Torsional response of assymetric multy story building thesis

CHAPTER 1

INTRODUCTION 1.1 GENERAL

Torsion responses in structures arise from two sources: Eccentricity in the mass

and stiffness distributions, causing a torsion response coupled with translation response;

and torsion arising from accidental causes, including uncertainties in the masses and

stiffness, the differences in coupling of the structural foundation with the supporting earth

or rock beneath and wave propagation effects in the earthquake motions that give a

torsion input to the ground, as well as torsion motions in the earth itself during the

earthquake. (1)

Horizontal twisting occurs in buildings when the center of mass (CM) does not

coincide with the centre of resistance (CR). The distance between them is called the

eccentricity (e). Lateral force multiplied by this (e) causes a torsion moment (T) that must

be resisted by the structure in addition to the normal seismic force.(2) The centre of

rigidity is the point through which the resultant of the restoring forces of a system acts.

The centre of mass corresponding to centre of gravity (c.g.) of the systems it is the point

through which the resultant of the masses of a system acts. (3) 1.2 THEORY

In general, the torsion arising from eccentric distributions of mass and stiffness

can be taken into account by ascribing an incremental torsion moment (T) in each storey =

the shear (V) in that storey multiplied by the eccentricity (e), measured perpendicular to

the direction of applied ground motion. A precise evaluation of the torsion response is

quite complicated because the coupled lateral- torsion vibration modes of the entire

structure are to be considered by performing a two – or three dimensional response

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calculations. (1) As an approximation, the torsion moment in each storey can be obtained

by summing from the top storey the incremental torsion moments.

The “static” torsion responses in each storey are then determined by computing

the twist in each storey obtained by dividing the total torsion storey moment by the storey

“rotational stiffness”. These twists are then added from the base upward to obtain the total

twisting or torsion response at each floor-level.(1) Since these are “static “responses, they

should be “amplified” for “dynamic” response using the response- spectrum amplification

factor for the fundamental torsion frequency of the structure. However, in many design

codes no amplification whatsoever is used. (1) “Accidental” torsion may arise in many

ways. Most current codes (4) use accidental eccentricity value of 5% of the plan dimension

of the storey perpendicular to the direction of applied ground motion. The accidental

torsion may be considered as an increase and also as a decrease in the eccentricity.

Corresponding to the distance between the centre of mass and resistance in various

storeys; with consideration of increases in all levels or decreases in all levels to get two

bounding values. The accidental torsion (or the total torsion) is computed in the same way

as the “real” torsion described above. (1) 1.3 DISTRIBUTION OF SHEAR AND MOMENTS

The storey shears arising from translation and from torsion response are

distributed over the height of the building in proportion to the stiffness of various

elements in the building the translational shears being affected by the translational

stiffness and the torsion shears being affected by the rotational stiffness of the building. (1)

The computed stiffness of the structure should take into account the stiffness of the floors

of floor structure acting as diaphragm or distributing element. If the floor diaphragm is

considered as infinitely rigid, and the storey stiffness are of importance. (1) However, if

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the floor diaphragm is flexible and deforms greatly, the distribution of forces becomes

more nearly uniform than determined by the method discussed above. A simplified

approach is possible by considering the relative displacements of the building due to

translation and that due to rotation of each storey separately, as affected by the diaphragm

or floor stiffness. The stiff nesses are determined by the forces corresponding to a unit

displacement in either translation or torsion. Respectively, then the shears due to

translation or rotation can be distributed in proportion to these stiff nesses.

The storey moments are distributed to the various frames and walls that make up

the lateral force system in a manner consistent with the distribution of storey shears. In

particular, the shears and moments in any frame or wall should be statically consistent.

Base or “overturning” moments: The flexural base moment is of importance in

connection with the foundation design. The corresponding flexural moments at each floor

level are important in connection with the calculation of vertical stresses in the columns

and walls of the structure. These moments can be computed from modal analysis or

equivalent lateral force analysis. 1.4 OLD CODE PROVISIONS

In 1984 version of Indian Seismic Code makes provision for the increase in shear

resulting from horizontal torsion due to the eccentricity (e) between the centre of mass

and the centre of rigidity. The torsion moment (T) at each storey = the shear (V) in that

storey multiplied by eccentricity (e). Since there could be quite a bit of variation in the

computed value of e, the code recommends that the design eccentricity (ed) be taken as

1.5e. Negative torsion shears shall be neglected. (3)

The net effect of this torsion is to increase the shear in certain structural elements

and reduction in certain others. The code recommends that reduction in shear on account

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of torsion should not be applied and only increased shear in the elements be considered.

(2)The torsion forces shall be distributed to the various vertical components of the seismic

resisting system with due consideration given to the relative stiff nesses of the vertical

components and the diaphragm. It is then corrected for torsion taking into account the

increases produced, but not the decreases (2) as specified in the code. (3) The following

steps are involved to determine the additional shears due to torsion in a building. Fig. 1.1

Let OX and OY be a set of rectangular coordinate axes, the origin O being taken

at the left corner of the building Fig. 1.1. If x and y are the coordinates of various

elements and Kx and Ky their stiff nesses in the two directions, the coordinates (Xr,Yr) of

the centre of rigidity or the point of rotation are computed as Xr = ΣKyx ……… 1 ΣKy Yr = ΣKxy ……… 2 ΣKx

The rotational stiffness Ip of the structure about the centre of rotation Cr is

given by Ip = Σ(KxY2 + KyX2) …… 3

If the torsional moment T= Ved …… 4

Where ed = 1.5e, the torsion shears Vx and Vy on any column line be computed as: Vx = T. Y. Kxx……… 5 Ip Vy = T. X. Kyy…… 6 Ip

Where Kxx, Kyy are the total stiff nesses of the column line under consideration and X and

Y are coordinates w.r.t the centre of rigidity Cr.

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Y 4 [email protected] 3 =22.5m Xr

Cr † Cm†

Yr 2 1 X A B C D E [email protected]=30m Fig: 1.1 Plan of an Asymmetric Building

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CHAPTER 2

LITERATURE SURVEY

2.1 GENERAL

It has been observed repeatedly in strong earthquakes that the presence of

asymmetry in the plan of a structure makes it more vulnerable to seismic damages. There

are reports of extensive damages to buildings that are attributed to excessive torsion

responses caused by asymmetry in earthquakes such as the 1972 Managua earthquake

(Pomares Calero5 1995), the 1985 Michanocan earthquake (Esteva6 1987) and the 1989

Loma Prieta earthquake (Mitchell et al7 (1990)). Fig. 2.1 shows damages in a multi-storey

building after the 1995 Hyogoken-Nanbu earthquake in Kobe, probably caused by

excessive torsion responses because its core was eccentrically located in plan.

Asymmetry in plan causes torsion in a building because the centre of mass and the

centre of rigidity do not coincide. The distance between the two centers is termed

structural eccentricity and the magnitude of this eccentricity can be estimated. Torsion

can also arise in a building due to other sources for which estimating their magnitude is

difficult. Some examples of these sources for the so-called accidental torsion are the

rotational components in the ground motion, an unfavorable distribution of live load, and

the difference between computed and actual stiffness/mass/yield strength of the elements.

All these factors cause coupling between the lateral and torsion motions in a building that

leads to non-uniform distribution of in-plan floor displacement. This results in uneven

demands on the lateral resisting elements at different locations of the system.

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Although torsion has long been recognized as a major reason for poor seismic

performance of multi-story buildings and many studies have been done on the seismic

torsion responses of single story buildings, the analytical and experimental studies on the

inelastic seismic response of multi-story buildings do not have a long history. The reason

as explained by De la Llera & Chopra8 (1995c) is that "most researchers have been

discouraged to look into the multi-story case in light of the already complex response of

single storey asymmetric buildings".

In most of the available studies on the seismic torsion response of multi-storey

buildings, simple building models such as shear walls are used and the conclusions of the

studies are based on the responses of buildings subjected to a limited number of

earthquake ground motions. Currently, there is no general agreement on how the torsion

effect should be allowed for in seismic design. These observations provided the

motivation for the study by A.S. Moghadam9 in order to provide a better understanding

of the problem of seismic damages caused by torsion in multi-storey reinforced concrete

frame buildings. Those investigations on torsion response that involve using the recorded

data in buildings during earthquakes are explained. Then experimental research is carried

out, and finally analytical work on the subject is explored.

2.2 STUDY ON RESPONSE OF BUILDINGS RECODRED IN EARTHQUAKES

Conducting experiments to study the inelastic response of a structure is not easy. To

obtain realistic estimations of the inelastic response, the test should be performed on a full-

scale prototype building. This is not practical for most structures. However, the recorded

motions of some instrumented buildings in earthquakes can provide valuable information

about the seismic performance of such buildings. Safak and Celebi10 (1990) introduced a

method to identify torsion vibration in an instrumented building. According to them,

similar methods can be used to identify inelastic behavior in vibrating structures. Lu and

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Hall11 (1992) studied the data from two low-rise, extensively instrumented buildings in the

1987 Whittier Narrows Earthquake. Their study involved the investigation of responses of

buildings, responding in the elastic and marginally inelastic range, by comparing the

behavior of the buildings with computer simulations. Both buildings were modeled as

frame structures using a shear wall idealization. The recorded data at the basements were

used as the ground motion input for the models. The results from unidirectional ground

motion input were found to provide a reasonably close match of the actual responses during

the earthquake. Using bi-directional ground motion inputs gave an even better match to the

measurements. Sedarat et al.12 (1994) studied the torsion response characteristics of three

regular buildings in California, by analyzing the strong motions recorded in these

buildings during three recent earthquakes: the 1989 Loma Prieta earthquake, the 1986 Mt.

Lewis earthquake, and the 1984 Morgan Hill earthquake. The responses of the buildings

were compared with responses of models designed using the provisions of the 1988 UBC.

The results of their investigation indicated that the code provision was not adequate to

account for the torsion responses of these buildings.

2.3 EXPERIMENTAL STUDIES

Some experiments on scaled models are reported in the literature. Bourahla and

Blakeborough13 (1994) examined the performance of knee braces in asymmetric frame

buildings by designing and testing a one-twelfth-scale building model using a shaking

table. The test structure was a four-storey frame, three bays deep and three bays wide.

Several symmetric and asymmetric arrangements of the frame were tested. The changes

in responses due to asymmetry and also due to the unbalanced strength were investigated.

It was found that the effect of the unbalanced strength in a nominally symmetric frame

buildings is less significant compared with other sources of asymmetry. The energy

dissipation capacities of the frames were also studied. Based on the experimental results,

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it is concluded that the magnitude of the eccentricity in itself is meaningless, but it is the

ability of the structure to resist torsion, which is critical.

2.4 ANALYTICAL STUDIES

Effects of torsion

Analytical studies have been done to compare the effects of torsion on the elastic

and inelastic behavior of buildings. Study of a seven-storey frame-wall structure (Sedarat

and Bertero 1990a14, 1990b15) demonstrated that linear dynamic analysis might

significantly underestimate the effect of torsion on the inelastic dynamic response of the

structure. On the other hand, the study of a thirteen storey regular space frame structure

Boroschek and Mahin16 (1992) showed that the effects of torsion were more severe if the

building is modeled as an elastic structure instead of an inelastic one, and the results were

found to be highly dependent on the characteristics of the earthquake motions. Therefore,

the issue of severity of torsion effect on the inelastic response of buildings has not been

settled.

Teramoto et al.17 (1992) presented some results of dynamic analyses of an

asymmetric 10-storey shear beam building. They used one earthquake record as the input

motion. A conclusion of this study is that mass eccentric and stiffness eccentric systems

behave differently. When mass eccentricity exists at upper floors only, the eccentricity

will also have some effects on the lower floors. However, stiffness eccentricity only

affects the floors where eccentricity exists.

Cruz and Cominetti18 (1992) used a five storey-building model in their study and

concluded that the overall ductility and the fundamental period of the building are the

parameters that most strongly affect the responses of the building.

In a study by De la Llera and Chopra19 (1996) they concluded that increasing the

torsion capacity of the building by introducing resisting planes in the orthogonal

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direction, and modifying the stiffness and strength distribution to localise yielding in

selected resisting planes, are the two most important corrective measures for asymmetric

buildings.

2.5 DESIGN PROCEDURES

Several issues related to the design of multi-storey buildings and evaluation of

building codes have been studied in the literature. Bertero20 (1992) developed formulae

with the objective of considering the elastic and inelastic torsion in the preliminary design

of tall buildings. Bertero21 (1995) used the classical theorems of plastic analysis to

estimate the reduction in the strength of a special class of buildings. De la Llera &

Chopra22 (1995a) proposed a procedure for including the effects of accidental torsion in

the seismic design of buildings. Ozaki et al.23 (1988) proposed a seismic design method

for multi-storey asymmetric buildings. Azuhata and Ozaki24 (1992) proposed a method

for safety evaluation of shear-type asymmetric multi-storey buildings. In both of these

studies, the damage potential due to torsion is evaluated based on the shear and torsion

strength capacity and the design shear force and torsion moment for each storey of the

building.

In a study by Duan and Chandler25 (1993) on an asymmetric multi-storey frame

building model, they concluded that application of the static torsion provisions of some

building codes may lead to non-conservative estimates of the peak ductility demand,

particularly for structures with large stiffness eccentricity. In another study they

(Chandler and Duan25 1993) proposed a modified approach for improving the

effectiveness of the static procedure for regular asymmetric multi-storey frame buildings.

2.6 SHORTCOMINGS OF THE PREVIOUS ANALYTICAL STUDIES

The number of parameters required to mathematically define the elastic and

inelastic properties of a representative model of an asymmetric multi-storey building is

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enormous. Therefore, all studies that have been reported in the literature involved using

simple models for the building and the conclusions are drawn based on a limited number

of earthquake records as ground motions input.

In almost all these studies, the multi-storey frame buildings are modelled as shear

buildings. The shear building model is not a good representative of the frame buildings in

a seismic zone because a shear building model has strong beams, which causes the plastic

hinges to occur at the columns. This is in contradiction to the strong column-weak beam

philosophy in earthquake design (Tso26 1994). A study by Moghadam and Tso27 (1996b)

has shown that shear-building modeling may lead to unreliable estimates of the important

design parameters. Rutenberg and De Stefano28 (1997) have pointed out that some of the

difference between the results of modeling a building as a shear building versus a ductile

moment resisting frame building in the study by Moghadam and Tso27 (1996b) might be

due to differences in the periods of the two compared models. Modeling of a building as a

shear building involves changing the stiffness of beams to very high values. This in turn

causes the period of the shear beam model to change. Therefore; modeling a ductile frame

building as a shear building will cause changes in not only the mode of failure, but also the

natural periods of the building. Thus, the relevance of observations of studies using shear

beam modeling to actual ductile moment resisting frame structures in seismic active

regions is questionable.

2.7 SIMPLIFIED METHODS

Some simplified approaches have been developed in the literature to estimate the

inelastic seismic responses of multi-storey buildings. De la Llera and Chopra8 (1995c)

developed a simple model for analysis and design of multi-storey buildings. Each storey

of the building is represented by a single super-element in the simplified model. The use of

storey shear and storey torque interaction surface (Kan and Chopra29 (1981), Palazzo and

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Fraternali30 (1988), De la Llera and Chopra31 (1995b)) is an important component of this

method. The storey shear and torque (SST) surface is basically the yield surface of the

storey due to the interaction between storey shear and torque. Each point inside the

surface represents a combination of storey shear and torque that the storey remains

elastic. On the other hand, each point on the surface represent a combination of shear and

torque that leads to the yielding of the storey. It is shown that the SST surfaces can be

used for single storey systems and multi-storey shear buildings. One major assumption

embedded in the method is that the stories of a multi-storey building are considered as

independent single storey systems. In other words, the floor diaphragms are assumed

rigid, both in-plane and out-of-plane. This assumption of out-of-plane rigid diaphragms

is equivalent to assuming rigid beams in the building. How realistic is such a model to

represent the behavior of ductile frame buildings in seismic regions is a subject that

requires further investigation.

In the performance based design codes and in the guidelines for retrofitting of

buildings, the use of different versions of a static inelastic response analysis procedure,

commonly known as pushover analysis, has been suggested as a valid tool to evaluate the

acceptability of any proposed design, or to assess the damage vulnerability of existing

buildings. Moghadam and Tso32 (1996a) extended the application of the pushover

analysis to asymmetrical buildings by using a 3-D inelastic program. Kilar and Fajfar33

(1997) developed a simple method to conduct pushover analysis for asymmetric buildings

by modeling the building as a collection of planar macro-elements. Another method

proposed by Tso and Moghadam34 (1997) incorporates the results of elastic dynamic

analyses of the building in the pushover procedure. A further simplification is achieved

by requiring only a two-dimensional inelastic analysis program to perform the pushover

analysis on asymmetrical multi-storey buildings (Tso and Moghadam34 1997, Moghadam

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and Tso35 1998). Rutenberg and De Stefano28 (1997) conducted pushover analyses on a 7-

storey wall-frame building and found reasonable agreement between results of pushover

and inelastic dynamic analyses.

