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## Contents

**ACKNOWLEDGEMENT**

**BSTRACT**

**CONTENTS**

**LIST OF TABLES**

**LIST OF FIGURES**

**NOTATIONS**

**CHAPTER-1 INTRODUCTION**

1.1 General

1.2 Strengthening of RCC building with shear wall

1.3 Methods of seismic analysis of structures

1.4 Objectives

**CHAPTER-2 THEORY AND REVIEW OF LITERATURE**

2.1 Necessity of dynamic analyses

2.1.1 Response spectra

2.1.2 Structures with more than a single mass

2.1.3 Modal analyses

2.1.4 Modal analysis using response spectra

2.1.5 Combination of modal maxima

2.2 Response spectrum modal analysis of building using IS 1893 (part 1)-2002

2.3 Review of literature

CHAPTER- 3 MODELLING AND METHODOLOGY

3.1 Details of the models

3.2 Details of the cases studied

CHAPTER- 4 RESULTS AND DISCUSSIONS

4.1 Effect of shear wall location on G+13 storey building with different position of shear wall

4.2 Effect of storey height on shear wall for G+13 and G+6 storied buildings

**CHAPTER- 5 CONCLUSIONS AND SCOPE FOR FURTHER STUDY**

5.1 conclusions drawn from the present study

5.2 Scope for further study

**REFERENCES**

## Acknowledgement

I would like to thank my thesis supervisor, **Dr. G.V. Rama Rao**, for giving me the opportunity to carry out the research work that has resulted in this thesis.

I also wish to express my special thanks to **Dr. K. Srinivasa Rao**, Professor, Department of Civil Engineering, Andhra University College of engineering, for giving me valuable insight and discussion while working on this thesis. I thank all the staff members of structures division for all their help, support and encouragement during the course of work.

I sincerely thank **Prof D.S.R Murty** Head, Department of Civil Engineering, Andhra University College of Engineering, for all his help rendered to me during the course work. I also thank **Prof. G.V.R Srinivasa Rao** (Chairman, Board of studies) for the aid provided during the progress of the report.

A thesis of this nature cannot be prepared without the tremendous background information made available by various research workers, authors of excellent books and technical articles which have been referred to and listed at the end of the thesis. I am thankful to them. My special thanks to my student, K. Suresh for his help in using the ETABS software.

I also express my thanks to my classmates, friends, colleagues and my juniors for their help and encouragement.

Last but definitely not least, I would like to thank my parents, my husband and my children for their immense and endless support and love. I would like to thank the almighty for his strength and courage.

*I.Siva Parvathi*

## ABSTRACT

Right from the evolution of the earth, earthquakes have been a cause of great disasters in the form of destruction of property, injury and loss of life to the population. The effective design and construction of earthquake resistant structures has much greater importance in this country due to the rapid industrial development and concentration of population in cities. Recently there has been a considerable increase in the construction of tall buildings both residential and commercial and the modern trend is towards more tall and slender structures. Thus the effect of lateral loads like wind loads, earthquake loads and blast forces are attaining increasing importance and almost every designer is facing the problems of providing adequate strength and stability against lateral loads. This is the new development as the earlier building designers designed the buildings for vertical loads and as an afterthought checked the final design for lateral loads as well. Now the situation is quiet different and a clear understanding of effect of the lateral loads on the building and the behavior of various components under these loads is essential.

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 resist large horizontal loads and support gravity loads, making them quite advantageous in many structural engineering applications. Incorporation of shear wall has become inevitable in multistorey building to resist lateral forces. It is very necessary to determine effective, efficient and ideal location of shear wall. The present study mainly aims to determine the solution for shear wall location in multi-storey building based on response spectrum method using ETABS.

In the present work, two multi storied buildings, one of six and other of thirteen storey have been modeled for earthquake zone V in India using response spectrum method as per IS: 1893 (Part 1) -2002. Five different types of position of shear walls are considered for studying their effectiveness in resisting lateral forces. The present work also deals with the effect of the variation of the building height on the structural response of the shear wall. Lateral displacements, storey shear, storey bending moment and storey drift were computed in all the cases and location of shear wall was established based upon the above computations.

## List of Tables

Table 2.1 Seismic Zone Factor *Z* as per IS:1893 (Part 1) - 2002 of the site where the building to be designed is located

Table 2.2 Importance Factor Z of buildings as per IS:1893 (Part 1) - 2002

Table 2.3 Response Reduction Factor *R* of buildings as per IS:1893 (Part 1) - 2002

Table 2.4 Proportion of live load to be considered in the estimate of seismic weight of buildings as per IS:1893-2002

Table 3.1 Structural details of the models studied

Table 4.1 Lateral displacement (mm) in longitudinal (Ux) and transverse (Uz) direction with different position of shear wall

Table 4.2 Storey drift (mm) with different position of shear wall

Table 4.3 Storey shear and storey moment with different position of shear wall

Table 4.4 Maximum base reaction and moment with different position of shear wall

Table 4.5 Modal period and frequencies with different position of shear wall

Table 4.6 Lateral displacement, storey shear and storey moment for G+13 and G+6 storied buildings

Table 4.7 Maximum values of lateral displacement, base shear, bending moment and top storey drift for G+13 and G+6 storied buildings

Table 4.8 Modal period and frequencies for G+13 and G+6 storied buildings

## LIST OF FIGURES

Fig. 1.1 Sketch of Seismic Zone Map of India(Source: IS:1893 (Part 1) - 2002)

Fig. 2.1 Single degree of freedom model of a structure

Fig. 2.2 El Centro may 1940, north-south accelerogram

Fig. 2.3 Displacement response spectrum

Fig. 2.4 Pseudo acceleration response spectrum

Fig. 2.5 Structure subjected to ground displacement

Fig. 2.6 Mode shapes of free-vibration

Fig. 2.7 Design Acceleration Spectrum for 5% damping

Fig. 3.1 Plan of building showing location of shear wall frame

Fig. 3.2 Plan and elevation of Model 1

Fig. 3.3 Plan and elevation of Model 2

Fig. 3.4 Plan and elevation of Model 3

Fig. 3.5 Plan and elevation of Model 4

Fig. 3.6 Plan and elevation of Model 5

Fig. 3.7 Plan and elevation of Model 6

Fig: 4.1 Storey shear for models with different position of shear wall

Fig: 4.2 Storey moments for models with different position of shear wall

Fig. 4.3 Max base shear for models with different position of shear wall

Fig. 4.4 Modal period for models with different position of shear wall

Fig. 4.5 Distribution of seismic load at each storey level for model 1

Fig. 4.6 Distribution of seismic load at each storey level for model 2

Fig. 4.7 Distribution of seismic load at each storey level for model 3

Fig. 4.9 Distribution of seismic load at each storey level for model 5

Fig. 4.11 Distribution of seismic load at each storey level for G+6 storied building

Fig. 4.12 First three mode shapes for Model-1

Fig. 4.13 First three mode shapes for Model-2

Fig. 4.14 First three mode shapes for Model-3

Fig. 4.15 First three mode shapes for Model-4

Fig. 4.16 First three mode shapes for Model-5

Fig. 4.17 First three mode shapes for Model-6

Fig. 4.10 Lateral displacements for G+13 and G+6 storied buildings

## NOTATIONS

Abbildung in dieser Leseprobe nicht enthalten

## CHAPTER 1

## INTRODUCTION

### 1.1 General

Amongst the natural hazards, earthquakes have the potential for causing the greatest damages to engineered structures. Since earthquake forces are random in nature & unpredictable, the engineering tools needs to be sharpened for analyzing structures under the action of these forces. India has a number of the world's greatest earthquakes in the last century. In fact, more than fifty percent area in the country is considered prone to damaging earthquakes. The northeastern region of the country as well as the entire Himalayan belt is susceptible to great earthquakes of magnitude more than 8.0.

