increase in storey stiffness when the number of columns increases. To account for this the column sizes have been suitable revised so that the storey stiffness matches with the other models. As evident from table 3.2 the column sizes have changed from model to model. However, these changes are minimal. Beam sizes have not been altered as minimum variations are observed and not much impact is seen on the stiffness. The analysis has been carried out for all seismic zones and for two types of soil as mentioned in the table. LL acting on roof has been considered as a separate load case so that the error of including roof LL in mass source can be eliminated.


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Table 3.1: Details of Modeling. Number of stories

5

Floor to floor height

3m

Slab thickness and type

150mm, membrane

Dead load

self weight of the slab + floor finish (inclusive of ceiling finish) = 3.75kN/m2 + 1.25 kN/m2 = 5 kN/m2

LL

3kN/m2

LL after applying reduction factor

3 X 0.25 = 0.75 kN/m2

Floor finish

1.25 kN/m2

LL on the roof

2kN/m2

Seismic zones

II, III, IV, V

Zone factor (Z)

0.10, 0.16, 0.24, 0.36

Importance factor

1

Soil type

Medium (II), hard (III)

Response reduction factor

5 (special moment resisting frame, SMRF)

Material used

M20 and Fe 415

Damping (ζ)

5%

Earthquake load

As per IS 1893 (PART 1) :2002

Beam dimension

200 x 300 (for all building models)

Column dimension

Control building

300 x 450

Type A

290 x 440

Type B

290 x 435

Type C

290 x 440

Type D

305 x 455


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3.6 LOAD COMBINATIONS: The various load combinations considered in the analysis and design of the structure subjected to seismic loading is as listed below. These load combinations are as per IS1893:2002. The most critical load combination for each member in a structure is identified and designed accordingly by the software. 1. 1.5 (DL + LL) 2. 1.2 (DL + LL + EL X) 3. 1.2 (DL + LL + EL Y) 4. 1.2 (DL + LL - EL X) 5. 1.2 (DL + LL - EL Y) 6. 1.5 (DL + EL X) 7. 1.5 (DL + EL Y) 8. 1.5 (DL - EL X) 9. 1.5 (DL - EL Y) 10. 0.9 (DL) + 1.5 (EL X) 11. 0.9 (DL) + 1.5 (EL Y) 12. 0.9 (DL) - 1.5 (EL X) 13. 0.9 (DL) - 1.5 (EL Y) Where DL = dead load LL = live load EL X = earthquake in X direction EL Y = earthquake in Y direction When linear dynamic analysis is performed i.e., response spectrum analysis there will be an addition of seven more load combinations which consists of the spectrum being applied in X and Y direction. Totally 20 load combinations will be applied.


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CHAPTER 4: METHODS OF SEISMIC ANALYSIS AND EVALUATION 4.1 OVERVIEW: The behaviour of the structure subjected to earthquake loading can be studied by performing seismic analysis. Also the analysis is essential in order to determine various characteristics of the building such as natural period of the building, stiffness and response quantities such as mode shapes, internal forces in various members of the structure and so on. Seismic analysis is a very important aspect in earthquake engineering as it interprets the structural behaviour and facilitates in seismic resistant design of buildings. Various methods of analysis are in use depending upon the codal provisions of their respective countries. Methods of analysis can be classified as follows [18]. ANALYSIS

EXTERNAL LOADS

STATIC ANALYSIS DYNAMIC ANALYSIS

STRUCTURAL / MATERIAL BEHAVIOUR

MODEL 3D, 2D, 1D

ELASTIC ANALYSIS INELASTIC ANALYSIS

FIGURE 4.1: flowchart representing classification of analysis methods Analysis can be classified based on external loads as static and dynamic analysis. Depending on the material behaviour analysis can be linear and non linear or elastic and inelastic analysis. The equivalent mathematical model of a structure can be of three, two or one dimensional and the corresponding analysis is performed.


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4.2 SEISMIC DESIGN PHILOSOPHY: The philosophy for seismic resistant design is as follows [18]: i.

The structure must be capable of resisting minor earthquake (less than Design Basis Earthquake,

ii.

DBE) which might occur frequently, without undergoing any damage.

The structure must be able to perform against moderate earthquake (DBE) which occurs occasionally by structural components not suffering any significant damage while non–structural components sustain repairable damages.

iii.

The structure must resist major earthquake (Maximum Considered Earthquake, MCE) which

is rare in occurrence, in which the structural members suffer severe damage but the building must not collapse. An actual force to which the structure is subjected during an earthquake is higher than the design forces calculated in accordance with the code. This is because complete protection against earthquakes of all magnitude is not economically feasible. However, this gap between the actual and design forces is balanced by making the structures more ductile. As a result, the structures can withstand more deformation due to the ductile nature thereby eliminating brittle failure.

4.3 ASSUMPTIONS: The following assumptions are made in the earthquake resistant design of structures: a) Earthquake generates impulsive ground motions which are highly erratic in nature and more complex, owing to changes in period and amplitude within a short interval of time. Therefore, resonance achieved in structures subjected to steady sinusoidal waves will not occur in this case as it needs more time to build up to resonance level. b) Earthquakes are not considered to occur simultaneously with other lateral loads such as wind, floods or sea waves. c) The material property such as elastic modulus considered is same as static analysis unless specified.


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4.4 METHODS TO DETERMINE THE DESIGN LATERAL FORCE: METHODS OF ANALYSIS

LINEAR ANALYSIS

STATIC

NON LINEAR ANALYSIS

DYNAMIC

DYNAMIC

STATIC

RESPONSE SPECTRUM ANALYSIS

PUSHOVER ANALYSIS

EQUIVALENT LATERAL FORCE ANALYSIS

NON LINEAR TIME HISTORY ANALYSIS

Figure 4.2: flow chart depicting various methods of analysis

4.4.1 Equivalent Lateral Force Procedure: Also known as seismic coefficient method is a linear static method applicable for regular buildings of limited height. This is the simplest method of all the four and requires less computational effort. The design lateral force is calculated from code based empirical formulae as explained below. The total base shear is distributed along the height of the building depending on the mass and stiffness distribution in each storey. 

Determination of design base shear:

The total base shear acting on a building is calculated by the following expression: VB = Ah W........................ (4.1) Where Ah = design horizontal seismic coefficient depending on the building and site characteristics. W = seismic weight of the building Ah shall be calculated using the formula as shown below.

Ah =

Z

I

Sa

2

R

g

............................ (4.2)


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Where Z = zone factor I = importance factor R = response reduction factor Sa/g = average response acceleration coefficient for soil and rock sites. Table 4.1: zone factor for various seismic zones SEISMIC ZONE



ZONE FACTOR

II

0.10

III

0.16

IV

0.24

V

0.36

The whole of India is divided into four seismic zones as shown in figure 4.3. each zone

has its own zone factor (Z) 

The zone factor is for the Maximum Considered Earthquake (MCE). Since, the structures

are designed for Design Basis Earthquake (DBE) which is half of MCE, only Z/2 is considered in calculating the base shear. This is a characteristic of the location where the structure is situated and the values are assigned based on their seismic zones.

Figure 4.3: Map Representing Seismic Zoning in India Dr. Ambedkar Institute of Technology, Bengaluru.

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IS 1893 (PART 1):2002 classifies the buildings into two categories depending on their

functional use. They are (i) important service and community buildings and (ii) all other buildings. The buildings falling under category 1 are assigned with an importance factor of 1.5 while the other with 1. 

The response reduction factor is a measure of ductile and damping behaviour in a

structure. More the ductility higher the value of R. Incorporation of this factor in the formula is to bring forward the inelastic characteristics of the structure in linear analysis. The reciprocal of this value is considered to significantly reduce the seismic demand on the structure based on its ductile capacity. 

Average response acceleration coefficient is a function of the soil site characteristic and

the natural period of the structure. The natural period of the structure is calculated from the formula as per IS1893 (PART 1): 2002 clause 7.6.1 and 7.6.2. Ta = 0.075 h0.75 for moment resisting RC frames without brick infill. Ta = 0.085 h0.75 for steel moment resisting frames without brick infill. Ta = 0.09 h/ √d all other buildings with brick infill walls. Where h = height of the building, m and d is the base dimension of building at the plinth level, m along the direction in which the lateral force is considered to be acting.

Figure 4.4: design spectra for rock and soil sites for 5% damping.


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Seismic Vulnerability of RC Frames with Re– Entrant Corners 2015 

Lateral Distribution of Base Shear along the Height of the Building:

The previously calculated base shear is distributed along the building height depending on the mass distribution. Indian code prescribes parabolic distribution of lateral force as per the following expression: Q i  VB

Wi h i

2

............... (4.3)

n

W h j1

j

2 j

Where Qi = design lateral force at floor i Wi = seismic weight of floor i hi = height of the floor i measure from the base.

4.4.2 Response Spectrum Analysis: This is a linear dynamic analysis also known as modal superposition method. Indian code prescribes that irregular buildings of height greater than 12m located in zone IV and V and of height greater than 40m located in zones II and III must be analyzed dynamically. The objective of this analysis is to obtain the lateral force distribution along the height of the building which is same as equivalent static method. The major difference between these two linear analysis is in their level of force and their distribution along the building height. The response of a building depends on the dynamic characteristics of the building such as fundamental natural period and damping. However, these are not taken into account in the previous analysis. Also, this analysis is applicable where modes along with fundamental mode affect the response of the building. Every individual mode will be analysed and the peak response quantities of all the modes will be combined by one of the following methods: 

Absolute sum (ABS) method: This method assumes that the maximum response

corresponding to each mode occurs at the same time interval. Therefore, the maximum response is the sum of the maximum absolute value of each mode. λ* = Ʃcr λc..................(4.4) This is applicable only for the closely spaced modes. 

Square root of sum of squares (SRSS): This is the most commonly used method for modal

combination as well as directional combination of modes. This method has been adopted in this study. This is applicable for well spaced modes. λ = √ Ʃk=1r (λk)2..................(4.5) Dr. Ambedkar Institute of Technology, Bengaluru.

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Seismic Vulnerability of RC Frames with Re– Entrant Corners 2015 

Complete quadratic combination (CQC): This is based on the theory of random vibration

and is an extension of SRSS method. It‟s applicable for undamped structure. The peak response quantity of all the modes is combines using the formula

𝑟 𝑖=1

𝜆=

𝑟 𝑗 =1 𝜆𝑖

𝜌𝑖𝑗𝜆𝑗 ................ (4.6)

Where r = number of modes being considered λi = response quantity in mode i, λj = response quantity in mode j, ρij= cross modal coefficient

𝜌𝑖𝑗 =

8𝜁 2 1+𝛽𝑖𝑗 𝛽 ^1.5

..................... (4.7) 1−𝛽𝑖 𝑗 2 +4𝜁 2 𝛽𝑖𝑗 1+𝛽𝑖𝑗 2

Where ζ = modal damping ratio, βij = frequency ratio = ωi/ωj, ωi = circular frequency in ith mode, ωj = circular frequency in jth mode. In the present study design spectra corresponding to medium soil and rock have been applied to various building models. These spectra are shown in fig. 4.5 and 4.6. The results of this analysis are presented in the subsequent chapter. The spectral coefficient for zone V is more when compared to other seismic zones implying the fact that buildings located in this zone are prone to severe damage. Also these values vary for different soil site conditions. Buildings located on hard soil experience more seismic action than the ones located on medium soil. This has been demonstrated in chapter 5.


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1

SPECTRAL ACCELERATION CO EFFICIENT (Sa/g)

0.9 0.8

ZONE 5

0.7

ZONE 4

0.6

ZONE 3

0.5

ZONE 2

0.4 0.3 0.2 0.1 0 0

2

4

6

8

10

12

PERIOD (S)

Figure 4.5: Design spectrum for various zones corresponding to medium soil site condition. 1 0.9 ZONE 2

SPECTRAL ACCELERATION CO EFFICIENT (Sa/g)

0.8 0.7

ZONE 3

0.6

ZONE 4

0.5

ZONE 5

0.4 0.3 0.2 0.1 0 0

2

4

6

8

10

12

PERIOD (S)

Figure 4.6: Design spectrum for various zones corresponding to rock site condition.