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A department Store in Kobe, Japan after 1995 Earthquake

r Collapse of this column due to excessive displacement demand initiated the progressive collapse in the building

The eccentric elevator core

Fig 2.1 Example of Structural collapse caused by torsion (Eccentric elevator core lead to significant torsion deformation and the collapse of corner columns)

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CHAPTER 3

STRUCTURAL MODEL, LOADINGS &

RESPONSE PARAMETERS OF INTEREST

3.1 INTRODUCTION

The study in this work is based on the analyses of a family of structural models

representing multi-story asymmetrical buildings. These models are subjected to both

critical and lateral loadings expected on buildings during an earthquake. A set of response

parameters is used to illustrate the effect of torsion in these buildings.

The purpose of this chapter is to present the basic assumptions and the tools utilized

in this work. The different building configurations are introduced first. Then the methods

and the loadings used in the analyses are discussed. Finally the chosen response

parameters are outlined. The material presented in this chapter prepares the background

information for the results to be presented in the subsequent chapters.

3.2 BUILDING CONFIGURATIONS

The basic structural model used throughout this a study is uniform nine-story building;

asymmetric with respect to both X and Y axis to demonstrate many of the features

expected from multi-story buildings subjected to seismic loading. The assumed plan of

building is shown in Fig. 3.1. It has an L-shape floor plan of dimensions 42.4 m by 53.0

m, and a uniform floor height of 4.2 m Fig. 3.2. The plan considered is asymmetric. For

convenience, the X-direction is referred to as the main direction and the Y-direction is

referred to as the transverse direction. To resist the lateral loads, there are 28 RC columns

supporting to flat slab. The flat slab is of thickness 0.25 m with column caps 3.6x3.6x0.5

m with (post tensioned) edge beams of size 0.6x0.5 m are provided through out the

building in all floors. All the columns are placed at strategic locations with spacing of

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10.6x10.6 m, having 5 bays in X direction & 4 bays in Y direction. The grids are marked

as 1 to 6 in X direction and A to E in Y direction as shown in Fig. 3.1. The Seismic

analysis is carried out as per the latest IS-1893-2002 code by the Response Spectrum

technique. The buildings are assumed to be located in zone-II, zone-V and located on

three types of soils (Hard, Medium; Soft soils). The Response quantities considered

includes axial forces, moments in X & Y directions, twisting moments, %steel, steel area

etc. for the columns; further both ordinary moment resisting frame (OMRF) and special

moment resisting frame (SMRF) are considered.

3.3 COMPUTER SOFTWARE STAAD.Pro 2006

The static and dynamic behavior of the multi-story asymmetric buildings in the

elastic range is the main focus of the study reported in this work. Therefore computer

program with the ability of performing 3-D elastic static and dynamic analysis was

necessary. The program STAAD.Pro-2006 has been chosen as the base computer

software in performing the analyses. To have a clear understanding of the analysis a study

has been carried out to evaluate this program by comparing its results with the responses

derived from the manual calculations.

3.4 BASIC ASSUMPTIONS IN MODELING

The following are the main modeling assumptions used in this study.

3.4.1 MODELING OF THE BUILDING

• Rigid slab: It is assumed that all the columns in the buildings are connected by

floor diaphragms that are rigid in their own plane. Therefore every floor has only

two translational and one rotational degrees of freedom. The in-plane

displacements of all the nodes on the floor are constrained by these degrees of

freedom. However, the nodes can have independent vertical displacements.

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• Fixed base: The columns of buildings are assumed to be fixed at their base on

rigid foundation. No soil-structure interaction effect is considered in this

study.

• One directional earthquake input: Only one direction of response values are

applied at the junction of columns and floor diaphragms. Due to the fixed base

assumption, all supports are assumed to move in phase. No vertical translation is

applied to the buildings.

• Lumped mass at floor level: The mass and the mass rotational moments of inertia

of the buildings are assumed to be lumped at the floor levels.

3.4.2 MODELING OF THE FRAMES

There are different analytical models available to simulate structural frames. In

this study an edge beam element with flat slab having and a column element are used to

model the elements of the frames in the buildings.

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CHAPTER 4

ANALYSIS & DESIGN OF ASYMMETRICAL MULTI-

STOREY BUILDINGS INCORPORATING TORSIONAL

PROVISIONS

4.1 INTRODUCTION

In a symmetric building, all the lateral load-resisting elements at different

locations in plan experience the same lateral displacement when subjected to

unidirectional forces. As a result, the force induced in each element is proportional to its

lateral stiffness. This observation leads to a guideline that calls for assigning the design

strength of the lateral load-resisting elements according to their stiffness. In an

asymmetric building, however, the location of a lateral load-resisting element affects the

share of load that it should resist because the loadings on the rigid floors of these

buildings are accompanied by torques caused by the structural eccentricity in the

building. The force induced in each element from the floor torques is proportional to its

contribution to the torsion stiffness of the building. The torque-induced force in an

element is called the torsion shear. The location of an element not only determines the

magnitude, but also the direction of the torsion shear. Depending on the direction of the

torque, the torsion shear should be added to or subtracted from the forces induced in that

element by the translational displacement of the floors.

To compensate the torsion effect on the performance of a building, different

approaches have been suggested to replace the rule of distribution of strength among the

elements proportional to their lateral stiffness. These approaches can collectively be referred to

as torsion provisions. The goal of this chapter is to evaluate the effectiveness of a few torsion

provisions to improve the seismic performance of asymmetric multistory buildings.

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The first approach that is studied here is distribution of the strength based on static

equilibrium consideration. Then the static torsion provisions based on the Indian seismic

code (IS: 1893-2002) are studied. Finally, the application of response spectrum analysis to

proportion the design strength of the elements is considered.

4.2 TORSIONAL PROVISIONS

Torsion provisions are incorporated in most building codes to redistribute the

strength among elements to minimize the torsion effects. Codes usually divide the

buildings into regular and irregular buildings and consider that static torsion provisions will

be suitable for regular buildings. For irregular buildings, design based on dynamic analysis,

such as the response spectrum method, is suggested.

4.3 I. S. CODE DESIGN PROVISIONS FOR TORSION

The static torsion provisions require the application of static torsion moments to

be included in the determination of the design forces. The product of the lateral force and

the design eccentricity determines the value of the torsion moment. The design

eccentricity can be different from the structural eccentricity in a building. To protect the

elements on both side of the building, codes require two separate load cases to be

considered involving two design eccentricities. The magnitudes of the two design

eccentricities are derived from equations:

(ed)x = l.5 e + 0.1 b ------- (4.1) ;

(ed)z = 0.5 e - 0.l b------ (4.2) ;

where (ed)x and (ed)z are the two design eccentricities, e is the structural eccentricity and

“b” is the width of the building. To design the elements, the forces required for resisting

the torsion moments (torsion shears) should be combined with the shear from

translational loading.

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4.4 CLASSIFICATION OF ASYMMETRICAL BUILDING USING FREE VIBRATION ANALYSIS

One procedure to classify a building is to carry out a free vibration analysis.1 The

nature of a mode can be identified using the modal mass information derived from the

free vibration analysis. The first two mode shapes of the buildings and also the effective

modal masses of the first 12 modes of the buildings are presented. The mode shapes of

the buildings are given in two formats. In one format, the displacements and rotations at

CM of the floors are given for each mode. In the second format, the lateral displacements

of the five frames are shown for each mode.

Based on structural dynamics, it can be shown that translation predominant modes

in general have larger modal masses than torsion predominant modes.1 In the figures, the

effective modal masses are shown in figure: against the natural periods of the building. It

can be seen that the first mode is translation predominant in X-direction of the building.

The first translation predominant mode is the second mode as can be seen by the large

modal masses associated with the second mode for Y-direction of the building. In the

case of third mode purely torsion predominant, where as in first and second modes also

very less torsion values will be appearing, but predominant case is translational.

A parameter defined here as effective modal moment of inertia provides a

quantitative way of identifying the contribution of different modes to the displacements of

edge 1 and edge 6 of a building.1 Depending on the sign of this parameter one can show

whether the effects of the rotational and translational components of a coupled mode are

additive or subtractive on each edge of the building. The effective modal moment of

inertia for the nth mode is defined as I*On (Chopra 1995, where this parameter is called

modal static response for base torque)1:

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N

I*On = Σ r2 Γ n m j φj θn

J = 1

This equation is developed for an asymmetric building with eccentricity in one

direction only, such that floor rotations are coupled with floor displacements in the In-

direction. In the equation, N= total number of floors, n= the mode number, r= mass

radius of gyration, m = mass of floor, φj θn= the rotational element on the jth floor in the

n-th vibration mode shape.

Γn is defined as:

N

Σ m j φj y n J = 1 Γn = -------------------------------------------------------- (4.3)

N N

Σ m j φ² j y n + r² Σ m j φ² j θ n J = 1 J =1

Where φj y n is the translational element on j th floor in the n th vibration mode. The

effective modal moment of inertia idea is based on the concept of modal expansion

(Chopra, 1995)1 that uses the effective modal mass and the effective modal moment of

inertia to expand the effective force vector of a structure. 4.5 TORSIONAL ANALYSIS OF AN L-SHAPED BUILDING

The calculations of torsion seismic shears 36 as per I.S. Code 2 is illustrated for the L-

shape building shown in Fig. 3.1 Imposed load floor 39 = 4kN/m²; Imposed load roof 39= 1.5 kN/m² Grade of concrete M35 and density 37 = 25 kN/m³, E 37 = 29.580 kN/m² Floor finishes 38 = 60mm of 20 kN/m³

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Column drop/cap = 3600x3600x0.5 depth (0.2 flat slab) Column size = 0.9x0.9 = 0.054675m4, Partitions load 38 = 1.25 kN/m²

∴ Total additional dead load on the slab = 1.25 + 1.2 = 2.45 kN/m² Note: - There is a 200mm thick block (brick) work around the building. Storey shears:- (i) Total weight of slab in a storey

a) 0.2(31.8 x 53+10.6 x 31.8)25 = 10112.4 kN b) 2.45(31.8 x 53+10.6 x 31.8) = 4955.08 kN

15067.5 kN

(ii) Total weight of column caps(18 numbers ) = 0.3(3.6 x 3.6 x 18 No’s) 25 = 1749.6 kN

(iii) Total weight of column in a storey (28 numbers) = 0.9 x 0.9 x 4.2 x 25 x 28 = 2381.4 kN

(iv) Total weight of walls in a storey (½ above & ½ below floor) @ 20 kN/m³

= (31.8+10.6+10.6+31.8+42.4+42.4) 0.2 x 4.2 x 20 = 2849.28 kN

(v) Live load (50% during earthquake for 4KN/m² class loading) = (31.8 x 53+10.6 x 31.8)0.5 x 4 = 4044.96 kN

Total weight lumped @ each floor of the 1st, 2nd, 3rd, 4th, 5th, 6th, 7th, 8th, roof (9th floor). W1 = W2 = W3 = W4 = W5 = W6 = W7 = W8

(15067.5 + 1749.6 +2381.4 + 2849.3 + 4044.96) = 26092.76kN Total weight lumped @ roof =W9 {15067.5 + 1749.6 +0.5(2381.4 + 2849.3) +0} = 19432.45 kN

- 24 -

Theoretical Base Shear = Vb = (Z/2 x I/R x Sa/g) W Time period (In shorter direction) T = 0.09H/√Ds =0.09 x 37.8/√42.4 = 0.522 sec Time period (In longer direction) T = 0.09H/√Ds =0.09 x 37.8/√53 = 0.497 sec In longer direction Sa/g = 2.5, in shorter direction = 2.5 ∴ VB = (0.1/2 x 1/3 x 2.5) 228174.53 kN = 9507.3 kN Vertical storey shear distribution for whole building can be determined using the equation:-

Qi= Vb x Wi hi2

Σ Wi hi2

Floor Wi in kN hi Wi hi

2 Qi Vi in kN 9(roof) 19433 37.8 27766648 2169.8 ≅2169.5

8 26093 33.6 29457953 2302 4471.5 7 26093 29.4 22553745 1762.44 6233.9 6 26093 25.2 16570099 1295 7528.9 5 26093 21.0 11507013 899.2 8428.1 4 26093 16.8 7364483 575.5 9003.6 3 26093 12.6 4142525 323.7 9327.3 2 26093 8.4 1841122 144 9471.3 1 26093 4.2 460280 36 9507.30

Σ Wi hi

2 = 121663873

CENTRE OF MASS IN X- DIRECTION:

The total height acting along each of column line 1-1 to 6-6 for storey 1, 2, 3, 4, 5, 6, 7, 8 & 9(roof) can be computed as below mentioned table:

WEIGHT CALCULATION IN X- DIRECTION

Column line

Weight of

beams in kN

Weight of slab in kN

Weight of

column in kN

Weight of

walls in kN

Live load in

kN

Total weight in 1 to 8

floors in kN

Live load

@ roof in kN

Total weight in 9th roof in

kN

1-1 145.8 1255.60 340.2 534.24 337.80 2612.92 - 2275.84 2-2 291.6 2511.20 340.2 178.08 674.16 3995.24 - 3321.08 3-3 340.2 2929.70 425.30 534.24 786.52 5013.96 - 4227.44 4-4 388.8 3348.30 425.30 356.16 898.88 5417.44 - 4518.56 5-5 388.8 3348.30 425.30 356.16 898.88 5417.44 - 4518.56 6-6 194.4 1674.20 425.30 890.4 449.44 3633.74 - 3184.30

ΣW=26090.74 ΣW=22045.78

- 25 -

WEIGHT CALCULATION IN Y- DIRECTION

Column line

Weight of

beams in kN

Weight of slab in kN

Weight of

column in kN

Weight of

walls in kN

Live load in

kN

Total weight in

1 to 8 floors in

kN

Live load @

roof in kN

Total weight in 9th

roof in kN

A-A 145.8 1255.60 340.2 534.24 337.08 2612.92 - 2275.84 B-B 388.8 3348.33 510.3 534.24 896.76 5678.43 - 4781.67 C-C 486.0 4185.4 510.3 356.16 1123.6 6661.46 - 5537.86 D-D 486.0 4185.4 510.3 356.16 1123.6 6661.46 - 5537.86 E-E 243.0 2092.7 510.3 890.4 561.8 4298.20 - 3736.40

ΣW=25912.47 kN ΣW=21869.63kN CENTRE OF MASS IN X- DIRECTION Taking moment of the weights @ about line “1-1” Cmx (for 1 to 8 floors) = (2612.92x0+3995.24x10.6+5013.96x21.2+5417.44x31.8+5417.44x42.4+3633.74x53) 26090.74 ∴ Cmx = 743207.764 = 28.49 m

26090.74

Cmx (for roof 9th floor) = (2275.84x0+3321.08x10.6+4227.44x21.2+4518.56x31.8+4518.56x42.4+3184.30x53) 22045.78

∴ Cmx (@ roof) = 628870.228 = 28.53 m 22045.78

CENTRE OF MASS IN Y – DIRECTION

Taking moment of the weights @ about line “A-A”

Cmz = (2612.92 x 0+5678.43 x 10.6+6661.46 x 21.2+6661.46 x 31.8+4298.20 x 42.4) 25912.47 (1 to 8 floors) ∴ Cmz = 595492.42= 22.98 m 25912.47

- 26 -

Cmz= (2275.84 x 0+4781.67 x 10.6+5537.86 x 21.2+5537.86 x 31.8+3736.4 x 42.4) 21869.63 (@ roof) ∴ Cmz (@ roof) = 502615.64 = 22.98 m

21869.63

CENTRE OF RIGIDITY IN X – DIRECTION

Lateral stiffness of column k = 12EI L3 For a square column (0.9x0.9 mts) (having) (using) M35 grade of “E” value same and also “L” are constant; kx = ky = k xr = Σ ky. X Σ ky = (4k x 0+4k x 10.6+5k x 21.2+5k x 31.8+5k x 42.4+5k x 53) 28k ∴ xr = 784.4k = 28.014 m 28k CENTRE OF RIGIDITY IN Y– DIRECTION

Zr= Σ kx.y Σ kx

= (4k x 0+6k x 10.6+6k x 21.2+6k x 31.8+6k x 42.4) 28k ∴ Zr = 636k = 22.714 m 28k Eccentricity:- For 1st, 2nd, 3rd, 4th, 5th, 6th, 7th, 8th floors ex = | Cmx - xr| = | 28.48 – 28.014| = 0.466 m ez = | Cmz - Zr| = | 22.981 – 22.714| = 0.267 m For 9th (roof) storey ex = | Cmx - xr | = | 28.53 – 28.014| = 0.516 m

- 27 -

ez = | Cmz - Zr | = | 22.983 – 22.714| = 0.269 m TORSIONAL STIFFNESS Ip = Σ (kX. Y 2 + kY. X 2 ) Σ kX.Y2 = k [4(22.714)2+6(22.714-10.6)2+6(22.714-21.2)2+6(22.714-31.8) 2+6(22.714-42.4) 2] Σ kX. Y2 = k [2063.703+880.494+13.75+495.33+2325.23] ∴ Σ kX. Y2 = 5778.51k m4