During the last century, 4 great earthquakes struck different parts of the country: Great Assam earthquake (1897), Kangra earthquake (1905), Bihar Nepal earthquake (1934) and Assam earthquake (1950). In recent times, damaging earthquakes experienced in our country include Bihar Nepal earthquake (1988), Uttarkashi earthquake (1991), Killari earthquake (1993), Jabalpur earthquake (1997), Chamoli earthquake (1999) and Bhuj earthquake (2001) and recently occurred West Bengal earthquake (2011). In all of these earthquakes there is huge loss of life and very large destruction of existing reinforced concrete (RC) buildings. Most recent constructions in the urban areas consist of poorly designed and constructed buildings. The older buildings, even if constructed in compliance with prevailing standards, may not comply with the more stringent specifications of the latest standards of IS 1893( Part 1):2002, IS 4326:1993 and IS 13920: 1993. The existing buildings can become seismically deficient since design code requirements are constantly upgraded due to advancement in Engineering knowledge.

Investigations of past and recent earthquake damage have illustrated that the building structures are vulnerable to severe damage and/or collapse during moderate to strong ground motion. An earthquake with a moderate magnitude is capable of causing severe damages of engineered buildings, bridges, industrial and port facilities as well as giving rise to great economic losses.

After the Bhuj earthquake (2001) considerable interest in this country has been directed towards the damaging effect of earthquakes and has increased the awareness of the threat of seismic events. Most of the mega cities in India are in seismically active zones and are designed for gravity loads only. The magnitude of the design seismic forces has been considerably enhanced in general, and the seismic zonation of some regions has also been upgraded as shown in Fig.1.1. Thus a large number of existing buildings in India needs seismic evaluation due to various above mentioned reasons. Hence evaluation growing concern.

Abbildung in dieser Leseprobe nicht enthalten

Fig. 1.1 Sketch of seismic zone map of India (Source: IS:1893 (Part 1) - 2002)

A large portion of India is susceptible to damaging levels of seismic hazards. Hence, it is necessary to take into account the seismic load for the design of high-rise structure. In tall building the lateral loads due to earthquake are a matter of concern. These lateral forces can produce critical stresses in the structure, induce undesirable stresses and vibrations in the structure cause excessive lateral sway of the structure (Duggal(2007)). Seismic design approaches are stated, as the structure should be able to ensure the minor and frequent shaking intensity without sustaining any damage, thus leaving the structure serviceable after the event. The structure withstands moderate level of earthquake ground motion without structural damage, but possibly with some structural as well as non-structural damage (Duggal (2007)).

The primary purpose of all kinds of structural systems used in the building type of structures is to transfer gravity loads effectively. The most common loads resulting from the effect of gravity are dead load, live load and snow load. Besides these vertical loads, buildings are also subjected to lateral loads caused by wind, blasting or earthquake. Lateral loads can develop high stresses, produce sway movement or cause vibration. Therefore, it is very important for the structure to have sufficient strength against vertical loads together with adequate stiffness to resist lateral forces.

### 1.2 Strengthening of RCC building with shear wall

Reinforced concrete (RC) buildings often have vertical plate-like RC walls called shear walls in addition to slabs, beams and columns. These walls generally start at foundation level and are continuous throughout the building height. Their thickness can be as low as 200mm, or as high as 400mm in high rise buildings [Ashish and Charkha(2012)]. Shear walls are usually provided along both length and width of buildings, they are like vertically oriented wide beams that carry earthquake loads downwards to the foundation. Properly designed and detailed buildings with shear walls have shown very good performance in past earthquakes [Mark Fintel (1992)]. 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 [Malik et al. (2012)]. Shear wall buildings are a popular choice in many earthquake prone countries, like Chile, New Zealand and USA [Mark Fintel (1992)]. 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 in terms of construction, cost and effectiveness in minimizing earthquake damage in structural and non-structural elements [Pande (2013) and Ashish and Charkha(2012)]. Most RC buildings with shear walls also have columns; these columns primarily carry gravity loads (i.e., those due to self-weight and contents of building). Shear walls provide large strength and stiffness to buildings in the direction of their orientation [Kumbhare **(** 2012 **)** ], which significantly reduces lateral sway of the building and thereby reduces damage to structure and its contents. Since shear walls carry large horizontal earthquake forces, the overturning effects on them are large. Thus, design of their foundations requires special attention. Shear walls should be provided along preferably both length and width. However, if they are provided along only one direction, a proper grid of beams and columns in the vertical plane (called a moment-resistant frame) must be provided along the other direction to resist strong earthquake effects[Rahul Rana, and Atila zekioglu (2004), Kumbhare **(** 2012 **)** ].

In tall buildings lateral loads are premier one which will increase rapidly with increase in height. The design takes care of the requirements of strength, rigidity and stability. The structural system designed to carry vertical load may not have the capacity to resist lateral load or even if it has, the design for lateral load will increase the structural cost substantially with increase in number of storey. To achieve economy in tall buildings special systems to resist lateral load should be adopted. Some of the systems are,

1. Moment Resistant Frames

2. Braced Frames

3. Shear Wall Structures

4. Tube Structures

5. Multi-Tube Structures.

**Moment Resistant Frames**: - This consists of linear, horizontal members (beams) in plane with linear vertical members (columns) by rigid or semi rigid joints.

**Braced Frames**: - Pure rigid frame systems are not efficient for buildings higher than about twenty storied as the deflection produced by bending of columns and girders and the buildings drift to be too large. A braced frame attempts to improve the efficiency of pure rigid frames by adding truss members such as diagonals between floor systems so that the shear is mainly absorbed by the diagonals [Zareian et al. (2008) and Quanfeng Wang et al. (2001)].

**Shear wall structures** *: -* A shear wall is a structural system providing stability against wind, earthquake and blast deriving its stiffness from inherent structural forms. The shear wall can be either planar, open sections, or closed sections around elevators and stair cores. These systems either can be constructed in steel or concrete or may either be solid or perforated. The shear walls behave as deep and slender cantilevers. Structurally these can be divided into coupled shear walls, shear wall frames, shear panel and staggered wall into two walls coupled by beams at each floor.

**Tube Structures** *: -* A tube structure may be defined as a three dimensional space frame composed of three or more frames, braced frames or shear walls joined at or near their edges to form a vertical tube like structural system capable of resisting lateral forces in any direction by cantilevering from foundation. There are different types of shear walls which areas given below:-

1. Cantilever shear walls

2. Flanged cantilever shear walls

3. Coupled shear walls

4. Shear wall with openings

5. Box system

Parameters influencing the response of shear walls:-

1. Height to Width Ratio

2. Type of Loading

3. Flexural Reinforcement

4. Shear reinforcement

5. Diagonal Reinforcement

6. Special Transverse reinforcement

7. Concrete Strength

8. Construction Joint

9. Axial Compressive stress

10. Moment to Shear Ratio.

Thus the design philosophy can be summarized with the following requirements.