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4.4.3 Pushover Analysis: 4.4.3.1 General: Non linear static analysis (NSA) also known as pushover analysis is performed by incrementally increasing the lateral loads while the vertical loads remain the same. These lateral loads represent the estimated seismic loads. In other words, the structure is pushed in small increments of the total estimated lateral load till the structure reaches its limit state. Once the structure has reached its limit state various failure modes of structure will be visible in the model determining the load at collapse and its ductile capacity. A graph of base shear versus roof displacement is obtained from the analysis (fig. 4.7), also known as pushover curve. The degradation in stiffness, the sequence of formation of plastic hinges in various members according to the displacement constraint laid on the structure can be determined. One of the analysis methods of doing NSA is capacity spectrum method (CSM) which uses the intersection of the capacity (pushover) curve of the structure with the demand curve of certain damping to estimate the performance of the structure in terms of spectral displacement. This study is based on CSM method.

Figure 4.7: Idealized Pushover Curve


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4.4.3.2 Methods of Pushover Analysis: There are various methods in which pushover analysis can be performed. However, these methods are classified into two types. i)

Force Control:

ii)

In force based method, lateral force is applied to the structure and the resulting displacement is measured. The type of load distribution being applied to the structure can be of two types a) fixed load and b) varying load. In fixed load distribution, the load to be applied at various levels of the building is prefixed and remains the same throughout the analysis. The list of distributions used under fixed load is as follows. 

A single concentrated lateral load at the top storey.



Uniform distribution of lateral load on all storeys.



Standard codal or triangular pattern of load distribution.



Loads are distributed at each level proportional to the product of the mass vector and their fundamental mode shapes.



Lateral loads are distributed based on the response spectrum analysis of the building. In varying load distribution, the loads are distributed based on the inertial forces acting at each level and their corresponding elastic deformation. In this case the load distribution varies as the storey displacement varies along the height of the building. Following are the various ways for variable load distribution.



The forces are distributed along various height of the building proportional to the product of their mass vector and fundamental mode till yielding occurs. In post yielding, the loads are distributed based on the deflection undergone by each storey. Then the load distribution is proportional to the product of the floor mass and its displacement.



Secant stiffness is used from which mode shapes are derived and distribution is based on those mode shapes.



Each storey offers its own resistance during each step of pushover analysis. Load distribution is based on this resistance.


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iii)

Displacement Control: In displacement based pushover analysis, the structure is subjected to displacement and the corresponding lateral forces are calculated. The storey displacement undergone by the structure is limited to 4% of the building height, the value of which will have to be specifies by the user and the sequence of formation of plastic hinges in the various members of the structure corresponding to displacement constraint is observed.

4.4.3.3 Methodology of Pushover Analysis: Pushover analysis is a technique in which the software models the building as specified by the user and the lateral load is applied to this model by one of the distribution methods as mentioned above in a certain shape such as parabolic, inverted triangle, uniform and so on (fig. 4.8). Lateral load is applied in gradually increasing manner in various steps while the gravity loads are same throughout the analysis till the prefixed roof displacement limit is reached. However, in displacement based pushover analysis the magnitude of lateral force at each floor level has no impact on the response of the structure but the ratio in which they are distributed at each floor level affects the response.

Figure.4.8: Static approximations in the pushover analysis The major benefit from this analysis is that the over strength can be measured and also the capacity of the structure to withstand the inelastic deformation can be studied. The loads acting on the structure contributed by various members of the structure are calculated by conventional method in accordance with IS 456: 2000 and are applied along with live loads which are applied with suitable reduction factor as per the guidelines of IS1893: 2002. The lateral loads and their distribution at each floor level are determined are calculated from equation 4.3. Dr. Ambedkar Institute of Technology, Bengaluru.

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Seismic Vulnerability of RC Frames with Re– Entrant Corners 2015 These loads are then applied in “PUSH - Analysis case” during the analysis. The structural members are then designed for the internal forces obtained from the analysis using IS 456: 2000 for the load combination 1.5 (DL + LL). Steps to perform pushover analysis: Following steps are followed in performing pushover analysis:  Modelling: A 3D model is created in the software using frame and shell elements of required dimensions.  Load application: Structural member elements are assigned with their respective loads.  Preliminary analysis/ linear analysis: Equivalent static analysis is performed for the applied gravity loads as well as lateral loads.  Design: Structural members are designed according to codal provisions of IS456: 2000 in the software.  Hinge assignment: Non linear / plastic hinges are assigned to beams and columns using the default hinge property. Columns are assigned with P-M2-M3 hinges where as beams are assigned with M3 hinges. Hinge properties are as defined in FEMA – 356.  Define load cases: non linear pushover cases are defined. A total of two cases are defines. One of the cases considers the gravity loads where as the other case considers the acceleration. First case is force controlled while the second is displacement controlled.  For displacement based pushover case the total displacement to which the structure is subjected to is limited to 4% of the building height.  Analysis: Non linear static analysis is run.  Interpretation of results. 4.4.3.4 Results from Pushover Analysis: Two important elements of pushover analysis are capacity and demand. Demand represents the characteristic of the applied ground motion where as capacity signifies the ability of the structure to resist the demand. The major objective of this analysis is to determine the capacity, demand and performance point. All the three parameters are briefly explained below. 

Capacity: The capacity of a structure depends upon the strength and deformability of all the individual components comprising the structure. To determine the performance of the structure beyond the elastic limit any of the non linear analysis must be performed. In pushover analysis a series of linear analysis is performed to determine the overall


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capacity of the structure. Then the model is adjusted to the reduced deformation ability of the structure and again lateral loads are applied in steps as explained earlier. The capacity curve represents the behaviour of the structure in post yielding stage. 

Demand: The displacement of the structure during ground motion is complex and has no fixed pattern. Monitoring this displacement at each and every time interval to match the structural requirements accordingly is impractical. Hence, linear analysis considers a peak value of acceleration and applied the loading along the height of the building using standard empirical formulae as specified by the code. In case of non linear analysis, displacement demands are laid on the structure and analysis is performed. Basically demand spectrum represents the expected behaviour of the structure during ground motion.



Performance point: This is of vital importance for designing a structure. The intersection of capacity and demand spectra is treated as performance point of the structure. This represents the structural and non structural behaviour in terms of damage states. The performance of the structure is compared with the acceptability criteria at the performance point.

All the three key elements are illustrated in fig. 4.9.

Figure 4.9: Determination of performance point.


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4.4.3.5. Seismic coefficients: There are two types of seismic coefficients namely, CA and CV which are functions of the seismic zone and the soil type. Various combinations of these two factors are represented in a matrix form in table 4.2 and 4.3. These values are provided for MCE as well as DBE. The basic form of this table is given in ATC 40 but the major drawback is that the method of soil classification and seismic zones is different when compared with the Indian scenario. Hence, suitable adaptation has been made to match with our criteria. Table.4.2: Seismic Coefficient Ca and Cv for MCE SOIL

CA FOR SHAKING INTENSITY

PROFILE TYPE

ZONE I

ZONE II

ZONE III

ZONE V

Type I

0.10

0.16

0.24

0.36

Type II

0.10

0.16

0.24

0.36

Type III

0.10

0.16

0.24

0.36

CV FOR SHAKING INTENSITY Type I

0.10

0.16

0.24

0.36

Type II

0.14

0.22

0.33

0.50

Type III

0.17

0.27

0.40

0.60


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Table.4.3: Seismic Coefficient Ca and Cv for DBE SOIL

CA FOR SHAKING INTENSITY

PROFILE TYPE

ZONE I

ZONE II

ZONE III

ZONE V

Type I

0.05

0.08

0.12

0.18

Type II

0.05

0.08

0.12

0.18

Type III

0.05

0.08

0.12

0.18

CV FOR SHAKING INTENSITY Type I

0.05

0.08

0.12

0.18

Type II

0.07

0.11

0.17

0.25

Type III

0.08

0.13

0.20

0.30

In the present study for zone 5 and medium soil type the value of CA and CV are taken as 0.18 and 0.25 respectively with respect to DBE.

4.4.4 NON LINEAR TIME HISTORY ANALYSIS: The non linear dynamic analysis makes use of the available ground motion data in analysing the structure. In this method, an environment is created which represents the exact real time ground motions and provides a more realistic picture about the possible deformations in a structure and collapse mechanism. Methodology is similar to that of static analysis except that no target displacement is fixed in this case. The deflections and other internal forces in structural members are measured as observed and this seismic response is very sensitive to the ground motion. This analysis can be carried out using an actual time history record of the previously occurred earthquakes or using a generated synthetic accelerogram. There are two methods to perform time history analysis and they are Modal Superposition Method i.e., Linear Time History Analysis and Direct Integration Time History Analysis or Non Linear Analysis. In this study non linear time history analysis is performed. Direct integration method is used when non linear analysis is to be performed on the structure. In this method Dr. Ambedkar Institute of Technology, Bengaluru.

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results are greatly affected by the time step size and hence, the step size must be small enough that the output or the results are no more affected from that. In the present study, two accelerogram have been utilized and they are El Centro (1940) earthquake and Bhuj (2001) earthquake. The details of these two earthquakes have been briefly explained in the subsequent sections and also listed in table 4.4.

Figure 4.10: Pictorial representation of the Non Linear Time History Analysis (Ecole doctoral Structures, CIVIL-706 Advanced Earthquake Engineering) 4.4.4.1 Details of the earthquake ground motions used in this study: 

Imperial valley earthquake or El Centro earthquake:

Figure 4.11: geographical location of the El Centro epicentre Dr. Ambedkar Institute of Technology, Bengaluru.

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Seismic Vulnerability of RC Frames with Re– Entrant Corners 2015 This earthquake took place on May 19th in 1940 at 21:35 (Pacific Standard Time) in the Imperial Valley near southern California at the international borders of United States and Mexico. It had a moment magnitude of 7.1 with an intensity of X (Intense) on Mercalli intensity scale. This became the first earthquake to be recorded by a seismograph which was located next to fault rupture. This caused a property damage which was estimated to be around $6million. The first shock damaged about 80% of buildings in Imperial Valley and also elevated water tanks in Holtville and Imperial collapsed. There was a huge break in the water mains leading to the breakage of the water pipes. Major canals were damaged such as Alamo canal which was the main feeder for the entire district had eight major breaks. The rail road tracks were displaced by a distance of 2m at Cocopah and 46cm at Meloland and many sand boils were observed near Gadsden on the Yuma project (fig4.12). A surface rupture of length 40 – 60 km with a maximum displacement of 4.5m was recorded near the border. It was a purely strike slip fault with no visible vertical displacement. There exists a plate boundary between the Pacific plate and the North American plate.

Figure 4.12: Displaced rail tracks during Northridge earthquake


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Figure 4.13: accelerogram of El Centro earthquake. 

Bhuj Earthquake:

Figure 4.14: geographical location of the Bhuj epicentre This event occurred on 26th January, India‟s 52nd republic day at 8:46 in the morning. It has been recorded that the earthquake lasted for about 42 seconds. The epicentre was about 9km south of Kutch district. This earthquake was of magnitude 7.9 on moment magnitude scale and an intensity of X (Intense) on Mercalli Intensity Scale. This earthquake caused a death toll of 20,000 people with the injured being 1, 67,000 people and about 4, 00, 000 homes were completely damaged. Gujarat is located at a distance of 400km from the plate boundary between the Indian and the Eurasian plate. However, the present tectonic movement is still governed by the collision along Dr. Ambedkar Institute of Technology, Bengaluru.

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this boundary. Figure 4.14 shows the geographical map of Bhuj. In this earthquake intra plate type of fault rupture was evidenced. Figure 4.15 depicts the ill effects of this earthquake and also the devastating condition in Kutch district. Figure 4.16 represents the accelerogram of the Bhuj earthquake being applied in the analysis.

Figure 4.15: Condition of Bachau in Kutch district after Bhuj earthquake (2001)

Figure 4.16: accelerogram of Bhuj earthquake.


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Table 4.4: Details of the earthquake used in this study Earth quake

El Centro

Bhuj

Date

18/05/1940

26/01/ 2001

Time

21:35

8:46:42

Magnitude

7.1

7.9

Latitude

32.733 N

23 02 N

Longitude

115.5 W

72 38 E

Initial Displacement (mm)

400

3.97

Peak acceleration (m/s2)

3.12

1.0382

4.4.4.2 Steps to perform Non Linear time History Analysis (NLTHA): As explained earlier this analysis makes use of the available ground motion data in predicting the structural behaviour to an actual earthquake. The time history record of the earthquake is loaded into the software while defining the time history function. The hinge assignment is similar to that of pushover analysis.