Σ kY.X 2 = k [4(28.014)2+4(28.014-10.6)2+5(28.014-21.2)2+5(28.014-31.8)2

+5(28.014-42.4)2+5(28.014-53)2] = k [3139.137+1212.99+232.153+71.669+1034.785+3121.500] ∴ Σ kY.X2 = 8812.234k m4 Ip = Σ (kX. Z2 + kY. X 2 ) Ip = (5778.51 + 8812.23) = 14590.74k m4 ADDITIONAL MOMENTS DUE TO SESMIC FORCE IN X- DIRECTION (b = 42.4 mts) 1st floor T1a = Vx (1.5 ez +0.05b) = 9507.3(1.5 x 0.267+ 0.05 x 42.4) T1a = 23963.15 kNm T1b = Vx (ez - 0.05b) = 9507.3 (0.267 - 0.05 x 42.4) T1b = - 17617 kNm 2nd floor T2a = 9471.3(1.5 x 0.267+0.05 x 42.4 T2a = 23872.4 kNm T2b = 9471.3 (- 1.853) = -17550.3 kNm

- 28 -

3rd floor T3a = 9327.3 (2.5205) = 23509.5 kNm T3b = 9327.3 (- 1.853) = -17283.5 kNm 4th floor T4a = 9003.6 (2.5205) = 22693.6 kNm T4b = 9003.6 (- 1.853) = -16683.7 kNm 5th floor T5a = 8428.1 (2.5205) = 21243.03 kNm T5b = 8428.1 (- 1.853) = -15617.3 kNm 6th floor T6a = 7528.9 (2.5205) = 18976.6 kNm T6b = 7528.9 (- 1.853) = -13951.05 kNm 7th floor T7a = 6233.9 (2.5205) = 15712.5 kNm T7b = 6233.9 (- 1.853) = -11551.4 kNm 8th floor T8a = 4471.5 (2.5205) = 11270.4 kNm T8b = 4471.5 (- 1.853) = -8285.7 kNm 9th floor (roof) T9a (roof) = 2169.8 (1.5 x 0.269 + 0.05 x 42.4) = 5475.5 kNm T9b (roof) = Vx ( ez -0.05b) 2169.8 (0.269 – 2.12) = -4016.3kNm

- 29 -

ADDITIONAL MOMENTS DUE TO SESMIC FORCE IN Y- DIRECTION:-

(b = 53.0 mts) T1a = Vz (1.5 ex - 0.05b) = 9507.3 (1.5*0.466+ 0.05*53) T1a = 31840 kNm T1b = Vz (ex - 0.05b) = 9507.3 (0.466- 0.05*53) T1b = - 20763.9 kNm

T2a = 9471.3 (3.349) = 31719.4 kNm

T2b = 9471.3 (- 2.184) = -20685.3 kNm

T3a = 9327.3 (3.349) = 31237.13 kNm T3b = 9327.3 (- 2.184) = -20370.8 kNm T4a = 9003.6 (3.349) = 30153.06 kNm T4b = 9003.6(-2.184) = -19663.9 kNm T5a = 8428.1(3.349) = 28225.7 kNm T5b = 8428.1 (-2.184) = -18406.9 kNm T6a = 7528.9 (3.349) = 25214.3 kNm T6b = 7528.9 (- 2.184) = -16443.12 kNm T7a = 6233.9 (3.349) = 20877.3 kNm T7b = 6233.9 (- 2.184) = -13614.8 kNm T8a = 4471.5 (3.349) = 14975.05 kNm T8b = 4471.5 (- 2.184) = -9765.7 kNm

T9a (roof) = Vz (1.5 ex + 0.05b) = 2169.8(1.5 x 0.516 + 0.05 x 53 = 7429.4 kNm T9b (roof) = Vz (ez - 0.05b) = 2169.8(0.516-0.05 x 53) = -4630.4 kNm

- 30 -

Table 4.1 Additional Shears for the L-shaped building due to earthquake forces acting in X- direction

p

xxxx I

KZTV =1 ∴Ip = 14590.74k m4

- 31 -

4.6 MODE SHAPES The mode shape coefficients outputted from STAAD are listed in Table-4.2 for the Master joints. The first few mode shapes are shown in Figures 4.1 to 4.8 for 3D building Fig 4.9 shows the top floor displacements in plan illustrating the torsion mode # 3 Table 4.2 Mode shape coefficients for Master slave joints Joint #

Mode # x-axis y-axis z-axis x-rotation y-rotation z-rotation

29 1 0.00177 -0.0023 -0.07244 -0.0006652 -0.0000009 -0.000024934 1 0.00177 -0.00235 -0.07052 -0.0006457 -0.0000009 -0.000008944 1 0.001 -0.00005 -0.07129 -0.0006252 -0.0000009 -0.000008547 1 0.00062 0.00239 -0.07244 -0.0006649 -0.0000009 0.000002849 1 0.00062 -0.00041 -0.07168 -0.0006095 -0.0000009 -0.000014653 1 0.00023 0.0024 -0.07168 -0.0006561 -0.0000009 0.000006456 1 0.00023 0.00228 -0.07052 -0.0006459 -0.0000009 -0.0000093

220 1 0.00547 -0.00432 -0.21437 -0.0008675 -0.0000030 -0.0000325225 1 0.00547 -0.00441 -0.20801 -0.0008385 -0.0000030 -0.0000141235 1 0.00293 -0.0001 -0.21056 -0.0008168 -0.0000030 -0.0000110238 1 0.00166 0.00448 -0.21437 -0.0008672 -0.0000030 0.0000033240 1 0.00166 -0.00075 -0.21183 -0.0008001 -0.0000030 -0.0000173244 1 0.00039 0.0045 -0.21183 -0.0008545 -0.0000030 0.0000087247 1 0.00039 0.00429 -0.20801 -0.0008387 -0.0000030 -0.0000094

410 1 0.00981 -0.00597 -0.37404 -0.0008932 -0.0000057 -0.0000342415 1 0.00981 -0.0061 -0.36224 -0.0008615 -0.0000057 -0.0000154425 1 0.0051 -0.00014 -0.36696 -0.0008397 -0.0000057 -0.0000114428 1 0.00274 0.0062 -0.37404 -0.0008929 -0.0000057 0.0000037430 1 0.00274 -0.00101 -0.36932 -0.0008232 -0.0000057 -0.0000176434 1 0.00038 0.00621 -0.36932 -0.0008791 -0.0000057 0.0000095437 1 0.00038 0.00593 -0.36224 -0.0008617 -0.0000057 -0.0000089

600 1 0.01417 -0.00725 -0.52997 -0.0008375 -0.0000083 -0.0000324605 1 0.01417 -0.00741 -0.51261 -0.0008067 -0.0000083 -0.0000152615 1 0.00723 -0.00017 -0.51955 -0.0007865 -0.0000083 -0.0000108618 1 0.00376 0.00753 -0.52997 -0.0008372 -0.0000083 0.0000034620 1 0.00376 -0.0012 -0.52302 -0.0007718 -0.0000083 -0.0000166624 1 0.00029 0.00754 -0.52302 -0.0008239 -0.0000083 0.0000090627 1 0.00029 0.0072 -0.51261 -0.0008069 -0.0000083 -0.0000079

790 1 0.0182 -0.00818 -0.67143 -0.0007366 -0.0000108 -0.0000288

795 1 0.0182 -0.00836 -0.6489 -0.0007090 -0.0000108 -0.0000138805 1 0.00919 -0.00019 -0.65791 -0.0006911 -0.0000108 -0.0000096808 1 0.00468 0.00849 -0.67143 -0.0007363 -0.0000108 0.0000028810 1 0.00468 -0.00132 -0.66242 -0.0006787 -0.0000108 -0.0000149814 1 0.00018 0.0085 -0.66242 -0.0007245 -0.0000108 0.0000078817 1 0.00018 0.00812 -0.6489 -0.0007092 -0.0000108 -0.0000068

- 32 -

980 1 0.0217 -0.0088 -0.79194 -0.0006065 -0.0000130 -0.0000240985 1 0.0217 -0.009 -0.76492 -0.0005833 -0.0000130 -0.0000119995 1 0.01089 -0.0002 -0.77573 -0.0005684 -0.0000130 -0.0000081998 1 0.00548 0.00914 -0.79194 -0.0006063 -0.0000130 0.0000021

1000 1 0.00548 -0.00138 -0.78113 -0.0005588 -0.0000130 -0.00001251004 1 0.00008 0.00915 -0.78113 -0.0005964 -0.0000130 0.00000631007 1 0.00008 0.00874 -0.76492 -0.0005834 -0.0000130 -0.0000054 1170 1 0.02455 -0.00918 -0.88735 -0.0004597 -0.0000147 -0.00001861175 1 0.02455 -0.00938 -0.85668 -0.0004415 -0.0000147 -0.00000951185 1 0.01228 -0.00021 -0.86895 -0.0004293 -0.0000147 -0.00000631188 1 0.00614 0.00953 -0.88735 -0.0004595 -0.0000147 0.00000141190 1 0.00614 -0.00141 -0.87508 -0.0004225 -0.0000147 -0.00001011194 1 0.00001 0.00953 -0.87508 -0.0004518 -0.0000147 0.00000461197 1 0.00001 0.00911 -0.85668 -0.0004416 -0.0000147 -0.0000041 1360 1 0.02669 -0.00937 -0.95587 -0.0003094 -0.0000160 -0.00001251365 1 0.02669 -0.00958 -0.92243 -0.0002960 -0.0000160 -0.00000781375 1 0.01332 -0.00022 -0.93581 -0.0002906 -0.0000160 -0.00000451378 1 0.00663 0.00973 -0.95587 -0.0003093 -0.0000160 0.00000021380 1 0.00663 -0.00141 -0.94249 -0.0002880 -0.0000160 -0.00000631384 1 -0.00006 0.00973 -0.94249 -0.0003038 -0.0000160 0.00000261387 1 -0.00006 0.0093 -0.92243 -0.0002961 -0.0000160 -0.0000019 1550 1 0.02821 -0.00944 -1 -0.0002053 -0.0000170 -0.00001061555 1 0.02821 -0.00965 -0.96454 -0.0001953 -0.0000170 -0.00000391565 1 0.01403 -0.00022 -0.97873 -0.0001788 -0.0000170 -0.00000281568 1 0.00694 0.00981 -1 -0.0002051 -0.0000170 0.00000221570 1 0.00694 -0.00141 -0.98582 -0.0001743 -0.0000170 -0.00000841574 1 -0.00015 0.0098 -0.98582 -0.0002011 -0.0000170 0.00000341577 1 -0.00015 0.00937 -0.96454 -0.0001954 -0.0000170 -0.0000028

29 2 0.07292 0.00237 0.00249 0.0000153 0.0000012 -0.000662334 2 0.07292 -0.0023 -0.00006 0.0000069 0.0000012 -0.000662644 2 0.07393 -0.00041 0.00096 0.0000082 0.0000012 -0.000617447 2 0.07444 0.00226 0.00249 0.0000317 0.0000012 -0.000677749 2 0.07444 0.00011 0.00147 0.0000033 0.0000012 -0.000626453 2 0.07495 0.00234 0.00147 0.0000224 0.0000012 -0.000684856 2 0.07495 -0.00235 -0.00006 -0.0000095 0.0000012 -0.0006823

220 2 0.21276 0.00445 0.00762 0.0000227 0.0000039 -0.0008478225 2 0.21276 -0.00431 -0.00047 0.0000060 0.0000039 -0.0008481235 2 0.216 -0.00077 0.00277 0.0000103 0.0000039 -0.0007987238 2 0.21762 0.00423 0.00762 0.0000412 0.0000039 -0.0008695240 2 0.21762 0.00021 0.00438 0.0000057 0.0000039 -0.0008101244 2 0.21923 0.00437 0.00438 0.0000275 0.0000039 -0.0008790247 2 0.21923 -0.00441 -0.00047 -0.0000126 0.0000039 -0.0008762

410 2 0.36806 0.00614 0.01354 0.0000241 0.0000070 -0.0008644

- 33 -

415 2 0.36806 -0.00595 -0.00114 0.0000050 0.0000070 -0.0008647425 2 0.37393 -0.00106 0.00473 0.0000103 0.0000070 -0.0008150428 2 0.37687 0.00584 0.01354 0.0000428 0.0000070 -0.0008877430 2 0.37687 0.0003 0.00767 0.0000057 0.0000070 -0.0008269434 2 0.37981 0.00603 0.00767 0.0000278 0.0000070 -0.0008977437 2 0.37981 -0.00609 -0.00114 -0.0000138 0.0000070 -0.0008948

600 2 0.51859 0.00744 0.01939 0.0000230 0.0000102 -0.0008057605 2 0.51859 -0.00721 -0.00194 0.0000039 0.0000102 -0.0008060615 2 0.52712 -0.00127 0.00659 0.0000094 0.0000102 -0.0007602618 2 0.53138 0.00708 0.01939 0.0000401 0.0000102 -0.0008280620 2 0.53138 0.00037 0.01086 0.0000051 0.0000102 -0.0007714624 2 0.53565 0.0073 0.01086 0.0000255 0.0000102 -0.0008376627 2 0.53565 -0.00738 -0.00194 -0.0000133 0.0000102 -0.0008349

790 2 0.6545 0.00839 0.02471 0.0000204 0.0000132 -0.0007059795 2 0.6545 -0.00813 -0.00276 0.0000028 0.0000132 -0.0007061805 2 0.66549 -0.00143 0.00823 0.0000080 0.0000132 -0.0006659808 2 0.67098 0.00797 0.02471 0.0000352 0.0000132 -0.0007258810 2 0.67098 0.00043 0.01372 0.0000040 0.0000132 -0.0006758814 2 0.67648 0.00821 0.01372 0.0000218 0.0000132 -0.0007343817 2 0.67648 -0.00831 -0.00276 -0.0000121 0.0000132 -0.0007320

980 2 0.76986 0.00902 0.02924 0.0000169 0.0000157 -0.0005789985 2 0.76986 -0.00874 -0.00354 0.0000017 0.0000157 -0.0005791995 2 0.78297 -0.00153 0.00957 0.0000063 0.0000157 -0.0005462998 2 0.78953 0.00857 0.02924 0.0000288 0.0000157 -0.0005955

1000 2 0.78953 0.00047 0.01613 0.0000028 0.0000157 -0.00055431004 2 0.79608 0.00882 0.01613 0.0000172 0.0000157 -0.00060271007 2 0.79608 -0.00894 -0.00354 -0.0000103 0.0000157 -0.0006007 1170 2 0.86074 0.0094 0.03282 0.0000128 0.0000178 -0.00043601175 2 0.86074 -0.00911 -0.00425 0.0000006 0.0000178 -0.00043621185 2 0.87557 -0.00159 0.01058 0.0000044 0.0000178 -0.00041051188 2 0.88299 0.00893 0.03282 0.0000217 0.0000178 -0.00044891190 2 0.88299 0.0005 0.01799 0.0000014 0.0000178 -0.00041671194 2 0.8904 0.00918 0.01799 0.0000123 0.0000178 -0.00045451197 2 0.8904 -0.00931 -0.00425 -0.0000083 0.0000178 -0.0004530 1360 2 0.92537 0.00959 0.03539 0.0000095 0.0000193 -0.00028831365 2 0.92537 -0.00929 -0.00489 -0.0000012 0.0000193 -0.00028841375 2 0.94148 -0.00162 0.01122 0.0000025 0.0000193 -0.00027561378 2 0.94954 0.00912 0.03539 0.0000140 0.0000193 -0.00029761380 2 0.94954 0.00052 0.01928 0.0000012 0.0000193 -0.00027941384 2 0.95759 0.00936 0.01928 0.0000071 0.0000193 -0.00030141387 2 0.95759 -0.0095 -0.00489 -0.0000058 0.0000193 -0.0003006 1550 2 0.96595 0.00966 0.03709 0.0000049 0.0000204 -0.00018721555 2 0.96595 -0.00936 -0.00547 0.0000002 0.0000204 -0.00018731565 2 0.98297 -0.00163 0.01155 0.0000014 0.0000204 -0.0001613

- 34 -

1568 2 0.99149 0.00918 0.03709 0.0000111 0.0000204 -0.00019401570 2 0.99149 0.00053 0.02007 -0.0000042 0.0000204 -0.00016521574 2 1 0.00942 0.02007 0.0000040 0.0000204 -0.00019741577 2 1 -0.00957 -0.00547 -0.0000061 0.0000204 -0.0001961

29 3 -0.05381 0.00068 0.07502 0.0006895 0.0000685 0.000497634 3 -0.05381 -0.00044 -0.0679 -0.0006235 0.0000685 0.000496844 3 0.00336 -0.00003 -0.01073 -0.0000937 0.0000685 -0.000028447 3 0.03194 -0.00135 0.07502 0.0006871 0.0000685 -0.000299649 3 0.03194 0.00013 0.01785 0.0001481 0.0000685 -0.000268553 3 0.06052 0.00136 0.01785 0.0001697 0.0000685 -0.000555656 3 0.06052 0.00021 -0.0679 -0.0006242 0.0000685 -0.000559057 3 -0.05381 0.01848 0.07017 0.0004234 0.0000685 0.0001155