- Structure must resist low intensity earthquakes without any structural damage. Thus, during small and frequent earthquakes all the structure should remain in elastic range.

- Structure should withstand an earthquake of moderate intensity with very light and repairable damage in the structural elements.

- Structure should withstand an earthquake of high intensity with a return period much longer than their design life without collapsing.

At present shear wall is a very important component in the earthquake resisting structure. So providing a shear wall in the different position and among them which position gives the best results are decided with the help of software.

### 1.3 Methods of seismic analysis of structures

Various methods of differing complexity have been developed for the seismic analysis of structures. They can be classified as follows.

1. Linear and Nonlinear Static Analysis

2. Linear and Nonlinear Dynamic Analysis.

Methods of Static Analysis

The method of static analysis used here is equivalent static method.

**Equivalent Static Analysis**

All the design against earthquake effects must consider the dynamic nature of the load. However, for simple regular structures, analysis by equivalent linear static methods is often sufficient. This is permitted in most codes of practice for regular, low- to medium-rise buildings and begins with an estimate of peak earthquake load calculated as a function of the parameters given in the code. Equivalent static analysis can therefore work well for low to medium-rise buildings without significant coupled lateral-torsional modes, in which only the first mode in each direction is of significance. Tall buildings (over, say, 75 m), where second and higher modes are important, or buildings with torsional effects, are much less suitable for the method, and require more complex methods to be used in these circumstances.

Methods of Dynamic Analysis

The methods of dynamic analysis are; Time history method and response spectrum method. **Time History Method**

Time-history analysis is a step-by-step analysis of the dynamical response of a structure to a specified loading that may vary with time. The analysis may be linear or non linear. Time history analysis is used to determine the dynamic response of a structure to arbitrary loading. **Response Spectrum Method**

The word spectrum in seismic engineering conveys the idea that the response of buildings having a broad range of periods is summarized in a single graph. For a given earthquake motion and a percentage of critical damping, a typical response spectrum gives a plot of earthquake- related responses such as acceleration, velocity, and deflection for a complete range, or spectrum of building periods. Thus, a response spectrum may be visualized as a graphical representation of the dynamic response of a series of progressively longer cantilever pendulums with increasing natural periods subjected to a common lateral seismic motion of the base.

### 1.4 Objectives

The main objectives of the present study are as follows, to conduct the dynamic analysis of reinforced concrete framed building with different position of shear wall using response spectrum method and to study the effect of the variation of the building height on the structural response of the shear wall.

## CHAPTER 2

## THEORY AND REVIEW OF LITERATURE

### 2.1 Necessity of dynamic analyses

Consider the single degree of freedom cantilever structure shown in Figure 2.1 where the mass M is supported on the top of the weightless column of length L and lateral stiffness K. If the column was prismatic with a flexural rigidity of EI, where E is Young's modulus and I is the second moment of area of the section, then the stiffness K would be 3EI/L. If a lateral force P is applied to top of the column, then the lateral deflection x at the top would be obtained by solving the equation In the majority of analysis carried out by engineers the forces are treated as static and even in situations where the forces are not actually constant with time they are considered to change sufficiently slowly that dynamic effects are not significant. If the force P acting on the structure changes at such a rate that the inertial and damping forces have a significant effect on the equation of equilibrium, then a dynamic analysis is required.

Abbildung in dieser Leseprobe nicht enthalten

Fig. 2.1 Single degree of freedom model of a structure

In a dynamic analysis where the applied force P(t) is changing with time, the unknowns are the displacement, velocity and acceleration of the mass but there is only a single equation of equilibrium, albeit a second order ordinary differential equation, Mx +Cx +K **x** = P(t) (2.2) where the dot denotes differentiation with respect to time.

In the case of an earthquake excitation, the external forces are, in fact, constant but the ground on which the structure is located is moving. If the foundation of the structure can be considered to move as a rigid body when subjected to a ground displacement Xg then the following observations may be made. The inertia force acting on the structure is proportional to the total acceleration, i.e. the sum of the acceleration of the structure and the acceleration of the ground. The elastic force in the structure is proportional to the deformation in the structure, i.e. the displacements of the mass relative to the foundation. It is the generally assumed that the damping force is also proportional to the relative velocity in the structure, i.e. the velocity of the structure mass relative to the foundation. This is expressed in the following equation.

Abbildung in dieser Leseprobe nicht enthalten

In this case the applied force P(t) is constant and represents the static force Po and the second term on the right hand side of the equation is often thought of as the equivalent earth quake force. This force is proportional to the mass of the structure and the ground acceleration. If the maximum acceleration of the ground is known the maximum equivalent lateral force can be computed and the maximum displacement of the structure can be found.

If the structure is allowed to freely vibrate with no external applied forces and no damping in a simple harmonic motion then the displacement has a sinusoidal variation with time such that

Abbildung in dieser Leseprobe nicht enthalten

Where A is the amplitude of the vibration and ro is the natural circular frequency of free-vibration whose units are radians per second. Substituting this solution into the equation of undamped motion yields,

Abbildung in dieser Leseprobe nicht enthalten

Where f is the natural frequency (Hertz) and T is the natural period (sec) of free vibration.

In the above equations of free-vibrations, the effects of damping have been ignored. In general, the observed equivalent amounts of damping in building structures appears to be small where the fraction of critical damping X is less than about 5%. This means that the difference between the undamped natural frequency ro and the damped natural frequency cod is insignificant. In the structure has damping and if the damping coefficient C is defined as

Abbildung in dieser Leseprobe nicht enthalten

Where X is the fraction of Critical Damping, then the response in a damped simple harmonic motion is x(t)=e **-Xrot** {AsinroDt+BcosroDt) (2.8)

Where the damped natural circular frequency roD is defined as

Abbildung in dieser Leseprobe nicht enthalten

If the structure is linearly elastic, the principle of superposition is valid and the solution for the response under a combination of loads can be obtained by superimposing the response obtained from each separate load. Therefore the static force solution can be added to that for the earthquake excitation. Athol J. Carr(1994) considering only the earthquake excitation response, if the ground acceleration history is known, then the equation of motion may be re-written as

Abbildung in dieser Leseprobe nicht enthalten

Substituting for C and K and dividing through by M gives

Abbildung in dieser Leseprobe nicht enthalten

The solution for this equation can be shown (Clough, 1992) to be

Abbildung in dieser Leseprobe nicht enthalten

This solution is usually obtained by a numerical integration such as the methods of Newmark (clough, 1993) etc.

An alternative approach to the solution for the structure subjected to the earth quake excitation is to use a response spectrum method where, given the natural period of free-vibration and fraction of critical damping of the structure, the maximum displacement and maximum acceleration of the structure can be determined.

Most engineers are familiar with the use of response spectrum method of carrying out the dynamic analysis of structures for design. These response spectrum methods reduce the dynamic response calculations to that of observing the maximum displacement or acceleration response of their structure to a given earth quake for which the spectrum has been determined or specified.

