optimum location of shear wall in tall buildings

ACKNOWLEDGEMENTS

I would like to express my deepest gratitude to Professor Dr. B.K.Raghu Prasad, Dept. of

Civil Engineering, The Oxford College of Engineering, for his continued encouragement and

knowledgeable advice throughout this dissertation work.

I acknowledge my gratitude to Dr. Amarnath. K, HOD, Department of Civil Engineering, The

Oxford College of Engineering and Dr.R.Nagaraj, Principal, The Oxford College of

Engineering for their valuable and constant support.

I personally express my regards to Mahanthesh.N.B, Assistant professor, Department of Civil

Engineering, The Oxford College of Engineering, Bangalore.

The completion of this project would not have been possible without the valuable help of staff

of Structures laboratory, Dept of civil Engineering, TOCE.

I am also in debt to all my friends for their constant support & encouragement during my

dissertation.

Finally my deepest thanks are reserved for my parents, who sacrifice all their lives in order to

give me advantages they never had dreamed at my age, cultivating my curiosity & teaching to

strive for a job well done.

I am grateful to one and all who helped me directly or indirectly in carrying out the Project.

SUJITH MATHEW

PUBLICATION

The Paper Entitled “OPTIMUM LOCATION OF SHEAR WALL IN MULTI–STOREY

BUILDING” by Sujith Mathew, B.K.Raghu Prasad, and Amarnath.K has been submitted to

Transstellar Journal Publication and Research Consultancy (TJPRC) (paper in journal of civil,

structural, Environmental, Water resource and Infrastructure Engg. Research ISSN (P): 2250-

1576, ISSN (E): 2278-9405, Impact Factor (JCC): 3.6528), publication is pending.

ABSTRACT

Pushover analysis is a static, nonlinear procedure using simplified nonlinear technique to

estimate seismic structural deformations. Pushover analysis is widely used for design and

seismic performance evaluation purposes. For structural design and assessment of reinforced

concrete members, the non-linear analysis has become an important tool.

Shear wall is one of the most commonly used lateral load resisting in high rise building. Shear

wall has high in plane stiffness and strength which can be used to simultaneously resist large

horizontal load and support gravity load.

In the present study, the non-linear Static analysis has been carried out using ETABS

with the intention of identification of effective shear wall location in multi-storey building

based on its both elastic and elasto-plastic behaviour. The load deformation curves and the

results so obtained have been compared to identify the optimum shear wall location in multi-

storey building.

CONTENTS

CERTIFICATE ................................................................................................................................... I

ACKNOWLEDGEMENTS .............................................................................................................. II

PUBLICATION ............................................................................................................................... III

ABSTRACT ..................................................................................................................................... IV

CONTENTS ...................................................................................................................................... V

TABLES ........................................................................................................................................... VI

FIGURES ........................................................................................................................................ VII

CHAPTER 1. INTRODUCTION

1.1 INTRODUCTION ......................................................................................................................... 1

1.2 OBJECTIVES ............................................................................................................................... 2

1.3 SCOPE OF THE PRESENT STUDY ............................................................................................ 2

1.4 ORGANISATION OF THE THESIS ............................................................................................ 3

CHAPTER 2. LITERATURE REVIEW

2.1 GENERAL ................................................................................................................................... 4

2.2 LITERATURE REVIEW ON EFFECT OF SHEAR WALL LOCATION & PUSHOVER

ANALYSIS ................................................................................................................................... 4-11

2.3 SCOPE OF THE PRESENT STUDY .......................................................................................... 12

CHAPTER 3. DUAL TYPE STRUCTURAL SYSTEM WITH L SHAPE SHEAR WALL

3.1 GENERAL DESCRIPTION OF STRUCTURE ......................................................................... 13

3.2 MATERIAL PROPERTIES ....................................................................................................... 13

3.3 MODEL GEOMETRY ............................................................................................................... 14

3.4.1 STRUCTURAL LAYOUT (MODEL I) ................................................................................... 14

3.4.2 ANALYSIS OUTPUT ........................................................................................................ 15-17

3.4.3 RESULTS ........................................................................................................................... 18-19

3.5.1 STRUCTURAL LAYOUT (MODEL II) ................................................................................. 20

3.5.2 ANALYSIS OUTPUT ........................................................................................................ 21-23

3.5.3 RESULTS ........................................................................................................................... 24-25

3.6.1 STRUCTURAL LAYOUT (MODEL III) ................................................................................ 26

3.6.2 ANALYSIS OUTPUT ........................................................................................................ 27-29

3.6.3 RESULTS ........................................................................................................................... 30-31

3.7.1 STRUCTURAL LAYOUT (MODEL IV) ................................................................................ 32

3.7.2 ANALYSIS OUTPUT ........................................................................................................ 33-35

3.7.3 RESULTS ........................................................................................................................... 36-37

3.8.1 STRUCTURAL LAYOUT (MODEL V) ................................................................................. 38

3.8.2 ANALYSIS OUTPUT ........................................................................................................ 39-41

3.8.3 RESULTS ........................................................................................................................... 42-43

3.9 RESULTS AND DISCUSSION ............................................................................................ 44-47

CHAPTER 4 DUAL TYPE STRUCTURAL SYSTEM WITH PLANE SHAPE SHEAR WALL



4.3 MODEL GEOMETRY ............................................................................................................... 49

4.4 STRUCTURAL LAYOUT (MODEL I) ...................................................................................... 49

4.5 ANALYSIS OUTPUT ........................................................................................................... 50-52

4.6 RESULTS .............................................................................................................................. 53-54


CHAPTER 5. DUAL TYPE STRUCTURAL SYSTEM WITH CHANNEL SHAPE SHEAR WALL



5.3 MODEL GEOMETRY ............................................................................................................... 59

5.4.1 STRUCTURAL LAYOUT (MODEL I) ................................................................................... 59

5.4.2 ANALYSIS OUTPUT ........................................................................................................ 60-62

5.4.3 RESULTS ........................................................................................................................... 63-64

5.5.1 STRUCTURAL LAYOUT (MODEL II) ................................................................................. 65

5.5.2 ANALYSIS OUTPUT ........................................................................................................ 66-67

5.5.3 RESULTS ........................................................................................................................... 68-69

5.6.1 STRUCTURAL LAYOUT (MODEL III) ................................................................................ 70

5.6.2 ANALYSIS OUTPUT ........................................................................................................ 71-72

5.6.3 RESULTS ........................................................................................................................... 73-74


CHAPTER 6. BARE FRAME STRUCTURE



6.3 MODEL GEOMETRY ............................................................................................................... 80

6.4 STRUCTURAL LAYOUT (MODEL I) ...................................................................................... 80

6.5 ANALYSIS OUTPUT ........................................................................................................... 81-83

6.6 RESULTS .............................................................................................................................. 84-85


CHAPTER 7. CONCLUSIONS AND RECOMMENDATIONS

7.1 GENERAL ................................................................................................................................. 89

7.2 CONCLUSIONS ................................................................................................................... 89-90

7.3 FUTURE WORK ....................................................................................................................... 90

REFERENCES ................................................................................................................................ 91-92

APPENDIX

LIST OF TABLES

Table 3.1: Summary of plastic hinging for pushover analysis at different damage levels (M-I)…..18

Table 3.2: Displacements, Drift Ratio & Storey Shear in X Direction for different stories (M-I)....18

Table 3.3: Force vs. Displacement (M-I)………………………………………………….…….....19

Table 3.4: Summary of plastic hinging for pushover analysis at different damage levels (M-II)….24

Table 3.5: Displacements, Drift Ratio & Storey Shear in X Direction for different stories (M-II)...24

Table 3.6: Force vs. Displacement (M-II)……………………………………………….……........25

Table 3.7: Summary of plastic hinging for pushover analysis at different damage levels (M-III)…30

Table 3.8: Displacements, Drift Ratio & Storey Shear in X Direction (M-III)…………………….30

Table 3.9: Force vs. Displacement (M-III)………………………...………………………...….....31

Table 3.10: Summary of plastic hinging for pushover analysis at different damage levels (M-IV)..36

Table 3.11: Displacements, Drift Ratio & Storey Shear in X Direction (M-IV)…………………….36

Table 3.12: Force vs. Displacement (M-IV)………………………………………………....….....37

Table 3.13: Summary of plastic hinging for pushover analysis at different damage levels (M-V)...42

Table 3.14: Displacements, Drift Ratio & Storey Shear in X Direction (M-V)……………………42

Table 3.15: Force vs. Displacement (M-V)……………………………………………….….….....43







Table 5.4: Summary of plastic hinging for pushover analysis at different damage levels (M-II).....68

Table 5.5: Displacements, Drift Ratio & Storey Shear in X Direction for different stories (M-II)...68

Table 5.6: Force vs. Displacement (M-II)……………………………...………………….…….....69

Table 5.7: Summary of plastic hinging for pushover analysis at different damage levels (M-III)....73

Table 5.8: Displacements, Drift Ratio & Storey Shear in X Direction (M-III)…………………….73

Table 5.9: Force vs. Displacement (M-III)………………………………………………..…….....74




LIST OF FIGURES

Fig 3.1: Floor plan of the dual system with L shape Shear wall (M-I)…………………...…..14

Fig 3.2: 3d view of the dual system with L shape Shear wall (M-I)……………………………15

Fig. 3.3: Displacement vs. Base shear (Pushover Curve) (M-I)…..………………………….…….....15

Fig 3.4: Spectral Displacement vs. Spectral Acceleration (Capacity Spectrum) (M-I)……………….15

Fig. 3.5 (a), (b): Step by step deformations (M-I)………………….……………….………….….16, 17

Fig 3.6: Force vs. Displacement (M-I)…………………………….…………..………………………19

Fig 3.7: Floor plan of the dual system with L shape Shear wall (M-II)………….…..………………..20

Fig 3.8: 3d view of the dual system with L shape Shear wall (M-II)……………………………...….20

Fig. 3.9: Displacement vs. Base shear (Pushover Curve) (M-II)…………………………………..….21

Fig 3.10: Spectral Displacement vs. Spectral Acceleration (Capacity Spectrum) (M-II)……..………21

Fig. 3.11 (a), (b): Step by step deformations (M-II)………………………………...…………….22, 23

Fig 3.12: Force vs. Displacement (M-II)……………………………………………………….……..25

Fig 3.13: Floor plan of the dual system with L shape Shear wall (M-III)……………………….……26

Fig 3.14: 3d view of the dual system with L shape Shear wall (M-III)…………………...…………..26

Fig. 3.15: Displacement vs. Base shear (Pushover Curve) (M-III)……………………………………27

Fig 3.16: Spectral Displacement vs. Spectral Acceleration (Capacity Spectrum) (M-III)……………27

Fig. 3.17 (a), (b): Step by step deformations (M-III)…………………………………………..….28, 29

Fig 3.18: Force vs. Displacement (M-III)……………………………………………………..………31

Fig 3.119: Floor plan of the dual system with L shape Shear wall (M-IV)………………….………..32

Fig 3.20: 3d view of the dual system with L shape Shear wall (M-IV)…………………………...…..32

Fig. 3.21: Displacement vs. Base shear (Pushover Curve) (M-IV)……………………………..…….33

Fig 3.22: Spectral Displacement vs. Spectral Acceleration (Capacity Spectrum) (M-IV)……………33

Fig. 3.23 (a), (b): Step by step deformations (M-IV)……………………………………...………34, 35

Fig 3.24: Force vs. Displacement (M-IV)……………………………………………………..………37

Fig 3.25: Floor plan of the dual system with L shape Shear wall (M-V)……………………….…….38

Fig 3.26: 3d view of the dual system with L shape Shear wall (M-V)……………………………..…38

Fig. 3.27: Displacement vs. Base shear (Pushover Curve) (M-V)………………………………...…..39

Fig 3.28: Spectral Displacement vs. Spectral Acceleration (Capacity Spectrum) (M-V)……….……39

Fig. 3.29 (a), (b): Step by step deformations (M-V)………………………………………………40, 41

Fig 3.30: Force vs. Displacement (M-V)……………………………………………………………...43

Fig. 3.31:Lateral Displacement for Dual Type structural system with L Shape of Shear

wall………………………………………………………………………………………...…………..45

Fig. 3.32: Storey Drift Ratio for Dual Type structural system with L Shape Shear wall (5 models)....46

Fig 4.1: Floor plan of the dual system with Plane shape Shear wall (M-I)………………...…………49

Fig 4.2: 3d view of the dual system with Plane shape Shear wall (M-I)……………………………...50

Fig. 4.3: Displacement vs. Base shear (Pushover Curve) (M-I)………………………………………50

Fig 4.4: Spectral Displacement vs. Spectral Acceleration (Capacity Spectrum) (M-1)………..……..50

Fig. 5.5 (a), (b): Step by step deformations (M-I)…………………………...…………………….51, 52

Fig 4.6: Force vs. Displacement (M-I)……………………………………...…………………………54

Fig. 4.7: Lateral Displacement for Dual Type structural system with Plane Shape Shear wall……....55

Fig. 4.8: Storey Drift Ratio for Dual Type structural system with Plane Shape Shear wall…………..56

Fig 5.1: Floor plan of the dual system with channel shape Shear wall (M-I)……………………..…..59

Fig 5.2: 3d view of the dual system with channel shape Shear wall (M-I)………………………...….60

Fig. 5.3: Displacement vs. Base shear (Pushover Curve) (M-I)…………………………………...….60

Fig 5.4: Spectral Displacement vs. Spectral Acceleration (Capacity Spectrum) (M-1)………………60

Fig. 5.5 (a), (b): Step by step deformations (M-I)………………………………………………..61, 62

Fig 5.6: Force vs. Displacement (M-I)…………………………………………………………...……64

Fig 5.7: Floor plan of the dual system with channel shape Shear wall (M-II)……………..………….65

Fig 5.8: 3d view of the dual system with channel shape Shear wall (M-II)………………..…………65

Fig. 5.9: Displacement vs. Base shear (Pushover Curve) (M-II)…………………………….………..66

Fig 5.10: Spectral Displacement vs. Spectral Acceleration (Capacity Spectrum) (M-II)………….….66

Fig. 5.11 (a), (b): Step by step deformations (M-II)…………………………………………………..67

Fig 5.12: Force vs. Displacement (M-II)………………………….…………………………………..69

Fig 5.13: Floor plan of the dual system with channel shape Shear wall (M-III)…………………..….70

Fig 5.14: 3d view of the dual system with channel shape Shear wall (M-III)………………...………70

Fig. 5.15: Displacement vs. Base shear (Pushover Curve) (M-III)………………………………..…..71

Fig 5.16: Spectral Displacement vs. Spectral Acceleration (Capacity Spectrum) (M-III)………...….71

Fig. 5.17 (a), (b): Step by step deformations (M-III)…………………………………...……………..72

Fig 5.18: Force vs. Displacement (M-III)……………………………………………………………..74

Fig 5.18: Lateral Displacement for Dual type Structural System with Channel shape of Shear wall (2

Models)………………………………………………………………………………………………..76

Fig. 5.19: Storey Drift Ratio for Dual Type structural system with Channel Shape Shear wall (2

models)………………………………………………………………….…………………………..…77

Fig 6.1: Floor plan of the Bare frame structure (M-I)………………………………………...……….80

Fig 6.2: 3d view of the dual system with channel shape Shear wall (M-II)………………..…………81

Fig 6.3: Displacement vs. Base shear (Pushover Curve) (M-I)………………………………...……..81

Fig 6.4: Spectral Displacement vs. Spectral Acceleration (Capacity Spectrum) (M-1)……………....81

Fig 6.5 (a), (b): Step by step deformations (M-I)……………………………………………….....82, 83

Fig 6.6: Force vs. Displacement (M-I)…………………………………………………...……………85

Fig 6.7: Lateral Displacement for Dual Type structural system with Bare frame structure…..………86

Fig 6.8: Storey Drift Ratio for Dual Type structural system with Bare frame structure……….……..87

OPTIMUM LOCATION OF SHEAR WALL IN MULTI-STOREY BUILDING

THE OXFORD COLLEGE OF ENGINEERING, Dept. of Civil Engg. Page 1

CHAPTER 1

INTRODUCTION AND SCOPE OF PRESENT STUDY

1.1 INTRODUCTION

Amongst the natural hazards, earthquakes have the potential for causing the greatest damages. Since

earthquake forces are arbitrary in nature &unpredictable, the engineering implements need to be

sharpened for analysing structures under the action of these forces. In recent years, the term Performance

Predicated Design is being utilized as a popular in the field of earthquake engineering, with the structural

engineer taking interest in its concepts due to its potential benefits in assessment, design and better

understanding of structural comportment during vigorous ground motion. The fundamental concept of

Performance Based Design is to conceive structures that perform desirably during various loading

scenarios. The distribution of shear through the building rather than the absolute value of design base

shear is now considered of importance, as endorsed by the capacity design principles. Concurrently, the

objective of most codes is to provide life safety performance during immensely colossal and infrequent

earthquakes. Earthquake loads are to be carefully modelled so as to assess the real behaviour of structure

with a clear understanding that damage is expected but it should be regulated.