220 3 -0.15722 0.00128 0.21977 0.0008859 0.0002004 0.0006365225 3 -0.15722 -0.00083 -0.1984 -0.0007983 0.0002004 0.0006356235 3 0.01005 -0.00005 -0.03113 -0.0001194 0.0002004 -0.0000380238 3 0.09369 -0.00254 0.21977 0.0008832 0.0002004 -0.0003846240 3 0.09369 0.00025 0.0525 0.0001933 0.0002004 -0.0003486244 3 0.17732 0.00255 0.0525 0.0002181 0.0002004 -0.0007140247 3 0.17732 0.0004 -0.1984 -0.0007991 0.0002004 -0.0007179

410 3 -0.27208 0.00177 0.38096 0.0009045 0.0003471 0.0006486415 3 -0.27208 -0.00114 -0.34337 -0.0008135 0.0003471 0.0006476425 3 0.01765 -0.00007 -0.05364 -0.0001210 0.0003471 -0.0000394428 3 0.16252 -0.0035 0.38096 0.0009017 0.0003471 -0.0003929430 3 0.16252 0.00034 0.09123 0.0001977 0.0003471 -0.0003561434 3 0.30739 0.00351 0.09123 0.0002231 0.0003471 -0.0007291437 3 0.30739 0.00055 -0.34337 -0.0008144 0.0003471 -0.0007329

600 3 -0.38332 0.00215 0.53729 0.0008428 0.0004893 0.0006036605 3 -0.38332 -0.00138 -0.48378 -0.0007572 0.0004893 0.0006027615 3 0.02511 -0.00008 -0.07535 -0.0001122 0.0004893 -0.0000370618 3 0.22933 -0.00425 0.53729 0.0008403 0.0004893 -0.0003661620 3 0.22933 0.00041 0.12886 0.0001844 0.0004893 -0.0003319624 3 0.43354 0.00425 0.12886 0.0002079 0.0004893 -0.0006795627 3 0.43354 0.00067 -0.48378 -0.0007580 0.0004893 -0.0006829

790 3 -0.48359 0.00242 0.67836 0.0007373 0.0006176 0.0005275795 3 -0.48359 -0.00156 -0.61036 -0.0006618 0.0006176 0.0005267805 3 0.0319 -0.00009 -0.09487 -0.0000978 0.0006176 -0.0000326808 3 0.28964 -0.00478 0.67836 0.0007351 0.0006176 -0.0003203810 3 0.28964 0.00046 0.16287 0.0001613 0.0006176 -0.0002902814 3 0.54739 0.00478 0.16287 0.0001818 0.0006176 -0.0005944817 3 0.54739 0.00075 -0.61036 -0.0006625 0.0006176 -0.0005974

980 3 -0.56848 0.0026 0.79788 0.0006031 0.0007263 0.0004310985 3 -0.56848 -0.00167 -0.71753 -0.0005409 0.0007263 0.0004303995 3 0.03768 -0.0001 -0.11136 -0.0000797 0.0007263 -0.0000269

- 35 -

998 3 0.34076 -0.00514 0.79788 0.0006013 0.0007263 -0.00026191000 3 0.34076 0.00049 0.19172 0.0001319 0.0007263 -0.00023731004 3 0.64384 0.00513 0.19172 0.0001486 0.0007263 -0.00048631007 3 0.64384 0.0008 -0.71753 -0.0005415 0.0007263 -0.0004886 1170 3 -0.63511 0.00271 0.89179 0.0004524 0.0008116 0.00032281175 3 -0.63511 -0.00174 -0.80165 -0.0004053 0.0008116 0.00032241185 3 0.04226 -0.0001 -0.12427 -0.0000593 0.0008116 -0.00002031188 3 0.38095 -0.00536 0.89179 0.0004512 0.0008116 -0.00019651190 3 0.38095 0.00051 0.21442 0.0000985 0.0008116 -0.00017751194 3 0.71964 0.00534 0.21442 0.0001113 0.0008116 -0.00036491197 3 0.71964 0.00084 -0.80165 -0.0004057 0.0008116 -0.00036651360 3 -0.68221 0.00277 0.95831 0.0002977 0.0008720 0.00021131365 3 -0.68221 -0.00178 -0.86112 -0.0002657 0.0008720 0.00021101375 3 0.04556 -0.0001 -0.13335 -0.0000388 0.0008720 -0.00001401378 3 0.40945 -0.00546 0.95831 0.0002971 0.0008720 -0.00012911380 3 0.40945 0.00052 0.23054 0.0000662 0.0008720 -0.00011841384 3 0.77333 0.00544 0.23054 0.0000731 0.0008720 -0.00024021387 3 0.77333 0.00085 -0.86112 -0.0002659 0.0008720 -0.0002410 1550 3 -0.71156 0.00279 1 0.0001934 0.0009097 0.00013721555 3 -0.71156 -0.00179 -0.89821 -0.0001719 0.0009097 0.00013681565 3 0.04772 -0.0001 -0.13892 -0.0000230 0.0009097 -0.00000841568 3 0.42736 -0.0055 1 0.0001926 0.0009097 -0.00008471570 3 0.42736 0.00052 0.24072 0.0000366 0.0009097 -0.00006851574 3 0.807 0.00548 0.24072 0.0000470 0.0009097 -0.00015621577 3 0.807 0.00086 -0.89821 -0.0001722 0.0009097 -0.0001570

4.7 MEMBER END FORCES

The axial forces, shear forces, bending moments and twisting moments obtained

for the Ground floor columns are given in Table 4.3. The same are illustrated in Fig. 4.10

to 4.13 The member end forces for different columns (central, edge, corners) considering

Ordinary moment resisting frame (OMRF, R=3) & special moment resisting frame

(SMRF, R=5) are given in Table 4.4 to 4.15 for different cases.

4.8 DISPLACEMENTS

The maximum displacements in column joints at various floors are shown in Figs

4.14 for the L- shaped building without considering torsion effects; with are regarded to

torsion effects the increased values are shown in Fig. 4.15. The relative displacements in

- 36 -

beams (edge) compared to that of columns is shown in Fig. 4.16 & 4.17 respectively. It is

observed that the max. Displacements are within the allowable limit 0.004H prescribed by

the IS code (1893-2002).

4.9 MOMENTS AND STRESSES IN THE FLAT SLAB

The contours for bending moments, twisting moments and stresses in flat slab of

Ground floor are shown in Fig. 4.18 to 4.22. The magnitudes are differentiated by

different coloures in the Figures.

Table 4.3 MEMBER END FORCES

MEMBER LOAD JT AXIAL SHEAR-Y

SHEAR-Z TORSION MOM-Y MOM-Z

KN KN KN KN.M KN.M KN.M

1 5 1 4366.64 97.66 97.95 1.69 -49.92 759.92 29 -3170.55 262.54 -62.35 1.6 -203.32 -99.72 6 1 2590.62 520.39 38.78 -8.44 33.47 2609.14 29 -2505.57 -520.39 -38.78 8.44 -196.34 -423.5

2 5 2 6368.84 229.44 159.3 1.25 -159.38 938.26 30 -6233.81 226.09 -141.12 1.15 -425.15 62.67 6 2 6354.63 746.66 138.76 -4.68 -134.57 2915.95 30 -6269.58 -746.66 -138.76 4.68 -448.23 220

3 5 3 6305.51 224.82 157.65 1.22 -164.4 934.61 31 -6189.21 228.7 -142.64 1.2 -428.16 48.99 6 3 6279.09 740.44 145.56 -4.61 -174.39 2912 31 -6194.04 -740.44 -145.56 4.61 -436.97 197.84

4 5 4 6305.06 227.4 155.74 1.18 -167.66 939.58 32 -6188.72 225.9 -144.44 1.23 -424.84 54.99 6 4 6297.23 743.53 153.58 -4.52 -214.69 2918.41 32 -6212.18 -743.53 -153.58 4.52 -430.36 204.43

5 5 5 6380.12 224.69 155.34 1.13 -167.13 936.97 33 -6224.18 230.31 -144.97 1.26 -421.98 44.37 6 5 6330.97 743.13 159.44 -4.51 -251.57 2918.07 33 -6245.92 -743.13 -159.44 4.51 -418.09 203.09

6 5 6 4351.6 261.3 91.19 1.68 -75.04 984.64 34 -3190.86 98.38 -68.89 1.76 -200.46 363.89 6 6 5030.56 685.13 117.83 -8.38 -229.06 2837.23

- 37 -

34 -4945.51 -685.13 -117.83 8.38 -265.85 40.327 5 7 6780.98 18.71 10.16 1.18 60.13 656.04

35 -5844.67 324.37 19.34 1.25 23.72 -276.77 6 7 5421.65 429.15 -33.99 -5.14 128.98 2523.76 35 -5336.6 -429.15 33.99 5.14 13.79 -721.31

8 5 8 10715.89 211.63 5.6 1.4 51.92 914.85

36 -

10601.16 204.58 16.76 1.42 22.18 82.24 6 8 10731.22 696.39 -21.5 -5.61 79.77 2881.65

36 -

10646.17 -696.39 21.5 5.61 10.54 43.199 5 9 10641.2 205.02 2.97 1.48 46.23 908.43

37 -

10545.57 209.29 14.72 1.5 18.32 65.29 6 9 10634.63 687.9 -11.19 -5.71 35.12 2873.39

37 -

10549.58 -687.9 11.19 5.71 11.87 15.810 5 10 10639.32 207.98 1.34 1.47 42.77 914.02

38 -10546.9 206.22 12.76 1.53 17.29 72.28 6 10 10637.2 690.94 -1.65 -5.67 -7 2879.25

38 -

10552.15 -690.94 1.65 5.67 13.92 22.7111 5 11 10714.82 203.21 0.8 1.4 41.81 909.13

39 -

10602.29 212.64 11.21 1.45 20.81 53.17 6 11 10671.08 688.1 8.15 -5.47 -49.06 2876.46

39 -

10586.03 -688.1 -8.15 5.47 14.84 13.5812 5 12 6781.77 323.23 3.61 1.24 44.94 1068.89

40 -5844.54 19.46 12.17 1.19 20.92 590.12 6 12 7290.36 733.76 20.63 -4.9 -95.87 2937.03 40 -7205.31 -733.76 -20.63 4.9 9.22 144.74

13 5 13 6750.84 21.45 20.53 1.24 50.16 660.89 41 -5824.39 326.03 10.24 1.23 -4.42 -279.37 6 13 5382.71 438.42 -26 -5.17 120.03 2567.74 41 -5297.66 -438.42 26 5.17 -10.82 -726.39

14 5 14 10637.85 213.52 20.65 1.38 34.17 918.45

42 -

10526.02 206.48 1.69 1.45 -23.33 80.69 6 14 10650.17 705.67 -6.15 -5.64 61.45 2925.4

42 -

10565.12 -705.67 6.15 5.64 -35.63 38.4315 5 15 10536.29 206.94 14.58 1.52 33.1 912.09

43 -

10438.22 210.71 3 1.52 -17.54 64.58 6 15 10536.61 696.27 1.25 -5.65 20.4 2915.24

43 -

10451.56 -696.27 -1.25 5.65 -25.64 9.0716 5 16 10499.42 209.56 9.3 1.54 34.78 917.31

44 - 207.38 5 1.59 -7.71 71.87

- 38 -

10407.03 6 16 10494.58 697.83 5.95 -5.74 -14.95 2918.48

44 -

10409.53 -697.83 -5.95 5.74 -10.05 12.4217 5 17 10579.71 204.31 8.02 1.46 34.12 912.02

45 -

10467.16 214.6 3.89 1.5 -2.06 50.79 6 17 10538.79 694.29 14.96 -5.55 -55.76 2914.5

45 -

10453.74 -694.29 -14.96 5.55 -7.07 1.5218 5 18 6691.44 324.03 7.8 1.23 40.98 1071.49

46 -5779.41 22.08 8.61 1.24 9.56 584.56 6 18 7209.58 738.09 24.5 -4.78 -97.53 2972.38 46 -7124.53 -738.09 -24.5 4.78 -5.38 127.61

19 5 19 4363.65 104.53 -72.42 1.69 155.6 772.62 47 -3193.38 270.21 88.83 2 234.58 -114.1 6 19 2645.84 552.03 -87.99 -3.73 202.4 2750.97 47 -2560.79 -552.03 87.99 3.73 167.15 -432.44

20 5 20 6409.14 237.68 -138.64 1.22 244.56 952.05 48 -6281.53 233.07 159.03 1.39 431.43 74.84 6 20 6427.86 787.34 -163.33 -6.17 271.72 3066.77 48 -6342.81 -787.34 163.33 6.17 414.25 240.04

21 5 21 8850.82 156.52 -48.31 1.26 136.92 846.76 49 -8545.37 291.23 79.26 1.2 197.3 -137.38 6 21 8991.27 678.84 -85.94 -4.57 136.77 2922.59 49 -8906.22 -678.84 85.94 4.57 224.17 -71.48

22 5 22 10644.96 216.29 10.55 1.41 34.91 928.2

50 -

10551.19 208.33 3.39 1.5 -13.34 75.52 6 22 10641.05 712.22 8.16 -5.21 -15.24 2966.19 50 -10556 -712.22 -8.16 5.21 -19.01 25.13

23 5 23 10692.56 208.62 9.61 1.39 34.37 919.81

51 -

10579.17 218.31 2.55 1.46 -8.62 47.13 6 23 10649.39 706.09 16.05 -5.2 -54.69 2958.43

51 -

10564.34 -706.09 -16.05 5.2 -12.71 7.1424 5 24 6770.52 328.76 10.05 1.19 40.13 1080.03

52 -5842.45 25.33 6.86 1.31 2.41 578.41 6 24 7318.89 748.68 25.82 -4.58 -95.69 3014.85 52 -7233.84 -748.68 -25.82 4.58 -12.75 129.62

25 5 25 4373.68 114.23 -78.25 1.78 146.66 792.47 53 -3248.98 268.85 85.69 1.62 240.98 -109.3 6 25 2648.29 559.37 -67.68 -0.72 110.91 2782.42 53 -2563.24 -559.37 67.68 0.72 173.33 -433.07

26 5 26 6375.7 244.21 -145.73 1.28 243.39 967.97 54 -6229.35 232.39 159.09 1.39 433.94 84.31 6 26 6376.04 791.89 -151.83 -5.05 199.38 3097.43 54 -6290.99 -791.89 151.83 5.05 438.28 228.5

27 5 27 6370.28 235.54 -148.13 1.36 240.35 958.32

- 39 -

55 -6250.91 241.23 156.73 1.33 443.32 57.57 6 27 6290.51 783.04 -140.26 -5.02 154.67 3087.05 55 -6205.46 -783.04 140.26 5.02 434.44 201.72

28 5 28 4380.75 273.15 -73.96 1.72 156.1 1008.14 56 -3180.81 109.71 90.88 1.73 234.74 343.17 6 28 5023.48 716.48 -81.93 -1 51.76 2994.79 56 -4938.43 -716.48 81.93 1 292.35 14.42 Due to large size input data such as member (Column) forces are skip the input data for minimizing the information

- 40 -

Table 4.4 Column forces, moments in X & Y direction , twisting moments & reinforcement for Zone II, Type-I soil, OMRF, R=3

For- ces

Column - Groups

9thfloor

8thfloor

7thfloor

6thfloor

5thfloor

4thfloor

3rdfloor

2ndfloor

1stfloor

Central Col 1247 2719 4190 5662 7132 8603 10073 11541 13008E1 Column 444 944 1430 1905 2369 2826 3277 3811 4336 B1 Column 443 942 1426 1900 2363 2819 3269 3861 4384 B3 Column 1022 2207 3397 4589 5784 6984 8187 9641 11004A3 Column 452 963 1458 1943 2415 2879 3333 3944 4554 A6 Column 472 1020 1574 2136 2702 3269 3833 4393 5113 E6 Column 473 1021 1576 2139 2706 3273 3838 4396 5003

P

Central Col 0.19 0.19 0.20 0.21 0.2 0.18 0.13 0.001 0.068 E1 Column 0.19 0.19 0.20 0.21 0.2 0.18 0.13 0.001 0.068 B1 Column 0.19 0.19 0.20 0.21 0.2 0.18 0.13 0.001 0.068 B3 Column 0.19 0.19 0.20 0.21 0.2 0.18 0.13 0.001 0.068 A3 Column 0.19 0.19 0.20 0.21 0.2 0.18 0.13 0.001 0.068 A6 Column 0.19 0.19 0.20 0.21 0.2 0.18 0.13 0.001 0.068 E6 Column 0.19 0.19 0.20 0.21 0.2 0.18 0.13 0.001 0.068

M x

Central Col 3.0 3.0 3.0 3.0 3.0 3.25 1.0 102 0.85 E1 Column 457 236 277 260 254 244 240 265 192 B1 Column 454 260 276 259 255 243 306 315 173 B3 Column 404 264 276 267 260 259 166 148 111 A3 Column 502 290 305 285 278 263 293 354 255 A6 Column 471 281 302 290 290 287 274 359 286 E6 Column 477 285 304 294 292 287 277 298 214

M y

Central Col 135 194 235 256 266 264 281 342 492 E1 Column 386 254 223 178 146 97 119 220 385 B1 Column 382 252 221 176 144 95 120 221 383 B3 Column 227 132 76 57 72 73 158 226 451 A3 Column 377 250 218 174 139 104 102 164 378 A6 Column 547 396 460 455 453 441 433 604 589 E6 Column 545 395 459 454 426 440 441 542 563