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CREATE A 3D MODEL OF THE STRUCTURE

ASSIGN THE FRAME PROPERTIES AND LOADS TO VARIOUS MEMBERS

DEFINE TIME HISTORY FUNCTION

DEFINE TIME HISTORY LOAD CASES

ASSIGN DEFAULT PLASTIC HINGES TO THE FRAME ELEMNTS

RUN ANALYSIS

INTERPRETATION OF RESULTS Figure 4.17: Flowchart representing the steps involved in performing NLTHA.

4.5 Seismic Evaluation/ Performance Based Evaluation: 4.5.1 General: Recent earthquakes have demonstrated the need for performance based seismic evaluation. The key element in this evaluation is a clear estimate of the inelastic behaviour of the structure as it is based on quantifying the response of the members and the structure as a whole in terms of deformation due to the lateral loads arising from the earthquake. This method has an advantage


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of giving more freedom in choosing the performance compared to limit state of collapse and serviceability. The flowchart below shows the steps involved in performance based assessment. DEFINE STRUCTURAL PERFORMANCE LEVEL

PRELIMINARY DESIGN

ANALYSIS

DEFINE SEISMIC HAZARD LEVEL

SELECTION OF THE PERFORMANCE OBJECTIVE

EVALUATION OF SEISMIC PERFORMANCE Figure.4.18. Performance-based Analysis Procedure 4.5.2 Performance Levels: A structural engineer decides the expected performance of the structure and its condition after being subjected to a sequence of ground motion. The building performance level is dependent on the condition of the structural and non structural components after the event has lapsed. The performance level of a structure is classified as follows [4] a) Immediate occupancy b) Life safety c) Collapse prevention


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Seismic Vulnerability of RC Frames with Re– Entrant Corners 2015 4.5.2.1 Immediate Occupancy Performance Level (S – 1)  This refers to a performance level wherein the structure has not suffered significant damage and the building can be occupied immediately and any repair works can be carried out after occupancy.  The main frame structure i.e., beams, columns and slabs which are the vertical and horizontal resisting elements of the structure have retained their strength and stiffness without significant degradation.  There can be hair line cracks in the framed structure and yielding might have been experienced at few places but crushing of concrete is improbable.  There will be no permanent drift while there can be a transient drift of 1%.  If there are brick infill walls, minor cracking or spalling of the plaster is evidenced.  There is no risk of life threatening injury since the structural damage is very less. 4.5.2.2 Damage Control Performance Level (S - 2)  Performance level in which the damage caused to the structure lies between that of immediate occupancy and life safety.  This level is desirable to minimize the time required for repair and when the cost of design for immediate occupancy is high.  The criteria for acceptability can be obtained by interpolating between immediate occupancy (S – 2) and life safety levels(S – 3). 4.5.2.3 Life Safety Performance Level (S – 3)  This represents a damage state where the structure has suffered significant structural damage but possess sufficient resistance against collapse.  Primary framing elements could be severely damaged, but has not given way to spalling off huge amount of debris.  Beams suffer maximum damage leading to spalling of concrete cover and columns suffer significant damage causing shear cracks.  A permanent drift of 1% and a transient drift of 2% are expected.  Brick infill experience cracking but are expected to remain intact.  The probability of life threatening injury due to structural damage is low though there might be minor injuries.  The damage must be repairable. However, it is not advisable from economical point of view. Dr. Ambedkar Institute of Technology, Bengaluru.

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4.5.2.4 Limited Safety Performance Level (S-4)  Structural Performance Level S-4, Limited Safety refers to a damage state between that of Life Safety and Collapse Prevention levels.  The criteria for acceptability can be obtained by interpolating between life safety (S – 3) and collapse prevention (S – 5) levels. 4.5.2.5 Collapse Prevention Performance Level (S-5)  Collapse Prevention level refers to a state where the building is on the verge of undergoing partial or complete collapse.  Structure has undergone excessive damage which involves degradation of stiffness and strength of the members resisting lateral loads. Building has been subjected to huge amount deformations.  Primary load resisting elements are subjected to excessive cracking and plastic hinges are formed in the framed elements.  A permanent drift of 4% or more is observed.  Brick infill walls would have developed large cracks and few walls would have collapsed due to out-of-plane bending,  There is a significant risk on life due to the injuries caused by the collapse of structural members or a part of a member.  The structure is neither fit for occupancy nor practical to repairs. 4.5.2.6 Structural Performance Not Considered (S-6):  Sometimes the owner or the client would like to rehabilitate non structural vulnerabilities without focussing on the structural damage. For instance parapet bracings, hazardous material storage containers are anchored. This kind of rehabilitation gain interest as they are of low cost and reduce the seismic risk considerably. The performance levels for the non-structural components are Operational (N-A), Immediate Occupancy (N-B), Life Safety (N-C) and Hazards Reduced (N-D). If the performance of the non structural components is neglected then it is addressed as Not Considered (N-E). The notations of the non structural performance levels are alphabetic with a prefix N. A building performance level is a combination of structural and non structural performance levels. The various combinations of these performance levels are listed in the table 4.5


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The notations of the building performance levels are alpha numeric, where the number corresponds to the structural performance level and the alphabet corresponds to non-structural performance level. Table 4.5 Building Performance levels (FEMA356)

Non structural Performance Levels

S–1

SP – 2

SP – 3

SP – 4

SP – 5

SP – 6

Immediate

Damage Control

Life Safety

Limited Safety

Collapse Prevention

Not Considered

2–A

NR

NR

NR

NR

2–B

3–B

NR

NR

NR

4–C

5–C

6–C

4–D

5–D

6–D

4–E

5–E Collapse Prevention

No rehabilitation

Occupancy

N–A

1–A

Operational

Operational

N–B

1–B Immediate Occupancy

Immediate Occupancy N–C

3–C 1–C

2–C

NR

2–D

Life Safety

Life Safety

N–D Hazards Reduced

3–D

N–E Not Considered

NR

NR

3–E

A more common way of representing standard structural performance levels is shown in Figure 4.18.


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Figure 4.19: Performance Levels 4.5.3 Seismic Hazard Levels In performance based seismic evaluation, seismic hazard level refers to the level of hazardous ground motion. The hazard level can be determined by two methods, a) Deterministic method b) Probabilistic method. 4.5.3.1 Deterministic method The characteristics of ground motion are represented by means of a response spectra or time history record. Response spectrum is a plot of acceleration varying against time period. This is used in linear dynamic analysis. A set of available ground motion time history data or synthetic ground motion data is made use of in non linear time history analysis. The important parameters in these accelerogram are peak ground acceleration and duration. The whole of India is divided into four seismic zones based on the seismic intensity levels from the previous seismic activity. This is an illustration of the deterministic method of quantifying the earthquake hazard level. 4.5.3.2 Probabilistic method Any seismic activity is associated with its probability of occurrence over the years to come. A normal probability distribution is assumed and the probability of exceedance (P) of an earthquake


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of certain specified level in a specified time interval (t in years) is related to its return period (N in years) which is given by the equation 4.8. N

t ln(1  p) ........................ (4.8)

The design life of a a structure is 50 years. Choosing the value of t = 50 years, five types of earthquake level can be defined for a particular building. Table.4.6: Earthquake Hazard Levels (FEMA 356) Earthquake levels

p

t (years)

N (years)

Approximate N (years)

Remarks

Serviceability earthquake – 1

50%

50

72

75

Frequent


20%

50

224

225

Occasional

Design basis earthquake

10%

50

475

500

Rare

5%

50

975 1000

Very rare

2500

Extremely rare

Maximum considered earthquake – 1 Maximum considered earthquake – 2

10%

100

949

2%

50

2475

10%

250

2373

4.5.4 Performance Objectives: Performance objective combines a building performance level and a seismic hazard level. If the performance objective includes two building performance levels under two earthquake levels, then it is a dual level performance objective. Similarly there can be multiple performance objectives. A basic safety objective (BSO) satisfies the dual requirement of Life Safety under DBE and Collapse Prevention under MCE (combinations k+p in below table.4.7). The aim of BSO is to have a low probability of life threatening injury during a moderate earthquake (as defined by DBE) and to eliminate the possibility of collapse of the vertical load resisting system during a severe earthquake (as defined by MCE)


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Table.4.7: Selection of Performance Objectives

Earthquake levels

Probability of exceedance in a period

Target building performance level

Operational

Immediate Occupancy

Life Safety

Collapse Prevention


50% in 50 years

a

b

c

d


20% in 50 years

e

f

g

h

Design basis earthquake (DBE)

10% in 50 years

i

j

k

l

Maximum considered earthquake – 2

2% in 50years

m

n

0

p

(MCE)

4.6 Vulnerability Index: Vulnerability index is an estimation of the damage caused to the building after the structure has been pushed to its target displacement. In other words, this index is calculated after performing non linear static analysis. It is a linear combination of the various hinges formed in the member along with a weightage factor assigned to each hinge state as shown in formula 4.8. The hinge status of each individual member constituting the structure with respect to the pre fixed target displacement is taken into account in calculating the vulnerability index. These hinges are considered either at the performance point of the structure or at the point where the analysis will be terminated [16]. However, in this study the hinge status corresponding to performance point of the structure has been considered.

𝑉𝐼 =

1.5

𝑖 𝑁𝑐 𝑋𝑖 + 𝑗 𝑁𝑏 𝑐 𝑏 𝑖 𝑁𝑐 + 𝑗 𝑁𝑏 𝑐 𝑏

𝑋𝑗

.................... (4.8)

Where Nc = number of hinges formed in columns Nb = number of hinges formed in beams Xi = weightage factor for that corresponding hinge state in columns (Table 4.8) Dr. Ambedkar Institute of Technology, Bengaluru.

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Xj = weightage factor for that corresponding hinge state in beams. Table 4.8 weightage factor for various performance ranges of hinges Serial no.

Performance range

Weightage factor

1

E

1

Where IO = immediate occupancy LS = life safety CP = collapse prevention C = collapse D, E refers to points on the moment curvature curve beyond collapse.


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CHAPTER 5: RESULTS AND DISCUSSION 5.1 OVERVIEW: The results are presented in three stages. In the First stage results obtained from response spectrum analysis are presented. These include storey drift, maximum storey displacement for various seismic zones and soil site condition. Also the drift has been compared for building models with and without shear walls to point out the importance of strengthening the re-entrant corners. Modal time periods of these building models are also presented. In the Second stage results of time history analysis are presented. Various columns located in critical locations are identified and the moment envelope along the height of the building is plotted. Along with this, the internal forces such as torsion in these columns have been tabulated. Comparison of the drift undergone by the models subjected to Bhuj and El Centro earthquake has been shown. Also the base shear response and floor response spectra has been presented In the Third stage results after performing pushover analysis has been presented. Pushover curve, performance point and the hinge status of various members in a structure have been plotted. The vulnerability index value has been tabulated and also pictorially shown in the form of bar graph. Comparison in terms of performance of the structure has been made for the building models.

5.2 RESULTS FROM RESPONSE SPECTRUM ANALYSIS: 5.2.1 Modal periods: Modal periods are characteristic of a building and no two buildings can have their natural period equal to each other unless they have their mass and stiffness also equal. Figure 5.1 represents the modal period of all the building models considered in this study. The number of modes considered in this analysis is twelve so that the modal participation factor is around 90% with reference to the codal provisions of IS 1893: 2002. As evident from the graph, in the first mode type A building model has higher natural period than the remaining models. But this is not the case in the next consecutive modes. Control building has performed consistently in all the modes when compared to other models. Dr. Ambedkar Institute of Technology, Bengaluru.

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Type A model has relatively higher natural period in almost all the modes. Type B and type C also have higher modal periods and are consistent with type A.

MODAL PERIOD (S)

1.8 1.6

CONTROL BLDG

1.4

TYPE A

1.2

TYPE B

1

TYPE C

0.8

TYPE D

0.6 0.4 0.2 0 1

2

3

4

5

6

7

8

9

10

11

12

MODES Figure 5.1: Modal Periods.

5.2.2 Mode shapes: Each building model has about twelve mode shapes out of which first three are significant and are presented in fig. 5.2. In the first two modes of vibration lateral sway is predominant. However, in third mode, torsion becomes more prominent as evident from the figure 5.2 for all the building models. Torsion in type A, B, C and D is more when compared to control building indicating the fact that plans of regular configuration are not subjected to significant torsion. Type D with vertical asymmetry also undergoes significant torsion though it has re-entrant corner only in the last storey.