In this context pushover analysis which is an iterative procedure shall be looked upon as an

alternative for the orthodox analysis procedures. Nonlinear static analysis has been developed over the

past twenty years and as a procedure. It is relatively simple and considers post elastic behaviour, it has

become the preferred analysis procedure for design and seismic performance evaluation purposes.

However, the procedure involves certain approximations and simplifications that some amount of

variation is always expected to exist in seismic demand prediction of pushover analysis.

Pushover analysis is an approximate analysis method in which the structure is subjected to

monotonically increasing lateral forces with an invariant height-wise distribution until a target

displacement is reached. The pushover analysis of a structure is a static non-linear analysis under

permanent vertical loads and gradually increasing lateral loads. The earthquake induced forces

approximately are represented by the equivalent static lateral loads. Any premature failure or weakness

developed in the structure can be determined from the total base shear versus top displacement (plot)

obtained from pushover analysis. The Nonlinear static analysis is carried out up to failure, which

helps to determine the collapse load and ductility capacity. This type of analysis enables weakness in the

structure to be identified. Based on the hinge states and the failure mechanisms, the need for retrofit and

the type of retrofit can be determined.



Shear walls are vertical elements of the horizontal force resisting system. Shear walls are

constructed to resist the effects of lateral load acting on a structure. In constructions, shear walls are

straight external walls that typically form a box which provides all of the lateral support for the building.

The shear walls are broadly classified based on their height-to-width aspect ratio as tall or short walls.

The in-plane lateral load verses drift behaviour of a tall wall is governed by flexural deformation. The

behaviour of a short wall is governed by shear deformation.

At present the seismic analysis and design of a building is being assessed on performance based

approach on quantifying the deformation of members and the building as a whole, under the lateral loads

of a certain level of seismic hazard. Since the deformations of the members are expected to go beyond

their elastic ranges, the performance based approach depends on the non-linear analysis.

1.2 OBJECTIVES

Shear wall systems are one of the most commonly used lateral load resisting in high rise building.

Shear wall has high in plane stiffness and strength which can be used to simultaneously resist large

horizontal loads and to support gravity loads. Inclusion of shear wall has become inevitable in multi-

storey buildings to resist lateral forces. It is always advisable to incorporate them in buildings built in

region likely to experience earthquake of large intensity or high winds.

The study is concerned with identification of effective shear wall location in multi-storey building

based on its both elastic and elasto-plastic behaviours. Five significant researches have been carried out to

design and analyse the shear wall. However, the decision about the optimum location of shear wall in

multi-storey building is not much discussed.

In the present study, RCC frames without and with shear walls of different shapes and at different

directions and different location under the loads up to the failure have been analysed using ETABS

software. The load deformation curves and the results so obtained have been compared to identify the

optimum shear wall location in multi-storey building

1.3 SCOPE OF THE PRESENT STUDY

RC multi-storey buildings are adequate for resisting both the vertical and horizontal load. When

such buildings are designed without shear walls, beam and column sizes are large and quite heavily

reinforced and there will be lot of congestion at these joint and it is difficult to place and vibrate concrete

at these places. Shear wall may become unavoidable from the point of view of economy and control of

lateral deflection.



The study is concerned with identification of effective shear wall shape and location in multi-

storey buildings based on its both elastic and elasto-plastic behaviour which minimizes the displacement

and the storey shear. The motivation is to make it very handy to the design office dealing with design of

multi storey buildings.

1.4 ORGANIZATION OF THE THESIS

The thesis is organized as per detail given below:

Chapter 1: Introduces to the topic of thesis in brief.

Chapter 2: Discusses the literature review i.e. the work done by various researchers in the field of

modelling of structural members by pushover analysis, effect of shear wall, optimum location of shear

wall.

Chapter 3: Dual Type Structural System with L Shape Shear Wall.

Chapter 4: Dual Type Structural System with Plane Shape Shear Wall.

Chapter 5: Dual Type Structural System with Channel Shape Shear Wall.

Chapter 6: Bare Frame Structure

Chapter 7: Finally, salient conclusions and recommendations of the present study are given in this

chapter followed by the references.

Chapter 8: Bibliography

APPENDIX



CHAPTER 2

LITERATURE REVIEW

2.1 GENERAL

To provide a detailed review of the literature related to modelling of structures in its entirety would be

difficult to address in this chapter. A brief review of previous studies on the effect of optimum location of

shear wall and application of the Non-linear Static Analysis of structures is presented is this section. This

literature review focuses on recent contributions related to pushover analysis of structures and past efforts

most closely related to the needs of the present work.

2.2 LITERATURE REVIEW ON EFFECT OF SHEAR WALL LOCATION &

PUSHOVER ANALYSIS

Ashish.S.Agrawal and S.D.Charkha, in their paper “Effect of Change in Shear wall Location on Storey

Drift of Multi-storey Building Subjected to Lateral Loads 1”

summarise that theShear wall systems are

one of the most commonly used lateral load resisting in high rise building. Shear wall has high in plane

stiffness and strength which can be used to simultaneously resist large horizontal loads and support

gravity loads. 25 storey building in zone V is considered for present study. Incorporation of shear wall has

become inevitable in multi-storey building to resist lateral forces from preliminary investigation reveals

that the significant effects on deflection in orthogonal direction by shifting the shear wall location.

Placing Shear wall away from centre of gravity resulted in increase in most of the members forces. From

analysis it may observed from tables that displacement at the building floor at top storey has been reduced

due to presence of shear wall placed at centre. When the lift core placed in eccentric position it develops

displacement in both the direction with application of seismic force in Y direction.

From studies it is cleared that drift is increased as height of building increased and reduced for top floor.

The column which placed at the edge of the building is heavily axially loaded due to seismic forces.

Location of shear wall effects on static and dynamic axial load on the column. The displacement of

building is uni-directional and uniform for all the grids in the case of zero eccentricity for seismic

loading. With the increase in eccentricity, the building shows non-uniform movement of right and left

edges of roof due to torsion and induces excessive moment and forces in member.



Anshuman.S and Dipendu Bhunia in their paper “Solution of Shear Wall location in Multi-storey

building 2”

summarise that Shear wall systems are one of the most commonly used lateral-load resisting

systems in high-rise buildings. Shear walls have very high in-plane stiffness and strength, which can be

used to simultaneously to resist large horizontal loads and support gravity loads, making them quite

advantageous in much structural engineering applications. The study shows the idea about the location for

providing the shear wall which was based on the elastic and inelastic analyses. It has been observed that

the top deflection was reduced and reached within the permissible deflection after providing the shear

wall in any of the 6th & 7th frames and 1st and 12th frames in the shorter direction.

Plan of the Building with Shear walls in 1st and 12th frames

Plan of the Building with Shear walls in 6th and 7th frames

It has been also observed that both bending moment and shear force in the 1st and 12th frame

were reduced after providing the shear wall in any of the 6th & 7th frames and 1st and 12th frames in the

shorter direction. It has been observed that the inelastic analysis performance point was small and within

the elastic limit. Thus results obtained using elastic analyses are adequate. Hence, it can be said that shear

wall can be provided in 6th and 7th frames or 1st and 12th frames in the shorter direction.



P.S. Kumbhare and A.C. Saoji in their paper “Effectiveness of Changing Reinforced Concrete Shear

Wall Location on Multi-storeyed Building3” summarize that shear wall is one of the most commonly

used lateral load resisting element in high rise buildings. Shear wall has high in plane stiffness and

strength which can be used to simultaneously resist large horizontal load and support gravity load. Shear

wall frame interaction systems are very effective in resisting lateral forces induced by earthquake.

Effectiveness of shear wall has been studied with the help of four different models. Model one is bare

frame structural system and other four models are dual type structural system. Building considered is the

commercial building having (G+11) stories. The study indicates the significant effect on shear force and

bending moment of column at different levels of the building by shifting the shear wall location. Placing

shear wall away from centre of gravity resulted in increase in the most of the members forces. It follows

that shear walls should be coinciding with the centroid of the building. For tall building shear walls can be

used as a primary vertical load carrying element, thus serving the load and dividing space. The frame type

structural system become economical as compared to the dual type structural system can be used for

medium rise residential building situated in high seismic zone.

Chandurkar and P.S. Pajgade in their paper “Seismic analysis of RCC Building with and without Shear

Wall 4” summarize that in the seismic design of buildings, reinforced concrete structural walls, or shear

walls, act as major earthquake resisting members. Structural walls provide an efficient bracing system and

offer great potential for lateral load resistance. The properties of these seismic shear walls dominate the

response of the buildings, and therefore, it is important to evaluate the seismic response of the walls

appropriately.

For this study, a Ten-Storey building with regular in plan is modelled. These buildings were designed in

compliance to the Indian Code of Practice for Seismic Resistant Design of Buildings. Models are studied

in all four zones comparing lateral displacement, Storey drift, percentage of Area of steel in column,

concrete quantity required, steel and total cost required in all zones for all models.

From the analysis, it is observed that in Ten Storey building, constructing building with shear wall in

short span at corner is economical as compared with other models. From this it can be concluded that

large dimension of shear wall is not effective in ten stories or below ten stories buildings. It is observed

that the shear wall is economical and effective in high rise building. Changing the position of shear wall

will affect the attraction of forces, so that wall must be in proper position. If the dimensions of shear wall

are large then major amount of horizontal forces are taken by shear wall. Providing shear walls at

adequate locations substantially reduces the displacements due to earthquake.



A.Kadid and A.Boumrkik, in their paper “Pushover Analysis of Reinforced Concrete Frame

Structures” say that, to evaluate the performance of framed buildings under future expected earthquakes,

a nonlinear static pushover analysis has been conducted. To achieve this objective, three framed buildings

with 5, 8 and 12 stories respectively were analyzed. The results obtained from this study show that

properly designed frames will perform well under seismic loads.

The performance of reinforced concrete frames was investigated using the Pushover analysis5. These are

the conclusions drawn from the analysis:

The pushover analysis is a relatively simple way to explore the nonlinear behaviour of

buildings

The behaviour of properly detailed reinforced concrete frame building is adequate as indicated

by the intersection of the demand and capacity curves and the distribution of hinges in the

beams and the columns. Most of the hinges developed in the beams and few in the columns

but with limited damage

The causes of failure of reinforced concrete during the Boumerdes earthquake may be

attributed to the quality of the materials of the used and also to the fact that most of buildings

constructed in Algeria are of strong beam and weak column type and not to the intrinsic

behaviour of framed structures.

The results obtained in terms of demand, capacity and plastic hinges gave an insight into the

real behaviour of structures.

Shahabodin and Zaregarizi in their paper “Comparative investigation of using Shear wall and infill to

improve Seismic Performance of existing Buildings6” says that large number of Reinforced concrete

framed buildings are constructed with unreinforced masonry (URM ) infill walls and lack both strength

and ductility , therefore there is a great need for efficient, effective and inexpensive rehabilitation

strategies. In this study two techniques one including shear wall and the other using concrete infills were

used for rehabilitation of a five Storey reinforced concrete building with URM infill walls as shown in

figure 2.1 and effectiveness of each structural element was studied through non-linear analysis.

Figure 2.1: Location of Concrete infills



Figure 2.2: Location of shear wall in RC frame (a) Without URM infills (b) With URM infills

Results from pushover analysis on the existing five storey frame indicated that the concrete infills

have a considerable strength while brick one has lower strength. The lateral strength of concrete infilled

frame is about 5 and 2.5 times, in comparison with bare frame and URM masonry infilled frame as shown

in figure 2.2. On the contrary large displacement acceptance capabilities in brick infills are higher than

concrete infills. So Combination of concrete and brick infills reduces the negative effect of brick and

concrete infills. Masonry infills as lateral resisting element have considerable strength and can prevent

collapse of buildings in modern earthquakes. Due to the high stiffness of an infill, only a limited number

of that is typically required in a structure. Therefore, it is possible to minimise disruption both during and

after construction. In addition Infills can be used to provide supplemental stiffness for structures where

existing shear walls are inadequate. Performance of a concrete infills is dependent on adjacent element

especially columns, so premature failure in column due to strong axial forces must be considered.

Mehmet Inel and Hayri Baytan Ozmen in their paper “Effects of plastic hinge properties in nonlinear

analysis of reinforced concrete buildings7” says that due to its simplicity, the structural engineering

profession has been using the nonlinear static procedure (NSP) or pushover analysis. Pushover analysis is

carried out for either user-defined nonlinear hinge properties or default-hinge properties, available in

some programs based on the FEMA-356 and ATC-40 guidelines. While such documents provide the

hinge properties for several ranges of detailing, programs may implement averaged values.

In this case interior frames of 4 and 7 Storey buildings were considered in pushover analyses to

represent low- and medium rise reinforced concrete (RC) buildings for study. Beam and Column elements

are modeled as nonlinear frame elements with by defining plastic hinges at both ends .The frames were

modeled with default and user-defined hinge properties to study possible differences in the results of

pushover analyses.