M z

Central Col 639 1393 2148 2903 3655 4409 5162 5915 7776 E1 Column 4787 920 733 976 114 1448 1679 1953 2222 B1 Column 4732 869 731 973 1211 1445 1675 1979 2247 B3 Column 1537 1131 1741 2352 2964 3579 4196 4941 5639 A3 Column 5016 1037 748 996 1238 1475 1709 2021 2334 A6 Column 5977 1868 1297 1095 1385 1675 1965 2251 2621

Steel area

E6 Column 6028 1871 1299 1096 1387 1678 1967 2253 2564

- 41 -

Central Col 0.17% 0.22% 0.28% 0.39% 0.46% 0.56% 0.67% 0.78% 0.97%E1 Column 0.60% 0.17% 0.17% 0.17% 0.17% 0.22% 0.22% 0.28% 0.28%B1 Column 0.60% 0.17% 0.17% 0.17% 0.17% 0.22% 0.22% 0.28% 0.28%B3 Column 0.22% 0.17% 0.22% 0.3% 0.39% 0.45% 0.56% 0.62% 0.73%A3 Column 0.62% 0.17% 0.17% 0.17% 0.17% 0.22% 0.22% 0.28% 0.3% A6 Column 0.78% 0.28% 0.17% 0.17% 0.22% 0.22% 0.28% 0.28% 0.35%

% of Steel

E6 Column 0.78% 0.28% 0.17% 0.17% 0.22% 0.22% 0.28% 0.28% 0.35%

Table 4.5 for Zone II, Type- II soil, OMRF, R=3

- 42 -

For- ces

Column - Groups

9thfloo

8thfloo

7thfloo

6thfloo

5thfloo

4thfloo

3rdfloo

2ndfloor

1stfloor

Central Col 1247 2719 4191 5661 7132 8602 10072 11541 13007E1 Column 440 931 1404 1863 2310 2746 3176 3691 4201 B1 Column 438 928 1400 1858 2303 2739 3169 3741 4250 B3 Column 1023 2208 3398 4593 5291 6993 8198 9656 11021A3 Column 447 851 1434 1903 2358 2802 3237 3828 4423 A6 Column 478 1033 1600 2177 2761 3348 3933 4512 5248 E6 Column 478 1035 1602 2181 2766 3353 3939 4516 5138

P


M x

Central Col 3.0 3.0 3.0 3.0 3.0 3.3 1.2 1.3 0.86 E1 Column 454 259 272 253 248 239 232 258 88 B1 Column 451 256 271 253 249 236 299 309 168 B3 Column 410 270 283 275 269 268 229 156 115 A3 Column 501 287 302 281 268 257 287 348 251 A6 Column 481 284 306 296 296 295 282 364 291 E6 Column 481 289 310 301 298 295 284 305 218

M y


M z


Steel area

Central Col 0.17% 0.22% 0.28% 0.4% 0.46% 0.56% 0.67% 0.78% 1.17%E1 Column 0.6% 0.17% 0.17% 0.17% 0.17% 0.22% 0.22% 0.28% 0.28%B1 Column 0.6% 0.17% 0.17% 0.17% 0.17% 0.22% 0.22% 0.28% 0.28%B3 Column 0.17% 0.17% 0.22% 0.3% 0.4% 0.45% 0.56% 0.61% 0.73%A3 Column 0.6% 0.17% 0.17% 0.17% 0.17% 0.22% 0.22% 0.28% 0.3% A6 Column 0.78% 0.28% 0.22% 0.17% 0.22% 0.22% 0.28% 0.3% 0.34%

% of Steel

E6 Column 0.78% 0.28% 0.22% 0.17% 0.22% 0.22% 0.28% 0.3% 0.34%

- 43 -

Table 4.6 for Zone II, Type-III soil, OMRF, R=3

For- ces

Column - Groups

9thfloor

8thfloor

7thfloor

6thfloor

5thfloor

4thfloor

3rdfloor

2ndfloor

1stfloor

Central Col. 1247 2719 4190 561 7132 8602 10072 11540 13007 E1 Column 435 919 1382 1827 2258 2678 3090 3588 4085 B1 Column 433 916 138 1822 2252 2671 3083 3638 4134 B3 Column 1023 2209 3400 4596 5796 7000 8209 9668 11036 A3 Column 443 940 1413 1869 2309 2736 3153 3727 4310 A6 Column 482 1045 1622 2213 2813 3417 4019 4615 5363 E6 Column 483 1046 1625 2217 2817 3422 4025 4619 5254

P

Central Col. 0.28 0.28 0.3 0.32 0.32 0.3 0.21 0.036 0.082 E1 Column 0.28 0.28 0.3 0.32 0.32 0.3 0.21 0.036 0.082 B1 Column 0.28 0.28 0.3 0.32 0.32 0.3 0.21 0.036 0.082 B3 Column 0.28 0.28 0.3 0.32 0.32 0.3 0.21 0.036 0.082 A3 Column 0.28 0.28 0.3 0.32 0.32 0.3 0.21 0.036 0.082 A6 Column 0.28 0.28 0.3 0.32 0.32 0.3 0.21 0.036 0.082 E6 Column 0.28 0.28 0.3 0.32 0.32 0.3 0.21 0.036 0.082

M x

Central Col. 7.0 3.0 3.0 3.0 3.0 3.4 1.2 0.655 0.869 E1 Column 451 256 268 248 242 233 227 253 185 B1 Column 448 253 267 248 244 230 294 271 72 B3 Column 415 254 289 281 277 276 237 163 52 A3 Column 500 285 299 277 268 252 281 343 248 A6 Column 476 287 309 301 298 299 287 309 295 E6 Column 484 292 208 306 304 301 290 311 220

M y

Central Col. 224 324 392 427 443 441 468 570 823.5 E1 Column 369 242 184 114 62 141 15 149 701 B1 Column 367 240 182 112 59 26 15 151 699 B3 Column 204 145 192 243 267 268 364 469 786 A3 Column 364 238 179 109 53 27 66 164 693 A6 Column 600 497 574 576 574 558 561 449 904 E6 Column 598 496 572 574 572 556 569 718 880

M z


Steel area

Central Col. 0.17% 0.22% 0.28% 0.4% 0.46% 0.56% 0.7% 0.8% 1.3%

- 44 -

E1 Column 0.56% 0.17% 0.17% 0.17% 0.17% 0.22% 0.22% 0.3% 0.3% B1 Column 0.56% 0.17% 0.17% 0.17% 0.17% 0.22% 0.22% 0.3% 0.3% B3 Column 0.17% 0.17% 0.22% 0.3% 0.4% 0.45% 0.56% 0.61% 0.73% A3 Column 0.6% 0.17% 0.17% 0.17% 0.17% 0.22% 0.22% 0.3% 0.3% A6 Column 0.79% 0.33% 0.3% 0.17% 0.22% 0.22% 0.3% 0.3% 0.4%

% of Steel

E6 Column 0.84% 0.34% 0.28% 0.17% 0.22% 0.22% 0.3% 0.3% 0.34%

Table 4.7 for Zone V, Type-I soil, OMRF, R=3

For- ces

Column - Groups

9thfloor

8thfloor

7thfloor

6thfloor

5thfloor

4thfloor

3rdfloor

2ndfloor

1stfloor


P


M x

Central Col 4.42 3066 3.8 3.7 3.45 3.7 1.6 1.62 1.3 E1 Column 303 236 242 217 206 1924 189 218 165 B1 Column 304 234 243 219 209 193 258 267 141 B3 Column 449 306 327 326 325 326 286 203 146 A3 Column 495 272 281 253 239 219 248 311 226 A6 Column 491 306 329 331 335 335 325 400 319 E6 Column 502 312 339 339 342 341 329 347 240

M y


M z

Central Col 639 1393 2147 2901 3655 4408 5161 9462 18792 E1 Column 3762 1367 653 823 993 1154 1309 1510 5689 B1 Column 3728 1362 710 820 990 1150 1305 1536 5422

B3 Column 1730 1134 1748 2366 2988 3613 4240 4996 13686

- 45 -

A3 Column 4029 1574 921 849 1026 1191 1349 1590 5175 A6 Column 7579 4705 4548 3251 1718 1969 2334 2693 5612 E6 Column 7645 4717 4646 3259 1721 1973 2339 2697 5208

Stee area

Central Col 0.17% 0.22% 0.28% 0.4% 0.46% 0.56% 0.67% 1.17% 2.33% E1 Column 0.46% 0.22% 0.17% 0.17% 0.17% 0.17% 0.17% 0.22% 0.73% B1 Column 0.46% 0.22% 0.17% 0.17% 0.17% 0.17% 0.17% 0.22% 0.67% B3 Column 0.22% 0.17% 0.22% 0.3% 0.39% 0.45% 0.56% 0.62% 1.7% A3 Column 0.5% 0.22% 0.17% 0.17% 0.17% 0.17% 0.17% 0.22% 0.67% A6 Column 0.95% 0.6 % 0.6% 0.45% 0.22% 0.28% 0.3% 0.33% 0.69%

% ofStee

E6 Column 0.95% 0.6% 0.6% 0.45% 0.22% 0.28% 0.3% 0.34% 0.67%

Table 4.8 for Zone V, Type-II soil, OMRF, R=3

For- ces

Column - Groups

9thfloor

8thfloor

7thfloor

6thfloor

5thfloor

4thfloor

3rdfloor

2ndfloor

1stfloor

Central Col. 1247 2718 4189 5660 7130 8600 10069 11537 13004E1 Column 389 799 1151 1456 1724 1965 2194 2516 2880 B1 Column 388 795 1146 1450 1717 1958 2186 2566 2928 B3 Column 1023 2215 3419 4632 5853 7081 8316 9801 11188A3 Column 401 828 1195 1514 1794 2047 2283 2684 3134 A6 Column 527 1165 1852 2583 3346 4128 4914 5685 6567 E6 Column 528 1168 1857 2590 3355 4138 4925 5695 6464

P


M x

Central Col. 5.1 4 4.1 4.0 3.73 4.0 1.81 1.8 0.93 E1 Column 24 204 225 196 178 165 160 194 152 B1 Column 295 221 227 199 183 154 234 218 125 B3 Column 472 328 352 356 357 359 262 231 163 A3 Column 349 264 269 229 213 182 224 290 212 A6 Column 500 319 347 347 357 360 350 420 335 E6 Column 515 326 358 362 367 368 354 371 253

M y

Central Col. 654 952 1148 1251 1299 1293 1369 1667 2418 E1 Column 445 494 536 598 346 504 619 985 2224 B1 Column 439 498 541 603 350 509 625 993 2217 B3 Column 368 815 1008 1140 1205 1117 1352 1643 2401 A3 Column 435 199 546 608 614 505 687 1017 2211 A6 Column 856 985 1120 1153 1155 1118 1180 1630 2422

M z

E6 Column 850 982 1116 1149 1150 1114 1183 1563 2403

- 46 -

Central Col. 1667 1393 2147 2901 3654 4408 6709 13600 25272E1 Column 3954 2816 2349 1827 1176 1007 1124 2321 12101B1 Column 3918 2840 2447 1959 1254 1003 1121 2499 12077B3 Column 3269 2620 1879 2374 3000 3629 4262 9042 20642A3 Column 4239 3044 2673 2124 1314 1049 1170 3164 11724A6 Column 8424 6198 6339 5121 3510 2116 2519 4953 12453E6 Column 8498 6217 6358 5136 3519 2121 2524 3794 12257

Steel area

Central Col. 0.22% 0.22% 0.28% 0.39% 0.46% 0.56% 0.84% 1.69% 3.15%E1 Column 0.5% 0.39% 0.3% 0.28% 0.17% 0.17% 0.17% 0.30% 1.55%B1 Column 0.5% 0.39% 0.34% 0.28% 0.17% 0.17% 0.17% 0.34% 1.50%B3 Column 0.45% 0.34% 0.28% 0.3% 0.39% 0.46% 0.56% 1.12% 2.64%A3 Column 0.56% 0.39% 0.34% 0.28% 0.17% 0.17% 0.17% 0.39% 1.45%A6 Column 1.06% 0.78% 0.8% 0.67% 0.45% 0.28% 0.34% 0.61% 1.55%

% of Steel

E6 Column 1.06% 0.78% 0.8% 0.67% 0.45% 0.28% 0.34% 0.50% 1.55%

Table 4.9 for Zone V, Type-III soil, OMRF, R=3

For-ces

Column - Groups

9thfloor

8thfloor

7thfloor

6thfloor

5thfloor

4thfloor

3rdfloor

2ndfloor

1st floor


P


M x


M y

Central Col. 803 1169 1409 1536 1595 1587 1682 2047 2969

E1 Column 471 662 723 796 803 776 831 1277 2751

- 47 -

B1 Column 465 666 729 802 808 780 838 1287 2743 B3 Column 532 1046 1291 1451 1530 1532 1693 2049 2959 A3 Column 460 668 736 809 503 785 902 1312 2737 A6 Column 944 1153 1309 1354 1356 1312 1394 1924 2947 E6 Column 938 1150 1304 1348 1350 1308 1395 1855 2929

M z


Steearea

Central Col. 0.39% 0.39% 0.34% 0.39% 0.46% 0.73% 1.29% 1.33% 3.97% E1 Column 0.56% 0.50% 0.50% 0.45% 0.39% 0.28% 0.28% 0.67% 2.17% B1 Column 0.56% 0.56% 0.50% 0.45% 0.39% 0.28% 0.34% 0.70% 2.17% B3 Column 0.60% 0.60% 0.60% 0.50% 0.45% 0.46% 0.89% 1.69% 3.39% A3 Column 0.60% 0.56% 0.56% 0.50% 0.45% 0.39% 0.39% 0.78% 2.17% A6 Column 1.17% 0.93% 0.99% 0.89% 0.67% 0.39% 0.34% 1.00% 2.33%

%of Stee

E6 Column 1.17% 0.95% 0.99% 0.89% 0.67% 0.39% 0.34% 0.89% 2.33%

Table 4.10 for Zone II, Type-I soil, SMRF, R=5

For- ces

Column - Groups

9thfloor

8thfloor

7thfloor

6thfloor

5tfloor

4thfloor

3rdfloor

2ndfloor

1stfloor


P


M x

Central Col. 2.9 2.7 2.9 2.95 2.8 3.2 1.03 1.13 0.85 E1 Column 461 267 282 266 262 254 247 272 196 B1 Column 457 264 281 265 262 250 314 323 178 B3 Column 397 257 268 257 250 248 210 140 105

M y A3 Column 503 292 309 290 284 269 300 360 259

- 48 -

A6 Column 468 277 296 284 283 279 267 352 281 E6 Column 474 281 299 287 284 279 269 291 210


M z


Steel area

Central Col. 0.17% 0.22% 0.28% 0.39% 0.47% 0.56% 0.67% 0.78% 0.97% E1 Column 0.67% 0.17% 0.17% 0.17% 0.17% 0.22% 0.22% 0.28% 0.30% B1 Column 0.62% 0.17% 0.17% 0.17% 0.17% 0.22% 0.22% 0.28% 0.30% B3 Column 0.28% 0.17% 0.22% 0.30% 0.405 0.44% 0.56% 0.62% 0.695% A3 Column 0.67% 0.17% 0.17% 0.17% 0.17% 0.22% 0.22% 0.28% 0.30% A6 Column 0.73% 0.22% 0.17% 0.17% 0.17% 0.22% 0.28% 0.28% 0.34%

% of Steel

E6 Column 0.73% 0.22% 0.17% 0.17% 0.17% 0.22% 0.28% 0.28% 0.34%

Table 4.11 for Zone II, Type-II soil, SMRF, R=5

For- ces

Column - Groups

9t floor

8thfloor

7tfloor

6thfloor

5thfloor

4tfloor

3rdfloor

2nhfloor

1shfloor


P


M x

- 49 -

Central Col 6.0 2.79 2.99 3.0 2.85 3.2 1.1 1.2 0.85 E1 Column 458 264 278 262 258 249 243 268 194 B1 Column 455 262 269 261 258 246 309 319 175 B3 Column 400 261 272 263 249 254 216 144 108 A3 Column 502 291 307 287 281 266 296 357 257 A6 Column 470 279 299 287 287 283 217 356 284 E6 Column 476 283 302 290 288 284 273 295 212

M y


M z


Steel area

Central Col 0.17% 0.22% 0.28% 0.40% 0.46% 0.56% 0.67% 0.78% 0.97% E1 Column 0.61% 0.17% 0.17% 0.17% 0.17% 0.22% 0.22% 0.28% 0.28% B1 Column 0.61% 0.17% 0.17% 0.17% 0.17% 0.22% 0.22% 0.28% 0.30% B3 Column 0.22% 0.17% 0.22% 0.30% 0.40% 0.45% 0.56% 0.62% 0.73% A3 Column 0.67% 0.17% 0.17% 0.17% 0.17% 0.22% 0.22% 0.28% 0.30% A6 Column 0.73% 0.22% 0.17% 0.17% 0.22% 0.22% 0.28% 0.28% 0.34%