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ST

CONTROL BUILDING 2nd MODE

3rd MODE

ST

1 MODE

TYPE A 2nd MODE

3rd MODE

1ST MODE

TYPE B 2nd MODE

3rd MODE

1 MODE


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ST

TYPE C 2nd MODE

3rd MODE

ST

TYPE D 2nd MODE

3rd MODE

1 MODE

1 MODE

Figure 5.2: Mode Shapes of the Building Models. 5.2.3 Storey Displacement: The analysis has been carried out for all the seismic zones and two types of soil such as medium and hard soil. The storey displacement of the models for all the seismic zones has been compared and also for the different soil condition. These graphs have been plotted and presented from fig. 5.3 to 5.6. Storey displacement represents the movement of each storey in the horizontal direction and this has been graphically shown along the height of the building. Also comparison has been made between model with and without shear walls to understand the impact of this lateral load resisting element on the displacement control. Dr. Ambedkar Institute of Technology, Bengaluru.

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Seismic Vulnerability of RC Frames with Re– Entrant Corners 2015 16 14

STOREY HEIGHT (m)

12 10

CONTROL BLDG

8

TYPE A

6

TYPE B

4

TYPE C

2

TYPE D

0 0

2

4

6

8

10

STOREY DISPLACEMENT (mm)

Figure 5.3: storey displacement corresponding to zone II and medium soil The displacement undergone by the model type D is highest while the control building experiences lesser displacement. In fact, control building has undergone lesser displacement when compared to other types. 16 14 12

STOREY HEIGHT (m)

10

CONTROL BLDG

8

TYPE A

6

TYPE B

4

TYPE C TYPE D

2 0 0

5

10

15

20


Figure 5.4: storey displacement corresponding to zone III and medium soil Similar performance has been evidenced in zone III as well with type D undergoing highest displacement. Control building has demonstrated lesser displacement when compared to other models. Dr. Ambedkar Institute of Technology, Bengaluru.

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16 14

STOREY HEIGHT (m)

12

CONTROL BLDG

10

TYPE A

8

TYPE B 6

TYPE C

4

TYPE D

2 0 0

5

10

15

20

25


Figure 5.5: storey displacement corresponding to zone IV and medium soil The storey displacement increases for higher seismic zones compared to lower seismic zones. The displacement undergone by all the models is higher in zone IV when compared with zone III. However, the performance of these models relative to one another remains the same. 16

STOREY HEIGHT (m)

14 12 10

CONTROL BLDG

8

TYPE A

6

TYPE B

4

TYPE C

2

TYPE D

0 0

10

20

30

40


Figure 5.6: storey displacement corresponding to zone V and medium soil


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The displacement undergone by the building models is highest in Zone V as the peak acceleration value is highest in this zone. Similar displacement results have been presented from fig. 5.7 to 5.10 for hard soil condition. The performance of the building models remains to be the same relative to one another but the values of this response quantity varies. Type D has been subjected to maximum storey displacement. 16

STOREY HEIGHT (m)

14 12

10

CONTROL BLDG

8

TYPE A

6

TYPE B

4

TYPE C TYPE D

2

0 0

2

4

6

8

10

12


Figure 5.7: storey displacement corresponding to zone II and hard soil 16

STOREY HEIGHT (m)

14 12 10

CONTROL BLDG

8

TYPE A

6

TYPE B

4

TYPE C TYPE D

2 0 0

5

10

15

20

STOREY DISPLACEMENT (mm) Figure 5.8: storey displacement corresponding to zone III and hard soil Dr. Ambedkar Institute of Technology, Bengaluru.

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In zone III for hard soil condition type D building has not suffered much of a displacement when compared to other cases. However, control building model continues to possess consistent performance. 16

STOREY HEIGHT (m)

14 12

CONTROL BLDG

10

TYPE A

8

TYPE B

6

TYPE C

4

TYPE D

2 0 0

5

10

15

20

25

30


Figure 5.9: storey displacement corresponding to zone IV and hard soil. The performance of type D model is quite different from the previous case. It has undergone greater displacement compared to other models. This indicates that vertical asymmetry is more vulnerable than other chosen models. 16

STOREY HEIGHT (m)

14 12

CONTROL BLDG

10

TYPE A

8

TYPE B

6

TYPE C

4

TYPE D

2 0 0

10

20

30

40

50


Figure 5.10: storey displacement corresponding to zone V and hard soil Dr. Ambedkar Institute of Technology, Bengaluru.

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The difference in seismic performance is influenced by the soil condition which has been presented from 5.11 to 5.14. The displacement undergone by the structures located on hard soil is more when compared to medium soil. 16

STOREY HEIGHT (m)

14 12 10 8

MEDIUM SOIL

6

HARD SOIL

4 2 0 0

10

20

30

40


Figure 5.11 comparison of storey displacement of control building in medium and hard soil for zone V. 16

STOREY HEIGHT (m)

14 12

10 8

MEDIUM SOIL

6

HARD SOIL

4 2 0 0

10

20

30

40


Figure 5.12 comparison of storey displacement of type A in medium and hard soil for zone V.


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16

STOREY HEIGHT (m)

14 12 10

8

MEDIUM SOIL

6

HARD SOIL

4 2 0 0

10

20

30

40

50

STOREY DISPLACEMENT (mm) Figure 5.13 comparison of storey displacement of type B in medium and hard soil for zone V. Seismic waves travel faster in such denser medium resulting in high energy dissipation into such medium which causes the structure located on that soil site condition experience higher displacement. 16

STOREY HEIGHT (m)

14 12 10 8

MEDIUM SOIL

6

HARD SOIL

4 2

0 0

10

20

30

40

50


Figure 5.14 comparison of storey displacement of type C in medium and hard soil for zone V.


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Type D model has undergone relatively higher storey displacement in both the soils when compared to other models. 16 14

STOREY HEIGHT (m)

12 10 8

MEDIUM SOIL

6

HARD SOIL

4 2

0 0

10

20

30

40

50

STOREY DISPLACEMENT (mm) Figure 5.15 comparison of storey displacement of type D in medium and hard soil for zone V.

5.2.4 Storey Drift: Drift is the relative motion of each storey with respect to its previous storey. Drifts indicate the lateral movement of the building model. This parameter has been plotted for all the building models for different soil conditions and seismic zones. Usually, buildings experience larger storey drifts in X direction as the applied seismic load is predominant in that direction. The storey drift in Y direction is less due to higher stiffness.This is one of the parameters to understand the seismic behaviour of the building in various seismic zones for varying soil condition. Also, it gives a better understanding about the vulnerability of re-entrant corners.


Page 67


16 14

STOREY HEIGHT (m)

12 10

CONTROL BLDG

8

TYPE A

6

TYPE B

4

TYPE C

TYPE D

2 0 0

0.0002

0.0004

0.0006

0.0008

0.001

DRIFT Figure 5.16: storey drift of building models for seismic zone II and medium soil Type D configuration has undergone larger drifts while type A has drifted the least as evident from the graph. 16 14

STOREY HEIGHT (m)

12 10

CONTROL BLDG TYPE A

8

TYPE B

6

TYPE C 4

TYPE D

2 0 0

0.0005

0.001

0.0015

DRIFT Figure 5.17: storey drift of building models for seismic zone III and medium soil


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The performance of the building models is similar to that of the previous case. Control building suffers lesser drift than other models implying the fact that they are relatively safer and the most desirable configuration when subjected to seismic activity. 16

CONTROL BLDG

STOREY HEIGHT (m)

14

TYPE A 12

TYPE B

10

TYPE C

8

TYPE D

6 4 2 0 0

0.0005

0.001

0.0015

0.002

DRIFT Figure 5.18: storey drift of building models for seismic zone IV and medium soil Type A and D have undergone significantly larger drifts in zone IV. Control building has shown consistent performance in all the seismic zones. Vertically asymmetrical building shows significant drift in the middle storeys. 16

CONTROL BLDG TYPE A

STOREY HEIGHT (m)

14

12

TYPE B 10

TYPE C

8 6 4 2 0 0

0.001

DRIFT

0.002

0.003

Figure 5.19: storey drift of building models for seismic zone V and medium soil Dr. Ambedkar Institute of Technology, Bengaluru.

Page 69


Building models experience larger drifts in seismic zone V when compared to other zones. Similar comparison of storey drift of all the building models for various seismic zones in hard soil condition has been plotted and presented here. 16

CONTROL BLDG

STOREY HEIGHT (m)

14

TYPE A

12

TYPE B

10

TYPE C

8

TYPE D

6 4 2 0 0

0.0002

0.0004

0.0006

0.0008

0.001

0.0012

DRIFT Figure 5.20: storey drift of building models for seismic zone II and hard soil Building model with asymmetry in vertical direction experience larger drift when compared to other models. 16

CONTROL BLDG TYPE A TYPE B TYPE C TYPE D

STOREY HEIGHT (m)

14 12 10 8 6 4 2 0

0

0.0005

0.001

0.0015

0.002

DRIFT Figure 5.21: storey drift of building models for seismic zone III and hard soil Dr. Ambedkar Institute of Technology, Bengaluru.

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16 14 STOREY HEIGHT (m)

12 CONTROL BLDG

10

TYPE A

8

TYPE B 6

TYPE C

4

TYPE D

2 0 0

0.001

0.002 DRIFT

0.003

Figure 5.22: storey drift of building models for seismic zone IV and hard soil Storey drift undergone by the control building which is of rectangular plan configuration is less when compared with other building models. Type A, B, C and D have undergone drifts in a similar manner. 16

CONTROL BLDG STOREY HEIGHT (m)

14

TYPE A

12

TYPE B

10

TYPE C

8

TYPE D

6 4 2 0 0

0.001

0.002

0.003

0.004

DRIFT Figure 5.23: storey drift of building models for seismic zone V and hard soil Dr. Ambedkar Institute of Technology, Bengaluru.

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Now that the models have been compared zone wise, further studies are carried out by comparing the performance of a model by varying the soil condition. The drift experienced in hard soil is more than medium soil.

STOREY HEIGHT (m)

16 14

MEDUIM SOIL

12

HARD SOIL

10

8 6 4 2 0 0

0.001

0.002

0.003

0.004

DRIFT Figure 5.24: comparison of storey drift of control building for medium and hard soil for seismic zone V.

STOREY HEIGHT (m)

16 14

MEDIUM SOIL

12

HARD SOIL

10 8 6 4 2 0 0

0.001

0.002

0.003

0.004

DRIFT Figure 5.25: comparison of storey drift of type A for medium and hard soil for seismic zone V. Dr. Ambedkar Institute of Technology, Bengaluru.

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16

MEDIUM SOIL

STOREY HEIGHT (m)

14

HARD SOIL

12 10 8 6 4 2 0 0

0.001

0.002

0.003

0.004

DRIFT Figure 5.26: comparison of storey drift of type B for medium and hard soil for seismic zone V. Building located on hard soil experiences larger drift than the ones situated on medium soil due to higher rigidity of the site conditions. 16

MEDIUM SOIL

STOREY HEIGHT (m)

14

HARD SOIL

12

10 8 6 4 2 0 0

0.001

0.002

0.003

0.004

DRIFT Figure 5.27: comparison of storey drift of type C for medium and hard soil for seismic zone V.


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STOREY HEIGHT (m)


16

MEDIUM SOIL

14

HARD SOIL

12 10 8 6 4 2 0 0

0.001

0.002

0.003

0.004

DRIFT Figure 5.28: comparison of storey drift of type D for medium and hard soil for seismic zone V. The difference in performance of buildings with and without lateral force resisting system such as shear wall was studied and the variation in the storey drift has been plotted. 16

CONTROL BLDG

14

CONTROL BLDG WITH SW

STOREY HEIGHT (m)

12 10 8 6 4 2 0 0

0.001

0.002

0.003

0.004

DRIFT Figure 5.29: comparison of storey drift of control building with and without shear wall for seismic zone V and medium soil


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16

TYPE A

STOREY HEIGHT (m)

14

TYPE A WITH SW

12 10 8 6 4 2 0

0

0.0005

0.001

0.0015

0.002

0.0025

0.003

0.0035

DRIFT Figure 5.30: comparison of storey drift of type A with and without shear wall for seismic zone V and medium soil. Models without shear walls have undergone larger drifts where as the models provided with shear walls have drifted negligibly as evident from the graphs fig. 5.29 to 5.32. All these comparison has been made for medium type of soil and seismic zone V. 16

TYPE B

STOREY HEIGHT (m)

14

TYPE B WITH SW

12 10 8 6 4 2 0 0

0.001

0.002

0.003

0.004

DRIFT Figure 5.31: comparison of storey drift of type B with and without shear wall for seismic zone V and medium soil. Dr. Ambedkar Institute of Technology, Bengaluru.