The following findings were observed:

i. The base shear capacity of models with the default hinges and with the user-defined hinges for

different plastic hinge length and transverse reinforcement spacing are similar; the variation in the

base shear capacity is less than 5%. Thus, the base shear capacity does not depend on whether the

default or user-defined hinge properties are used.

ii. Displacement capacity depends on the amount of transverse reinforcement at the potential hinge

regions. Comparisons clearly point out that an increase in the amount of transverse

iii. Reinforcement improves the displacement capacity. The improvement is more effective for

smaller spacing. For example reducing the spacing from 200 mm to 100 mm provides an increase

of up to 40% in the displacement capacity, while reducing the spacing from 200 mm to 150 mm

provides an increase of only 12% for the 4-Storey frame.

iv. Time-history results point out that pushover analysis is reasonably successful in capturing hinging

patterns for low and medium-rise buildings, except that the plastic hinge formation in the upper

levels is not estimated adequately by pushover analysis, as observed by other researchers.

Although the capacity curve for the default-hinge model is reasonable for modern code compliant

buildings, it may not be suitable for others. Considering that most existing buildings in Turkey and some

other countries do not conform to requirements of modern code detailing, the use of default hinges needs

special care. Some programs (i.e. SAP2000) provide default-hinge properties based on the ATC-40 or

FEMA-356 documents to make modeling practical for nonlinear analyses. Based on the observations in

this study, it is clear that, although default-hinge properties provided in SAP2000 are suitable for modern

code compliant buildings, the displacement capacities are quite high for other buildings. In the case of

evaluating existing buildings constructed according to pre-modern codes, the user should either modify

the default hinge properties based on ATC-40 or FEMA-356 documents or use the user-defined hinges

based on moment–curvature analysis. The observations clearly show that the user-defined hinge model is

better than the default-hinge model in reflecting nonlinear behavior compatible with element properties.

However, if the default-hinge model is preferred due to simplicity, the user should be aware of what is

provided in the program and should definitely avoid the misuse of default-hinge properties.

Hasan Kaplan, Salih Yilmaz, Nihat Cetinkaya& Ergin Atimtay in their paper “Seismic strengthening of

RC structures with exterior shear walls8 ”summarize that vulnerable buildings and their rehabilitation are

important problems for earthquake regions. In this study, a new strengthening alternative for RC

structures, namely exterior shear walls, has been experimentally investigated under reversed cyclic

loading. Using the proposed technique, it is possible to strengthen structures without disturbing their users

or vacating the building during renovation. In this technique, shear walls are installed in parallel to the



building‟s exterior sides. It has been observed that the usage of exterior shear walls considerably improve

the capacity and sway stiffness of R.C structures.

In this study, an experimental investigation on seismic strengthening of the RC buildings by exterior

shear walls has been carried out. Structures of the two storey framed model were tested under the

imposed reversed cyclic lateral sway to simulate seismic loadings. It is observed that he implementation

of shear walls to the structural system has improved the capacity of the bare frame as expected.

Main conclusions of the study are as follows:

i. It was observed and measured that the newly added external shear wall and the connected end

columns and beams behave like a monolithic member. Minor cracks between new and existing

elements have been formed after 1% drift. Even after these minor cracks, the shear walls did not

lose their load bearing capacity.

ii. The first cracking occurred at the bottom of the exterior shear walls due to bending in initial stages

of the experiment. During the subsequent cycles, sliding shear capacity of the shear walls dropped

due to the rupturing of the longitudinal bars and in addition, shear sliding behaviour was observed

at the bottom of the walls. This had an adverse effect on ductility and energy absorption capacity

of the system. To prevent such damage, additional shear reinforcement is required at the web of

the wall.

iii. Response reduction factor (R) is an important parameter for the seismic design of buildings. In the

experimental study, the strengthened model reached yield strength at about 4 to 5 mm roof

displacement, where the base shear capacity started to fall after 23 mm of roof displacement.

Therefore, a response reduction factor of 4 to 5 can be used for E.S.W strengthened buildings to

determine the design force demand for the External Shear Walls.

iv. Application of the proposed technique to asymmetric buildings requires a carefully performed

design to minimize the effects of torsional loads by minimizing the eccentricity, which can be

compensated by an appropriate arrangement of the new shear walls. Since the model used in this

study was loaded uniaxially, it was strengthened with respect to that direction only. However,

existing seismically deficient buildings are vulnerable to seismic forces from any direction.

Therefore, buildings must be strengthened at right angles in real-life applications of exterior shear

walls.

v. Addition of shear walls to a structure will definitely improves its lateral load capacity. This fact

has been demonstrated by many experimental studies carried out for infill strengthening walls.

However, an infill wall with poorly designed dowels can even improve strength performance

considerably by providing bracing effect. On the other hand, exterior shear walls cannot improve



the capacity in case of dowel failure. The key point of this study is that exterior shear walls can be

successfully applied to existing vulnerable buildings to improve seismic capacity provided that the

dowels are well-designed.

A. Shuraim , A. Charif in their paper “Performance of Pushover Procedure in Evaluating the Seismic

Adequacy of Reinforced Concrete frames9” summarise thatthe nonlinear static analytical procedure

(Pushover) as introduced by ATC-40 has been utilized for the evaluation of existing design of a new

reinforced concrete frame, in order to examine its applicability. Potential structural deficiencies in RC

frame, when subjected to a moderate seismic loading, were estimated by the code seismic-resistant design

and pushover approaches. In the first method the design was evaluated by redesigning under one selected

seismic combination in order to show which members would require additional reinforcement. It was

shown that most columns required significant additional reinforcement, indicating their vulnerability if

subjected to seismic forces. On the other hand, the nonlinear pushover procedure shows that the frame is

capable of withstanding the presumed seismic force with some significant yielding at all beams and one

column. Vulnerability locations from the two procedures are significantly different. The paper has

discussed the reasons behind the apparent discrepancy which is mainly due to the default assumptions of

the method as implemented by the software versus the code assumptions regarding reduction factors and

maximum permissible limits. In new building design, the code always maintains certain factor of safety

that comes from load factors, materials reduction factors, and ignoring some post yielding characteristics

(hardening). In the modeling assumptions of ATC-40, reduction factor is assumed to be one, and

hardening is to be taken into consideration. Hence, the paper suggests that engineering judgment should

be exercised prudently when using the pushover analysis and that engineer should follow the code limits

when designing new buildings and impose certain reductions and limits in case of existing buildings

depending on their conditions. In short software should not substitute for code provisions and engineering

judgment.



CLOSURE

The literature review has suggested that use of Pushover analysis for R.C frame with and without

shear wall is useful. So it has been decided to use ETABS for the modeling. With the help of the software

study of R.C frame has been done. It gives the nonlinear load deflection curve of the building.

Further from the literature study it has been observed that not much focus is placed on the optimum

location of shear wall. ETABS software package is used for modeling. Therefore in the present study, a

typical multistory R.C structure with and without shear wall is analyzed by pushover analysis.With the

help of this, results so obtained have been compared to identify the optimum shear wall location in Multi-

storey building.



CHAPTER 3

DUAL TYPE STRUCTURAL SYSTEM WITH „L‟SHAPE

SHEARWALL

3.1 GENERAL DESCRIPTION OF STRUCTURE

One of the major objectives of this work is to test an existing real- life structure under pushover loads. In

this chapter Eleven storey R.C frame structure incorporated with L Shape Shear wall is being modelled by

using ETABS software. The selection of building configuration is basically done as per IS: 456 and the

loading details are taken as per IS: 875 provisions. Beams and columns are modelled as two noded beam

elements with six DOF at each node. Shear walls are modelled using shell element. Pushover analysis is

performed on the models. Based on analysis results parameters such as displacement, base shear, storey

drift and storey shear, Ductility demand, Work done by force are evaluated for each model.

In this chapter 6 models with L shape shear wall are discussed.

3.2 MATERIAL PROPERTIES

The material used for construction is Reinforced concrete with M-25 grade concrete and Fe-500 grade

reinforcing steel. The Stress-Strain relationship used is as per I.S.456:2000. The basic material properties

used are as follows:

Modulus of Elasticity of concrete, Ec = 24516.63MPa

Density of concrete = 25 KN/m3

Density of Steel = 78.5 KN/m3

Characteristic strength of concrete, fck = 25 MPa

Yield stress for steel, fy = 500 MPa



3.3 MODEL GEOMETRY

The structure analysed is for an eleven storey building with moment-resisting frame of reinforced

concrete with properties as specified above. The concrete floors are modelled as rigid. The details of the

model are given as:

Number of stories = 11

Number of bays along X-direction = 5

Number of bays along Y-direction = 5

Storey height = 3.0 meters

Bottom storey (ground storey) height = 4.15 meters

Bay width along X-direction = 6.5 meters

Bay width along Y-direction = 4.5 meters

Shear wall thickness = 180 mm

Depth of slab = 175 mm

Size of interior column from second floor = 500 mm*500 mm

Size of beams in longitudinal and transverse direction = 300 mm* 450mm

Size of exterior column = 600 mm*600mm

Zone = II

Response Reduction Factor = 3

Importance Factor = 1.5

Soil Condition Medium

Dual type structural System with L shape shear wall at various locations and in different

directions

Model – i

3.4.1 STRUCTURAL LAYOUT

Fig 3.1: Floor plan of the dual system with L shape Shear wall



Fig 3.2: 3-D view of the dual system with L shape Shear wall

3.4.2 ANALYSIS OUTPUT

Pushover Curve

Fig. 3.3: Displacement vs. Base shear (Pushover Curve)

Capacity Spectrum

Fig 3.4: Spectral Displacement vs. Spectral Acceleration (Capacity Spectrum)



Hinge Formation

STEP 0

STEP1

STEP2

Fig.3.5 (a): Step by step deformations



STEP 3

STEP 4

STEP5

Fig. 3.5(b): Step by step deformations

The colour shade of hinges defines the status of hinges, i.e., where it is along its force-displacement

curve. Based on the hinge states and the failure mechanisms, the need for retrofit and the type of retrofit

can be determined.



3.4.3 RESULTS

Table 3.1: Summary of plastic hinging for pushover analysis at different damage levels

Number of Hinges in the different state of damage

Step

Displacement Base Force A-B B-IO IO-LS LS-CP CP-C C-D D-E >E TOTAL

0

-0.0024 0 2110 2 0 0 0 0 0 0 2112

1

0.0415 4582.584 1397 679 36 0 0 0 0 0 2112

2

0.1777 14676.71 1189 615 265 43 0 0 0 0 2112

3

0.3167 21431.27 1091 575 341 104 0 1 0 0 2112

4

0.3952 24797.89 1089 576 338 106 0 1 1 1 2112

5

0.2549 9887.621 2112 0 0 0 0 0 0 0 2112

Note: The state of damages is indicated by colour code following the ATC

DISPLACEMENTS, DRIFTS& STOREY SHEAR

Table 3.2: Displacements, Drift Ratio & Storey Shear in X Direction for different stories

Storey Story Height (m) Displacement (m) Story Drift Ratio Story Shear (kN)

STOREY11 34.15 0.39519 0.00489 787.66

STOREY10 31.15 0.38054 0.00647 1683.74

STOREY9 28.15 0.36114 0.00786 2579.71

STOREY8 25.15 0.33756 0.0093 3475.59

STOREY7 22.15 0.30965 0.01084 4371.38

STOREY6 19.15 0.27714 0.01236 5267.05

STOREY5 16.15 0.24005 0.01382 6162.59

STOREY4 13.15 0.19858 0.01512 7057.94

STOREY3 10.15 0.15321 0.016 7953.07

STOREY2 7.15 0.10521 0.01602 8847.97

STOREY1 4.15 0.05714 0.01377 9780.29

DUCTILITY DEMAND

Ductility can be defined as the “ability of material to undergo large deformations without rupture before

failure”. The correct estimate of the yield point and the selection of the ultimate or failure loads are

essential for the calculation of the ductility ratio (µ). In this study, the ratio (∆failure/∆ yield) was used to

determine the level of ductility demand in the whole structure.

µ = ∆failure/∆ yield.

= (.3952/.0415) = 9.523



AREA UNDER CURVE

To detremine the work done by the force in each model, area under force-displacement curve is

computed. Excel software is used to compute the area under curve, as the total area of the trapezoids

under these line segments using the formula

Area= (Vb1+Vb2)/2*(δ2-δ1)

Where Vb1,Vb2 = Base shear force

δ 2,δ1 = Displacements

Fig 3.6: Force vs. Displacement

Displacement (m) Base shear force (Vb) kN Area (kN-m)

0 0 125

0.05 5000 350

0.1 9000 537.5

0.15 12500 712.5

0.2 16000 856.25

0.25 18250 975

0.3 20750 1093.75

0.35 23000 1080.28

0.3952 24800

Total Area 5730.28 kN-m

Table 3.3: Work done by force

0

5000

10000

15000

20000

25000

30000

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45

B

a

s

e

R

e

a

c

t

i

o

n

Displacement (m)



o Model–ii

Dual Type Structural System with L shape of Shear wall at various locations and in

different directions

Material property and Model geometry is same as in Model-I



Fig 3.8: 3-D viewof the dual system with L shape Shear wall




Pushover Curve

Fig 3.9: Displacement vs. Base shear (Pushover Curve)

Capacity Spectrum




Hinge Formation

STEP 0

STEP 1

STEP2

Fig 3.11 (a): Step By Step Deformations



STEP 3

STEP 4

Fig 3.11 (b): Step By Step Deformations

The colour shade of hinges defines the status of hinges, i.e., where it is along its Force-Displacement


can be determined.



3.5.3 RESULTS



Step Displacement Base Force A-B B-IO IO-LS LS-CP CP-C C-D D-E >E TOTAL

0 -1.90E-04 0 2111 1 0 0 0 0 0 0 2112

1 0.0208 5288.738 1442 627 42 1 0 0 0 0 2112

2 0.1525 29851.77 1361 567 163 20 0 1 0 0 2112

3 0.2164 39074.57 1360 568 163 20 0 1 0 0 2112

4 0.1051 11395.99 2112 0 0 0 0 0 0 0 2112


DISPLACEMENTS, STOREY DRIFTS RATIO& STOREY SHEAR


Storey Storey Height (m) Displacement (m) Storey Drift Ratio Storey Shear (kN)

STOREY11 34.15 0.21612 0.00579 897.79

STOREY10 31.15 0.19875 0.00667 1929.09

STOREY9 28.15 0.17873 0.00697 2960.39

STOREY8 25.15 0.15784 0.00716 3991.7

STOREY7 22.15 0.13636 0.00732 5023

STOREY6 19.15 0.1144 0.00739 6054.3

STOREY5 16.15 0.09224 0.0073 7085.61

STOREY4 13.15 0.07034 0.007 8116.91

STOREY3 10.15 0.04934 0.00644 9148.21

STOREY2 7.15 0.03002 0.00557 10179.5

STOREY1 4.15 0.01332 0.00321 11257.8

DUCTILITY DEMAND


failure”. The correct estimate of the yield point and the selection of the ultimate or failure loads are

essential for the calculation of the ductility ratio (µ). In this study, the ratio (∆failure/∆ yield) was used to

determine the level of ductility demand in the whole structure


= (.2164/.0208) = 10.4



AREA UNDER CURVE


computed. Excel software is used to compute the area under curve as the total area of the trapezoids


Area= (Vb1+Vb2)/2*(δ 2-δ1)





0 0 80

0.025 6400 215

0.05 10800 325

0.075 15200 440

0.1 20000 560

0.125 24800 675

0.15 29200 780

0.175 33200 875

0.2 36800 622.175

0.2164 39075

Total area 4572.15 kN-m


0

5000

10000

15000

20000

25000

30000

35000

40000

45000

0 0.05 0.1 0.15 0.2 0.25

B

a

s

e

R

e

a

c

t

i

o

n

Displacement



Model – iii

Dual Type Structural System with L shape Shear wall at various locations and in different

directions

Material property and Model geometry is same as in case -I



Fig 3.14: 3-D viewof the dual system with L shape Shear wall




Pushover Curve


Capacity Spectrum




Hinge Formation

STEP 0

STEP 1

STEP 2




STEP 3

STEP 4


The shade of hinges defines the status of hinges, i.e., where it is along its Force-Displacement curve.