% of Steel

E6 Column 0.78% 0.22% 0.17% 0.17% 0.22% 0.22% 0.28% 0.28% 0.34%

Table 4.12 for Zone II, Type-III soil, SMRF, R=5

For-ces

Column - Groups

9thfloor

8thfloor

7thfloor

6thfloor

5thfloor

4thfloor

3rdfloor

2ndfloor

1stfloor

Central Col. 1247 2719 4190 5662 7132 8603 10072 11541 13007 E1 Column 444 944 1430 1904 2369 2825 3276 3810 4335 B1 Column 443 941 1426 1899 2363 2818 3269 3860 4384 B3 Column 1022 2207 3396 4588.7 2784 6984 8187 9641 11004 A3 Column 452 963 1458 1942 2415 2878 3333 3943 4553 A6 Column 472 1020 1574 2136 2702 3269 3834 4394 5114 E6 Column 473 1021 1576 2139 2706 3274 3839 4396 5004

P

Central Col. 0.192 0.196 0.204 0.21 0.20 0.18 0.13 0 0.068 E1 Column 0.192 0.196 0.204 0.21 0.20 0.18 0.13 0 0.068

B1 Column 0.192 0.196 0.204 0.21 0.20 0.18 0.13 0 0.068

- 50 -

B3 Column 0.192 0.196 0.204 0.21 0.20 0.18 0.13 0 0.068 A3 Column 0.192 0.196 0.204 0.21 0.20 0.18 0.13 0 0.068 A6 Column 0.192 0.196 0.204 0.21 0.20 0.18 0.13 0 0.068 E6 Column 0.192 0.196 0.204 0.21 0.20 0.18 0.13 0 0.068

M x


M y

Central Col. 135 195 235 256 266 265 282 342 493.4 E1 Column 387 254 223 178 146 97 122 220 386 B1 Column 382 252 118 176 144 95 120 220 384 B3 Column 226 132 76 57 73 74 159 226 452 A3 Column 376 250 218 174 138 104 102 163 379 A6 Column 547 396 461 456 454 425 433 603 590 E6 Column 545 396 460 455 453 440 442 543 564

M z


Steearea


% ofStee

E6 Column 0.78% 0.285 0.22% 0.17% 0.22% 0.22% 0.28% 0.28% 0.34%

- 51 -

Table 4.13 for Zone V, Type-I soil, SMRF, R=5

For- ces

Column - Groups

9thfloor

8thfloor

7thfloor

6thfloor

5thfloor

4thfloor

3rdfloor

2ndfloor

1stfloor


P


M x


M y


M z


Steel area

Central Col. 0.17% 0.22% 0.28% 0.39% 0.47% 0.56% 0.67% 0.78% 1.45% E1 Column 0.56% 0.17% 0.17% 0.17% 0.17% 0.17% 0.22% 0.22% 0.28%

B1 Column 0.56% 0.17% 0.17% 0.17% 0.17% 0.17% 0.22% 0.22% 0.28%

- 52 -

B3 Column 0.17% 0.17% 0.22% 0.30% 0.39% 0.45% 0.56% 0.62% 0.73% A3 Column 0.56% 0.17% 0.17% 0.17% 0.17% 0.17% 0.22% 0.28% 0.28% A6 Column 0.84% 0.39% 0.39% 0.17% 0.22% 0.22% 0.28% 0.34% 0.39%

% of Steel

E6 Column 0.84% 0.39% 0.39% 0.17% 0.22% 0.22% 0.28% 0.34% 0.39%

Table 4.14 for Zone V, Type-II soil, SMRF, R=5

For- ces

Column - Groups

9th floor

8th floor

7thfloor

6thfloor

5thfloor

4thfloor

3rdfloor

2ndfloor

1stfloor


P


M x


M y


M z

Central Col. 639 1393 2147 2901 3655 4408 5161 7097 15552 E1 Column 659 715 662 862 1050 1229 1403 1623 2221 B1 Column 3643 668 659 859 1046 1225 1399 1649 2251 B3 Column 961 1133 1746 2363 2982 3604 4229 4982 9667

Steel A3 Column 3940 881 680 886 1080 1263 1441 1700 1972

- 53 -

A6 Column 7180 3903 3752 2330 1549 1894 3240 2581 2991 E6 Column 7221 3983 3761 2335 1552 1898 2244 2584 2936

area


% ofSteel

E6 Column 0.89% 0.50% 0.47% 0.30% 0.22% 0.28% 0.28% 0.34% 0.39%

Table 4.15 for Zone V, Type-III soil, SMRF, R=5

For- ces

Column - Groups

9th floor

8thfloor

7thfloor

6thfloor

5thfloor

4thfloor

3rdfloor

2ndfloor

1stfloor


P


M x


M y

Central Col. 482 701 846 922 957 953 1009 1229 1781 E1 Column 415 300 318 368 372 360 374 647 1616 B1 Column 410 303 323 372 376 363 378 654 1611 B3 Column 180 547 683 782 830 832 957 1174 1756 A3 Column 407 304 327 376 382 365 439 676 1605 A6 Column 753 790 902 923 923 894 933 1290 1816

M z

E6 Column 749 788 899 919 919 891 937 1225 1794

- 54 -


Steel area


% of Steel

E6 Column 0.95% 0.60% 0.60% 0.45% 0.22% 0.28% 0.30% 0.34% 0.67%

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- 56 -

- 57 -

- 58 -

- 59 -

- 60 -

- 61 -

- 62 -

- 63 -

- 64 -

- 65 -

- 66 -

- 67 -

CHAPTER-5

DISCUSSION ON RESULTS 5.1 INTRODUCTION

In the previous chapters dynamic analysis was carried out employing STAAD

Pro and manually using SP-22 and IS 1893-2002 I.S codal provisions. The basic plan of

the L-shaped building was kept same as, for easy comparison. In this thesis studies are

carried out on the variation of axial forces, twisting moment, moments in X, Y direction,

Percentage of steel and steel area of building due to variation of seismic zones (zone II,

zone V) and types of foundation soil for both OMRF and SMRF and considering type of

building as flat slab with edge beams for lateral loading in X- direction only. L-shaped

building was chosen as it as asymmetric relative to both X and Y-axis in plan.

Analytically torsion response is studied in this thesis, which is the main cause of failure

of most of the building during earthquakes. The difference in the results obtained by

manual and Staad-pro- 2006 for zone II, OMRF and type III soil have been compared.

These results have been captured along with the figures (4.5 to 4.12).

5.2 MODES OF VIBRATION OF BUILDING In the previous chapter STAAD Pro out-put of modes shape coefficients is shown in

Table 4.2 for master-slave joints of the L-Shaped building. First few mode shapes are

captured in Figs. 4.1 to 4.9. It is observed that the first 3 mode shapes in X- direction are

shown in Figs 4.1, 4.3, & 4.5, while Fig 4.2, 4.4 & 4.6 show the first 3 mode shapes in Z-

direction. All those are mainly translational modes. The dominant torsional mode is

illustrated by the top floor plan in Fig 4.9.

- 68 -

5.3 COMPARISION OF AXIAL LOADS Tables 4.4--4.15 show the Axial loads for Central, Edge, Corner columns, Obtained

for 9 storey L-shaped building using Staad pro; for zone-II, zone-V, OMRF & SMRF in

type-II & type-III soils. These values gradually increased from Top floor to Bottom floor

by more than 10 times as seen from the Tables.

5.4 COMPARISION OF MOMENTS MY Tables 4.4--4.15 show the Moments MY for Central, Edge, Corner Columns,

obtained for 9 storey L-shaped building using Staad pro; for zone-II, zone-V, OMRF &

SMRF in type-II & type-III soils. These moments are found to increase from Bottom

floor to Top floor by more than 2 times for all columns in general. MY moments in

Corner columns are more compared with Edge columns, MY moments are least for

Central columns.

5.5 COMPARISION OF MOMENTS MZ Tables 4.4--4.15 show the Moments MZ for Central, Edge, Corner Columns, obtained

for 9 storey L-shaped building using Staad pro; for zone-II, zone-V, OMRF & SMRF in

type-II & type-III soils. The variation of MZ moments is similar tot that of MY moments.

However for most of the columns MZ moments are greater than MY moments.

5.6 COMPARISION OF TWISTING MOMENTS MX Tables 4.4--4.15 show the Twisting moments for Central, Edge, Corner Columns,


SMRF in type-II & type-III soils. It is observed that the MX moments for all columns at

any floor level are same. This is due to selection of Master slave joint option in STAAD

to reduce the DOF’s.

- 69 -

5.7 COMPARISION OF REINFORCEMENT (% STEEL) Tables 4.4--4.15 show the Reinforcement for Central, Edge, Corner Columns,


SMRF in type-II & type-III soils. These are found to decrease from first storey to top

storey for Central columns and reverse trend is observed for Corner & Edge columns.

5.8 COMPARISION OF DISPLACEMENTS Figures 4.14--4.17 show the Floor Displacements obtained for 9 storey L-shaped

building using Staad pro; for zone-II, zone-V, OMRF & SMRF in type-II & type-III soils.

Deflections in columns are found to be less than the permissible values as per IS 1893-

2002 codal provisions. Eg. Max top displacement of 104.722 mm from Fig. 4.15 is less

than permissible deflection 151.2 mm. ( 0.004 H = 0.004x 37.8).

5.9 COMPARISION OF AXIAL FORCES, MOMENTS IN X-DIRECTION WITH AND WITHOUT ACCEDENTAL TORSION Figures 4.10 to 4.13 illustrate torsion effect on the columns (5A to 5F grid columns

which is having edge beam for easy evaluation of difference) due to accidental torsion

consideration in analytical values inputting in Staad-pro-2006 and without torsion

consideration of I S code and without torsion considering in the problem. These figures

are helpful in pictorially studying the variation in Moments due to consideration of

accidental torsion.

5.10 MOMENTS & STRESSES IN THE FLAT SLAB Figures 4.18 to 4.22 show the variation of stresses & Bending moments in flat slab

bottom, top & local XY Direction, From this figures we can easily visualize the behavior

of the flat slab by the Moments & stress contours with different colours.

- 70 -

CHAPTER-6

CONCLUSIONS

Based on the investigations carried out on the seismic torsion response of

Asymmetrical multy storey buildings, the following conclusions are drawn:

1. The 3rd, 6th & 9th modes are the dominant torsion modes while the 1st, 2nd, 4th, 5th

& 7th, 8th modes include mainly transitional modes 2 in X- direction & 2 in Z –

direction.

2. The axial forces in columns are found to increase from top storey to Bottom storey

by more than 10 times.

3. Both MY, MZ moments in columns are observed to increase from ground floor to

top floor by more than 2 times, The Mz moments are greater than MY moments

for buildings studied.

4. The twisting moments in columns in columns are represented by MX, The

variations in maximum and minimum twisting moments is found to be more than

10 times in the building studied.

5. The reinforcements required for Central columns are found to decrease from first

storey to top storey. However for Corner and edger columns the steel requirement

is reverse.

6. The max top floor displacement for all the buildings studied are found to be less

than permissible deflections of 0.004 H, where H = total height of the building.

7. Similarly the inter storey drifts are found to be less than the permissible value of

0.004 h, where h = floor height.

8. The effect of accidental eccentricity on the variation of bending moments can be

illustrated nicely pictorially as shown in Fig. 4.12, 4.13.

9. The variation of bending moments and stresses in flat slabs can be illustrated

nicely by stress and moments contours drawn in different colours.

- 71 -

CHAPTER-7

RECOMMENDATIONS FOR FURTHER STUDY

In this study STAAD Pro 2006 has been used other software’s like

ETABS, ANSYS etc can be used.

In this study the effect of height of building has not been done; High-rise

Or Tall buildings (25, 30, 40 stories) can be studied for torsion effects.

Here linear analysis has been performed; Non-linear analysis can be done

for same building.

L-shaped building with exclusive flat plate (without column drops) can be

studied; instead of flat slabs in the present study.

Dynamic analysis can be carried out for asymmetric multi-storey buildings

using actual earthquake records by Time History Analysis.

Soil-Foundation structure interaction can be studied.

L-shape building with un-equal spans in both orthogonal directions for tall

Buildings can be studied (greater than 160’-0” height).

- 72 -

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Published by Nemchand & Bros., Roorkee.

37) IS 456-2000, Code of practice for plain & reinforced concrete.

38) IS 875 (Part-1) -1987 code of practice for design load (other than earthquake) for buildings and Structures unit weight of buiding materials & stored materials

39) IS 875 (Part-2) -1987 code of practice for design load (other than earthquake) for buildings and Structures Imposed (Live) loads.

40) Jack P. Mochale.,PEER,USA—Sesimic analysis,design and review for tall

buildings in journal paper The structural design of tall &special buildings in 2006. pages(495-513)

41) Ductility reinforcement for flat slabs in seismic areas by C.E Broms (Royal institute of technology—Sweden) in magazine of concrete research journal paper in 2006 pages (243-254).

42) M.Tech dissertation by Suresh (MES) on Seismic analysis & design of multi story buildings-- JNTU, Hyderabad in 2006.

43) M.Tech dissertation by Shaista Begum on Torsional analysis of asymmetric buildings-- JNTU, Hyderabad in 2007.

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APPENDIX – A

SEISMIC ANALYSIS USING STAAD.Pro The L-Shaped building analyzed using STAAD package assuming it to be located in zone-II on soft soil (type-III) part of Input & Output files are furnished. **************************************************** * * * STAAD.Pro * * Version 2006 Bld 1002.US * * Proprietary Program of * * Research Engineers, Intl. * * Date= FEB 5, 2009 * * Time= 15: 9:49 * * * * USER ID: * **************************************************** 1. STAAD SPACE TORSIONAL RESPONSE BUILDING INPUT FILE: L_S_BStatic23.01.STD 2. START JOB INFORMATION 3. JOB NAME ASYMETRIC MULTI-STOREY BUILDING 4. JOB CLIENT JNTU COLLEGE OF ENGINEERING 5. JOB PART TORSIONAL BUILDING 6. ENGINEER NAME PNCHARY 7. CHECKER NAME PROF.ASTHANA 8. ENGINEER DATE 17-SEP-06 9. CHECKER DATE 05.02.07 10. END JOB INFORMATION 11. INPUT WIDTH 79 12. UNIT METER KN 13. JOINT COORDINATES 14. 1 0 0 0; 2 10.6 0 0; 3 21.2 0 0; 4 31.8 0 0; 5 42.4 0 0; 6 53 0 0; 7 0 0 10.6 15. 8 10.6 0 10.6; 9 21.2 0 10.6; 10 31.8 0 10.6; 11 42.4 0 10.6; 12 53 0 10.6 16. 13 0 0 21.2; 14 10.6 0 21.2; 15 21.2 0 21.2; 16 31.8 0 21.2; 17 42.4 0 21.2 17. 18 53 0 21.2; 19 0 0 31.8; 20 10.6 0 31.8; 21 21.2 0 31.8; 22 31.8 0 31.8 18. 23 42.4 0 31.8; 24 53 0 31.8; 25 21.2 0 42.4; 26 31.8 0 42.4; 27 42.4 0 42.4 19. 28 53 0 42.4; 29 0 4.2 0; 30 10.6 4.2 0; 31 21.2 4.2 0; 32 31.8 4.2 0 20. 33 42.4 4.2 0; 34 53 4.2 0; 35 0 4.2 10.6; 36 10.6 4.2 10.6; 37 21.2 4.2 10.6 21. 38 31.8 4.2 10.6; 39 42.4 4.2 10.6; 40 53 4.2 10.6; 41 0 4.2 21.2 22. 42 10.6 4.2 21.2; 43 21.2 4.2 21.2; 44 31.8 4.2 21.2; 45 42.4 4.2 21.2 23. 46 53 4.2 21.2; 47 0 4.2 31.8; 48 10.6 4.2 31.8; 49 21.2 4.2 31.8 24. 50 31.8 4.2 31.8; 51 42.4 4.2 31.8; 52 53 4.2 31.8; 53 21.2 4.2 42.4 25. 54 31.8 4.2 42.4; 55 42.4 4.2 42.4; 56 53 4.2 42.4; 57 0 4.2 1.76667 26. 58 1.76667 4.2 1.76667; 59 1.76667 4.2 0; 60 0 4.2 3.53333 27. 61 1.76667 4.2 3.53333; 62 0 4.2 5.3; 63 1.76667 4.2 5.3; 64 0 4.2 7.06667 28. 65 1.76667 4.2 7.06667; 66 0 4.2 8.83333; 67 1.76667 4.2 8.83333 29. 68 1.76667 4.2 10.6; 69 3.53333 4.2 1.76667; 70 3.53333 4.2 0 30. 71 3.53333 4.2 3.53333; 72 3.53333 4.2 5.3; 73 3.53333 4.2 7.06667 31. 74 3.53333 4.2 8.83333; 75 3.53333 4.2 10.6; 76 5.3 4.2 1.76667; 77 5.3 4.2 0 32. 78 5.3 4.2 3.53333; 79 5.3 4.2 5.3; 80 5.3 4.2 7.06667; 81 5.3 4.2 8.83333