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STOREY HEIGHT (m)


16

TYPE C

14

TYPE C WITH SW

12 10 8

6 4 2 0 0

0.0005

0.001

0.0015

0.002

0.0025

0.003

0.0035

DRIFT Figure 5.32: comparison of storey drift of type C with and without shear wall for seismic zone V and medium soil.

Of all the building models, control building as undergone least storey drift in both the configurations i.e., with and without shear wall. Type C model with asymmetry in both the directions has undergone significantly larger drifts in both the configuration when compared to other models. However, both type A and B have performed in a similar pattern.


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5.3

RESULTS FROM NON LINEAR TIME HISTORY ANALYSIS:

5.3.1 Base Shear Response: The variation of base shear with respect to time of the building models when subjected to El Centro and Bhuj have been presented in this section. Depending on the number of output steps and step size the range of output data available will be decided by the software. In this number of steps and step size has been considered as 1000 and 0.01 respectively. As a result, the data is available up to first 10 seconds. 1000

EL CENTRO

800

BHUJ

BASE SHEAR , kN

600 400 200 0 -200

0

2

4

6

8

10

12

-400 -600 -800 -1000

TIME (S)

Figure 5.33: base shear response of type A building model. The base shear response corresponding to El Centro has larger variations and also the peak values are much higher when compared to that of Bhuj. This is due to the fact that the initial displacement and peak ground acceleration of El Centro is greater than that of Bhuj. For the first two seconds no significant base shear has been evidenced due to Bhuj ground motion. In case of El Centro ground motion there are successive crests and troughs implying highly erratic nature of the earthquake. The peak value of base shear has not exceeded 200kN in type A building when subjected to Bhuj ground motion. However, in case of El Centro the base shear exceeds 800 kN.


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1000 800

EL CENTRO

600

BHUJ

BASE SHEAR , kN

400 200 0 -200

0

2

4

6

8

10

12

-400 -600 -800 -1000

TIME (S)

Figure 5.34: base shear response of type B building model. The peak value of base shear response of type B building model when subjected to El Centro ground motion is around 900kN and 250kN for Bhuj earthquake.

BASE SHEAR , kN

1000

800

EL CENTRO

600

BHUJ

400 200 0 -200

0

2

4

6

8

10

12

-400 -600 -800 -1000

TIME (S)

Figure 5.35: base shear response of type C building model.


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1000 EL CENTRO

800

BHUJ

BASE SHEAR , kN

600 400 200 0 -200

0

2

4

6

8

10

12

-400 -600 -800

TIME (S)

-1000

Figure 5.36: base shear response of type D building model.

5.3.2 Floor response spectra: The floor response spectra are a characteristic of every building model and vary for each storey in a building. In this section, plot of peak spectral acceleration (PSA) against period has been plotted. This response characteristic can be used to derive spectral displacement (Sd) and peak spectral velocity (PSV) using the inter relationship formula.

Sa = ωn2 Sd = ωn Sv Where Sa = spectral acceleration Sd = spectral displacement Sv = spectral velocity ωn = natural frequency The peak spectral acceleration at the base of the building is highest among other storeys with a value of around 2800mm/s2. This holds good for all the building models. The next highest peak response is corresponding to first storey. This response goes on decreasing Dr. Ambedkar Institute of Technology, Bengaluru.

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for higher storeys but for the last storey there is significant increase in the peak response quantity. There are variations among other storeys for different building models. The building with vertical asymmetry has demonstrated peak response among other models. 3000

STOREY 5 PSEUDO SPECTRAL ACCELERATION (PSA), mm/s2

2500

STOREY 4 STOREY 3

2000

STOREY 2 STOREY 1

1500

BASE

1000

500

0 0

1

2

3

4

5

6

PERIOD (S) Figure 5.37: floor response spectra of control building.

PSEUDO SPECTRAL ACCELERATION (PSA), mm/s2

3000

STOREY 5 STOREY 4

2500

STOREY 3 2000

STOREY 2 STOREY 1

1500

BASE

1000

500

0 0

1

2

3

4

5

6

PERIOD (S) Figure 5.38: floor response spectra of type A model. Dr. Ambedkar Institute of Technology, Bengaluru.

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3000

STOREY 5 STOREY 4

2500

STOREY 3 STOREY 2

2000

STOREY 1 1500

BASE

1000

500

0 0

1

2

3

4

5

6

PERIOD (S) Figure 5.39: floor response spectra of type B model.


3000

STOREY 5 STOREY 4

2500

STOREY 3 STOREY 2

2000

STOREY 1 1500

BASE

1000

500

0 0

1

2

3

4

5

6

PERIOD (S)

Figure 5.40: floor response spectra of type C model.


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3000

story 5 story 4 story 3 story 2 story 1 BASE


2500 2000 1500 1000 500 0 0

1

2

3

4

5

6

PERIOD (S) Figure 5.41: floor response spectra of type D model.

5.3.3 Moment in critical columns: At the re-entrant corners columns experiences excessive moment due to stress concentration at the notch. The moments developed in the columns corresponding to the critical load combination has been considered. Along with this, few other columns such as columns located at the corner, on the edge and in the interior of the plan have been considered. Comparison of the moments developed in these columns has been made to understand the condition of the re-entrant columns. For the control building as there are no re entrant corners only three columns are considered. Since, it‟s a regular building with rectangular plan interior column experiences larger moments. The edge column considered in this direction is not on the side facing the seismic loading from X direction. Hence, the moment developed is less. However, negative moments are developed in this column and require more attention in design and detailing. In type A building, edge column has developed larger moments because the column is located in such a way that it is subjected to maximum seismic loading. Corner columns have lesser moments in this case. The moment developed in the column located near the re-entrant corner is quite less than expected because the location of the column is such Dr. Ambedkar Institute of Technology, Bengaluru.

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that the load due to seismic activity on the column is less. Interior columns have developed significant moment in this type of plan configuration. 16

CORNER COLUMN

STOREY HEIGHT (m)

14

INTERIOR COLUMN

12

EDGE COLUMN

10 8

6 4 2 0

-20.00

0.00

20.00

40.00

60.00

80.00

100.00

120.00

MOMENT (kN-m)

Figure 5.42: moment envelope along the height of the control building. 16

CORNER COLUMN

STOREY HEIGHT (m)

14

RE-ENTRANT COLUMN

12

INTERIOR COLUMN

10

EDGE COLUMN

8

6 4

2 0 0.00

20.00

40.00

60.00

80.00

100.00

120.00

MOMENT (kN-m)

Figure 5.43: moment envelope along the height of the type A building. In type B building model, edge column has developed lesser moments but includes negative moment. Corner columns have performed moderately. Re-entrant columns have developed larger moments implying the fact that stress concentration at the notch has an impact on the building


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performance. However, there is a linear variation in the moment developed along the height of the building for the re – entrant columns. 16

CORNER COLUMN RE-ENTRANT COLUMN INTERIOR COLUMN EDGE COLUMN

14

STOREY HEIGHT (m)

12

10 8 6 4 2 0

-20.00

0.00

20.00

40.00

60.00

80.00

100.00

120.00

MOMENT (kN-m) Figure 5.44: moment envelope along the height of the type B building. 16

CORNER COLUMN

14

EDGE COLUMN RE-ENTRANT COLUMN

10

INTERIOR COLUMN

STOREY HEIGHT (m)

12

8 6 4 2 0

0.00

20.00

40.00

60.00

80.00

100.00

120.00

MOMENT (kN-m) Figure 5.45: moment envelope along the height of the type C building. The performance of C type building is similar to that of B. Re-entrant column has developed larger moment when compared with other columns. The moment at the first storey is Dr. Ambedkar Institute of Technology, Bengaluru.

Page 84


approximately 100kN-m while at the top storey is around 25kN-m. In this case, edge column and interior columns have behaved in a similar manner. 16 14

RE- ENTRANT COLUMN

STOREY HEIGHT (m)

12

EDGE COLUMN

10

INTERIOR COLUMN 8 6 4 2 0 0.00

20.00

40.00

60.00

80.00

100.00

120.00

140.00

MOMENT (kN-m) Figure 5.46: moment envelope along the height of the type D building. Type D building model is a regular building till the fourth storey and has re-entrant corner only in the last storey. Hence, the behaviour of the columns located at the re-entrant corner, edge and interior have similar performance. Interior column has developed moment of around 130 kN-m at the first storey which is significantly higher than the moment developed by any of the column in any of the model that has been studied here. Table 5.1: torsion in re-entrant columns. MODEL

TYPE A

TYPE B

TYPE C

TYPE D

STOREY 5

0.83

0.00

0.53

0.91

STOREY 4

1.13

0.01

0.35

1.07

STOREY 3

1.32

0.00

0.45

1.42

STOREY 2

1.38

0.00

0.25

1.46

STOREY 1

0.82

0.01

0.29

1.23

Significant torsion in the columns is observed in type A and type D building models implying that these building models are more active under torsional action.


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5.4 RESULTS FROM PUSHOVER ANALYSIS: 5.4.1 Performance point : The intersection of the capacity spectrum and demand spectrum gives the performance point of the structure. Performance point is a measure of the seismic resistance of a structure. This combines the performance of both structural and non structural components in a building. It expresses the building performance in terms of damage states. Buildings are designed considering various parameters corresponding to this point. However, in our study the results are used for quantifying vulnerability. 0.2

capacity

spectral acceleration (Sa)

0.18

demand

0.16 0.14 0.12 0.1 0.08 0.06 0.04 0.02 0 0

0.05

0.1

0.15

0.2

0.25

spectral displacement (Sd) Figure 5.47: performance point of control building without shear wall. There is an improvement in the performance of the structure when shear walls are provided. The spectral displacement of control building without shear wall is around 0.1m where as that of the same model with shear wall is about 0.01 or less than that. This demonstrates the fact that shear walls do have an impact on the performance of the building and makes the structure more seismic resistant. Spectral values of acceleration and displacement are considered in defining the performance point of the structure.


Page 86


7


6 5

4 3

capacity

2

demand

1 0 -0.02

-1

0

0.02

0.04

0.06

0.08

0.1

spectral displacement (Sd)

Figure 5.48: performance point of control building with shear wall. Similar results have been evidenced in other building models as well. The performance of the building models provided with shear wall is better than the same model without shear wall.

0.2 0.18

capacity


0.16

demand

0.14 0.12 0.1 0.08 0.06 0.04 0.02 0 0

0.05

0.1

0.15

0.2

0.25


Figure 5.49: performance point of type A model without shear wall.


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3.5 3


2.5 2

capacity

1.5

demand 1 0.5 0

-0.02

0

0.02

0.04

0.06

0.08

0.1

spectral displacement (Sd) Figure 5.50: performance point of type A model with shear wall.

0.2 0.18

capacity

0.16

demand


0.14 0.12 0.1 0.08 0.06 0.04

0.02 0 0

0.05

0.1

0.15

0.2


Figure 5.51: performance point of type B model without shear wall.


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5 4.5 4


3.5 3 2.5

capacity

2

demand

1.5 1 0.5 0

0

0.02

0.04

0.06

0.08

0.1

0.12

spectral displacement (Sd) Figure 5.52: performance point of type B model with shear wall.

0.2

capacity

0.18

demand


0.16 0.14 0.12 0.1 0.08 0.06 0.04 0.02 0 0

0.05

0.1

0.15

0.2

0.25


Figure 5.53: performance point of type C model without shear wall.


Page 89


3


2.5 2 1.5

capacity 1

demand

0.5 0 0

0.02

0.04

0.06

0.08

0.1


Figure 5.54: performance point of type C model with shear wall. Shear walls impart more structural stiffness to the structure. As they are lateral load resisting elements the performance of the structure has seen improvement in resisting seismic load.


0.2 0.18

capacity

0.16

demand

0.14 0.12 0.1 0.08 0.06 0.04 0.02 0 0

0.05

0.1

0.15

0.2

0.25

spectral displacement (Sd) Figure 5.55: performance point of type D model.


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5.4.2 Pushover curve: Plot of base shear against displacement is known as pushover curve. This shows the behaviour of the building model beyond the yield point. As evident from figure 5.57 the building has undergone significant displacement beyond the yield point. However, not much inelastic deformation has been observed after introducing lateral load resisting system (fig. 5.58).