Based on the hinge states and the failure mechanisms, the need for retrofit and the type of retrofit can be

determined.



3.6.3RESULTS




DISPLACEMENTS, STOREY DRIFT RATIOANDSTOREY SHEAR



STOREY11 34.15 0.373096 0.010714 5109.54

STOREY10 31.15 0.340954 0.011892 10978.9

STOREY9 28.15 0.305277 0.01226 16848.4

STOREY8 25.15 0.268498 0.012488 22718

STOREY7 22.15 0.231034 0.012634 28587.7

STOREY6 19.15 0.193131 0.012632 34457.5

STOREY5 16.15 0.155235 0.012398 40327.5

STOREY4 13.15 0.118042 0.011821 46197.8

STOREY3 10.15 0.082579 0.010755 52068.2

STOREY2 7.15 0.050314 0.009229 57938.9

STOREY1 4.15 0.022628 0.005452 64077.2

DUCTILITY RATIO


failure”. In this study, the ratio (∆failure/∆ yield) was use determine the level of ductility demand in the

whole structure


= (.3052/.0388) = 7.86


0 0.0022 0 2108 4 0 0 0 0 0 0 2112

1 0.0388 9589.653 1392 672 48 0 0 0 0 0 2112

2 0.1693 34032.59 1336 220 508 48 0 0 0 0 2112

3 0.3052 54837.57 1264 240 442 166 0 0 0 0 2112

4 0.3735 64864.83 2112 0 0 0 0 0 0 0 2112



AREA UNDER CURVE




Area= (Vb1+Vb2)/2*(δ 2-δ1)





0

10000

20000

30000

40000

50000

60000

70000

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4

B

a

s

e

R

e

a

c

t

i

o

n

Displacement


0 0 177.6

0.037 9600 486.4

0.075 16000 710.4

0.112 22400 980.5

0.149 30600 1280.6

0.187 36800 1457.8

0.224 42000 1665

0.261 48000 1945.6

0.299 54400 2101.6

0.336 59200 2295.2

0.373 64860




o Model–iv

Dual Type Structural System with L Shape of Shear wall at various locations and in

different directions

Material property and Model geometry is same as in case -I


Fig 3.19: Floor plan of the dual system with L shape shear wall

Fig 3.20: 3-D view of the dual system with L shape shear wall




Pushover Curve


Capacity Spectrum




Hinge Formation

STEP 1

STEP 2

STEP 3




STEP 4

STEP5

STEP 6 STEP 7


The colour of hinges defines the status of hinges, i.e., where it is along its Force-Displacement curve.


determined.



3.7.3 RESULTS




0 3.58E-06 0 2110 2 0 0 0 0 0 0 2112

1 0.0457 5972.84 1367 732 13 0 0 0 0 0 2112

2 0.1776 18478.22 1154 695 253 10 0 0 0 0 2112

3 0.3109 28074.51 1124 675 290 23 0 0 0 0 2112

4 0.3284 29266.49 1124 674 291 23 0 0 0 0 2112

5 0.3284 29180.01 1025 594 414 79 0 0 0 0 2112

6 0.402 34225.23 1024 589 416 82 0 1 0 0 2112

7 -0.0645 -13211.6 2112 0 0 0 0 0 0 0 2112


DISPLACEMENTS, STOREY DRIFT RATIOAND STOREY SHEAR



STOREY11 34.15 0.402 0.00857 1040.82

STOREY10 31.15 0.3763 0.01026 2236.43

STOREY9 28.15 0.34553 0.01132 3432.04

STOREY8 25.15 0.31157 0.01233 4627.65

STOREY7 22.15 0.27457 0.01335 5823.26

STOREY6 19.15 0.23451 0.01419 7018.87

STOREY5 16.15 0.19193 0.01467 8214.48

STOREY4 13.15 0.14794 0.0146 9410.09

STOREY3 10.15 0.10415 0.0137 10605.7

STOREY2 7.15 0.06303 0.01161 11801.4

STOREY1 4.15 0.02821 0.0068 13051.4

DUCTILITY RATIO


failure”. In this study, the ratio (∆failure/∆ yield) was used to determine the level of ductility demand in

the whole structure


= (.402/.0457) = 8.796



AREA UNDER CURVE




Area= (Vb1+Vb2)/2*(δ 2-δ1)



Fig 3.24 Force vs. Displacement


0

5000

10000

15000

20000

25000

30000

35000

40000

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45

B

a

s

e

R

e

a

c

t

i

o

n

Displacement

Displacement (m) Baseshear force (Vb) kN Area (kN-m)

0 0 210

0.06 7000 600

0.12 13000 930

0.18 18000 1230

0.24 23000 1500

0.3 27000 1740

0.36 31000 1560

0.402 34000

Total Area 7770 kN-m



o Model–v

Dual Type Structural System with L Shape of shear wall provided at four corners of the

periphery

Material property and Model geometry is same as per case -I


Fig 3.25: Floor plan of the dual system with L shape shear wall

Fig 3.26: 3-D view of the dual system with L shape shear wall



3.8.2ANALYSIS OUTPUT

Pushover Curve


Capacity Spectrum

Fig 3.28: Spectral Displacement vs. Spectral Acceleration



Hinge Formation

STEP 0

STEP 1

STEP 2




STEP 3 STEP 4

STEP 5

STEP 6




determined



3.8.3RESULTS




0 1.20E-05 0 2110 2 0 0 0 0 0 0 2112

1 0.0246 10488.55 1520 572 20 0 0 0 0 0 2112

2 0.1118 39574.88 1520 572 20 0 0 0 0 0 2112

3 0.1118 39550.38 1422 620 68 2 0 0 0 0 2112

4 0.1383 47287.9 1422 618 70 2 0 0 0 0 2112

5 0.1383 47226.52 1308 598 150 54 0 2 0 0 2112

6 0.217 70452.73 2112 0 0 0 0 0 0 0 2112





STOREY11 34.15 0.217142 0.00706 5440.75

STOREY10 31.15 0.195963 0.007207 11808.2

STOREY9 28.15 0.174342 0.007362 18175.65

STOREY8 25.15 0.152257 0.007465 24543.1

STOREY7 22.15 0.129862 0.00749 30910.55

STOREY6 19.15 0.107391 0.007411 37278

STOREY5 16.15 0.085158 0.007165 43645.44

STOREY4 13.15 0.063664 0.006715 50012.88

STOREY3 10.15 0.04352 0.00597 56380.31

STOREY2 7.15 0.025611 0.004877 62747.73

STOREY1 4.15 0.01098 0.002646 69445.57

DUCTILITY DEMAND


failure”. In this study the ratio (∆failure/∆ yield) was used to determine the level of ductility demand in

the whole structure


= (.2167/.025)

= 8.68



AREA UNDER CURVE




Area= (Vb1+Vb2)/2*(δ 2-δ1)





0

10000

20000

30000

40000

50000

60000

70000

80000

0 0.05 0.1 0.15 0.2 0.25

B

a

s

e

R

e

a

c

t

i

o

n

Displacement


0 0 140

0.025 11200 380

0.05 19200 580

0.075 27200 780

0.1 35200 980

0.125 43200 1180

0.15 51200 1370

0.175 58400 1550

0.2 65600 1156.425

0.217 70450




3.9 RESULTS AND DISCUSSION

The section here deals with the observations and interpretations obtained from the Pushover analysis.

Nonlinear static analysis is performed for Dual Type structural system with L shape Shear wall and it is

being modelled by using computer software. The frame was subjected to design earthquake forces as

specified in the IS code for Zone II along X directions. Pushover curves for Dual type structural system

with L shape of Shear wall for different models in X directions as shown in figures. These curves show

the behaviour of the frame in terms of its stiffness and ductility. Average base shear and the

corresponding displacement for different model (Dual Type Structural System with L-Shape of Shear

Wall) obtained from analysis are mentioned below.

Model I: - average base shear from analysis is 25*103 kN for a displacement of 395 mm in X

direction.

Model II: -average base shear from analysis is 39*103 kN for a displacement of 219mm in X

direction

Model III: -average base shear from analysis is 64.86*103 kN for a displacement of 373 mm in X

direction

Model IV: -average base shear from analysis is 34*103 kN for a displacement of 402 mm in X

direction

Model V: - average base shear from analysis is 70.4*103 kN for average displacement of 216mm

in X direction

From the above analysis results it is observed that model V is having lower displacement and larger base

force as compared to other models.

Capacity spectrum is the capacity curve spectral acceleration vs. spectral displacement (Sa vs. Sd) co-

ordinates. The „performance point‟ is the point where the capacity curve crosses the demand curves. The

performance point is obtained by superimposing demand spectrum on capacity curve and transformed

into spectral coordinates. From analysis it is observed that the performance point attained for different

model is cited below.

Model I: -The performance point obtained at a base shear level of 10*103

kN for a displacement of

118 mm in the X direction.

Model II: -The performance point obtained at a base shear level of 14.8*103

kN for a displacement

of 72 mm in the X direction.

Model III:-The performance point obtained at a base shear level of 16.8*103





Model IV: - The performance point obtained at a base shear level of 11*103



Model V: -The performance point obtained at a base shear level of 22*103



From the above analysis results it is observed that model V is having lower displacement and larger base


HINGE STATUS

Model-V is having considerable strength and stiffness due to the provision of L shape shear wall at four

corners. Hinges developed in Limited safety performance range (LS-CP) in Model-V (54 numbers for a

maximum displacement of 138mm) is very less as compared to other models (I, II, III, and IV). In Model-

V majority of the hinges were developed in, Immediate occupancy performance level (IO-LS) in which

structural damage occurred is limited. Number of hinges in the complete state of damage (CP, D & E) in

Model V is appreciably less as compared to other models. In model V (for a maximum displacement of

138mm) 2 number of hinges were developed in Collapse Prevention performance level, means the

structural element or building is on the verge of experiencing partial or total collapse.

LATERAL DISPLACEMENT

Lateral displacement for different Models at each floor level is shown in Fig 3.31.

Fig. 3.31:Lateral Displacement for Dual Type structural system with L Shape of Shear wall (5 models)

The Figure presented in this chapter were developed with the intent to determine the lateral displacement

for different models.In this chapter Dual type Structural system with L Shape of Shear wall (5 cases)

were considered. From results it is observed that the displacements occurs in Model II & Model V

0

2

4

6

8

10

12

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45

S

t

o

r

e

y

Displacement (m)

Model 1

Model 2

Model 3

Model 4

model 5



reduced up to 45 % as compared with other Models (I,III,IV). The graphs show that generally the

displacement increases as the stiffness increases. Stiffness of Model (I,III,IV) is very less as compared to

other models (II,V). The displacement is inversely proportional to the stiffness..

STORY DRIFT RATIO

Story drift is the displacement of one level relative to the other level above or below. Story drift ratio

according to each model is shown in fig 3.32.

Story drift ratio = (difference between displacement of two stories / height of one story)

In terms of seismic design, lateral deflection and drift can affect the structural elements that are part of the

lateral force resisting system. Without proper consideration of the expected movement of the structure,

the lateral force resisting system might experience premature failure and a corresponding loss of strength.

Fig. 3.32: Storey Drift Ratio for Dual Type structural system with L Shape Shear wall (5 models)

The Figure presented in this chapter were developed with the intent to determine maximum and minimum

value of storey drift ratio occurs in different models. Expected movement of the structure can be

determined with the help of maximum and minimum value of storey drift ratio. In this chapter Dual type

Structural system with L-Shape of Shear Wall (5 models) were considered for analysis. From the figure it

is observed that the story drift ratio is maximum for model I i.e. (Dual type Structural system with L

Shape of Shear wall provide at one corner) as compared to other model. Models (III,VI) has the minimum

value of story drift ratio as compared to other models.

DUCTILTY AND AREA UNDER CURVE

In this chapter Dual type Structural system with L shape of Shear wall (5 models) was considered for

analysis. The ratio (∆failure/∆ yield) was used to determine the level of ductility demand in the whole

0

2

4

6

8

10

12

0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 0.018

S

t

o

r

e

y

Storey Drift Rato

Model 1

Model 2

Model 3

Model 4

Model 5



structure. From the results it is observed that dutility ratio for model III (7.86) is very less as compared

with other models . Ductiliy demand for model II (10.4) is approximately 25 % larger as compared with

other respective models. Ductility so obtained in this mode II is quite large, thus allowing the structure to

undergo large deformations before failure.

To detremine the work done by the force in each model Area under force-displacement curve is

computed. From results it has been observed that work done by Model III (13100 kN-m) is approximately

50 % more as compared with Model I (5730 kN-m). Work done by force in models (II,IV,V) is

appreciably less as compared to model III.



CHAPTER 4

DUAL TYPE STRUCTURAL SYSTEM WITH PLANE SHAPE

SHEARWALL



this chapter, Eleven storey R.C frame structure incorporated with Plane Shape of Shear wall is being

modelled by using ETABS software. The selection of building configuration is basically done as per IS-

456 and the loading details are taken as per IS: 875 provisions. Beams and columns are modelled as two

noded beam elements with six DOF at each node. Shear walls are modelled using shell element. Pushover

analysis is performed on the models. Based on analysis result, parameters such Displacement, Base shear,

Storey drift and Storey shear, Ductility demand, Work done by force are explored.



reinforcing steel. The Stress-Strain relationship used is as per IS 456:2000. The basic material properties









4.3 MODEL GEOMETRY

The structure analysed is for an eleven storey building with moment-resisting frame of reinforced

concrete with properties as specified above. The concrete floors are modelled as rigid. The details of the

model are given as:













Zone = II




4.4 STRUCTURAL LAYOUT

Dual Type Structural System with Plane shape of Shear wall provided at the periphery

of the structure

Fig.4.1: Floor plan of the dual system with plane shape shear wall



Fig.4.2: 3-D view of the dual system with plane shape shear wall

4.5 ANALYSIS OUTPUT

Pushover Curve


Capacity Spectrum

Fig. 4.4: Spectral Displacement vs. Spectral Acceleration (Capacity Spectrum)



Hinge Formation

STEP 0

STEP 1

STEP 2




STEP 3

STEP 4


The colour shade of hinges defines the status of hinges, i.e., where it is along its Force-Displacement


can be determined.