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33. 82 5.3 4.2 10.6; 83 7.06667 4.2 1.76667; 84 7.06667 4.2 0 34. 85 7.06667 4.2 3.53333; 86 7.06667 4.2 5.3; 87 7.06667 4.2 7.06667 35. 88 7.06667 4.2 8.83333; 89 7.06667 4.2 10.6; 90 8.83333 4.2 1.76667 36. 91 8.83333 4.2 0; 92 8.83333 4.2 3.53333; 93 8.83333 4.2 5.3 37. 94 8.83333 4.2 7.06667; 95 8.83333 4.2 8.83333; 96 8.83333 4.2 10.6 38. 97 10.6 4.2 1.76667; 98 10.6 4.2 3.53333; 99 10.6 4.2 5.3 39. 100 10.6 4.2 7.06667; 101 10.6 4.2 8.83333; 102 12.3667 4.2 1.76667 40. 103 12.3667 4.2 0; 104 12.3667 4.2 3.53333; 105 12.3667 4.2 5.3 41. 106 12.3667 4.2 7.06667; 107 12.3667 4.2 8.83333; 108 12.3667 4.2 10.6 42. 109 14.1333 4.2 1.76667; 110 14.1333 4.2 0; 111 14.1333 4.2 3.53333 43. 112 14.1333 4.2 5.3; 113 14.1333 4.2 7.06667; 114 14.1333 4.2 8.83333 44. 115 14.1333 4.2 10.6; 116 15.9 4.2 1.76667; 117 15.9 4.2 0 45. 118 15.9 4.2 3.53333; 119 15.9 4.2 5.3; 120 15.9 4.2 7.06667 46. 121 15.9 4.2 8.83333; 122 15.9 4.2 10.6; 123 17.6667 4.2 1.76667 47. 124 17.6667 4.2 0; 125 17.6667 4.2 3.53333; 126 17.6667 4.2 5.3 48. 127 17.6667 4.2 7.06667; 128 17.6667 4.2 8.83333; 129 17.6667 4.2 10.6 49. 130 19.4333 4.2 1.76667; 131 19.4333 4.2 0; 132 19.4333 4.2 3.53333 50. 133 19.4333 4.2 5.3; 134 19.4333 4.2 7.06667; 135 19.4333 4.2 8.83333 51. 136 19.4333 4.2 10.6; 137 21.2 4.2 1.76667; 138 21.2 4.2 3.53333 52. 139 21.2 4.2 5.3; 140 21.2 4.2 7.06667; 141 21.2 4.2 8.83333 53. 142 22.9667 4.2 1.76667; 143 22.9667 4.2 0; 144 22.9667 4.2 3.53333 54. 145 22.9667 4.2 5.3; 146 22.9667 4.2 7.06667; 147 22.9667 4.2 8.83333 55. 148 22.9667 4.2 10.6; 149 24.7333 4.2 1.76667; 150 24.7333 4.2 0 56. 151 24.7333 4.2 3.53333; 152 24.7333 4.2 5.3; 153 24.7333 4.2 7.06667 57. 154 24.7333 4.2 8.83333; 155 24.7333 4.2 10.6; 156 26.5 4.2 1.76667 58. 157 26.5 4.2 0; 158 26.5 4.2 3.53333; 159 26.5 4.2 5.3; 160 26.5 4.2 7.06667 59. 161 26.5 4.2 8.83333; 162 26.5 4.2 10.6; 163 28.1797 4.2 1.76667 60. 164 28.1797 4.2 0; 165 28.1797 4.2 3.53333; 166 28.1797 4.2 5.3 61. 167 28.1797 4.2 7.06667; 168 28.1797 4.2 8.83333; 169 28.1797 4.2 10.6 62. 170 30.0333 4.2 1.76667; 171 30.0333 4.2 0; 172 30.0333 4.2 3.53333 63. 173 30.0333 4.2 5.3; 174 30.0333 4.2 7.06667; 175 30.0333 4.2 8.83333 64. 176 30.0333 4.2 10.6; 177 31.8 4.2 1.76667; 178 31.8 4.2 3.53333 65. 179 31.8 4.2 5.3; 180 31.8 4.2 7.06667; 181 31.8 4.2 8.83333 66. 182 33.5667 4.2 1.76667; 183 33.5667 4.2 0; 184 33.5667 4.2 3.53333 67. 185 33.5667 4.2 5.3; 186 33.5667 4.2 7.06667; 187 33.5667 4.2 8.83333 68. 188 33.5667 4.2 10.6; 189 35.3333 4.2 1.76667; 190 35.3333 4.2 0 69. 191 35.3333 4.2 3.53333; 192 35.3333 4.2 5.3; 193 35.3333 4.2 7.06667 70. 194 35.3333 4.2 8.83333; 195 35.3333 4.2 10.6; 196 37.1 4.2 1.76667 71. 197 37.1 4.2 0; 198 37.1 4.2 3.53333; 199 37.1 4.2 5.3; 200 37.1 4.2 7.06667 72. 201 37.1 4.2 8.83333; 202 37.1 4.2 10.6; 203 38.8667 4.2 1.76667 73. 204 38.8667 4.2 0; 205 38.8667 4.2 3.53333; 206 38.8667 4.2 5.3 74. 207 38.8667 4.2 7.06667; 208 38.8667 4.2 8.83333; 209 38.8667 4.2 10.6 75. 210 40.6333 4.2 1.76667; 211 40.6333 4.2 0; 212 40.6333 4.2 3.53333 76. 213 40.6333 4.2 5.3; 214 40.6333 4.2 7.06667; 215 40.6333 4.2 8.83333 77. 216 40.6333 4.2 10.6; 217 42.4 4.2 1.76667; 218 42.4 4.2 3.53333 78. 219 42.4 4.2 5.3; 220 42.4 4.2 7.06667; 221 42.4 4.2 8.83333 79. 222 44.1667 4.2 1.76667; 223 44.1667 4.2 0; 224 44.1667 4.2 3.53333 80. 225 44.1667 4.2 5.3; 226 44.1667 4.2 7.06667; 227 44.1667 4.2 8.83333 81. 228 44.1667 4.2 10.6; 229 45.9333 4.2 1.76667; 230 45.9333 4.2 0 82. 231 45.9333 4.2 3.53333; 232 45.9333 4.2 5.3; 233 45.9333 4.2 7.06667 83. 234 45.9333 4.2 8.83333; 235 45.9333 4.2 10.6; 236 47.7 4.2 1.76667 84. 237 47.7 4.2 0; 238 47.7 4.2 3.53333; 239 47.7 4.2 5.3; 240 47.7 4.2 7.06667 85. 241 47.7 4.2 8.83333; 242 47.7 4.2 10.6; 243 49.4667 4.2 1.76667 86. 244 49.4667 4.2 0; 245 49.4667 4.2 3.53333; 246 49.4667 4.2 5.3

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87. 247 49.4667 4.2 7.06667; 248 49.4667 4.2 8.83333; 249 49.4667 4.2 10.6 88. 250 51.2333 4.2 1.76667; 251 51.2333 4.2 0; 252 51.2333 4.2 3.53333 89. 253 51.2333 4.2 5.3; 254 51.2333 4.2 7.06667; 255 51.2333 4.2 8.83333 90. 256 51.2333 4.2 10.6; 257 53 4.2 1.76667; 258 53 4.2 3.53333; 259 53 4.2 5.3 91. 260 53 4.2 7.06667; 261 53 4.2 8.83333; 262 0 4.2 12.3667 92. 263 1.76667 4.2 12.3667; 264 0 4.2 14.1333; 265 1.76667 4.2 14.1333 93. 266 0 4.2 15.9; 267 1.76667 4.2 15.9; 268 0 4.2 17.6667 94. 269 1.76667 4.2 17.6667; 270 0 4.2 19.5303; 271 1.76667 4.2 19.5303 95. 272 1.76667 4.2 21.2; 273 3.53333 4.2 12.3667; 274 3.53333 4.2 14.1333 96. 275 3.53333 4.2 15.9; 276 3.53333 4.2 17.6667; 277 3.53333 4.2 19.5303 ............................................................................... Due to Large size input data such as joint incidencies, member & element incidencies skip the input data for minimizing the information. ............................................................................. 4612. MEMBER PROPERTY INDIAN 4613. 100 TO 119 121 123 125 127 130 137 144 151 164 171 178 185 192 205 212 219 - 4614. 226 233 246 253 260 267 274 287 294 301 308 315 322 324 326 328 330 333 335 - 4615. 337 339 341 512 514 516 518 520 523 525 527 529 531 533 540 547 554 561 574 - 4616. 581 588 595 602 712 714 716 718 720 723 725 727 729 731 733 740 747 754 761 - 4617. 774 781 788 795 802 815 822 829 836 843 845 847 849 851 853 884 TO 991 1668 - 4618. 1669 TO 1775 2452 TO 2559 3236 TO 3343 4020 TO 4127 4804 TO 4911 5588 TO 5695 - 4619. 6372 TO 6479 PRIS YD 0.6 ZD 0.5 4620. SUPPORTS 4621. 1 TO 28 FIXED 4622. CUT OFF MODE SHAPE 20 4623. ****************************************************************************** 4624. **1893 EARTH QUAKE LOAD 4625. ***ZONE II COFFICIENT =0.1 4626. ***RESPONSE REDUCTION FACTOR = 3.0 4627. ***IMPORTANCE FACTOR = 1 4628. ****SOFT SOIL FACTOR = 3 4629. ***TYPE OF STRUCTURE :R.C.C = 1.0 4630. ******************************************************************************* 4631. DEFINE 1893 LOAD 4632. ZONE 0.1 RF 3 I 1 SS 3 ST 1 DM 0.05 DT 3 4633. *ZONE 0.1 RF 3 I 1 SS 2 ST 1 DM 0.05 DT 3 4634. *ZONE 0.1 RF 3 I 1 SS 1 ST 1 DM 0.05 DT 3 4635. *ZONE 0.1 RF 5 I 1 SS 3 ST 1 DM 0.05 DT 3 4636. *ZONE 0.1 RF 5 I 1 SS 2 ST 1 DM 0.05 DT 3 4637. *ZONE 0.1 RF 5 I 1 SS 1 ST 1 DM 0.05 DT 3 4638. *ZONE 0.36 RF 3 I 1 SS 3 ST 1 DM 0.05 DT 3 4639. *ZONE 0.36 RF 3 I 1 SS 2 ST 1 DM 0.05 DT 3 4640. *ZONE 0.36 RF 3 I 1 SS 1 ST 1 DM 0.05 DT 3 4641. *ZONE 0.36 RF 5 I 1 SS 3 ST 1 DM 0.05 DT 3 4642. *ZONE 0.36 RF 5 I 1 SS 2 ST 1 DM 0.05 DT 3 4643. *ZONE 0.36 RF 5 I 1 SS 1 ST 1 DM 0.05 DT 3 4644. SELFWEIGHT ............................................................................ Due to Large size input data such as nodal seismic weight was skip the input data for minimizing the information. .............................................................................

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4926. CHECK SOFT STORY 4926. LOAD 1 DEAD LOAD 4927. SELFWEIGHT Y -1 4928. *ELEMENT LOAD 4929. *120 122 124 126 128 129 131 TO 136 138 TO 143 145 TO 150 152 TO 163 - 4930. *165 TO 170 172 TO 177 179 TO 184 186 TO 191 193 TO 204 206 TO 211 - 4931. *213 TO 218 220 TO 225 227 TO 232 234 TO 245 247 TO 252 254 TO 259 - 4932. *261 TO 266 268 TO 273 275 TO 286 288 TO 293 295 TO 300 302 TO 307 - 4933. *309 TO 314 316 TO 321 323 325 327 329 331 332 334 336 338 340 342 TO 511 - 4934. *513 515 517 519 521 522 524 526 528 530 532 534 TO 539 541 TO 546 - 4935. *548 TO 553 555 TO 560 562 TO 573 575 TO 580 582 TO 587 589 TO 594 - 4936. *596 TO 601 603 TO 711 713 715 717 719 721 722 724 726 728 730 732 - 4937. *734 TO 739 741 TO 746 748 TO 753 755 TO 760 762 TO 773 775 TO 780 - 4938. *782 TO 787 789 TO 794 796 TO 801 803 TO 814 816 TO 821 823 TO 828 - 4939. *830 TO 835 837 TO 842 844 846 848 850 852 854 855 992 TO 1639 1776 TO 2423 - 4940. *2560 TO 3207 3344 TO 3991 4128 TO 4775 4912 TO 5559 5696 TO 6343 - 4941. *6480 TO 7127 PR GY -2.45 4942. *MEMBER LOAD 4943. *100 TO 119 121 123 125 127 130 137 144 151 164 171 178 185 192 205 212 219 - 4944. *226 233 246 253 260 267 274 287 294 301 308 315 322 324 326 328 330 333 335 - 4945. *337 339 341 512 514 516 518 520 523 525 527 529 531 533 540 547 554 561 574 - 4946. *581 588 595 602 712 714 716 718 720 723 725 727 729 731 733 740 747 754 761 - 4947. *774 781 788 795 802 815 822 829 836 843 845 847 849 851 853 884 TO 991 1668 - 4948. *1669 TO 1775 2452 TO 2559 3236 TO 3343 4020 TO 4127 4804 TO 4911 5588 TO 5695 4949. *6372 TO 6479 UNI GY -16.8 4950. LOAD 2 LIVE LOAD 4951. ELEMENT LOAD 4952. 120 122 124 126 128 129 131 TO 136 138 TO 143 145 TO 150 152 TO 163 - 4953. 165 TO 170 172 TO 177 179 TO 184 186 TO 191 193 TO 204 206 TO 211 - 4954. 213 TO 218 220 TO 225 227 TO 232 234 TO 245 247 TO 252 254 TO 259 - 4955. 261 TO 266 268 TO 273 275 TO 286 288 TO 293 295 TO 300 302 TO 307 - 4956. 309 TO 314 316 TO 321 323 325 327 329 331 332 334 336 338 340 342 TO 511 - 4957. 513 515 517 519 521 522 524 526 528 530 532 534 TO 539 541 TO 546 - 4958. 548 TO 553 555 TO 560 562 TO 573 575 TO 580 582 TO 587 589 TO 594 - 4959. 596 TO 601 603 TO 711 713 715 717 719 721 722 724 726 728 730 732 - 4960. 734 TO 739 741 TO 746 748 TO 753 755 TO 760 762 TO 773 775 TO 780 - 4961. 782 TO 787 789 TO 794 796 TO 801 803 TO 814 816 TO 821 823 TO 828 - 4962. 830 TO 835 837 TO 842 844 846 848 850 852 854 855 992 TO 1639 1776 TO 2423 - 4963. 2560 TO 3207 3344 TO 3991 4128 TO 4775 4912 TO 5559 5696 TO 6343 PR GY -4 4964. 6480 TO 7127 PR GY -2 4965. LOAD 3 SESMIC ALONG X 4966. SELFWEIGHT X 1 4967. SELFWEIGHT Y 1 4968. SELFWEIGHT Z 1 4969. MEMBER LOAD 4970. 100 TO 119 121 123 125 127 130 137 144 151 164 171 178 185 192 205 212 219 - 4971. 226 233 246 253 260 267 274 287 294 301 308 315 322 324 326 328 330 333 335 - 4972. 337 339 341 512 514 516 518 520 523 525 527 529 531 533 540 547 554 561 574 - 4973. 581 588 595 602 712 714 716 718 720 723 725 727 729 731 733 740 747 754 761 - 4974. 774 781 788 795 802 815 822 829 836 843 845 847 849 851 853 884 TO 991 1668 - 4975. 1669 TO 1775 2452 TO 2559 3236 TO 3343 4020 TO 4127 4804 TO 4911 5588 TO 5695 - 4976. 6372 TO 6479 UNI GX 16.8 4977. 100 TO 119 121 123 125 127 130 137 144 151 164 171 178 185 192 205 212 219 -