80000

1200

70000

1000

60000

BASE SHEAR (KN)

BASE SHEAR (KN)

CONTROL BLDG

800 600 400 200 0

CONTROL BLDG WITH SW

50000 40000 30000 20000 10000 0

0

0.1

0.2

0.3

-0.05-10000 0

DISPLACEMENT (m)

0.05

0.1

0.15

DISPLACEMENT (m)

Figure 5.56: Pushover curve of control building without and with shear wall. TYPE A

1200

TYPE A WITH SW BASE SHEAR (KN)

40000

BASE SHEAR (KN)

1000 800 600 400

35000 30000 25000 20000 15000

200

10000

0

5000

0.00E+00

1.00E-01

2.00E-01

0

3.00E-01

-5.00E-02 0.00E+00 5.00E-02 1.00E-01 1.50E-01

DISPLACEMENT (m)

DISPLACEMENT (m)

Figure 5.57: Pushover curve of type A model without and with shear wall.


Page 91


TYPE B WITH SW

TYPE B

1200

60000

BASE SHEAR (KN)

BASE SHEAR (KN)

1000 800 600 400 200

50000 40000 30000 20000 10000 0

0 0

0.1

0.2

0

0.3

0.005

0.01

0.015

DISPLACEMENT (m)

DISPLACEMENT (m)

Figure 5.58: Pushover curve of type B model without and with shear wall.

TYPE C WITH SW

1200

35000

1000

30000

800

25000

BASE SHEAR (KN)

BASE SHEAR (KN)

TYPE C

600

400 200 0

20000 15000 10000 5000 0

-1.00E-01 0.00E+00 1.00E-01 2.00E-01 3.00E-01

-1.00E-02 0.00E+00 1.00E-02 2.00E-02 3.00E-02

DISPLACEMENT (m)

DISPLACEMENT (m)

Figure 5.59: Pushover curve of type C model with out and with shear wall. 1200

TYPE D

BASE SHEAR (KN)

1000

-1.00E-01

800 600 400 200 0 0.00E+00

1.00E-01

2.00E-01

3.00E-01

DISPLACEMENT (m) Figure 5.60: Pushover curve of type D model. Dr. Ambedkar Institute of Technology, Bengaluru.

Page 92


5.4.3 Hinge formation: When the structure is pushed to its full capacity hinges are formed in various members of the structure indicating different stages of performance. Few hinges can be in immediate occupancy level while few can be in collapse prevention level. Colour coded hinges are represented in the structure each colour representing a different hinge state. For example dark blue indicated immediate occupancy where as yellow indicates collapse. In fig. 5.66 majority of hinges are blue indicating life safety and the rest orange representing post collapse load stage. This indicates that structure is more vulnerable as most of the members are on the verge of failure. Majority of the hinges are formed in the beams and very few in columns establishing strong column weak beam concept in the structure. hence, the chosen sizes of the beams and columns and their orientation is correct.

Figure 5.61: formation of hinges in control building In the control building provided with shear walls majority of the hinges are within immediate occupancy stage. This shows that the structure is safe against seismic activity. Very few hinges are in collapse condition which can be taken care of in design.


Page 93


Figure 5.62: formation of hinges in control building with shear wall

Figure 5.63: formation of hinges in type A model


Page 94


In type A building model also similar performance has been observed. Building models equipped with lateral load resisting system perform better than the same models without them.

Figure 5.64: formation of hinges in type A model with shear wall.

Figure 5.65: formation of hinges in type B model Dr. Ambedkar Institute of Technology, Bengaluru.

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Figure 5.66: formation of hinges in type B model with shear wall

Figure 5.67: formation of hinges in type C model Dr. Ambedkar Institute of Technology, Bengaluru.

Page 96


Figure 5.68: formation of hinges in type C model with shear wall

Figure 5.69: formation of hinges in type D model Dr. Ambedkar Institute of Technology, Bengaluru.

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5.5 Vulnerability index:

0.4 0.3 0.2 0.1 0 control building

type a

Vulnerability Index with shear wall type b

Vulnerability Index with out shear wall

type c

Figure 5.70: comparison of vulnerability index of models with and without shear wall. Table 5.2: Vulnerability Index Model

Without shear wall

With shear wall

control building

0.324

0.212

type a

0.36

0.305

type b

0.31

0.26

type c

0.369

0.29

The vulnerability index of type D building model is 0.53. The vulnerability of this building is quite higher when compared to other models and hence, requires retrofitting. Vertical asymmetry is a practical case which can be observed in recent times in tower like structure with the last few storeys kept as a pent house with an open balcony causing a re-entrant corner.


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CHAPTER 6 A CASE STUDY 6.1 INTRODUCTION: After conducting parametric study it has been understood that re-entrant corners pose a serious threat to the structure. To further demonstrate this case study has been considered in which plan of a regular existing building has been considered and a suitable plan with re-entrant corners has been created to compare both of them in understanding the vulnerability of re-entrant corners. The plan area of both the models has been matched so that the floor loads are almost same facilitating the comparison.

6.2 STRUCTURAL MODELING DETAILS: Two building models have been considered. One of the models has irregular plan with re-entrant corners and another model with regular plan. The details of the model have been mentioned in table 6.1. The plan and the three dimensional view of the building models chosen for the study has been shown in fig. 6.1 and 6.2.

A

B

C

L

Figure 6.1: Plan and 3D model of the re-entrant building. Dr. Ambedkar Institute of Technology, Bengaluru.

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Figure 6.2 Plan and 3D model of the regular building. Table 6.1 structural details of the model. Plan area of re-entrant building Plan area of regular building Number of stories Floor to floor height Beam sizes Column sizes Slab thickness Shear wall Dead load Live load Live load after applying reduction factor Roof live load Seismic zones Zone factor Importance factor Soil type Response reduction factor Material used

210m2 216m2 5 3m 250 x 400mm, 200 x 350mm & 300 x 450mm 300 x 450mm & 300 x 600mm 150mm 200mm self weight of the slab + floor finish (inclusive of ceiling finish) = 3.75kN/m2 + 1.3 kN/m2 = 5.05 kN/m2 3kN/m2 3 X 0.25 = 0.75 kN/m2 2kN/m2 II, III, IV, V 0.10, 0.16, 0.24, 0.36 1 Medium (II) 5 M20 and Fe 500


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6.3 Results and Discussion: The re entrant percentage of each corner has been calculated as follows. Re – entrant percentage: A/L = 0.428. B/L = 0.50. C/L = 0.232. The joint displacement of all the three re-entrant corners for various zones after performing response spectrum analysis has been shown in figure 6.3, 6.4 and 6.5. Buildings undergo relatively higher joint displacement in zone V. It is evident from the graph that corner with 42.85% re-entrant has undergone larger displacement when compared to other two joints as this joint is subjected more seismic loading when applied in X direction. However, the joint displacement in the other two joints is similar. The displacement undergone by these joints in seismic zone V is large due to higher peak acceleration. And this value is least in seismic zone II.

Figure 6.3: joint displacement with 42.85% re - entrant corner.


Page 101


16 14

STOREY HEIGHT (m)

12 10 ZONE 2

8

ZONE 3

6

ZONE 4

4

ZONE 5

2 0 0.00

2.00

4.00

6.00

8.00

10.00

12.00

JOINT DISPLACEMENT (mm)

Figure 6.4: joint displacement with 23.2% re - entrant corner. 16 14

STOREY HEIGHT (m)

12 10 ZONE 2 8

ZONE 3

6

ZONE 4

4

ZONE 5

2 0 0.00

2.00

4.00

6.00

8.00

10.00

12.00


Figure 6.5: joint displacement with 50% re - entrant corner. The storey displacement undergone by the structure is highest in zone V due to the same explanation given above. Also the storey drift for various seismic zones have been plotted. The building has undergone significantly higher drift in storey2 and storey 3 as shown in figure 6.7.


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16

STOREY HEIGHT (m)

14 12 10 ZONE 2 8

ZONE 3

6

ZONE 4 ZONE 5

4 2 0 0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

MAX. DISPLACEMENT (m)

Figure 6.6: maximum storey displacement for re-entrant building.

STOREY HEIGHT (m)

16

ZONE 2

14

ZONE 3

12

ZONE 4

10

ZONE 5

8 6 4

2 0 0

0.0005

0.001

0.0015

0.002

0.0025

0.003

DRIFT

Figure 6.7: storey drift for re-entrant building The columns located near the re-entrant corner experience maximum forces as illustrated in the parametric study. The column forces in all the three re-entrant corners has been plotted.


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35

COLUMN 2

COLUMN FORCES (kN)

30

COLUMN 3 COLUMN 1

25 20 15 10 5 0

STORY 5 STORY 4 STORY 3 STORY 2 STORY 1

Figure 6.8: column forces The storey drift of both the building models have been compared after performing non linear time history analysis. Re-entrant buildings undergo larger drifts when compared with regular building due to the irregularity present in the plan. 16 RE ENTRANT 14

REGULAR

STOREY HEIGHT (m)

12 10 8 6 4 2 0 0

0.001

0.002

0.003

DRIFT

Figure 6.9: comparison of storey drift between regular and re - entrant building.


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MODAL PERIODS 1

PERIOD (SEC)

0.8 0.6

re entrant

0.4

regular

0.2 0 1

2

3

4

5

6

7

8

9 10 11 12

MODES

Figure 6.10: Modal Periods The modal periods of both the building models have been compared. The time period of regular building is higher in all the modes implying the fact that they are less susceptible to earthquakes of higher frequency. Re-entrant buildings with lesser modal periods are susceptible to earthquakes even of small natural period making it more vulnerable. 16 14

STOREY HEIGHT (m)

12 10

joint 4 - bhuj joint 7 - Bhuj

8

joint 10 - Bhuj 6

joint 4 - El

Joint 7 - EL

4

joint 10 - El 2 0 0

200

400

600

800


Figure 6.11: joint displacement from time history analysis.


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The joint displacement has been compared for both the ground motions in figure 6.11. The joint displacement when subjected to El Centro ground motion is higher when compared to Bhuj. This is due to the fact that the initial displacement and peak acceleration of El Centro ground motion is larger than Bhuj. 16 14 12

Col 1 - El

10

Col 1 - Bhuj

8

Col 2 - El

6

Col 2 - Bhuj Col 3 - El

4

Col 3 - bhuj 2 0 0

10

20

30

40

Figure 6.12: column forces in re-entrant columns from time history analysis. The columns located near re-entrant corners experience larger forces under the influence of El Centro ground motion. All the three columns have shown considerably larger forces in El Centro condition than Bhuj.

PEAK SPECTRAL ACCELERATION (PSA), mm/S2

4000

STOREY 5 STOREY 4 STOREY 3 STOREY 2 STOREY 1

3500 3000 2500 2000 1500 1000 500 0

0

1

2

3

PERIOD (S)

4

5

6

Figure 6.13: floor response spectra of re-entrant building


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The floor response spectra of both the building models have been plotted. The peak value of spectral acceleration is highest for storey V for both the models.

PEAK SPECTRAL ACCELERATION (PSA), mm/S2

140

STOREY 5 120

STOREY 4

100

STOREY 3 STOREY 2

80

STOREY 1

60 40 20 0 0

1

2

3

4

PERIOD (S)

5

6

Figure 6.14: floor response spectra of regular building. The base shear response of both the building models has been plotted. The response corresponding to El Centro is higher when compared to Bhuj. 1500

EL CENTRO 1000

BHUJ

500

0 0

5

10

15

-500

-1000

-1500

TIME (S)

Figure 6.15: base shear response of re-entrant building.


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40000 EL CENTRO

BASE SHEAR (kN)

30000

BHUJ

20000 10000 0 -10000

0

2

4

6

8

10

12

-20000 -30000 -40000

TIME (S)

Figure 6.16: base shear response of regular building. The hinge formation in both the building models has been depicted in fig. 6.18 and 6.19.

Figure 6.17: formation of plastic hinges in the re entrant building.