4.6 RESULTS




0 2.41E-06 0 2108 4 0 0 0 0 0 0 2112

1 0.0299 6558.205 1400 640 72 0 0 0 0 0 2112

2 0.161 25098.93 1376 234 428 72 0 2 0 0 2112

3 0.2716 37452 1374 236 428 72 0 2 0 0 2112

4 0.1376 9071.27 2112 0 0 0 0 0 0 0 2112





STOREY11 34.15 0.27117 0.00791 714.64

STOREY10 31.15 0.24746 0.00854 1535.57

STOREY9 28.15 0.22183 0.0088 2356.49

STOREY8 25.15 0.19544 0.00905 3177.41

STOREY7 22.15 0.16831 0.00924 3998.34

STOREY6 19.15 0.14058 0.00933 4819.26

STOREY5 16.15 0.1126 0.00922 5640.18

STOREY4 13.15 0.08493 0.00882 6461.11

STOREY3 10.15 0.05848 0.00799 7282.03

STOREY2 7.15 0.0345 0.00662 8102.96

STOREY1 4.15 0.01465 0.00353 8961.24

DUCTILITY RATIO

In this study, the ratio (∆failure/∆ yield) was used to determine the level of ductility demand in the whole

structure

µ = ∆failure/∆ yield

= (0.2716/0.0299) = 9.08



AREA UNDER CURVE

To detremine the work done by the force in each model, Area under force-displacement curve is



Area= (Vb1+Vb2)/2*(δ 2-δ1)





0 0 102

0.03 6800 264

0.06 10800 384

0.09 14800 510

0.12 19200 648

0.15 24000 768

0.18 27200 858

0.21 30000 954

0.24 33600 1101.275

0.271 37450



0

5000

10000

15000

20000

25000

30000

35000

40000

0 0.05 0.1 0.15 0.2 0.25 0.3

B

a

s

e

R

e

a

c

t

i

o

n

Displacement





Nonlinear static analysis is performed for Dual type structural system with Plane shape of Shear wall and

it is being modelled by using the computer software. The frame was subjected to design earthquake forces

as specified in the IS code for Zone II along X directions. Pushover curves for Dual type Structural

system with Plane Shape of Shear wall in X directions as shown in Figure. These curves show the

behaviour of the frame in terms of its stiffness and ductility.

Average base shear for Dual type Structural System with plane shape of Shear Wall obtained from

analysis is 37.3*103 kN for a displacement of 270 mm in X direction.




into spectral coordinates. From capacity spectrum curve it is observed that the performance point is

obtained at a base shear level of 14.4*103 kN for a displacement of 84 mm in the X direction.


Lateral displacement for Dual type Structural system with Plane shape of Shear wall at each floor level is

shown in Fig 4.7.

Fig 4.7: Lateral Displacement for Dual type Structural System with plane shape of Shear Wall


for the model.In this chapter Dual type Structural system with Plane shape of Shear wall were considered.

From results it has been observed that the displacements occurs in Dual type structural system with Plane

shape of Shear wall increased up to 20 % as compared with Dual type structural system with L-shape of

0

2

4

6

8

10

12

0 0.05 0.1 0.15 0.2 0.25 0.3

S

t

o

r

e

y

Displacement



Shear wall (Model-V). The graphs show that generally the displacement increases as the stiffness

decreases. Stiffness of Model with rectangular shape of shear wallis very less as compared to model with

L- shape of shear wall. The displacement is inversely proportional to the stiffness.

STORY DRIFT RATIO


according to each model is shown in Fig 4.8.


Fig 4.8: Storey Drift Ratio for Dual type Structural System with Rectangular shape of Shear Wall

The figure presented in this chapter were developed with the intent to determine maximum and minimum

value of storey drift occurs in model. Expected movement of the structure can be determined with the

help of maximum and minimum value of storey drift ratio .Without proper consideration of the expected

movement of the structure,the lateral force resisting system might experience premature failure and a

corresponding loss of strength. As from the observation, maximum value of storey drift ratio in this

model is 9.33.

HINGE STATUS

For a Model with plane shape shear wall, majority of the hinges (432 Numbers for a maximum

displacement of 271 mm) in the model were developed in Damage control performance range in which

structural damage occurred is limited. For a maximum displacement of 271 mm, number of hinges

developed in Limited safety performance range (LS-CP) is 72, means the continuous range of damage

states between the Life Safety and Collapse Prevention levels. For a Model incorporated with plane shape

of shear wall (for a maximum displacement of 271 mm) 2 numbers of hinges were developed in Collapse

0

2

4

6

8

10

12

0 0.002 0.004 0.006 0.008 0.01

S

t

o

r

e

y

Storey Drift Ratio



Prevention performance level, means the structural element or building is on the verge of experiencing

partial or total collapse.


In this chapter type Dual type Structural system with Plane shape of Shear wall were considered for

analysis. The ratio (∆failure/∆ yield) was used to determine the level of ductility demand the whole

structure. From the results it is observed that dutility demand obtained from model is 9.08. Ductility so

obtained in this model is quite large thus allowing the structure to undergo large deformations before

failure.

To detremine the work done by the force in each model Area under force-displacement curve is

computed. From results it has been observed that work done by force in Dual type structural sytem with

plane shape of shear wall is 5590 kN-m.



CHAPTER 5

DUAL TYPE STRUCTURAL SYSTEM WITH CHANNEL

SHAPE SHEAR WALL



this chapter Eleven storey R.C frame structure incorporated with Channel shape of Shear wall and it is

being modelled by using ETABS software. The selection of building configuration is basically done as

per IS: 456 and the loading details are taken as per IS: 875 provisions. Beams and columns are modelled

as two noded beam elements with six DOF at each node. Shear walls are modelled using shell element.

Pushover analysis is performed on the models. Based on analysis result, parameters such Displacement,

Base shear, Storey drift Storey shear, Ductility ratio and Work done by force are evaluated for each

model.

In this chapter 3 models with Channel shape shear wall are discussed.



reinforcing steel. The Stress-Strain relationship used is as per IS 456:2000. The basic material properties









5.3 MODEL GEOMETRY

The structure analysed for an eleven storey building with moment-resisting frame of reinforced concrete

with properties as specified above. The concrete floors are modelled as rigid. The details of the model are

given as:













Zone = II




Model–i

Dual Type Structural System with Channel Shape Shear wall provided at centre of the

structure


Fig 5.1: Floor plan of the dual system with channel shape shear wall



Fig 5.2: 3-D view of the dual system with channel shape shear wall


Pushover Curve


Capacity Spectrum




Hinge Formation

STEP 0 STEP 1

STEP 2

STEP 3




STEP 4

STEP 5

STEP 6




determined.



5.4.3 RESULT




0 -2.99E-06 0 2109 3 0 0 0 0 0 0 2112

1 0.0369 6162.247 1395 704 13 0 0 0 0 0 2112

2 0.1686 22985.85 1110 740 248 14 0 0 0 0 2112

3 0.301 35669.78 971 581 439 121 0 0 0 0 2112

4 0.4352 47065.37 893 496 498 224 0 1 0 0 2112

5 0.5085 52515.21 893 496 497 225 0 1 0 0 2112

6 0.2874 18279.34 2112 0 0 0 0 0 0 0 2112


DISPLACEMENTS AND DRIFTS, STOREY DRIFT RATIOANDSTOREY SHEAR



STOREY11 34.15 0.50849 0.008251 1448.98

STOREY10 31.15 0.483736 0.009861 3103.89

STOREY9 28.15 0.454152 0.011334 4758.79

STOREY8 25.15 0.420151 0.013028 6413.69

STOREY7 22.15 0.381067 0.014907 8068.6

STOREY6 19.15 0.336345 0.016809 9723.5

STOREY5 16.15 0.285919 0.018484 11378.41

STOREY4 13.15 0.230465 0.019682 13033.32

STOREY3 10.15 0.171418 0.019969 14688.23

STOREY2 7.15 0.111511 0.018669 16343.13

STOREY1 4.15 0.055504 0.013374 18070.06

DUCTILITY RATIO



the whole structure


= (.5085/.0369) = 13.78



AREA UNDER CURVE




Area= (Vb1+Vb2)/2*(δ 2-δ1)





0 0 252

0.06 8400 756

0.12 16800 1224

0.18 24000 1620

0.24 30000 1980

0.3 36000 2304

0.36 40800 2610

0.42 46200 2898

0.48 50400 1466.539

0.5085 52515



0

10000

20000

30000

40000

50000

60000

0 0.1 0.2 0.3 0.4 0.5 0.6

B

a

s

e

R

e

a

c

t

i

o

n

Dsiaplacement



o Model – ii

Dual Type Structural System with Channel Shape Shear wall provided at periphery (4

corners) of the structure







Pushover Curve


Capacity Spectrum




Hinge Formation

STEP 0 STEP 1

STEP 2

STEP 3

Fig 5.11(a): Step By Step Deformations



5.5.3 RESULTS




0 2.16E-05 0 2110 2 0 0 0 0 0 0 2112

1 0.0198 12385.76 1384 592 136 0 0 0 0 0 2112

2 0.1524 75613.44 1260 432 274 144 0 2 0 0 2112

3 0.2667 119549.1 2112 0 0 0 0 0 0 0 2112




Storey Storey Height (m) Displacement (m) Storey Drift ratio Storey Shear (kN)

STORY11 34.15 0.266819 0.009277 9032.84

STORY10 31.15 0.238989 0.009355 19822.4

STORY9 28.15 0.210924 0.009439 30612

STORY8 25.15 0.182606 0.009456 41401.6

STORY7 22.15 0.154238 0.00937 52191.6

STORY6 19.15 0.126126 0.009152 62982.3

STORY5 16.15 0.09867 0.008717 73773.9

STORY4 13.15 0.07252 0.00804 84563.5

STORY3 10.15 0.0484 0.006987 95351.6

STORY2 7.15 0.027437 0.005381 106140

STORY1 4.15 0.011293 0.002721 117564

DUCTILITY RATIO


structure


= (0.2667/0.0198)

= 13.46



AREA UNDER CURVE


computed. Excel software is used to compute the, Area under curve, as the total area of the trapezoids


Area= (Vb1+Vb2)/2*(δ 2-δ1)





0 0 288

0.03 19200 774

0.06 32400 1170

0.09 45600 1584

0.12 60000 2016

0.15 74400 2412

0.18 86400 2754

0.21 97200 3096

0.24 109200 3053.799

0.2667 119549

Total Area 17147 kN-m


0

20000

40000

60000

80000

100000

120000

140000

0 0.05 0.1 0.15 0.2 0.25 0.3

B

a

s

e

R

e

a

c

t

i

o

n

Displacement



o Model – iii

Dual Type Structural System with Channel Shape Shear wall provided at periphery

(centre) of the structure







Pushover Curve


Capacity Spectrum




Hinge Formation

STEP 0 STEP 1

STEP 2

STEP 3

Fig 5.17: Step By Step Deformations



5.6.3 RESULTS




0 2.87E-04 0 2106 6 0 0 0 0 0 0 2112

1 0.0256 12903.1 1352 658 98 2 0 2 0 0 2112

2 0.1455 60624.9 1350 660 98 2 0 2 0 0 2112

3 0.0282 2142.21 2112 0 0 0 0 0 0 0 2112




Storey Storey Height (m) Displacement (m) Storey Drift ratio Storey Shear (kN)

STOREY11 34.15 0.14571 0.0044 164.16

STOREY10 31.15 0.13252 0.00468 357.67

STOREY9 28.15 0.11848 0.0048 551.18

STOREY8 25.15 0.10408 0.00491 744.69

STOREY7 22.15 0.08936 0.00497 938.2

STOREY6 19.15 0.07446 0.00495 1131.7

STOREY5 16.15 0.05962 0.00483 1325.21

STOREY4 13.15 0.04514 0.00457 1518.72

STOREY3 10.15 0.03144 0.00411 1712.23

STOREY2 7.15 0.0191 0.00348 1905.75

STOREY1 4.15 0.00867 0.00209 2109.77

DUCTILITY RATIO


structure


= (0.1455/0.0256)

= 5.68



AREA UNDER CURVE


computed. Excel software is used to compute the, Area under curve, as the total area of the trapezoids


Area= (Vb1+Vb2)/2*(δ 2-δ1)





0

10000

20000

30000

40000

50000

60000

70000

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16

B

a

s

e

R

e

a

c

t

i

o

n

Displacement


0 0 60

0.015 8000 168

0.03 14400 264

0.045 20800 354

0.06 26400 438

0.075 32000 528

0.09 38400 624

0.105 44800 714

0.12 50400 798

0.135 56000 612.276

0.1455 60624

Total area 4560 kN-m





Nonlinear static analysis is performed for Dual type structural system with Channel shape of Shear wall is

being model by using the computer software. The frame was subjected to design earthquake forces as

specified in the IS code for Zone II along X directions. Pushover curves for Dual type structural system

with Channel shape of Shear wall in X directions as shown in Figure. These curves show the behaviour of

the frame in terms of its stiffness and ductility. Average base shear and the corresponding displacement

for different model (Dual Type structural system with Channel shape of Shear wall) obtained from

analysis are mentioned below.

Model I: - average base shear from analysis is 52*103 kN for a displacement of 508 mm in X

direction.

Model II: - average base shear from analysis is 119.6*103 kN for a displacement of 266 mm in X

direction

Model III: - average base shear from analysis is 60.6*103 kN for a displacement of 145 mm in X

direction

From the above analysis results it is observed that model II is having lower displacement and larger Base





into spectral coordinates. From figure it is observed that the performance point attained for different

model is cited below.

Model I: - The performance point obtained at a base shear level of 13.2*103



Model III: -The performance point obtained at a base shear level of 27.6*103 kN for a

displacement of 50 mm in the X direction.

Model III: -The performance point obtained at a base shear level of 25.6*103

kN for a

displacement of 56 mm in the X direction.

From the above analysis results it is observed that model II is having lower displacement and larger base

force as compared to Model I& II.



HINGE STATUS

Model III is having considerable strength and stiffness due to the provision of Channel shape shear wall

provided at periphery. Hinges developed in Limited safety performance range (LS-CP) in Model II (2

numbers for a maximum displacement of 145mm) is very less as compared to other model I and model II.

In Model III majority of the hinges were developed in, Immediate occupancy performance level in which

structural damage occurred is limited. Number of hinges in the complete state of damage (CP, D and E) in

Model III is appreciably less as compared other models.

In all Models, incorporated with channel shape of shear wall, 2 number of hinges were developed in

Collapse prevention performance level, means the structural element or building is on the verge of

experiencing partial or total collapse.


Lateral displacement for different models at each floor level is shown in Fig 5.19

Fig 5.19: Lateral Displacement for Dual type Structural System with Channel shape of Shear wall (3 Models)


for different models.In this chapter Dual type Structural system with Channel shape of Shear wall (3

Models) were considered for analysis. From results it is observed that the displacements occurs in Model

III reduced up to 45-72 % as compared with Models I and model II.From the figure (5.19) it is observed

that the displacement increases as the stiffness increases. Stiffness of Model I and Model II is very less as

compared to model III. The displacement is inversely proportional to the stiffness.