#### 2.1.1 Response spectra

Response spectra are derived from the response of a single degree of freedom system subjected to an earthquake ground acceleration excitation. The maximum absolute value of the displacement of the mass is obtained from

Abbildung in dieser Leseprobe nicht enthalten

Where Sd is the spectral displacement, Sv is the pseudo spectral velocity and Sa is the pseudo spectral acceleration. The pseudo spectral velocity is the maximum value of the integral term above which is an integration of accelerationwith respect to time and therefore has the units of velocity. It is not the maximum velocity of the mass, the spectral velocity, but it is related to it. The pseudo spectral acceleration, usually differs from the spectral acceleration, which is the maximum total acceleration of the structure, by only one or two percent. The period used in the calculation of the modal response is that of the structure in undamped free-vibration. These spectra are usually published for several levels of viscous damping, usually 0%, 2%, 5%,10% and 20% of critical viscous damping. Spectra in the various New Zealand design codes have been based on 5% of critical viscous damping. With the low levels of damping encountered in building structures the natural period is little affected by viscous damping.

The maximum value of the base shear V can be obtained from

Abbildung in dieser Leseprobe nicht enthalten

The maximum displacement of a structure with a give natural period of free-vibration and a given fraction of critical damping subjected to El Centro ground accelerogram shown in Figure 2.2, can be read off the displacement spectrum shown in Figure 2.3.

Abbildung in dieser Leseprobe nicht enthalten

Fig.2.2El Centro may 1940, north-south accelerogram

Abbildung in dieser Leseprobe nicht enthalten

Fig. 2.3 Displacement response spectrum

Abbildung in dieser Leseprobe nicht enthalten

The maximum acceleration of the mass of the structure subjected to the El Centro ground accelerogram can be obtained from the acceleration spectrum for the El Centro ground accelerogram

Abbildung in dieser Leseprobe nicht enthalten

The code specified response spectra are smoothed response spectra based on an earthquake with a specified probability of exceedance during the expected design life of the structure. If a different level of risk is desired, or the expected life of the structure is much different from that of normal buildings, then the spectral values may need to be adjusted accordingly.

Many building codes supply the design acceleration spectra with the units being fractions of the acceleration of gravity so that the engineer may use the weight of the structure rather than the mass of the structure in computing the base shear.

However, these response spectrum methods are applicable only to single degree of freedom structures. For a multi-degree of freedom structure, which covers nearly all real structures, the answer requires the simultaneous solution for the displacements of every degree of freedom of the structure as a time-history. This time-history may then be enveloped to obtain the maximum values of the displacements and member forces. The displacement of the structure cannot now be described as a function of a single variable and the structure does not have a single natural frequency of free-vibration and so the simple application of response spectra techniques is no longer available to the designer. This means that for these structures a different approach must be made to their dynamic analysis. The following example of a building subjected to a horizontal ground motion will illustrated some of the differences in behavior when compared with a single degree of freedom system.

#### 2.1.2 Structures with more than a single mass

For the structure shown in Figure 2.5, the ground is assumed to move initially to the right. The base of the structure has to move with the ground but upper parts of the structure have not yet followed the lower structure. It takes time for the shear forces, caused by deformation of the structure, to accelerate the masses of upper floors. The speed of propagation of the wave motion of the structure is governed by the stiffness of the stories and masses of the floors. By the time that the upper part of the structure has started to follow its base, the ground may well have started move back in the reverse direction. The deformation pattern of the structure may take on a complex form.

Abbildung in dieser Leseprobe nicht enthalten

Fig. 2.5 Structure subjected to ground displacement

The inertia forces acting on the various levels of the structure are proportional to the masses and total accelerations of the floors and are derived from Newton's laws. These accelerations are the second derivatives of the displacements with respect to time and exhibit a much greater variation with respect to time than are shown by the displacements of the structure.

The number of degrees of freedom in a structure is defined as the number of variables required to uniquely define the inertia forces or the displacements. For any real structure with distributed mass, the number of degrees of freedom is infinite. However, most computational methods reduce the number of degrees of freedom by restricting the displacements of the members, or elements, with in the structure to a limited class of functions. For example, for beam or column members in a conventional frame analysis, the lateral displacements of the beam are usually assumed to have a cubic variation along their length so that their displacements can be uniquely defined by the displacements of the joints, or nodes, at the member ends. In dynamic analyses, the number of degrees of freedom may be further reduced by lumping the mass of the structure at a selected number of joints or levels. Those degrees of freedom without mass are no longer independent variables but are dependent on the displacements of those degrees of freedom that do have mass associated with them.

In most building structures with stiff in-plane floor diaphragms the mass representation maybe reduced to two horizontal inertias, the mass of the floor acting into in two orthogonal horizontal directions, and a rotational inertia of the floor about a vertical axis , generally through the centre of mass of the floor. The latter is related to the polar moment of inertia of the floor mass about the vertical axis.

The equation of motion can now be written as

Abbildung in dieser Leseprobe nicht enthalten

Where [M], [C] and [K] are the mass, damping and stiffness matrices, {x} is the vector of displacements. The vector{r} is the influence vector for the ground displacement where each term is the displacement in the structure associated with a unit foundation movement in the direction of the earthquake excitation.

#### 2.1.3 Modal analyses

The natural frequency of free vibration associated with a single degree of freedom system vibrating in simple harmonic motion has its equivalent in multi-degree of freedom systems. At each natural frequency of free vibration the structure vibrates in simple harmonic motion where the displaced shape, or mode shape, of the structure is constant but the amplitude of the displacement is varying in a sinusoidal manner with time. A system with N degrees of freedom has N natural frequencies of free vibration and N mode shapes of free vibration {(p[, one associated with each natural frequency. This set of N mode shapes forms a basis set of displacement vectors in that any displacement shape of the structure can be made up of a combination of these linearly independent mode shapes. Luckily, most engineers are generally only concerned with a small number of these modes , i.e. those associated with the few lowest natural frequencies of free vibration.

When assuming simple harmonic motion the displacement in mode shape can be written as

Abbildung in dieser Leseprobe nicht enthalten

Where A is an, as yet, undetermined constant and the equation of undamped free-vibration becomes

Abbildung in dieser Leseprobe nicht enthalten

The mode shapes, or vectors, have the very important property in that they are orthogonal with respect to the mass and stiffness's matrices of the structure. This means that, provided one assumes that the mode shapes are also orthogonal with respect to the damping matrix of the structure, one can consider the structure vibrating in any of the modes of free vibration as a single degree of freedom system with the natural frequency, or period, of that mode. The normally coupled N degree of freedom system behaves as N single degree of freedom systems, each one associated with a natural mode of free vibration. The shape of each mode of free vibration is unique but the amplitude of the mode shape in undefined. The mode shapes are usually normalized such that the largest term in the vector is 1.0 as is shown in the top of Figure 2.6. Alternatively the sum of the squares of the terms in the vector is 1.0 or, in the case of some of the computer programs in common engineering usage the vectors are normalized so that the generalized mass M* is 1.0 i.e.

Abbildung in dieser Leseprobe nicht enthalten

It must be noted in this last case that the 1.0 has the units of mass.