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Figure 6.18: formation of plastic hinges in regular building. By making use of this colour coded display of hinges the vulnerability is quantified and the results are shown in table 6.2 The vulnerability index implies that re-entrant building is more vulnerable than regular building. Table 6.2 vulnerability index Model

index

Re entrant

0.624

regular

0.418


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CHAPTER 7 CONCLUSION 7.1 GENERAL: Seismic evaluation of the performance of the irregular buildings has been done in two stages. In the first stage which is parametric study, different configurations of building plans had been considered and their behaviour was studied using linear and non linear dynamic analysis. To quantify the vulnerability of this irregularity pushover analysis has been performed. In the second stage a case study was considered and similar methods of analysis were adopted. The results of both the stages have been presented in chapters 5 and 6.

7.2 CONCLUSIONS: The following conclusions were able to reach after a thorough analysis of the building models. 1. The modal periods of the control building with rectangular plan exhibits consistent performance in all the modes. The other building models have shown significant variation in their period from mode to mode. Also, it can be concluded that building model with lower time period are susceptible to minor earthquakes. 2. Mode shapes of the building models demonstrate the fact that first three modes are highly significant in understanding the behaviour of the structure. In the first two modes lateral sway is significant while in third mode torsion is significant in the building. Hence, these torsional effects must be studied in detail and taken care of. 3. The storey displacement and drift undergone by type D model is more than other types of models. Also, these response quantity show higher values in case of Zone V when compared to other seismic zones. When this quantity was compared among different soil types, higher values of drift and displacement has been shown for hard soil. This is due to the fact that high energy seismic waves travel faster into the harder medium when compared with the softer medium. 4. The drift and displacements are controlled when the lateral load resisting elements such as shear wall is provided. 5. The base shear response of the models is more for El Centro ground motion when compared with Bhuj. This is due to higher peak acceleration of El Centro earthquake. Dr. Ambedkar Institute of Technology, Bengaluru.

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6. From the floor response spectra it can be inferred that base storey experiences more acceleration than the other storeys by a factor of 66.67%. 7. Moment developed in the columns is usually higher for re-entrant columns when compared to other columns such as corner, edge and interior columns. It also depends on the location of the column in a plan. 8. Among the chosen building models, the ones with shear walls provide better performance than the ones without that. 9. The inelastic deformation is minimized when shear walls are provided. This is due to the fact that shear walls impart more stiffness to the structure and makes the structure seismic resistant. 10. The hinge status in various members corresponding to the fixed target displacement was studied. The hinges are moving towards the collapse stage in models which are not provided with shear walls. Majority 11. The vulnerability index for all the models was calculated and it has been observed that type C model i.e., two way asymmetric building plan is the most vulnerable among all of them. And also, installation of shear walls ahs best worked for this case. 12. From the case study, it can be inferred that re-entrant buildings are more seismically vulnerable than the buildings of regular plan configuration.

7.3 SCOPE OF FUTURE WORK:  Plans with higher percentage of re-entrant corner can be considered and its impact on the seismic performance can be studied.

 Instead of shear walls variety of bracings can be used to improve the seismic behaviour of the buildings.

 Time history analysis can be carried out for the recent Nepal earthquake that took place in April 2015.

 Fragility analysis can be carried out for the same and vulnerability curves can be developed in a conventional manner.


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REFERNCES [1] A. Cinitha.A, P.K. Umesh , Nagesh R. Iyer (2012), “Nonlinear Static Analysis to Assess Seismic Performance and Vulnerability of Code - Conforming RC Buildings” [2] Amin Alavi, Prof. P. Srininvasa Rao (2013), “Effect of Plan Irregular RC Buildings in High Seismic Zone”, Australian Journal Of Basic And Applied Sciences. [3] An Introduction to Vulnerability Atlas of India (2006), BMTPC. [4] ATC 40 (1996), “Seismic Evaluation and Retrofit of Concrete Buildings”, Applied Technology Council, USA, Vol.1. [5] Chopra A.K. (1995), “Dynamics of Structures: Theory and Applications to Earthquake Engineering”, Prentice Hall Publishers. [6] Computers and Structures, INC. CSI Analysis Reference Manual for ASP 2000, ETABS and SAFE, Berekeley, California.,2009. [7] Divyashree . M, Gopi siddappa, “Seismic Behaviour of RC Buildings with Re-Entrant Corners and Strengthening”, IOSR Journal of Mechanical and Civil Engineering.

[8] Federal Emergency Management Agency, Prestandard and Commentary for the Seismic Rehabilitation of Buildings (FEMA 356), Washington D.C. November 2000.

[9] FEMA-356 (2000), “Prestandard and commentary for the seismic rehabilitation of buildings”, Federal Emergency Management Agency, Washington, D.C.

[10] IS 456-2000, Indian Standard Plain and Reinforced Concrete - Code of Practice, Bureau of Indian Standards. [11] IS: 875(Part 2) – 1987, Code of Practice for Design Loads (other than earthquake) for Buildings and Structures, Bureau of Indian Standards

[12] IS 1893 (Part 1) – 2002, Indian Standard Criteria for Earthquake Resistant Design of Structures, Bureau of Indian Standards. [13]Jonathan Chambers and Trevor Kelly, “Nonlinear Dynamic Analysis – The Only Option For Irregular Structures”, 13th World Conference on Earthquake Engineering, Vancouver, B.C., Canada, August 1-6, 2004 [14] Mehmed Causevic, Sasa Mitrovic,(2010) “Comparison between non-linear dynamic and static seismic analysis of structures according to European and US provisions”, Bull Earthquake Eng, DOI 10.1007/s10518-010-9199-1 [15] Mohammed yousuf, P.M. shimpale, “Dynamic Analysis of Reinforced Concrete Building with Plan Irregularities”, International Journal of Emerging Technology and Advanced Engineering, September 2013. [16] Neha P. Modakwar1, Sangita S. Meshram, Dinesh W. Gawatre, “Seismic Analysis of Structures with Irregularities”, IOSR Journal of Mechanical and Civil Engineering (IOSR-JMCE)


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Seismic Vulnerability of RC Frames with Re– Entrant Corners 2015 [17] P.B Prajapati, Prof. Mayor G Vanza, “Influence Of Plan Irregularity On Seismic Response Of Buildings.”, International Journal Of Engineering Research And Applications. [18] Pankaj Agarwal and Manish Shrikhande (2006), “Earthquake Resistant Design of Structures”, Prentice Hall of India Pt. Ltd. [19] Putul Haldar, Yogendra Singh, “Seismic Performance And Vulnerability Of Indian Code designed Rc Frame Buildings”, ISET Journal of Earthquake Technology,March 2009. [20] Ravi Kanth Mittal, P.Prashanth (2012), “Response Spectrum Modal Analysis Of Buildings Using Spreadsheets”, International Journal Of Modern Engineering Research(IJMER). [21] S.Varadharajan, “Study of Irregular RC Buildings under Seismic effect”, a Ph.D thesis submitted to National Institute of Technology Kurukshethra, 2014 [22] Seismic Vulnerability Assessment of Building Types in India - Technical Document on Typology of Buildings in India by Seismic Vulnerability Assessment Project Group of IIT Bombay, IIT Guwahati, IIT Kharagpur, IIT Madras and IIT Roorkee Submitted to National Disaster Management Authority, Government of India. [23] T. Mahdi, V. Soltangharaie, “Static and Dynamic Analyses of Asymmetric Reinforced Concrete Frames”, WCEE 2012. [24] Wikipedia .org [25] www. nptel.ac.in

.


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LIST OF PUBLICATIONS Sl. no

Title

Authors

Seminar -

Place/ College -

Journal publications International Journal of Engineering Research and Technology (IJERT) May - 2015 -

1.

A case study on B. Shivakumara seismic response swamy, Shreyasvi of buildings with C re-entrant corners.

2.

Comparative Study Of Regular And Irregular Building Plan Using Non Linear Time History Analysis

B. Shivakumara swamy, Shreyasvi C

Conference On R. V. Advances In College Of Research & Engineering Development , Bengaluru. And Dissemination Of Interdisciplinar y Developments For Sustainability

3.

Comparative Study Of Regular And Irregular Building Plan Using Non Linear Time History Analysis


Conference On Futuristic Technology In Civil Engineering For Sustainable Development

4.

Seismic Response of Buildings with Re - Entrant Corners in Different Seismic Zones


Conference On Ghousia International Advances In college of journal of Structural, engineering, research in Highway And bengaluru engineering CADD and technology Engineering (IJRET) May - 2015


S.J.B. Institute of Technology

-

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Page 115



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International Journal of Engineering Research & Technology (IJERT) ISSN: 2278-0181 Vol. 4 Issue 05, May-2015

A Case Study on Seismic Response of Buildings with Re Entrant Corners Shreyasvi .C

B. Shivakumaraswamy

PG student, Department of Civil Engineering, Dr. Ambedkar Institute of Technology, Karnataka, India.

Professor and Head, Department of Civil Engineering, Dr. Ambedkar Institute of Technology, Karnataka, India.

Abstract— Plan irregular configuration of buildings has been one of the major issues to be addressed, for those located in earthquake prone areas. This paper deals with re-entrant corner irregularity. There have been many researches on buildings with re – entrant corners by considering few standard shapes such as L, H, T shapes and analyzed using linear dynamic analysis. There is a need for extensive study on re-entrant corners using non linear dynamic analysis. The objective of this study is to compare a building containing re-entrant corners with a building of regular plan configuration by performing non linear time history analysis and also to study the behavior of the re-entrant building located in different seismic zones. A regular residential building with re-entrant corners has been chosen. While modeling, the plan area of the re – entrant and the regular building models has been made approximately equal in order to facilitate the comparison. Linear and non linear dynamic analysis has been carried out. The results obtained of both the models have been compared for maximum storey displacement, storey drift, and modal periods. Re-entrant buildings undergo larger displacement when compared with regular buildings. The floor response curves of these structures have been presented to understand the difference in their behavior due to plan irregularity. Also, the performance of the re – entrant building in different seismic zones has been studied. Buildings with reentrant corner are more vulnerable to seismic damages and are susceptible to earthquakes corresponding to time periods of lower order. Hence, the building plan must be of regular configuration to possess significant seismic resistance. Keywords— Re-entrant corner; Response spectrum analysis (RSA); Non linear time history analysis; El Centro earthquake; Bhuj earthquake.

I.

IS 1893 (PART 1): 2002 states that any corner in a plan of a structure is considered as a re – entrant corner, if both the projections of the structure beyond that corner are greater than 15% of its plan dimension in the given direction. Also, buildings having projection less than 15% of its plan dimension in the given direction is safe. Whereas 15 to 20% is considered deficient and greater than 20% is treated as highly deficient. Re – entrant corners mainly cause two problems, one is torsion and the other is difference in the stress induced in different wings of the building causing stress concentration at the corner. This paper presents an overview of the progress in research regarding seismic response of plan irregular buildings in various seismic zones of India.

INTRODUCTION

In the present scenario, majority of the buildings have irregular configurations which can be either in plan or elevation or both. Any irregularity will lead to an abrupt change in strength or stiffness of the structure. Past earthquake experiences implicate that, buildings with irregularity are prone to earthquake damages. Therefore, it is essential to study the seismic response of the structure especially the irregular ones even in low seismic zones to reduce the damages in building as in future these buildings have the probability of being subjected to more devastating earthquakes. In such a case, it is necessary to understand the behavior of the structures in order to make it possess sufficient seismic resistance.

IJERTV4IS051043

The present study makes an attempt to study the effect of re-entrant corners in a building plan on its seismic performance. In order to assess the seismic performance of the considered irregularity, two analytical approaches are performed which includes both linear and nonlinear analysis. Two residential building models are chosen for the analysis. One of the models chosen has re – entrant corners. While the other model has regular plan configuration.

Fig. 1 - Damages caused to the roof diaphragm at the re- Entrant Corner of West Anchorage High School, Alaska, during 1964 Earthquake.

www.ijert.org (This work is licensed under a Creative Commons Attribution 4.0 International License.)

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II.

As per IS 1893 (PART 1): 2002, clause 7.8.1(b) response spectrum method shall be performed for irregular buildings of height greater than 12m in zones IV & V (zone factor, Z = 0.24 & Z = 0.36 respectively) and those greater than 40m in zones II & III ( Z = 0.10 & Z = 0.16 respectively). Code design practices use the concept of force based design, in which individual components of the structure are designed for strength based on the results obtained from elastic analysis. The seismic analysis of structures carried out by considering the peak values of ground acceleration as in case of equivalent static method or linear static method is not sufficient to understand its behavior, as the response of the structure depends on the natural frequency content and dynamic properties of ground motion. Buildings having plan irregularity must be analyzed dynamically. In linear dynamic analysis i.e., response spectrum analysis (RSA), maximum response of the building is estimated directly from design spectrum which represents the design earthquake considering the site condition and the characteristics of the building. In RSA, seismic forces are based on the natural vibration modes of the building based on the distribution of mass and stiffness over the height of the building. Square root of sum of squares (SRSS) method has been adopted for modal combination as well as directional combination. However, this method ignores behavior of the structure in non linear region. Hence, non linear dynamic analysis (time history analysis) has been employed to completely understand the seismic performance of building.