0

2

4

6

8

10

12

0 0.1 0.2 0.3 0.4 0.5 0.6

S

t

o

r

e

y

Displacement (m)

Model 1

Model 2

Model 3



STORY DRIFT RATIO


according to each model is shown in Fig 5.20. In Software value of story drift is given in ratio.


In terms of seismic design, lateral deflection and drift can affect the structural elements that are part of the

lateral force resisting system.

Without proper consideration of the expected movement of the structure, the lateral force resisting system

might experience premature failure and a corresponding loss of strength.

Fig. 5.20: Storey Drift Ratio for Dual Type structural system with channel Shape Shear wall (3 models)

The Figurepresented in this chapter were developed with the intent to determine maximum and minimum

value of storey drift ratio occurs in different models. Expected movement of the structure can be

determined with the help of maximum and minimum value of storey drift ratio. In this chapter Dual type

Structural System with Channel shape of Shear wall (3 models) were considered for analysis. From the

figure (5.20) it is observed that the story drift ratio is maximum for Model I and II as compared with

Model III (4.97 ).


In this chapter Dual type structural system with Channel Shape of Shear wall (3 models) were considered

for analysis. The ratio (∆failure/∆ yield) was used to determine the level of ductility demand in the whole

structure. From the results it is observed that dutility ratio for model III (5.68) is very less as compared

with other models. Ductiliy ratio for model I (13.78) and model II (13.46) is approximately 58 % larger as

0

2

4

6

8

10

12

0 0.005 0.01 0.015 0.02 0.025

S

t

o

r

e

y

Storey Drift Ratio

Model 1

Model 2

Model 3



compared Model III. Ductility so obtained in this Model I is quite large, thus allowing the structure to

undergo large deformations.


computed. From results it has been observed that work done by Model I (15110 kN-m) and Model II

(17147 kN-m) is approximately 70-75 % more as compared with Model III (4560 kN-m). Work done by

force in the Model III is appreciably less as compared to other models.



CHAPTER 6

BARE FRAME WITHOUT SHEAR WALL



this chapter Eleven storey RC Bare frame structure without shear wall is being modelled by using ETABS

software. The selection of building configuration is basically done as per IS: 456 and the loading details

are taken as per IS: 875 provisions. Beams and columns are modelled as two noded beam elements with

six DOF at each node. Shear walls are modelled using shell element. Pushover analysis is performed on

the model. Based on analysis result parameters such Displacement, Base shear, Storey drift and Storey

shear, Ductility demand, Work done by force are explored.



reinforcing steel. The Stress -Strain relationship used is as per IS 456:2000. The basic material properties



Density of concrete = 25 kN/m3

Density of Steel = 78.5 kN/m3





6.3 MODEL GEOMETRY

The structure analysed for an Eleven storey building with moment-resisting frame of reinforced concrete

with properties as specified above. The concrete floors are modelled as rigid. The details of the model are

given as:












Zone = II




6.4 STRUCTURAL LAYOUT

Fig 6.1: Floor plan of the bare framed structure



Fig 6.2: 3-D view of the bare framed structure

6.5 ANALYSIS OUTPUT

Pushover Curve


Capacity Spectrum




Hinge Formation

STEP 0

STEP 1

STEP 2




STEP 3

STEP 4

STEP 5




determined.



6.5 RESULTS






Storey Story Height (m) Displacement (m) Storey Drift Ratio Story Shear (kN)

STOREY11 34.15 0.32839 0.00127 432.47

STOREY10 31.15 0.32457 0.0022 919.41

STOREY9 28.15 0.31797 0.00358 1406.35

STOREY8 25.15 0.30724 0.00527 1893.29

STOREY7 22.15 0.29143 0.00713 2380.24

STOREY6 19.15 0.27005 0.00907 2867.18

STOREY5 16.15 0.24285 0.01107 3354.12

STOREY4 13.15 0.20965 0.0131 3841.06

STOREY3 10.15 0.17036 0.01515 4328

STOREY2 7.15 0.1249 0.01717 4814.95

STOREY1 4.15 0.0574 0.01769 5320.69

DUCTILITY DEMAND



the whole structure


= (.3283/.0356) = 9.23


0 5.39E-06 0 2110 2 0 0 0 0 0 0 2112

1 0.0356 2865.862 1648 370 94 0 0 0 0 0 2112

2 0.1481 8788.435 1570 192 182 168 0 0 0 0 2112

3 0.289 12828.58 1560 180 154 216 0 2 0 0 2112

4 0.3283 13938.16 1560 180 154 216 0 2 0 0 2112

5 0.2203 5373.037 2112 0 0 0 0 0 0 0 2112



AREA UNDER CURVE



under these line segments using the formula.

Area= (Vb1+Vb2)/2*(δ 2-δ1)




Displacement Base shear force (Vb) Area (kN-m)

0 0 60

0.04 3000 162

0.08 5100 252

0.12 7500 333

0.16 9150 387

0.2 10200 429

0.24 11250 477

0.28 12600 640.941

0.3283 13940

Total area 2790.94 kN-m


0

2000

4000

6000

8000

10000

12000

14000

16000

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35

B

a

s

e

R

e

a

c

t

i

o

n

Dispalcement





Nonlinear static analysis is performed for Bare frame and it is being modelled by using the computer

software. The frame was subjected to design earthquake forces as specified in the IS code for Zone II

along X directions. Pushover curves for RC Bare frame structure without shear wall in X directions as

shown in Figure. These curves show the behaviour of the frame in terms of its stiffness and ductility.

Average base shear for RC Bare frame structure without shear wall obtained from analysis is 139.3*103

kN for a displacement of 328 mm in X direction.




into spectral coordinates. From capacity spectrum curve it is observed that the performance point is

obtained at a base shear level of 8.75*103 KN for a displacement of 150 mm in the X direction.


Lateral displacement for Dual type Structural System with Rectangular shape of Shear Wall at each floor

level is shown in Fig 6.7.

Fig 6.7: Lateral Displacement for bare frame structure without shear wall


for different models.In this chapter bare frame structure without shear wall was considered for analysis.

From results it is observed that the displacements occurs after yielding in Bare frame structure without

0

2

4

6

8

10

12

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35

S

t

o

r

e

y

Displacement



shear wall is 328mm. The graphs show that generally the displacement increases as the stiffness

decreases. Stiffness of Bare frame model without shear wall is very less as compared to dual type

structural system with different shapes of shear wall. The displacement is inversely proportional to the

stiffness.

STORY DRIFT RATIO


according to each model is shown in Fig 6.8.


Fig. 6.8: Storey Drift Ratio for Bare frame structure without Shear wall

The figure presented in this chapter were developed with the intent to determine maximum and minimum

value of storey drift ratio occurs in the Model. Expected movement of the structure can be determined

with the help of maximum and minimum value of storey drift ratio without proper consideration of the

expected movement of the structure,the lateral force resisting system might experience premature failure

and a corresponding loss of strength.As from the observation, maximum value of storey drift ratio in this

Model is 17.69 mm in the bare frame structure,as the storey shear drift ratio uniformly decreased with the

storey level which is considerably more from those in other dual type systems.

HINGE STATUS

For a Model with bare framed structure, majority of the hinges (216 numbers for a maximum

displacement of 328 mm) in the model were developed in Limited safety performance range (LS-CP) in

which structural damage occurred is severe. For a maximum displacement of 328 mm, number of hinges

0

2

4

6

8

10

12

0 0.005 0.01 0.015 0.02

S

t

o

r

e

y

Storey Drift ratio



developed in Immediate occupancy performance level (IO-LS) is 154 in which structural damage

occurred is limited. For a Model with bare frame structure (for maximum displacement of 348 mm) 2

number of hinges were developed in Collapse Prevention performance level, means the structural element

or building is on the verge of experiencing partial or total collapse.


In this chapter bare frame structure without shear wall was considered for analysis. The ratio (∆failure/∆

yield) was used to determine the level of ductility demand in the whole structure. From the results it is

observed that dutility ratio obtained from model is9.23.

To detremine the work done by the force in each model. Area under Force-Displacement curve is

computed. From the results it has been observed that work done by force in Bare frame structure without

shear wall is 2790 kN-m.



CHAPTER 7

CONCLUSIONS AND RECOMMENDATIONS

7.1 GENERAL

In the present study, the non-linear response of RCC frame using ETABS under the loading has been

carried out with the intention to study the relative importance of shearwall and to identify theoptimum

location of shear wall in multi-storey building.

7.2 CONCLUSIONS

The pushover analysis is a simple way to investigate the nonlinear behavior of the buildings. Eleven

storey RC frame structure with and without shear wall is being modelled using ETABS software. The

selection of building configuration is basically done as per IS: 456 and the loading details are taken as per

IS: 875 provisions. From the results it is clear that shear wall frame interaction systems are very effective

in resisting lateral forces induced by earthquake. Placing the shear wall away from center of gravity

results in a decrease in displacements. Changing the position of shear wall will affect the attraction of

forces, so that wall must be in proper position.

i. The Top deflection is reduced and is within the permissible deflection as per IS-456 provision for

the dual type system with channel type shear wall compared to other strutures incorporated with

typical types of shear wall systems.

ii. Drift ratio is very small in lower stories and reaches a maximum in the middile stories and again

reaches a low value towards the top. In some cases (Bare frame model, dual system with L shape

shear wall-Model I, Dual system with channel shape shear wall-Model I) top drift ratio is much

less as compared to bottom. In the bare frame without shear wall, drift ratio uniformly decreases

towards the top. The drift ratio is within the permissible limit as per ATC-40

iii. Most effective location of the shear wall is when it is farther away from centre of gravity. It also

reduce the effect due to torsion of the floor plan.

iv. Amongst the various strutures incorporated with typical types of shear wall systems, Dual type

system with Channel shape shear wall provided at periphery is having considerable strength and

stiffness. Hinges developed in Limited safety performance range in Model III (dual system with

channel shape of shear wall) is appreciably very less as compared to other models incorporated

with L shape or Plane shape shear wall. Large yielding towards upper stories is very less in dual

system with channel shape of shear wall (Model III) as compared to other models.



v. Ductilty demand obatined from every model is quite large and this should not be mistaken for

member ductility. As the demanded ductility is within the elastic limit, ductility ratio for dual type

system with channel shape shear wall (Model III) is quite small.

vi. Work done by the force indual type system with channel type shear wall (Model III) is quite small

as compared to the other models. Dual type system with channel shape shear wall provided at the

periphery shows a response which is within the elastic limit. Due to high stiffness and strength of

the channel shape shear wall provided around the periphery, yielding in this model is very less as

compared to other models incorporated with L shape or Plane shape shear wall.

7.3 FUTURE WORK

Future work has to be done to obatin Member ductilities. It will help to obtain more detailed design for

Top Expendable stories.



REFERENCES

1) Ashish.S.Agrawal and S.D.Charkha, “Effect of Change in Shear wall Location on Storey Drift

of Multi-storey Building Subjected To Lateral Loads”, International Journal of Engineering

Research and Applications (IJERA), Vol. 2, Issue 3, May-Jun 2012 , pp.1786-1793.

2) Anushman.S and Dipendu Bhunia, “Solution of Shear Wall location in Multi-storey building”,

International journal of Civil and Structural Engineering (IJCSE), Volume 2, No 2, 2011

3) P.S.Kumbhare and A.C.Saoji, “Effectiveness of Changing Reinforced Concrete Shear Wall

Location on Multi-storeyed Building”, International Journal of Engineering Research and

Applications (IJERA) Vol. 2, Issue 5, September- October 2012, pp.1072-1076

4) Chandurkar, Dr.P.S.Pajgade, “Seismic analysis of RCC Building with and without Shear Wall”,

P. P. International Journal of Modern Engineering Research (IJMER) Vol. 3, Issue. 3, May -

June 2013 pp-1805-1810

5) A.Kadid and A.Boumrkik, “Pushover Analysis of Reinforced Concrete Frame Structures”,

Asian Journal of Civil Engineering (Building and Housing) Vol. 9, Issue. 1 (2008) Pages 75-83.

6) Shahabodin and Zaregarizi, “Comparative investigation of using Shear wall and infill to

improve Seismic Performance of existing Buildings”, The 14th

World conference on Earthquake

Engineering October 12-17, 2008, Beijing, China.

7) Mahomet Intel, Hairy Bay tan Omen, “Effects of plastic hinge properties in nonlinear analysis

of reinforced concrete buildings”, Engineering Structures 28 (2006) pp. 1494–1502

(www.Science Direct.com).

8) Hasan Kaplan, Salih Yilmaz & Ergin Atimtay ,“Seismic strengthening of RC structures with

exterior shear walls”, Indian Academy of Sciences, Vol. 36, Part 1, February 2011, pp. 17–34.

9) A.Shuraim and A.Charif “Performance of Pushover Procedure in Evaluating the Seismic

Adequacy of Reinforced Concrete Frames” (King Saud University 2007).

10) Sigmund A. Freeman “Review of The Development of The Capacity Spectrum Method” ISET

Journal of Earthquake Technology, Paper No. 438, Vol. 41, No. 1, March 2004, pp. 1-13.

11) Peter Fajfar, “Capacity Spectrum Method Based on Inelastic demand Spectra”, Earthquake

Engineering and Structural Dynamics 28, 979-993 (1999).

12) A.S.Elnashai, “Advanced inelastic static (pushover) analysis for earthquake applications”,

Structural Engineering and Mechanics, Vol. 12, No. 1, (2001), pp. 51-69.

13) “Effect of Internal and External Shear Wall Location on Strengthening Weak RC Frames”, Vol.

17, No. 4, pp. 312-323, Sharif University of Technology, August 2010.



14) Dr. Saraswati Setia and Vineet Sharma, “Seismic Response of R.C.C Building with Soft Storey”,

International Journal of Applied Engineering Research, Vol.7 ,No.11 (2012)

15) Y.M.Fahjan, J.Kubin & M.T.Tan, “Nonlinear Analysis Methods for Reinforced Concrete

Buildings with Shear walls”, 14 ECEE 2010.

16) Rahiman G. Khan1, Prof. M. R. Vyawahare, “Push Over Analysis of Tall Building with Soft

Stories at Different Levels ”International Journal of Engineering Research and Applications

(IJERA) ,Vol. 3, Issue 4, Jul-Aug 2013, pp.176-185.

17) Computers and Structures Inc. (CSI), 1995, ETABS: Three Dimensional Analysis of Building

Systems, Berkeley, California.

18) Rahiman G. Khan1, Prof. M. R. Vyawahare, “Push Over Analysis of Tall Building with Soft

Stories at Different Levels ”International Journal of Engineering Research and Applications

(IJERA) Vol. 3, Issue 4, Jul-Aug 2013, pp.176-185

19) “Seismic evaluation and Retrofit of concrete Buildings”, ATC-40.

20) Federal Emergency Management Agency (FEMA), 1997, NEHRP Guidelines for the Seismic

Rehabilitation of Buildings, FEMA-273.

21) FEMA-440,Federal Emergency Management Agency ,Improvement of Non-Linear Static

Seismic Analysis Procedure (2004-2005), Applied Technology Council (ATC-55 Project) 201

Redwood Shores Parkway, Suite 240, Redwood city, California, Federal Emergency

Management Agency Washington D.C.