If the modes shapes are assumed to be orthogonal with respect to the damping matrix as well as the mass and stiffness matrices, then damping will have no effect on the mode shapes but the natural frequency for each mode will be the damped frequency as was discussed earlier for the single mass Where Xi is the fraction of critical damping in the ith mode of free vibration.

Abbildung in dieser Leseprobe nicht enthalten

Fig. 2.6 Mode shapes of free-vibration

If the structure has symmetry in both stiffness and mass with respect to two orthogonal horizontal axes of the structure, then the mode shapes will un coupled the motion in the two horizontal two axis directions and it may be possible to speak of, say x and y direction mode shape as well as torsional modes. However, if these symmetries are not present and eccentricity of mass and /or stiffness is to be considered, then such a directional uncoupling is unlikely. This means that any translation of the structure in an axis direction will involve translation in the orthogonal direction and also rotation about the vertical axis. In design, even though the structure may appear to be symmetrical, this is not guaranteed by the materials and in the yield properties. This is one reason for code requiring designers to make provision in the design for some torsion about the vertical axis.

The uncoupling of the degrees of freedom means that one can use response spectrum methods to obtain the response of each mode in the structure and thus for each mode obtain the displacements and accelerations or forces. The difficulty, however, is that response spectrum methods have lost parts of the information relevant to the dynamic behavior of the structure. Un answered questions are, when has the peak response occurred, what sign should be associated with it and what any other mode with a different natural frequency was doing at that time the peak response occurred in the mode of interest. It is thus impossible to combine these modal responses to obtain the maximum response of the multidegree of freedom system. The problem is usually resolved by relying on a statistical combination of the modal responses.

These modal methods are only applicable to linearly elastic structure undergoing small deflection responses in that these are the requirements for the principle of superposition to be valid. If these conditions are not met, then the natural modes and frequencies of free vibration do not have a meaning because the frequency and mode shapes depend on the amplitude of the displacement and the resulting free vibration in each mode is no longer simple harmonic. Further, if the principle of superposition is no longer valid, then the combination of the modal responses to get the total structural response is also invalid.

#### 2.1.4 Modal analysis using response spectra

The response of the structure in each mode can be written as

Abbildung in dieser Leseprobe nicht enthalten

Where Yi is the amplitude of the ith mode where the displacement of the structure in the ith mode may be expressed as

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To obtain the maximum displacement of the structure in the ith mode, the procedure is very similar to that for single degree of freedom system.

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Once the displacements have been obtained from ith mode, then the inter-storey drifts, the member forces and moments can all be obtained for the ith mode.

It can be shown that the maximum base shear for the ith mode can be written as

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And if the equivalent inertia forces {f}i associated with each degree of freedom is required , then they are given by

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These forces may be applied to the structures and actions evaluated with an equivalent static analysis. This is unnecessary with most modern programs as the member forces in the structure follow immediately from the computed displacements.

Mass participation factors.

The multiplier of the ground acceleration, L*/M* in the equation of motion for the ith mode, is the participation factor for the ith mode of the structure. It is a function of the mode shape, the mass distribution of the structure, and the direction of the earth quake excitation. If the vibration components of the mode shape are orthogonal to the direction of the ground excitation, the participation factor for that mode is zero. Negative participation factors may also be observed. In general, the magnitude of the participation factors diminish with increasing mode number and at some point it may be considered that the remaining higher modes do not significantly affect the displacements.

The participation factor shows how strongly a given mode contributes to the response of the structure when subjected to a specified direction of ground acceleration. An important point to note concerning participation factors is that the numbers obtained are dependent on the normalization method used in computing the mode shapes of free-vibration. Thus the participation factors computed from one computer program should not be compared with those from another program unless they both use the same methods of normalizing the mode shapes. This normalization does not affect the solution for the displacements or member actions as the modal amplitude Yi has to be multiplied by the mode shape and any effect of the normalization is cancelled out. It is only the modal amplitude Yi that is affected by the choice of normalization method.

Number of modes to be used:

The number of modes needed depends on the structure, the direction of the earth quake excitation and the degree of coupling between the translational and torsional modes. Sufficient mode should be used to ensure that most of structure's mass is contributing to the excitation in each direction of excitation. One measure that can be used to investigate the participation factors for each mode. These will show which modes are participating in the particular direction of excitation, which modes are orthogonal to the excitation and at which mode number the contributions from the higher modes are becoming insignificant.

A more significant method uses the effective mass of each mode (L*)^{2}/M* which is seen in the expression for the maximum base shear in each mode. The sum of the effective masses for all modes must equal the total mass of the structure. The effective mass associated with a mode usually diminishes rapidly as the mode number i increases. The number of modes used in the analysis should be large enough so that the modes used represent at least 90% of the total mass of the structure.

#### 2.1.5 Combination of modal maxima

The use of response spectra techniques for multi-degree of freedom structures is complicated by the difficulty of combining the modal responses. The combinations are usually achieved by using statistical methods. Response spectra calculations have lost all information on sign or when the maximum displacement etc. occurred. Therefore, proper combinations of modes are not possible. In each mode structural members are in equilibrium and all actions in members have the appropriate of signs. However, what contribution or sign other modes should have at the same time are unknown.

Let Ri be the modal quantity (Base shear, Nodal displacement, Nodal force, Member stress etc.). values of Ri have been found for all modes (or for as many as are significant). Most design codes require designers to use a sufficient number of modes so that the error associated with the omitted modes is only a small percentage of the total response, at least 3 modes in each direction to be considered.

R max = *Ri max* Would be true only if all maxima occurred at the same instant of time and all had the same sign.

In general,

R max < SiLi *Ri max* and in almost all cases the inequality holds.

There are several accepted statistical combination methods.

(a) **Maximum possible response**: *sum of absolutes*. This is very conservative and is very seldom sued except in some codes for say two or three modes for very short period structures.

(b) **Maximum likely response**: square root of some of squares, SRSS or root sum square. This is the most commonly used method. It is not root mean square.

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The root sum square method was initially used when two dimensional structural analysis were the norm. In a two dimensional structure no two lateral frequencies are close, and so no strong correlation between model responses is likely. The root sum square method impulse no correlation between the responses of the different modes, the maximum of each mode is independent of the maximum in other modes. In a uniform moment resisting frame undergoing a shear-type sway deformation the natural frequencies of free vibration increase roughly in ratios of 1:3:5:7:9 etc. and whilst the relative ratios between the frequencies of the higher modes tend towards 1.0 the contribution of these higher modes is rapidly diminishing because their participation factors become smaller with increasing mode number .

In three-dimensional structures, different modes in different directions may have very similar frequencies. If one of these modes is strongly excited by the earthquake at a given instant then the other mode, with a similar frequency, is also likely to be strongly excited at the same instant. In these cases root sum square combinations have been shown to give non-conservative estimates of the maximum likely response.