Column sizes Slab thickness Shear wall

self weight of the slab + floor finish (inclusive of ceiling finish) = 3.75kN/m2 + 1.3 kN/m2 = 5.05 kN/m2

Dead load

3kN/m2

Live load Live load after applying reduction factor Roof live load Seismic zones Zone factor Importance factor Soil type

3 X 0.25 = 0.75 kN/m2

Response reduction factor Material used Damping

2kN/m2 II, III, IV, V 0.10, 0.16, 0.24, 0.36 1 Medium (II) 5 (special moment resisting frame, SMRF) M20 and Fe 415 5%

TABLE II: DETAILS OF TIME HISTORY DATA Earth quake

El Centro

Bhuj

Date

18/05/1940

26/01/ 2001

Time

21:35

8:46:42

Magnitude

7.1

7.6

Latitude

32.733 N

23 02 N

Longitude

115.5 W

72 38 E

Initial Displacement (mm)

400

3.97

Peak acceleration (m/s2)

3.12

1.0382

This analysis is aims at setting up an environment which imitates the real time earthquake ground motions and gives a more realistic picture of the possible deformation and collapse mechanism formed in a structure. Time history method of analysis makes use of ground motion data of previously occured earthquakes to assess the structural behavior. In this method, the structure will be assigned with plastic hinges to study the structural behavior in the non linear region or in other words material non linearity is considered. In this study, the ground motions of El Centro (1940) and Bhuj (2001) has been considered. The whole of dynamic analysis has been carried out using FE software. III.

x 450mm 300 x 450mm & 300 x 600mm 150mm 200mm

METHODS OF ANALYSIS

C

STRUCTURAL MODELLING DETAILS:

Two building models with ground and four upper stories were considered. One building model with a re-entrant corner (Fig. 2) and another of regular plan configuration (Fig. 3). The plan area of both the building models has been made approximately equal so that the floor loads acting on the models is same, facilitating the comparison as shown in Fig.4 and Fig. 5. TABLE I: STRUCTURAL DETAILS Plan area of re-entrant 210m2 building Plan area of regular building 216m2 Number of stories 5 Floor to floor height 3m Beam sizes 250 x 400mm, 200 x 350mm & 300

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B

A

L Fig. 2 - Plan of re-entrant building.


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The percentage re-entrant is calculated by the ratio A/L for joint 1, B/L for joint 2 and C/L for joint 3[3]. Therefore, the percentage re-entrant for joints 1, 2 & 3 are 23.8%, 42.8% & 50% respectively.

Fig. 5 - regular building model Fig. 3 - plan of regular building

IV.

RESULTS AND DISCUSSION

The response spectrum analysis was carried out for all the four seismic zones and their respective design spectrum showing spectral acceleration co efficient varying with period is shown in fig. 6. The acceleration experienced by the buildings is least in seismic zone II and highest in zone V as evident from the graph below. The peak acceleration co efficient for zone II, III, IV & V is 0.10, 0.16, 0.24, and 0.36 respectively.

Fig. 4 - re-entrant building model Fig. 6 – design spectrum

The displacement undergone by joints located near reentrant corner is an important case of study in understanding the behavior of re-entrant corners. There are three such joints with a re-entrant percentage of 42.85%, 23.2% and 50%. Figures 7, 8 & 9 shows the displacement of these joints

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respectively. Joints undergo maximum displacement in case of zone V when compared with other seismic zones. Also, the displacement increases with increase in zone factor. Joint with re-entrant of 42.85% re-entrant undergo larger displacement as evident from fig. 9.

The maximum displacement of each storey is also of major interest in this study. Buildings located in seismic zone V undergo larger displacement while that in zone II undergoes smaller displacement. Fig. 10 shows maximum displacement along the height of the building for different seismic zones.

Fig. 7 – displacement of joint 1 Fig. 10 – maximum storey displacement.

Displacement is an absolute term whereas drift is a relative term. The displacement undergone by an upper storey with respect to its immediate lower storey is termed as drift. Building undergoes maximum drift near second and third storey as evident from fig. 11. Also the drift experienced by the building is highest in zone V. Fig. 11 represents the storey drift for re-entrant building along the storey height for various seismic zones. The percentage increase in drift from zone 2 to zone 3 is around 60.20%, whereas from zone 3 to zone 4 is about 49.68% and from zone 4 to zone 5 is 50%.

Fig. 8 - displacement of joint 2.

Fig. 11 – storey drift

Fig. 9 – displacement of joint 3.

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The columns located near re-entrant corners are subjected to huge forces when compared to other columns as there is local stress concentration near the re-entrant corners. Column located near the corner with 50% re-entrant is subjected to highest force as shown in fig. 12.


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Fig. 12 – column forces at the re- entrant corner.

The comparison of building performance with re-entrant corners for various seismic zones was studied from fig. 6 to 11. However, fig. 13 gives a comparison between regular and re-entrant building in terms of joint displacement. Joint 1, 2 & 3 has a re-entrant of 23.2%, 50% and 42.85%. Reentrant building undergoes larger joint displacement when compared to regular building.

Fig. 14 - storey drift

The modal periods are characteristic of a building as it depends on the building stiffness and its seismic weight. According to IS1893 (PART 1) : 2002, the number of modes to be used in the analysis should be such that the total sum of modal masses of all modes considered is at least 90% of the seismic mass. Hence, the number of modes considered is 12. The modal period of regular building is higher than that of re-entrant building which makes the re-entrant building more susceptible to earthquakes with period of lower order. Fig. 15 shows the modal periods for different modes.

Fig. 15 – modal periods. Fig. 13 - comparison of joint displacement between regular and re-entrant building.

The storey drift undergone by a re-entrant building is more than the regular building as evident from fig. 14. However, the drift observed in the top most storey is slightly higher in regular building. Fig. 14 represents the storey drift along the height of the building for both re-entrant as well as regular building.

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The time histories of Bhuj and El Centro were applied to the building models. The accelerogram of these two earthquakes have been shown in fig. 16 & 17. The details of these earthquakes have been shown in table 2. The following graphs (fig. 16 & 17) are a plot of acceleration against time recorded by the accelerogram.


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These ground motion data were applied to the building to study the behavior of the building under an actual earthquake.

Fig. 16 - accelerogram of El Centro earthquake. Fig. 19 – floor acceleration response spectrum of re-entrant building to El – Centro earthquake.

Fig. 17 - accelerogram of Bhuj earthquake.

The floor acceleration response spectra of the models after the application Bhuj and El Centro earthquake time history is shown in fig. 18, 19, 20 &21.

Fig. 20 - floor acceleration response spectrum of regular building to Bhuj earthquake.

Fig. 21 – floor acceleration response spectrum of regular building to El centro earthquake. Fig. 18 - floor acceleration response spectrum of re-entrant building to Bhuj earthquake.

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The story displacement of both the building models have been compared for both the ground motions as shown in table 3. The storey displacement of re-entrant buildings is higher than that of the regular building, irrespective of the ground motion. TABLE 3: STOREY DISPLACEMENT (mm) regular

Bhuj

El Centro

Bhuj

El Centro

storey 5

25.062

788.714

5.985

328.011

storey 4

22.374

690.228

5.202

258.278

storey 3

17.805

558.232

4.049

184.062

storey 2

11.696

387.807

2.602

109.016

storey 1

4.806

181.505

1.069

41.637

Also, the story drift of both the models has been compared in table 4. However, the storey drifts have responded quite differently when compared to displacement. Both the building models subjected to El Centro have shown maximum drift with re-entrant building showing highest response among the two.

Storey height, m

re-entrant

The moment distribution in various columns located near re-entrant corners varying over the height of the building is shown in fig. 23. It is evident from this graph that the columns possess considerably higher moments when subjected to El – Centro than Bhuj. Also the moment is maximum at the base and decreases as the height increases, which is in agreement with the conceptual understanding of the moment developed in columns over the height of the building.

Moment (kN – m)

TABLE 4: STOREY DRIFT

storey 5

re-entrant Bhuj El centro 0.0009 0.0328

regular Bhuj El centro 0.0003 0.0233

storey 4

0.0015

0.0440

0.0004

0.0247

storey 3

0.0020

0.0568

0.0005

0.0250

storey 2

0.0023

0.0688

0.0005

0.0225

storey 1

0.0016

0.0605

0.0004

0.0139

Fig. 23 - moment envelope along the height of the building.

V.

Joint displacement at the re-entrant corners is as shown in fig. 22. Similar to the drift behaviour, joint displacements are maximum for El centro time history. These joints undergo larger displacement when subjected to El Centro ground motion.

Fig. 22 - joint displacement at the re-entrant corner

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CONCLUSION

In the present study, an attempt has been made to compare an irregular building consisting of re-entrant corner with a regular building of rectangular configuration. Mainly the difference in their response to ground motion was studied and also the response of the re-entrant building located in different seismic zones was compared and the conclusion about various aspects has been listed below. 1. The ground acceleration to which the structure is subjected to is higher in zone V when compared to zone II. The peak acceleration increases from zone II to zone V. 2. The displacement undergone by the joint with reentrant of 42.85% is highest when compared to other two joints. Also the joint displacement is highest in zone V. 3. The drifts and maximum storey displacement undergone by a re – entrant building is highest when located in zone V and least in zone II. 4. As re-entrant buildings have lesser time periods, they are more susceptible to ground motions and the probability of undergoing damage due to high frequency ground motions is high. 5. The columns located near the re-entrant corners experience more seismic loads as compared to other interior columns. Hence, they require higher ductile detailing when compared to other columns. 6. Also, longer the cantilever projection of the building from the re-entrant corner greater the force experienced by the column located near to it.


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7. As observed from table 3 and 4, re-entrant buildings undergo larger displacements and drifts when compared with regular buildings. 8. Maximum drift is observed in case of El Centro earthquake in both the type of building models when compared with Bhuj ground motion. 9. Building model with higher percentage of re-entrant corner undergo larger joint displacements. 10. Moment to which a column is subjected to is greater in case of El Centro earthquake when compared with Bhuj earthquake.

REFERENCES: [1] Agarwal, P. and Shrikhande, M., Earthquake Resistant Design of Structures, Prentice hall of India Pvt. Ltd.,2006. [2] Chopra A.K., Dynamics Of Structures, 3rd edition, Prentice Hall Of India., 2007. [3] STANDARDS, BUREAU OF INDIAN, 2002. Criteria for Earthquake Resistant Design of Structures IS 1893(Part 1): 2002. In part 1 general provisions and buildings, New Delhi. [4] Dubey, S.K and Sangamnerkar., Seismic Behaviour of Asymmetric Rc Buildings., International journal of advanced engineering technology, 2(4): 296-301., 2011. [5] Ravi Kanth Mittal, P.Prashanth (2012), Response Spectrum Modal Analysis Of Buildings Using Spreadsheets, International Journal Of Modern Engineering Research(IJMER)., volume 2, issue 6, pg – 4207 to 4210, 2012. [6] Divyashree . M, Gopi siddappa, Seismic Behaviour Of RC Buildings With Re-Entrant Corners And Strengthening, IOSR Journal Of Mechanical And Civil Engineering., pg – 63 to 69. [8] Amin Alavi, P. Srinivasa Rao, Effect of Plan Irregular RC Buildings in High Sesimic Zones, Australian Journal of Basic and Applied Sciences, 7(13) November 2013, Pages: 1-6 [7] ASCE, FEMA 356, Pre standard and commentary for seismic rehabilitation of buildings, Reston, Virginia, USA, 2000. [8] Computers and Structures, INC. CSI Analysis Reference Manual for ASP 2000, ETABS and SAFE, Berekeley, California.,2009. [9] Mehmed Causevic · Sasa Mitrovic, Comparison between non-linear dynamic and static seismic analysis of structures according to European and US provisions, Bull Earthquake Eng., DOI 10.1007/s10518-010-9199-1,8July2010. [10] Murthy. C. V. R (2005), “Earthquake Tips”, Learning Earthquake Design and Construction.

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