22) Muhammed Tekin, Ali Gürbüz, and Ali Demir,” Comparison of Nonlinear Static And Dynamic

Analyses on a R/C Building” Mathematical and Computational Applications, Vol. 18, No. 3, pp.

264-272, 2013

23) IS 1893(Part1): 2002.”Criteria for Earthquake Resistant Design of Structures”, Bureau of

Indian Standards, New Delhi, 2002.

24) IS 456 - 2000 “Code of practice for plain and reinforced concrete”.Bureau of Indian standards,

New Delhi.

25) IS 875 Part 1 “Code of practice for Unit weight of material”.

26) IS 875 Part 2 “Code of practice for Live loads”

27) Sermin Oguz. A thesis on “Evaluation of Pushover Analysis Procedures for Frame Structures,

April, 2005.

28) Science Direct.com

29) Wikepedia.com


THE OXFORD COLLEGE OF ENGINEERING, Dept. of Civil Engg.

APPENDIX



PUSHOVER ANALYSIS (NON LINEAR STATIC ANALYSIS)

OVERVIEW

Pushover Analysis option will allow engineers to perform pushover analysis as per

FEMA -356 and ATC-40. Pushover analysis is a static, nonlinear procedure using simplified

nonlinear technique to estimate seismic structural deformations. It is an incremental static

analysis used to determine the force-displacement relationship, or the capacity curve, for a

structure or structural element. The analysis involves applying horizontal loads, in a

prescribed pattern, to the structure incrementally, i.e. pushing the structure and plotting the

total applied shear force and associated lateral displacement at each increment, until the

structure or collapse condition. (Sermin, 2005).

BACKGROUND

Nonlinear static analysis, or pushover analysis, has been developed over the past

twenty years and has become the preferred analysis procedure for design and seismic

performance evaluation purposes as the procedure is relatively simple and considers post-

elastic behaviour. However, the procedure involves certain approximations and

simplifications that some amount of variation is always expected to exist in seismic demand

prediction of pushover analysis. But certain limitations are associated with traditional

pushover analysis.

Improved pushover procedures have been proposed to overcome the certain limitations of

traditional pushover procedures. However, the improved procedures are mostly

computationally demanding and conceptually complex that use of such procedures is

impractical in engineering profession and codes. As traditional pushover analysis is widely

used for design and seismic performance evaluation purposes.

A predefined lateral load pattern which is distributed along the building height is then

applied. The lateral forces are increased until some members yield. The structural model is

modified to account for the reduced stiffness of yielded members and lateral forces are again

increased until additional members yield. The process is continued until a control

displacement at the top of building reaches a certain level of deformation or structure



becomes unstable. The roof displacement is plotted with base shear to get the global capacity

curve.

The purpose of pushover analysis is to evaluate the expected performance of

structural systems by estimating performance of a structural system by estimating its strength

and deformation demands in design earthquakes by means of static inelastic analysis, and

comparing these demands to available capacities at the performance levels of interest. The

evaluation is based on an assessment of important performance parameters, including global

drift, Interstorey drift, and inelastic element deformations

Pushover analysis can be performed as force-controlled or displacement-controlled. In

force-controlled pushover procedure, full load combination is applied as specified, i.e., force-

controlled procedure should be used when the load is known (such as gravity loading). Also,

in force-controlled pushover procedure some numerical problems that affect the accuracy of

results occur since target displacement may be associated with a very small positive or even a

negative lateral stiffness because of the development of mechanisms.

Pushover analysis has been the preferred method for seismic performance evaluation

of structures by the major rehabilitation guidelines and codes because it is conceptually and

computationally simple. Pushover analysis allows tracing the sequence of yielding and failure

on member and structural level as well as the progress of overall capacity curve of the

structure (Girgin, 2007).The nonlinear static procedure or pushover analysis is increasingly

used to establish the estimations of seismic demands for building structures. Since structures

exhibit nonlinear behaviour during earthquakes, using the nonlinear analysis is inevitable to

observe whether the structure is meeting the desirable performance or not.

Pushover analysis is a technique by which a computer model of the building is

subjected to a lateral load of a certain shape (i.e., inverted triangular or uniform). The

intensity of the lateral load is slowly increased and the sequence of cracks, yielding, plastic

hinge formation, and failure of various structural components is recorded. Pushover analysis

can provide a significant insight into the weak links in seismic performance of a structure. A

series of iterations are usually required during which, the structural deficiencies observed in

one iteration, are rectified and followed by another. This iterative analysis and design process

continues until the design satisfies pre-established performance criteria. The performance



criteria for pushover analysis are generally established as the desired state of the building

given roof-top or spectral displacement amplitude.

Pushover analysis is a performance based analysis. According to ATC 40, there are

two key elements of a performance-based design procedure - demand and capacity. Demand

is the representation of earthquake ground motion or shaking that the building is subjected to.

In nonlinear static analysis procedures, demand is represented by an estimation of the

displacements or deformations that the structure is expected to undergo. Capacity is a

representation of the structure‟s ability to resist the seismic demand. The performance is

dependent on the manner that the capacity is able to handle the demand. In other words, the

structure must have the capacity to resist demands of the earthquake such that the

performance of the structure is compatible with the objectives of the design.

PURPOSE OF DOING PUSHOVER ANALYSIS

The pushover is expected to provide information on many response characteristics

that cannot be obtained from an elastic static or dynamic analysis. The purpose of pushover

analysis is to evaluate the expected performance of structural systems by estimating

performance of a structural system by estimating its strength and deformation demands in

design earthquakes by means of static inelastic analysis, and comparing these demands to

available capacities at the performance levels of interest.

The evaluation is based on an assessment of important performance parameters,

including global drift, Interstorey drift, inelastic element deformations (either absolute or

normalized with respect to a yield value), deformations between elements, and element

connection forces (for elements and connections that cannot sustain inelastic deformations

The following are the examples of such response characteristics:

Consequences of the strength deterioration of individual elements on behaviour of the

structural system.

Identification of the critical regions in which the deformation demands are expected to

be high and that have to become the focus through detailing.

Estimates of the inter-Storey drifts that account for strength or stiffness discontinuities

and that may be used to control the damages.

Consequences of the strength detoriation of the individual elements on the behaviour



of the structural system.

Identification of the critical regions in which the deformation demands are expected to

be high and that have to become the focus through detailing.

3.6 BUILDING PERFORMANCE LEVELS AND RANGES (ATC, 1997a)

The ATC-40 and FEMA-273 documents have developed modelling procedures, acceptance

criteria and analysis procedures for pushover analysis. These documents define force-

deformation criteria for hinges used in pushover analysis. Seismic performance of a structure

is described by designating the maximum allowable damage state for an identified seismic

hazard. ATC-40 describes standard performance levels for structural and non-structural

systems and several commonly used combinations of structural and non-structural levels as

(a) Operational, (b) Immediate occupancy, (c) Damage control, (d) Life safety, (e) Structural

stability and (f) Not considered.

The performance level of a building is determined based up on its function and importance.

Structures like hospital buildings, telecommunication centres, transportation facilities etc. are

expected to have a performance level of operational or immediate occupancy for an identified

seismic hazard that can occur for the structure. Meanwhile a residential building must have a

performance level of damage control or life safety.

Temporary structures or unimportant buildings or structures came under the performance

level of structural stability or sometimes are not considered. The force deformation

relationship as well as the performance levels of a structure as well as a structural element is

given in fig 1.

Fig.1. Force-Deformation relationship of a typical plastic hinge (FEMA 356)



3.6.1 PERFORMANCE LEVEL: the intended post-earthquake condition of a building; a

well-defined point on a scale measuring how much loss is caused by earthquake damage. In

addition to casualties, loss may be in terms of property and operational capability.

3.6.2 PERFORMANCE RANGE: a range or band of performance, rather than a discrete

level.

DESIGNATIONS OF PERFORMANCE LEVELS AND RANGES: Performance is

separated into descriptions of damage of structural and non-structural systems; structural

designations are S-1 through S-5 and non-structural designations are N-A through N-D.

BUILDING PERFORMANCE LEVEL

The combination of a Structural Performance Level and a Non-structural Performance Level

to form a complete description of an overall damage level.

Fig. 2: Building Performance Level (ATC, 1997a)



Methods and design criteria to achieve several different levels and ranges of seismic

performance are defined. The four Building Performance Levels are Collapse Prevention,

Life Safety, Immediate Occupancy, and Operational. These levels are discrete points on a

continuous scale describing the building‟s expected performance, or alternatively, how much

damage, economic loss, and disruption may occur.

Each Building Performance Level is made up of a Structural Performance Level that

describes the limiting damage state of the structural systems and a Non-structural

Performance Level that describes the limiting damage state of the non-structural systems.

Three Structural Performance Levels and four Non-structural Performance Levels are used to

form the four basic Building Performance Levels listed above. Other structural and non-

structural categories are included to describe a wide range of seismic rehabilitation intentions.

The three Structural Performance Levels and two Structural Performance Ranges consist of:

S-1: Immediate Occupancy Performance Level

S-2: Damage Control Performance Range (extends between Life Safety and

Immediate Occupancy Performance Levels)

S-3: Life Safety Performance Level

S-4: Limited Safety Performance Range (extends between Life Safety and Collapse

Prevention Performance Levels)

S-5: Collapse Prevention Performance Level

In addition, there is the designation of S-6, Structural Performance Not Considered, to cover

the situation where only non-structural improvements are made.

The four Non-structural Performance Levels are:

N-A: Operational Performance Level

N-B: Immediate Occupancy Performance Level

N-C: Life Safety Performance Level

N-D: Hazards Reduced Performance Level

Building performance is a combination of the performance of both structural and non-

structural components. Independent performance definitions are provided for structural and



non-structural components. Structural performance levels are identified by both a name and

numerical designator. Non-structural performance levels are identified by a name and

alphabetical designator

STRUCTURAL PERFORMANCE LEVELS (ATC, 1997a)

IMMEDIATE OCCUPANCY PERFORMANCE LEVEL (S-1)

Structural Performance Level S-1, Immediate Occupancy, means the post-earthquake

damage state in which only very limited structural damage has occurred. The basic vertical

and lateral-force-resisting systems of the building retain nearly all of their pre-earthquake

strength and stiffness. The risk of life threatening injury as a result of structural damage is

very low, and although some minor structural repairs may be appropriate, these would

generally not be required prior to re-occupancy.

DAMAGE CONTROL PERFORMANCE RANGE (S-2)

Structural Performance Range S-2, Damage Control, means the continuous range of

damage states that entail less damage than that defined for the Life Safety level, but more

than that defined for the Immediate Occupancy level. Design for Damage Control

performance may be desirable to minimize repair time and operation interruption; as a partial

means of protecting valuable equipment and contents; or to preserve important historic

features when the cost of design for Immediate Occupancy is excessive.

Acceptance criteria for this range may be obtained by interpolating between the

values provided for the Immediate Occupancy (S-1) and Life Safety (S-3) levels.

LIFE SAFETY PERFORMANCE LEVEL (S-3)

Structural Performance Level S-3, Life Safety, means the post-earthquake damage

state in which significant damage to the structure has occurred, but some margin against

either partial or total structural collapse remains. Some structural elements and components

are severely damaged, but this has not resulted in large falling debris hazards, either within or

outside the building. Injuries may occur during the earthquake; however, it is expected that

the overall risk of life-threatening injury as a result of structural damage is low. It should be

possible to repair the structure; however, for economic reasons this may not be practical.



LIMITED SAFETY PERFORMANCE RANGE (S-4)

Structural Performance Range S-4, Limited Safety, means the continuous range of

damage states between the Life Safety and Collapse Prevention levels. Design parameters for

this range may be obtained by interpolating between the values provided for the Life Safety

(S-3) and Collapse Prevention (S-5) levels.

COLLAPSE PREVENTION PERFORMANCE LEVEL (S-5)

Structural Performance Level S-5, Collapse Prevention, means the building is on the

verge of experiencing partial or total collapse. Substantial damage to the structure has

occurred, potentially including significant degradation in the stiffness and strength of the

lateral force resisting system, large permanent lateral deformation of the structure and to

more limited extent degradation in vertical-load-carrying capacity.

However, all significant components of the gravity load resisting system must

continue to carry their gravity load demands. Significant risk of injury due to falling hazards

from structural debris may exist. The structure may not be technically practical to repair and

is not safe for reoccupancy, as aftershock activity could induce collapse.

NONSTRUCTURAL PERFORMANCE LEVELS (ATC, 1997a)

OPERATIONAL PERFORMANCE LEVEL (N-A)

Non-structural Performance Level A, Operational, means the post-earthquake damage

state of the building in which the non-structural components are able to support the building‟s

intended function. At this level, most non-structural systems required for normal use of the

building including lighting, plumbing, etc. are functional, although minor repair of some

items may be required. This performance level requires considerations beyond those that are

normally within the sole province of the structural engineer.

IMMEDIATE OCCUPANCY LEVEL (N-B)

Non-structural Performance Level B, Immediate Occupancy, means the post-

earthquake damage state in which only limited non-structural damage has occurred. Basic

access and life safety systems, including doors, stairways, elevators, emergency lighting, fire

alarms, and suppression systems.

Presuming that the building is structurally safe, it is expected that occupants could



safely remain in the building, although normal use may be impaired and some clean up may

be required. In general, components of mechanical and electrical systems in the building are

structurally secured and should be able to function if necessary utility service is available.

However, some components may experience misalignments or internal damage and be non-

operable. Power, water, natural gas, communications lines, and other utilities required for

normal building use may not be available. The risk of life-threatening injury due to non-

structural damage is very low.

LIFE SAFETY LEVEL (N-C)

Non-structural Performance Level C, Life Safety, is the post-earthquake damage state

in which potentially significant and costly damage has occurred to non-structural components

but they have not become dislodged and fallen, threatening life safety either within or outside

the building. Egress routes within the building are not extensively blocked. While injuries

may occur during the earthquake from the failure of non-structural components, it is expected

that, overall, the risk of life-threatening injury is very low. Restoration of the non-structural

components may take extensive effort.

HAZARDS REDUCED LEVEL (N-D)

Non-structural Performance Level D, Hazards Reduced, represents a post-earthquake

damage state level in which extensive damage has occurred to non-structural components, but

large or heavy items that pose a falling hazard to a number of people such as parapets,

cladding panels, heavy plaster ceilings, or storage racks are prevented from falling. While

isolated serious injury could occur from falling debris, failures that could injure large

numbers of persons either inside or outside the structure should be avoided. Exits, fire

suppression systems, and similar life-safety issues are not addressed in this performance

level.

PLASTIC ANALYSIS

An elastic analysis does not give information about the loads that will actually collapse a

structure. An indeterminate structure may sustain loads greater than the load that first causes

a yield to occur at any point in the structure. In fact, a structure will stand as long as it is able

to find redundancies to yield. It is only when a structure has exhausted all of its redundancies

will extra load causes it to fail. Plastic analysis is the method through which the actual failure



load of a structure is calculated, and as will be seen, this failure load can be significantly

greater than the elastic load capacity.