With an increasing realization that three-dimensional analysis were important in the response of real structures to earthquake excitation and the increasing concern of torsional behavior, improvements in the modal combination methods were sought. For very short period structures where all the natural frequencies are low, and are therefore, in an absolute sense, close together, the few modes were often combined by taking the maximum response as the sum of the absolute of the model responses. In these structures, which are inherently massive, the excessively conservative nature of the combinations is unlikely to be a problem. In the 1972 Los Angeles proposal it was suggested that the worst of the SRSS of a minimum of three modes are the sum of absolutes of any two modes be used for design. In a three dimensional structure it is likely that natural frequencies of modes in one translational direction will be similar to the natural frequencies of modes in the orthogonal translational direction of to the natural frequencies of the torsional modes.

Other modal combination methods that have been proposed are, in general, all related to the statistical combination of natural mode responses when the structure is subjected to a white noise excitation. It has been shown that these methods give reasonable combinations when applied to earthquake excitation. Similarly, the method proposed by Humar was initially developed for the torsional response of structures subjected to lateral ground excitation.

All the modal combination methods may be expressed in the form

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Where Xi and Xj are the fractions of critical damping in the ith and jth modes and œ, and œj are the natural circular frequencies of the modes.

**DSC [Rosenblueth and Elorduy(1969)] (Double sum combination**).

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S is the time duration of the white noise segment of the earthquake record. For actual records, for example, the duration of the strong motion segment characterized by extremely irregular accelerations of roughly equal intensity should be taken.

### 2.2 Response spectrum modal analysis of building using IS 1893 (part 1)-2002

As per IS 1893 (part1)-2002, Dynamic analysis shall be performed to obtain the design seismic force, and its distribution to different levels along the height of the building and to the various lateral load resisting elements, for the following buildings:

**a) Regular buildings** -Those greater than 40 m in height in Zones IV and V, and those greater than 90 m in height in Zones II and III.

**b) Irregular buildings** - All framed buildings higher than 12 m in Zones IV and V, and those greater than 40 m in height in Zones II and III.

Dynamic analysis may be performed by the response spectrum method. Procedure is summarized in following steps.

**a) Modal mass (M k )** - Modal mass of the structure subjected to horizontal or vertical as the case may be, ground motion is a part of the total seismic mass of the structure that is effective in mode k of vibration. The modal mass for a given mode has a unique value, irrespective of scaling of the mode shape.

Abbildung in dieser Leseprobe nicht enthalten

**b) Modal Participation factor (P k)** - Modal participation factor of mode k of vibration is the amount by which mode k contributes to the overall vibration of the structure under horizontal or vertical earthquake ground motions. Since the amplitudes of 95 percent mode shape can be scaled arbitrarily, the value of this factor depends on the scaling used for the mode shape.

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Table 2.1 Seismic zone factor *Z* as per IS: 1893 (Part 1) - 2002 of the site where the building to be designed is located

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Table 2.2 Importance factor I of buildings as per IS: 1893 (Part 1) - 2002

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In Eq. (2.1), *W* is the *seismic weight* of the building. For the purpose of estimating the seismic weight of the building, full dead load and part live load are to be included. The proportion of live load to be considered is given by IS: 1893 (Part 1) as per Table 2.4; live load need not be considered on the roofs of buildings in the calculation of design earthquake force.

Table 2.3 Response reduction factor *R* of buildings as per IS: 1893 (Part 1) - 2002

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Table 2.4 Proportion of live load to be considered in the estimate of seismic weight of buildings as per IS: 1893-2002

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Dynamic analysis may be performed either by time history method or by the response spectrum method. However in either method, the design base shear *VB* shall be compared with a base shear ( VB) calculated using a fundamental period *Ta*. When *VB* is less than all the response quantities shall be multiplied by VB/ Vb.

### 2.3 Review of literature

Shear wall mainly resists two types of forces: shear forces and uplift forces. To resist the horizontal earthquake forces, shear wall should provide the necessary lateral strength and to prevent the roof or floor above from excessive side-sway, shear walls also should provide lateral stiffness. Shear walls are classified into different types. They are coupled shear wall, core type shear wall, column support shear wall, frame wall with infill frame, rigid frame shear wall etc.

Anshuman et al. (2011) presented the solution for shear wall location in multi-storey building based on its both elastic and elasto-plastic behavior. An earthquake load is calculated and applied to a building of fifteen stories located in zone IV. Elastic and elasto-plastic analyses were performed using both STAAD Pro and SAP software packages. Shear forces, bending moment and story drift were computed in both the cases and location of shear wall was established based upon the above computations. By providing shear wall in some frames, the top deflection was reduced to permissible deflection. Also it has been observed that both bending moment and shear force in some frames were reduced after providing the shear wall. Thus result 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.

Romy Mohan and Prabha (2011) studied two multi storey buildings, one of six and other of eleven storeys have been modeled using software package SAP 2000 for earthquake zone V in India. Six different types of shear walls with its variation in shape are considered for studying their effectiveness in resisting lateral forces. It also deals with the effect of the variation of the building height on the structural response of the shear wall. They have concluded that, square shaped shear wall is the most effective and L shaped is the least effective.

From the past records of earthquake, there is an increase in the demand of earthquake resisting building which can be fulfilled by providing the shear wall systems in the buildings. For achieving economy in reinforced concrete building structures, design of critical section is carefully done to get reasonable concrete sizes and optimum steel consumption in members. Anuj Chandiwala (2012) had tried to get moment occur at a particular column including the seismic load, by taking different lateral load resisting structural systems, different number of floors, with various positions of shear wall for earthquake zone III in India has been found *.*

The earthquake analysis of 20 Storied building was done by Pravin et al. (2012) by seismic coefficient method and response spectrum method. The main parameters considered in this study are to compare the seismic performance of different zones i.e. II and V are base shear, storey moment and lateral forces. In response spectrum method, the time periods, natural frequencies and mode shape coefficients are calculated by STAAD program then remaining process was done by manually. The modal combination rule for response spectrum analysis is SRSS.

Kumbhare and Saoji (2012) have discussed the effectiveness of changing reinforced concrete shear wall location on multi-storied building. Shear wall frame interaction systems are very effective in resisting lateral forces. Abdur Rahman et al. (2012) have discussed the analysis of drift due to wind loads and earthquake loads on tall structures. The drift on high rise structures has to be considered as it has a notable magnitude.

Ashish Agrawal and Charkha (2012) carried out 25 storey building in zone V is presented with some preliminary investigation which is analysed by changing various position of shear wall with different shapes for determining parameters like bending moment, base shear and storey drift by using standard package ETABS. From preliminary investigation, it reveals that the significant effects on deflection in orthogonal direction and base shear by shifting the shear wall location. Placing Shear wall away from centre of gravity resulted in increase in most of the members forces. 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.

Three storey and six storey building models with plus shape shear wall have been considered by Oni and Vanakudre (2013). Equivalent static method and response spectrum methods are carried out as per IS: 1893 (Part 1) -2002 using finite element analysis software ETABS. Seismic performance is assessed by pushover analysis as per ATC-40 guidelines for earthquake zone V in India. It also deals with the effect of the variation of the building height on the structural response of the shear wall. They have concluded that plus shaped shear wall can effectively resist the lateral forces coming on the structure.

Patil et al. (2013) describes seismic analysis of high-rise building using program in STAAD Pro. with various conditions of lateral stiffness system. Some models are prepared with bare frame, brace frame and shear wall frame. Analysis is done with response spectrum method. Test results including base shear, story drift and story deflections are presented and get effective lateral load resisting system. A significant amount of increase in the lateral stiffness has been observed in all models of brace frame and shear wall frame as compared to bare frame.

Srikanth and Ramesh (2013) studied the earthquake response of symmetric multi-storied building by seismic coefficient method and response spectrum method. The responses obtained by above methods in two extreme zones as mentioned in IS code 1893 (part1) i.e. zone II and V are then compared. Test results base shears, lateral forces and storey moments are compared.

Alfa Rasikan and Rajendran (2013) presented the study and comparison of the difference between the wind behavior of buildings with and without shear wall using STAAD Pro. They found that, the displacement for a 15 storey building with shear wall was 20.18% less than the 15 storey building without shear wall and the displacement for 20 storey building with shear wall was 14.6% less than the 20 storey building without shear wall.

The structural behavior of RC building with and without infill walls and shear walls and also behavior of building on leveled and sloped ground are studied by Rayyan and Vidyadhara (2013). The results were obtained for storey displacements and base shear. The analysis is carried based on IS codes using equivalent static, response spectrum and pushover analysis.

Sway or drift is the magnitude of the lateral displacement at the top of the building relative to its base. Traditionally, seismic design approaches are stated, as the structure should be able to ensure the minor and frequent shaking intensity without sustaining any damage, thus leaving the structure serviceable after the event. The structure should withstand moderate level of earthquake ground motion without structural damage, but possibly with some structural as well as non-structural damage. This limit state may correspond to earthquake intensity equal to the strongest either experienced or forecast at the site.

Kevadkar and Kodag (2013) presents, R.C.C. building is modeled and analyzed in three Parts 1) Model without bracing and shear wall 2) Model with different shear wall system 3) Model with different bracing system. The computer aided analysis is done by using ETABS to find out the effective lateral load system during earthquake in high seismic areas. The performance of the building is evaluated in terms of lateral displacement, storey shear and storey drifts, base shear and demand capacity (performance point). It is found that the X type of steel bracing system significantly contributes to the structural stiffness and reduces the maximum inter story drift, lateral displacement and demand capacity (performance point) of R.C.C building than the shear wall system.

Shear wall is a structural element used to resist horizontal forces parallel to the plane of the wall. Shear wall has highly in plane stiffness and strength which can be used to simultaneously resist large lateral loads and support gravity loads. Shear walls are specially designed structural walls include in the buildings to resist horizontal forces that are induced in the plane of the wall due to wind, earthquake and other forces. They are mainly flexural members and usually provided in high rise buildings to avoid the total collapse of the high rise buildings under seismic forces. Shahzad and Umesh (2013) presented study of 25 storied building in zone V is presented with some investigation which is analyzed by changing various location of shear wall for determining parameters like storey drift, storey shear and displacement is done by using standard package ETABS. Creation of 3D building model for both linear static and linear dynamic method of analysis and influence of concrete core wall provided at the center of the building.

## CHAPTER 3

## MODELLING AND METHODOLOGY

### 3.1 Details of the models

For the present work, response spectrum method as per IS:1893-2002 is carried out for reinforced concrete moment resisting frame having G+13 and G+6 storied buildings situated in zone V. The floor to floor height of the building is 3.1m. The total height of building for G+13 is 43.4m. The ETABS (Extended Three-dimensional Analysis of Building Systems) software is used to develop 3D model and to carry out the analysis. The lateral loads to be applied on the buildings are based on the Indian standards as per IS 875:part1&2 (Dead load, Live Load) IS 1893:2002 (Earthquake load) and the study is performed for seismic zone V. The building consists of reinforced concrete and brick masonry elements. G+13 storied building is analyzed for seismic and gravity forces and building analyzed with different types of shear wall systems. Shear walls are modeled as wall piers. To find out effectiveness of shear wall to RCC building there is a need to study the parameters viz lateral displacement, story shear, storey moment and story drift. The material properties and geometry of models are described below. The building consists of 4 bays of 6.5 m in X- direction and 3 bays of 6.0 m in Z- direction in plan as shown in Fig. 3.1. The structural details of the models studied are given in Table 3.1.

**Gravity Loads:**

(i) Dead loads:

Self-weight: Self weight is calculated by the software based on sectional properties and material constants provided.

Super imposed dead load (floor finishes or water proofing) =1.5kN/m^{2}

Wall load =11.96 kN/m, Parapet load= 2.3 kN/m

(ii) Live Loads:

Live load on floor =5.0 kN/m^{2} Live load on roof =1.5 kN/m^{2} Note: Except self-weight there is no load that is applied on ground floor. **Lateral loads:**

(i) Response Spectrum Method:

Z = 0.36 considering zone factor for zone V (Table 2.1)

I = 1.5 considering residential building (Table 2.2)

R = 5.0 considering special RC moment resistant frame (SMRF) (Table 2.3)

The response spectrum analysis is carried out using the spectra for medium soil (type-II) as per IS 1893 (Part 1) 2002 for seismic zone V and 5% damping. The spectral acceleration coefficient (Sa/g) values are calculated (from Fig. 2.7).Load combinations considered in this analysis are: i) 1.5(DL+LL) ii) 0.9DL+1.5EQX iii) 0.9DL-1.5EQX)

Table 3.1 Structural details of the models studied

Abbildung in dieser Leseprobe nicht enthalten

### 3.2 Details of the cases studied

Case 1: Effect of shear wall location on G+13 storey building with different position of shear wall using response spectrum method (for models 1, 2, 3, 4 and 5)

Case 2: Effect of storey height on shear wall for G+13 and G+6 storied buildings using response spectrum method (for model 1 and model 6)

**Shear wall location and models under Study**

**Model 1** Shear wall at location A in plan- Shear wall is centrally located at exterior frame of Z direction throughout height as shown in Figure 3.2.

**Model 2** Shear wall at location B in plan- Shear wall is centrally located at exterior frame of X direction throughout height as shown in Figure 3.3.

**Model 3** Shear wall at location A and B in plan- Shear wall is centrally located at exterior frame of both X and Z direction throughout height as shown in Figure 3.4.

**Model 4** Shear wall at location C in plan- Shear wall is located at exterior frame end corners of both X and Z direction throughout height as shown in Figure 3.5..

**Model 5** Shear wall at location D in plan- Shear wall is centrally located at interior frame of both X and Z direction throughout height as shown in Figure 3.6.

**Model 6** Shear wall at location A in plan for G+6 storey - Shear wall is centrally located at exterior frame of Z direction throughout height as shown in Figure 3.7.

Abbildung in dieser Leseprobe nicht enthalten

Fig. 3.2 Plan and elevation of Model 1

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Fig.3.3 Plan and elevation of Model 2

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Fig.3.5 Plan and elevation of Model 4

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Fig. 3.7 Plan and elevation of Model 6

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## CHAPTER 4

## RESULTS AND DISCUSSIONS

### 4.1 Effect of shear wall location on G+13 storey building with different position of shear wall

Lateral Displacements Results obtained from the analysis are recorded in tabular form for the five cases of the building separately for comparison of storey shear, bending moment, storey drift and lateral displacement.