PLASTIC HINGE MECHANISM

Plastic hinge is used to describe the deformation of a section of a beam where plastic

bending occurs. Formation of a plastic hinge at the face of the column results in yielding of

beam reinforcing bars at the face of the column and in the beam-column joint, as well.

Yielding of the reinforcing bars in the joint core results in bond deterioration between the

reinforcing bars and the surrounding concrete. This causes the deterioration of the stiffness

and strength of the joints.

In plastic limit analysis of structural members subjected to bending, it is assumed that

an abrupt transition from elastic to ideally plastic behaviour occurs at a certain value of

moment, known as plastic moment (Mp).Note that once the plastic moment capacity is

reached, the section can rotate freely – that is, it behaves like a hinge, except with moment of

at the hinge. This is termed a plastic hinge, and is the basis for plastic analysis. At the plastic

hinge stresses remain constant, but strains and hence rotations can increase. Plastic hinges

occur in the sections that have bending moments that exceed the nominal bending moment

associated with yielding of the section.

Fig. 3: Plastic Hinge Formation

Plastic hinge formation mechanisms have been obtained at the displacement points

corresponding to global yielding and ultimate displacements. The global yielding point

corresponds to the displacement on the capacity curve where the system starts to soften.

Whenever plastic hinge forms in the structure, equilibrium is obtained. As the result the

degree of static indeterminacy reduces by one with the formation of one plastic hinge.



CAPACITY SPECTRUM

INTRODUCTION TOCAPACITY SPECTRUM

The CSM was first introduced in the 1970s as a rapid evaluation procedure in a pilot project

for assessing seismic vulnerability of buildings at the Puget Sound Naval Shipyard (Freeman

et al., 1975). In the 1980s, it was used as a procedure to find a correlation between earthquake

ground motion and building performance (ATC, 1982). The method was also developed into

a design verification procedure for the Tri-services (Army, Navy, and Air Force) “Seismic

Design Guidelines for Essential Buildings” manual (Freeman et al., 1984; Army, 1986). The

procedure compares the capacity of the structure (in the form of a pushover curve) with the

demands on the structure (in the form of a response spectrum). The graphical intersection of

the two curves approximates the response of the structure. In order to account for non-linear

inelastic behaviour of the structural system, effective viscous damping values are applied to

the linear-elastic response spectrum similar to an inelastic response spectrum

CAPACITY SPECTRUM METHOD (CSM)

Capacity Spectrum Method is extensively employed compared to other Non Linear Static

Procedures due to its visual and graphical nature, and its ability to provide rapid assessment

of the relationship between supply and demand. Capacity Spectrum Method is used to

determine the displacement demand imposed on a structure which is expected to deform

beyond its elastic range. The Capacity Spectrum Method (CSM), a performance-based

seismic analysis technique, can be used for a variety of purposes such as rapid evaluation of a

large inventory of buildings, design verification for new construction of individual buildings,

evaluation of an existing structure to identify damage states, and correlation of damage states

of buildings to various amplitudes of ground motion. The procedure compares the capacity of

the structure (in the form of a pushover curve) with the demands on the structure (in the form

of response spectra). The graphical intersection of the two curves approximates the response

of the structure. In order to account for non-linear inelastic behaviour of the structural system,

effective viscous damping values are applied to linear-elastic response spectra similar to

inelastic response spectra.

By converting the base shears and roof displacements from a non-linear pushover to

equivalent spectral accelerations and displacements and superimposing an earthquake



demand curve, the non-linear pushover becomes a capacity spectrum. The earthquake

demand curve is represented by response spectra, plotted with different levels of “effective”

or “surrogate” viscous damping (e.g. 5%, 10%, 15%, 20% and sometimes 30% to

approximate the reduction in structural response due to the increasing levels of damage).

Capacity spectrum method as a tool for estimating and visualizing the likely behaviour of the

structure under a given earthquake in a simple graphical manner. By formatting the results in

the acceleration-displacement response-spectrum format (Mahaney, 1993) in lieu of the

traditional spectral acceleration (Sa) versus period (T) format, the graphical and intuitive

nature of the capacity spectrum method become even more apparent.

The Acceleration} Displacement Response Spectrum (ADRS) format is used, in which

spectral accelerations are plotted against spectral displacements, with the periods „T‟

represented by radial lines. The intersection of the capacity spectrum and the demand

spectrum provides an estimate of the inelastic acceleration (strength) and displacement

demand.

Fig.4: Capacity spectrum

By means of a graphical procedure, the capacity spectrum method compares the capacity of a

structure with the demands of earthquake ground motion on it. The graphical presentation

makes possible a visual evaluation of how the structure will perform when subjected to

earthquake ground motion. The method is easy to understand. The capacity of the structure is

represented by a force-displacement curve, obtained by non-linear static (pushover) analysis.

The base shear forces and roof displacements are converted to the spectral accelerations and



spectral displacements of an equivalent Single-Degree-Of-Freedom (SDOF) system,

respectively. These spectral values define the capacity spectrum.

CONVERSION TO ADRS SPECTRA

Application of the capacity spectrum technique requires both the demand response spectra

and structural capacity (or Pushover) curve can be plotted in the spectral acceleration vs.

spectral displacement domain. Spectra plotted in the format are known as Acceleration –

Displacement Response Spectra (ADRS) after Mahoney, 1993.

Every point on a response spectrum has associated with it a unique Spectral acceleration Sa,

Spectral velocity Sv, Spectral displacement Sd and Period T. Convert the design spectrum

from the standard pseudo acceleration, (Sa/g), versus natural period Tn, format to ADRS

(Acceleration Demand Response Spectrum) curve.

( )

Fig. Standard Spectrum Fig. ADRS Spectrum

(Sa vs. T) (Sa vs. Sd)

Figure 5. Response spectra in Traditional and ADRS Formats

Develop the capacity spectrum from the capacity (or pushover) curve, Convert the pushover

curve to a capacity diagram. This is for performance evaluation of building. Base shear is

calculated using seismic coefficient in equivalent static analysis. Any point (V-Δ roof) on the

capacity curve is converted to the corresponding points Sa vs. Sd on the capacity spectrum

using the equations



V = Ah*W…………………………………………………………….……………………….......... (i)

………………………………………………………………….… (ii)

…………………………………………….. (iii)

Where

α = modal mass coefficient

PF = modal participation factors for the first natural mode of the structure

Φ roof = roof level amplitude of the first mode.

α = modal mass coefficient for the first natural mode

V = base shear



W = building dead weight plus likely live load

S a = spectral acceleration

S d = spectral displacement

Once the capacity curve and demand displacements are defined a performance check can be

done. Performance check verifies that structural and non-structural components are not

damaged beyond acceptable limits of performance objective.

REQUIRED COMPONENTS OF THE CSM

The two essential components of CSM are the capacity and demand diagrams. Capacity

diagrams are obtained through conversion from the widely used pushover curves which are

characteristic nonlinear lateral force-displacement relationships for structures. So as to

perform CSM, capacity and demand curves are needed to be represented in Acceleration-

Displacement (AD) format, also called Acceleration-Displacement-Response Spectrum

(ADRS)

As opposed to a traditional spectrum, in AD format the horizontal axis shows spectral

displacement whereas the period is represented by radial lines drawn from the origin to any

point on the demand or capacity diagrams. Idealization of capacity diagrams is required for

structural assessment using CSM, this is achieved with bilinear representations. The equal

energy rule, i.e. same area under the actual curve and its bilinear representation, is used here

and elastic stiffness is taken as the initial tangent stiffness of the original capacity diagram.

Fig.6: Bilinear representation of capacity diagram using equal energy principle.



DEMAND SPECTRUM AND PERFORMANCE POINT

The spectral acceleration and spectral displacement, as calculated from the linear elastic

response spectrum for a certain damping (initial value 5%), is plotted in the Acceleration

Displacement Response Spectrum (ADRS) format. With increasing on-linear deformation of

the components, the equivalent damping and the natural period increase. The spectral

acceleration and displacement values can be modified from the 5% damping curve by

multiplying a factor corresponding to the effective damping (refer Table 3, IS 1893:2002).

Thus, the instantaneous spectral acceleration and displacement point (demand point) shifts to

a different response spectrum for higher damping.

The locus of the demand points in the ADRS plot is referred to as the demand spectrum. The

demand spectrum corresponds to the inelastic deformation of the building.

The „performance point‟ is the point where the capacity curve crosses the demand curves. If

the performance point exists and the damage state at this point is acceptable, the building

satisfies the target performance level. The output from the analysis contains the pushover

curve, the demand and capacity spectra curves.

Performance point



SHEAR WALL

Shear wall is one of the most commonly used lateral load resisting in high rise building.

Shear wall has high in plane stiffness and strength which can be used to simultaneously resist

large horizontal load and support gravity load. To resist lateral force due to wind and

earthquakes R.C shear walls are used in building. They are normally provided between

column lines, in stair wells, lift wells, in shafts that house other utilities. Shear wall provide

lateral load resisting by transferring the wind or earthquake load to foundation. Besides, they

impart lateral stiffness to the system and also carry gravity loads.

They are commonly used in tall building to avoid collapse of buildings. Shear wall may

become inevitable from the point of view of economy and control of lateral deflection. When

shear wall are situated in advantageous positions in the building they can form an efficient

lateral force resisting system. Many building codes instruct the use of such walls to make

homes safer and more stable

.

Fig.7: Reinforced concrete shear walls in buildings

In addition to the weight of structure and occupants, create powerful twisting (torsional)

forces. These forces can literally tear (shear) a building apart. Reinforcing a frame by



attaching or placing a rigid wall inside it maintains the shape of the frame and prevents

rotation at the joints.

FUNCTIONS OF A SHEAR WALL

Shear walls must provide the adequate lateral strength to withstand horizontal

earthquake forces. When shear walls are strong enough, they will transfer these horizontal

forces to the next element in the load path below them. These other components in the load

path may be other shear walls, floors, foundation walls, slabs or footings

Shear walls also provide adequate lateral stiffness to prevent the roof or floor from excessive

side-sway. When shear walls are stiff enough, Shear wall will prevent floor and roof framing

members from moving off their supports. Also, buildings that are sufficiently stiff will

usually suffer less non-structural damage.

PURPOSE OF CONSTRUCTING SHEAR WALLS

Shear walls are not only designed to resist gravity / vertical loads (due to its self-

weight and other living / moving loads), but they are also used to provide firmness to the

structure. The walls are structurally incorporated with diaphragms and other lateral walls

running across at right angles, thereby giving the three dimensional stability for the building

structures.



Walls have to resist the uplift forces caused by the pull of the wind. Walls have to resist the

shear forces that endeavour to push the walls over. Walls have to resist the lateral force of the

wind that endeavours to push the walls in and pull them away from the building.

FORCES ON SHEAR WALL

Shear walls resist two types of forces: shear forces and uplift forces. Shear forces are

engendered in stationary buildings by expeditions resulting from ground movement and by

external forces like wind and waves. This action generates shear forces throughout the height

of the wall between the top and bottom shear wall connections.

Uplift forces exist on shear walls because the horizontal forces are applied to the top of the

wall. These uplift forces try to pull up one end of the wall and push the other end down. In

some cases, the uplift force is immensely large enough to tip the wall over. Uplift forces are

greater on tall short walls and less on low long walls. Bearing walls have less uplift than non-

bearing walls because gravity loads on shear walls avail them resist uplift. Shear walls need

hold down at each end when the gravity loads cannot resist all of the uplift. The hold down

contrivance then provides the essential uplift resistance.

Shear walls should be located on each level of the structure including the crawl space. To

compose an efficient box structure, equal length shear walls should be placed symmetrically

on all four exterior walls of the building. Shear walls should be integrated to the building

interior when the exterior walls cannot provide sufficient vigour and stiffness.

ADVANTAGES OF SHEAR WALLS IN BUILDINGS

Properly designed and detailed buildings with shear walls have shown very good

performance in past earthquakes. Shear walls in high seismic regions require special

detailing. However, in past earthquakes, even buildings with sufficient amount of walls that

were not specially detailed for seismic performance (but had enough well-distributed

reinforcement) were saved from collapse.



Shear wall buildings are a popular choice in many earthquake prone countries, like Chile,

New Zealand and USA. Shear walls are easy to construct, because reinforcement detailing of

walls is relatively straight forward and therefore easily implemented at site. Shear walls are

efficient, both interims of construction cost and effectiveness in minimizing earthquake

damage in structural and non-structural elements like glass windows and building contents.

Thus shear walls are one of the most effective building elements in resisting lateral forces

during earthquake. By constructing shear walls damages due to effect of lateral forces due to

earthquake and high winds can be minimized. Shear walls construction will provide larger

stiffness to the buildings there by reducing the damage to structure and its contents.

OVERALL GEOMETRY OF SHEAR WALLS

Shear walls are oblong in cross-section, i.e., one dimension of the cross-section is much

larger than the other. While rectangular cross-section is common, L- and U-shaped sections

are also used .Thin-walled hollow RC shafts around the elevator core of buildings also act as

shear walls, and should be taken advantage of to resist earthquake forces. However, some

combinations of planar walls are also used in the structural systems. Typical non-planar shear

wall sections used in the building structures are given in Figure

Fig.7: Typical non-planar shear wall sections



COMPARISONS OF SHEAR WALL WITH CONSTRUCTION OF

CONVENTIONAL LOAD BEARING WALLS

Load bearing masonry is very brittle material. Due to different kinds of stresses such as shear,

tension, torsion, etc., caused by the earthquakes, the conventional unreinforced brick masonry

collapses instantly during the capricious and sudden earthquakes.

On the other hand even moderately designed shear wall structures not only more stable, but

withal comparatively quite ductile. In safety terms it signifies that, during very rigorous

earthquakes they will not suddenly collapse causing death of people. They give enough

indicative warnings such as widening structural cracks, yielding in structures, before they

totally collapse.

For structural purposes we consider the exterior walls as the shear-resisting walls. Forces

from the ceiling and roof diaphragms make their way to the outside along presumed paths,

enter the walls, and exit at the foundation.



PROCEDURE OF PUSHOVER ANALYSIS IN ETABS

The following general sequence of steps is involved in performing a static nonlinear

analysis:

Create a model just like you would for any other analysis. Note that material

nonlinearity is restricted to frame and link elements, although other element types

may be present in the model.

Define the static load cases, if any, that are needed for use in the static nonlinear

analysis (Define > Static Load Cases command). Define any other static and dynamic

analysis cases that may be needed for steel or concrete design of frame elements.

Define hinge properties, if any (Define > Frame Nonlinear Hinge Properties

command).

Assign hinge properties, if any, to frame/line elements (Assign > Frame/Line > Frame

Nonlinear Hinges command).

Run the basic linear and dynamic analyses (Analyse> Run command).

Define the static nonlinear load cases (Define > Static Nonlinear/Pushover Cases

command).

Run the static nonlinear analysis (Analyse> Run Static Nonlinear Analysis

command).

Review the static nonlinear results (Display > Show Static Pushover Curve

command), (Display > Show Deformed Shape command), (Display > Show Member

Forces/Stress Diagram command), and (File > Print Tables > Analysis Output

command).

Perform any design checks that utilize static nonlinear cases.

Revise the model as necessary and repeat.

optimum location of shear wall in tall buildings

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