The presence of shear wall can affect the seismic behavior of framed structure to a large extent, and the shear wall increases the strength and stiffness of the structure. From Table 4.1, it reveals that the significant effects on deflection in orthogonal direction by shifting the shear wall location. In case of shear wall at exterior corners the structure is subjected to less displacement against the structure with shear wall at centre. Placing shear wall away from centre of gravity resulted in an increase in most of the deflections for model 5. Among all the models under study, the minimum lateral deflections are observed for models 2 and 3.

Storey Drifts Story drift, which is defined as the relative horizontal displacement of two adjacent floors, can form the starting point for assessment of damage to non-structural components such as facades and interior partitions. As per IS 1893-2002, 7.11.1, the storey drift in any storey due to the minimum specified design lateral force, with partial load factor of 1.0 shall not exceed 0.004 times the storey height, so that minimum damage would take place during earthquake. The maximum storey drifts of different models along longitudinal (Ux) and transverse directions (Uz) are as shown in Table 3. For buildings on normal ground the maximum drift allowed is 12.4 mm. Hence it can be said that all models are within permissible drifts.

From table 4.1 and 4.2, it has been found that the model 3 shows better location of shear wall since lateral displacements and inter-storey drift are less as compared to other models. From the above study we conclude that model 3 shows better performance among the other models.

Table 4.1 Lateral displacement (mm) in longitudinal (Ux) and transverse (Uz) direction with different position of shear wall

Abbildung in dieser Leseprobe nicht enthalten

Table 4.2 Storey drift (mm) with different position of shear wall

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Storey shear and moment

Storey shear and storey moment are presented for different models in Table 4.3 and maximum base reactions and moments are presented in Table 4.4. From Tables 4.3 and 4.4, it is observed that, the maximum storey shear force has appeared in model 4 and minimum in model 5. So it can be said that addition of shear wall will increase the base shear. Whereas maximum base moment is observed in model 1 and minimum is observed in model 5.From the Table 4.3 and Figs. 4.1, 4.2 and 4.3, minimum base shear and moment are observed in model 5 but due to placing shear wall away from centre of gravity resulted in increase in deflections and storey drift.

Table 4.3 Storey shear and storey moment with different position of shear wall

Abbildung in dieser Leseprobe nicht enthalten

Table4.4 Maximum base reaction and moment with different position of shear wall

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Fig: 4.1 Storey shear for models with different position of shear wall

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Fig: 4.2 Storey moments for models with different position of shear wall

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Fig. 4.3 Max base shear for models with different position of shear wall

Modal period and frequencies

From Table 4.5 and Fig.4.4, a significant amount of decrease in time period has been observed in models 3 and 4with shear wall frame. As base shear increases, the time period of models decreases and vice versa. Building with short time period tends to suffer higher accelerations but smaller displacement. Therefore, from Tables 4.1and 4.2 it is clear that the story deflections and drift are also observed to be minimum for models 2 and 3 with shear wall frame.

The stiffer the structure the higher natural frequency of the same mass and the shorter natural period observed. For models 2 and 3, the lateral stiffness system is centrally located at exterior frame of X direction throughout height and lateral stiffness system is centrally located at exterior frame of X & Z direction throughout height shows better performance compared to other models.

The distribution of seismic load at each storey is as shown in Figs. 4.5 to 4. 9 for models 1, 2, 3, 4 and 5. From the above figures it is observed that by adding the shear wall the seismic load is also increased.

Table 4.5 Modal period and frequencies with different position of shear wall

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Fig. 4.4 Modal period for models with different position of shear wall

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Fig.4.5 Distribution of seismic load at each storey level for model 1

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Fig.4.6 Distribution of seismic load at each storey level for model 2

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Fig.4.8 Distribution of seismic load at each storey level for model 4

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Fig.4.9 Distribution of seismic load at each storey level for model 5

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### 4.2 Effect of storey height on shear wall for G+13 and G+6 storied buildings

From Tables 4.6 and 4.7, maximum base shear, moment and storey drift are high in G+13 when compared to G+6 storied building. From Table 4.8, shows that the time period is less for G+6 model when compared to G+13 model with shear wall frame. As building height increases, the time period of model increases. Distribution of seismic load at each storey level for G+6 storied building is shown in Fig.4.11.With the decrease in height the magnitude of seismic load decreases. The first three mode shapes of all the models under study are presented in Fig. 4.12

Table 4.6 Lateral displacement, storey shear and storey moment for G+13 and G+6 storied buildings

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Table 4.7 Maximum values of lateral displacement, base shear, bending moment and top storey drift for G+13 and G+6 storied buildings

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Table 4.8 Modal period and frequencies for G+13 and G+6 storied buildings

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Fig 4.10 Lateral displacements for G+13 and G+6 storied buildings

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Fig. 4.12 First three mode shapes for Model-1

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Fig. 4.13 First three mode shapes for Model-2

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Fig. 4.14 First three mode shapes for Model-3

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Fig. 4.15 First three mode shapes for Model-4

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Fig. 4.16 First three mode shapes for Model-5

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Fig. 4.17 First three mode shapes for Model-6

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## CHAPTER 5

## CONCLUSIONS

### 5.1 Following are the conclusions drawn from the present study:

1. From the seismic analysis of reinforced concrete framed structure by dynamic analysis, significant effect on deflection in orthogonal direction have been observed by shifting the shear wall location. In case of shear wall on exterior frame the structure experienced smaller deflections against the structure with shear wall at centre.

2. Minimum base shear and moment are observed in Model 5 which has shear wall at lift core. However, placing shear wall away from centre of gravity of the structure resulted in increase in lateral deflections and storey drift. It has been observed that maximum base shear is developed in Model 4 which has shear wall at corners as compared to the other models. So it can be concluded that addition of shear wall increases the base shear.

3. The presence of shear wall can affect the seismic behavior of framed structure to large extent, and the shear wall increases the strength and stiffness of the structure. It has been observed that the Models 2 and 3 (i.e. lateral stiffness system is centrally located at exterior frame of X direction throughout height and lateral stiffness system is centrally located at exterior frame of X & Z direction throughout height) show better location of shear wall since lateral displacement and inter-storey drift are less as compared to other models.

4. A significant amount of decrease in time period and story drift has been observed in Models 3 and 4 (i.e. lateral stiffness system is centrally located at exterior frame of X & Z direction throughout height and shear wall is located at exterior frame end corners of both X and Z direction throughout height) compared to other models. Also Model 3 gives less storey deflection and storey drift than other models.

5. For unsymmetrical plans, it can be concluded that Model 3 (i.e, lateral stiffness system is centrally located at exterior frame of X & Z direction throughout height) shows better performance compared to other models.

6. As building height increases time period of model increases. With the decrease in height the magnitude of seismic load decreases. However, maximum base shear, moment and storey drift are high in G+13 when compared to those obtained in G+6 storied building.

### 5.2 Scope for further study

Further investigation is needed to consider the nonlinear effects, so that push over analysis and time history analysis can be carried out. The analysis can be carried over with symmetrical plan and plan irregularity with torsional effects.

## REFERENCES

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- Quote paper
- Injam Siva Parvathi (Author), 2014, Seismic Performance Evaluation of Reinforced Concrete Framed Buildings with Shear Walls, Munich, GRIN Verlag, https://www.grin.com/document/538286

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