- 80 -

4978. 226 233 246 253 260 267 274 287 294 301 308 315 322 324 326 328 330 333 335 - 4979. 337 339 341 512 514 516 518 520 523 525 527 529 531 533 540 547 554 561 574 - 4980. 581 588 595 602 712 714 716 718 720 723 725 727 729 731 733 740 747 754 761 - 4981. 774 781 788 795 802 815 822 829 836 843 845 847 849 851 853 884 TO 991 1668 - 4982. 1669 TO 1775 2452 TO 2559 3236 TO 3343 4020 TO 4127 4804 TO 4911 5588 TO 5695 - 4983. 6372 TO 6479 UNI GY 16.8 4984. 100 TO 119 121 123 125 127 130 137 144 151 164 171 178 185 192 205 212 219 - 4985. 226 233 246 253 260 267 274 287 294 301 308 315 322 324 326 328 330 333 335 - 4986. 337 339 341 512 514 516 518 520 523 525 527 529 531 533 540 547 554 561 574 - 4987. 581 588 595 602 712 714 716 718 720 723 725 727 729 731 733 740 747 754 761 - 4988. 774 781 788 795 802 815 822 829 836 843 845 847 849 851 853 884 TO 991 1668 - 4989. 1669 TO 1775 2452 TO 2559 3236 TO 3343 4020 TO 4127 4804 TO 4911 5588 TO 5695 - 4990. 6372 TO 6479 UNI GZ 16.8 4991. ******************************************************************************* 4992. ELEMENT LOAD 4993. 120 122 124 126 128 129 131 TO 136 138 TO 143 145 TO 150 152 TO 163 - 4994. 165 TO 170 172 TO 177 179 TO 184 186 TO 191 193 TO 204 206 TO 211 - 4995. 213 TO 218 220 TO 225 227 TO 232 234 TO 245 247 TO 252 254 TO 259 - 4996. 261 TO 266 268 TO 273 275 TO 286 288 TO 293 295 TO 300 302 TO 307 - 4997. 309 TO 314 316 TO 321 323 325 327 329 331 332 334 336 338 340 342 TO 511 - 4998. 513 515 517 519 521 522 524 526 528 530 532 534 TO 539 541 TO 546 - 4999. 548 TO 553 555 TO 560 562 TO 573 575 TO 580 582 TO 587 589 TO 594 - 5000. 596 TO 601 603 TO 711 713 715 717 719 721 722 724 726 728 730 732 - 5001. 734 TO 739 741 TO 746 748 TO 753 755 TO 760 762 TO 773 775 TO 780 - 5002. 782 TO 787 789 TO 794 796 TO 801 803 TO 814 816 TO 821 823 TO 828 - 5003. 830 TO 835 837 TO 842 844 846 848 850 852 854 855 992 TO 1639 1776 TO 2423 - 5004. 2560 TO 3207 3344 TO 3991 4128 TO 4775 4912 TO 5559 5696 TO 6343 - 5005. 6480 TO 7127 PR GX 2.45 5006. 120 122 124 126 128 129 131 TO 136 138 TO 143 145 TO 150 152 TO 163 - 5007. 165 TO 170 172 TO 177 179 TO 184 186 TO 191 193 TO 204 206 TO 211 - 5008. 213 TO 218 220 TO 225 227 TO 232 234 TO 245 247 TO 252 254 TO 259 - 5009. 261 TO 266 268 TO 273 275 TO 286 288 TO 293 295 TO 300 302 TO 307 - 5010. 309 TO 314 316 TO 321 323 325 327 329 331 332 334 336 338 340 342 TO 511 - 5011. 513 515 517 519 521 522 524 526 528 530 532 534 TO 539 541 TO 546 - 5012. 548 TO 553 555 TO 560 562 TO 573 575 TO 580 582 TO 587 589 TO 594 - 5013. 596 TO 601 603 TO 711 713 715 717 719 721 722 724 726 728 730 732 - 5014. 734 TO 739 741 TO 746 748 TO 753 755 TO 760 762 TO 773 775 TO 780 - 5015. 782 TO 787 789 TO 794 796 TO 801 803 TO 814 816 TO 821 823 TO 828 - 5016. 830 TO 835 837 TO 842 844 846 848 850 852 854 855 992 TO 1639 1776 TO 2423 - 5017. 2560 TO 3207 3344 TO 3991 4128 TO 4775 4912 TO 5559 5696 TO 6343 - 5018. 6480 TO 7127 PR GY 2.45 5019. 120 122 124 126 128 129 131 TO 136 138 TO 143 145 TO 150 152 TO 163 - 5020. 165 TO 170 172 TO 177 179 TO 184 186 TO 191 193 TO 204 206 TO 211 - 5021. 213 TO 218 220 TO 225 227 TO 232 234 TO 245 247 TO 252 254 TO 259 - 5022. 261 TO 266 268 TO 273 275 TO 286 288 TO 293 295 TO 300 302 TO 307 - 5023. 309 TO 314 316 TO 321 323 325 327 329 331 332 334 336 338 340 342 TO 511 - 5024. 513 515 517 519 521 522 524 526 528 530 532 534 TO 539 541 TO 546 - 5025. 548 TO 553 555 TO 560 562 TO 573 575 TO 580 582 TO 587 589 TO 594 - 5026. 596 TO 601 603 TO 711 713 715 717 719 721 722 724 726 728 730 732 - 5027. 734 TO 739 741 TO 746 748 TO 753 755 TO 760 762 TO 773 775 TO 780 - 5028. 782 TO 787 789 TO 794 796 TO 801 803 TO 814 816 TO 821 823 TO 828 - 5029. 830 TO 835 837 TO 842 844 846 848 850 852 854 855 992 TO 1639 1776 TO 2423 - 5030. 2560 TO 3207 3344 TO 3991 4128 TO 4775 4912 TO 5559 5696 TO 6343 -

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5031. 6480 TO 7127 PR GZ 2.45 5032. ****************************************************************************** 5033. 120 122 124 126 128 129 131 TO 136 138 TO 143 145 TO 150 152 TO 163 - 5034. 165 TO 170 172 TO 177 179 TO 184 186 TO 191 193 TO 204 206 TO 211 - 5035. 213 TO 218 220 TO 225 227 TO 232 234 TO 245 247 TO 252 254 TO 259 - 5036. 261 TO 266 268 TO 273 275 TO 286 288 TO 293 295 TO 300 302 TO 307 - 5037. 309 TO 314 316 TO 321 323 325 327 329 331 332 334 336 338 340 342 TO 511 - 5038. 513 515 517 519 521 522 524 526 528 530 532 534 TO 539 541 TO 546 - 5039. 548 TO 553 555 TO 560 562 TO 573 575 TO 580 582 TO 587 589 TO 594 - 5040. 596 TO 601 603 TO 711 713 715 717 719 721 722 724 726 728 730 732 - 5041. 734 TO 739 741 TO 746 748 TO 753 755 TO 760 762 TO 773 775 TO 780 - 5042. 782 TO 787 789 TO 794 796 TO 801 803 TO 814 816 TO 821 823 TO 828 - 5043. 830 TO 835 837 TO 842 844 846 848 850 852 854 855 992 TO 1639 1776 TO 2423 - 5044. 2560 TO 3207 3344 TO 3991 4128 TO 4775 4912 TO 5559 5696 TO 6343 PR GX 2 5045. 6480 TO 7127 PR GX 1 5046. 120 122 124 126 128 129 131 TO 136 138 TO 143 145 TO 150 152 TO 163 - 5047. 165 TO 170 172 TO 177 179 TO 184 186 TO 191 193 TO 204 206 TO 211 - 5048. 213 TO 218 220 TO 225 227 TO 232 234 TO 245 247 TO 252 254 TO 259 - 5049. 261 TO 266 268 TO 273 275 TO 286 288 TO 293 295 TO 300 302 TO 307 - 5050. 309 TO 314 316 TO 321 323 325 327 329 331 332 334 336 338 340 342 TO 511 - 5051. 513 515 517 519 521 522 524 526 528 530 532 534 TO 539 541 TO 546 - 5052. 548 TO 553 555 TO 560 562 TO 573 575 TO 580 582 TO 587 589 TO 594 - 5053. 596 TO 601 603 TO 711 713 715 717 719 721 722 724 726 728 730 732 - 5054. 734 TO 739 741 TO 746 748 TO 753 755 TO 760 762 TO 773 775 TO 780 - 5055. 782 TO 787 789 TO 794 796 TO 801 803 TO 814 816 TO 821 823 TO 828 - 5056. 830 TO 835 837 TO 842 844 846 848 850 852 854 855 992 TO 1639 1776 TO 2423 - 5057. 2560 TO 3207 3344 TO 3991 4128 TO 4775 4912 TO 5559 5696 TO 6343 PR GY 2 5058. 6480 TO 7127 PR GY 1 5059. 120 122 124 126 128 129 131 TO 136 138 TO 143 145 TO 150 152 TO 163 - 5060. 165 TO 170 172 TO 177 179 TO 184 186 TO 191 193 TO 204 206 TO 211 - 5061. 213 TO 218 220 TO 225 227 TO 232 234 TO 245 247 TO 252 254 TO 259 - 5062. 261 TO 266 268 TO 273 275 TO 286 288 TO 293 295 TO 300 302 TO 307 - 5063. 309 TO 314 316 TO 321 323 325 327 329 331 332 334 336 338 340 342 TO 511 - 5064. 513 515 517 519 521 522 524 526 528 530 532 534 TO 539 541 TO 546 - 5065. 548 TO 553 555 TO 560 562 TO 573 575 TO 580 582 TO 587 589 TO 594 - 5066. 596 TO 601 603 TO 711 713 715 717 719 721 722 724 726 728 730 732 - 5067. 734 TO 739 741 TO 746 748 TO 753 755 TO 760 762 TO 773 775 TO 780 - 5068. 782 TO 787 789 TO 794 796 TO 801 803 TO 814 816 TO 821 823 TO 828 - 5069. 830 TO 835 837 TO 842 844 846 848 850 852 854 855 992 TO 1639 1776 TO 2423 - 5070. 2560 TO 3207 3344 TO 3991 4128 TO 4775 4912 TO 5559 5696 TO 6343 PR GZ 2 5071. 6480 TO 7127 PR GZ 1 5072. SPECTRUM SRSS 1893 TOR X 0.0167 ACC SCALE 2.2254 DAMP 0.05 LIN MIS 5073. SOIL TYPE 3 5074. CHECK SOFT STOREY 5075. *LOAD 4 SESMIC ALONG Z 5076. *SELFWEIGHT X 1 5077. *SELFWEIGHT Y 1 5078. *SELFWEIGHT Z 1 5079. *SPECTRUM SRSS 1893 TOR Z 0.0167 ACC SCALE 2.2893 DAMP 0.05 LIN MIS 5080. *SOIL TYPE 3 5081. LOAD 4 SP-22 LOAD 5082. JOINT LOAD 5083. 29 TO 34 53 TO 56 FX 60.3

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5084. 732 TO 737 756 TO 759 FX 60.05 5085. 1435 TO 1440 1459 TO 1462 FX 59.13 5086. 2138 TO 2143 2162 TO 2165 FX 57.26 5087. 2841 TO 2846 2865 TO 2868 FX 53.37 5088. 3544 TO 3549 3568 TO 3571 FX 47.93 5089. 4247 TO 4252 4271 TO 4274 FX 39.52 5090. 4950 TO 4955 4974 TO 4977 FX 28.35 5091. 5653 TO 5658 5677 TO 5680 FX 9.75 5092. 35 TO 52 FX 120.55 5093. 738 TO 755 FX 120.1 5094. 1441 TO 1458 FX 118.26 5095. 2144 TO 2161 FX 114.51 5096. 2847 TO 2864 FX 106.74 5097. 3550 TO 3567 FX 95.46 5098. 4253 TO 4270 FX 79.04 5099. 4956 TO 4973 FX 56.7 5100. 5659 TO 5676 FX 19.5 ******************************************************************************* 5102. *LOAD COMB 8 1.5(S.W+F.L+M.L+L.L) 5103. *4 1.5 5 1.5 6 1.5 7 1.5 5104. LOAD COMB 5 COMBINATION LOAD CASE 5 5105. 1 1.0 2 1.0 3 1.0 5106. LOAD COMB 6 LOAD COMB 6 5107. 1 1.0 2 1.0 4 1.0 5108. *LOAD COMB 10 1.0(FL+ML)+0.5LL 5109. *5 1.0 6 1.0 7 0.5 5110. PERFORM ANALYSIS PRINT STATICS CHECK P R O B L E M S T A T I S T I C S ----------------------------------- NUMBER OF MODES REQUESTED = 20 NUMBER OF EXISTING MASSES IN THE MODEL = 18981 NUMBER OF MODES THAT WILL BE USED = 20 CALCULATED FREQUENCIES FOR LOAD CASE 3 MODE FREQUENCY(CYCLES/SEC) PERIOD(SEC) ACCURACY 1 0.416 2.40503 1.041E-15 2 0.427 2.33990 1.232E-15 3 0.481 2.07866 1.167E-15 4 1.346 0.74290 9.933E-16 5 1.378 0.72556 7.580E-16 6 1.545 0.64705 0.000E+00 7 2.536 0.39438 4.479E-16 8 2.582 0.38733 1.512E-15 9 2.881 0.34713 1.215E-15 10 4.052 0.24681 7.362E-08 11 4.106 0.24355 1.142E-07 12 4.373 0.22868 1.152E-05

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13 4.449 0.22477 9.371E-05 14 4.512 0.22164 1.920E-03 15 4.568 0.21889 1.639E-04 16 4.576 0.21853 2.623E-04 17 4.632 0.21587 1.484E-03 18 4.735 0.21121 2.696E-04 19 4.738 0.21105 2.822E-04 20 4.769 0.20970 4.527E-04 21 4.800 0.20834 1.868E-04 22 4.803 0.20819 1.650E-04 23 4.864 0.20560 2.048E-03 24 4.870 0.20535 8.723E-04 25 4.875 0.20515 3.784E-03 26 4.891 0.20448 6.149E-03 MODE SPECTRAL ACCELERATION DESIGN SEISMIC COEFFICIENT ---- --------------------- ------------------------------ X Y Z 1 0.69438 0.0258 0.0000 0.0000 2 0.71371 0.0265 0.0000 0.0000 3 0.80340 0.0299 0.0000 0.0000 4 2.24794 0.0835 0.0000 0.0000 5 2.30167 0.0855 0.0000 0.0000 6 2.50000 0.0929 0.0000 0.0000 7 2.50000 0.0929 0.0000 0.0000 8 2.50000 0.0929 0.0000 0.0000 9 2.50000 0.0929 0.0000 0.0000 10 2.50000 0.0929 0.0000 0.0000 11 2.50000 0.0929 0.0000 0.0000 12 2.50000 0.0929 0.0000 0.0000 13 2.50000 0.0929 0.0000 0.0000 14 2.50000 0.0929 0.0000 0.0000 15 2.50000 0.0929 0.0000 0.0000 16 2.50000 0.0929 0.0000 0.0000 17 2.50000 0.0929 0.0000 0.0000 18 2.50000 0.0929 0.0000 0.0000 19 2.50000 0.0929 0.0000 0.0000 20 2.50000 0.0929 0.0000 0.0000 FLOOR PEAK STOREY SHEAR IN KN ----- ------------------------ X Z 10 1555.70 0.00 9 2632.05 0.00 8 3310.42 0.00 7 3797.11 0.00 6 4190.21 0.00 5 4613.16 0.00 4 5059.28 0.00 3 5493.07 0.00 2 5721.28 0.00

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1 5721.28 0.00 RESPONSE LOAD CASE 3 CSM GROUPING MODAL COMBINATION METHOD USED. MISSING MASS METHOD USED. DYNAMIC WEIGHT X Y Z 2.479661E+05 2.479661E+05 2.479661E+05 KN MISSING WEIGHT X Y Z -1.072770E+04 -8.784135E+04 -1.085082E+04 KN MISSING WEIGHT X Y Z -1.072770E+04 -8.784135E+04 -1.085082E+04 KN MODAL WEIGHT X Y Z 2.372384E+05 1.601247E+05 2.371153E+05 KN FLOOR PEAK STOREY SHEAR IN KN INCLUDING MISSING MASS CORRECTION ----- ---------------------------------------------------------- X Z 10 1558.87 0.00 9 2632.05 0.00 8 3312.63 0.00 7 3797.42 0.00 6 4192.43 0.00 5 4614.60 0.00 4 5062.30 0.00 3 5498.10 0.00 2 5750.60 0.00 1 5750.60 0.00 ZPA 3.23695 ZPAFREQ 33.00000 MASS PARTICIPATION FACTORS IN PERCENT BASE SHEAR IN KN -------------------------------------- ------------------ MODE X Y Z SUMM-X SUMM-Y SUMM-Z X Y Z 1 0.03 0.00 78.13 0.027 0.000 78.128 1.76 0.00 0.00 2 78.37 0.00 0.03 78.399 0.000 78.153 5154.58 0.00 0.00 3 0.05 0.00 0.09 78.449 0.000 78.246 3.68 0.00 0.00 4 0.00 0.00 10.38 78.452 0.000 88.631 0.63 0.00 0.00 5 10.31 0.00 0.00 88.763 0.000 88.633 2187.06 0.00 0.00 6 0.00 0.00 0.01 88.766 0.000 88.641 0.80 0.00 0.00 7 0.00 0.00 4.44 88.767 0.000 93.077 0.12 0.00 0.00 8 4.39 0.00 0.00 93.156 0.000 93.077 1011.19 0.00 0.00 9 0.00 0.00 0.00 93.156 0.000 93.078 0.07 0.00 0.00 10 0.00 0.00 2.54 93.156 0.001 95.622 0.11 0.00 0.00 11 2.52 0.00 0.00 95.673 0.001 95.623 579.75 0.00 0.00 12 0.00 57.15 0.00 95.673 57.153 95.623 0.00 0.00 0.00 13 0.00 0.00 0.00 95.673 57.156 95.623 0.09 0.00 0.00 14 0.00 0.48 0.00 95.673 57.639 95.624 0.01 0.00 0.00 15 0.00 0.10 0.00 95.673 57.736 95.624 0.00 0.00 0.00 16 0.00 5.94 0.00 95.673 63.679 95.624 0.00 0.00 0.00 17 0.00 0.64 0.00 95.673 64.323 95.624 0.00 0.00 0.00

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18 0.00 0.00 0.00 95.673 64.327 95.624 0.00 0.00 0.00 19 0.00 0.07 0.00 95.673 64.395 95.624 0.00 0.00 0.00 20 0.00 0.18 0.00 95.674 64.575 95.624 0.07 0.00 0.00 ZPA 4.33 0.00 0.00 100.000 0.000 0.000 579.91 0.00 0.00 --------------------------- TOTAL SRSS SHEAR 5748.73 0.00 0.00 TOTAL 10PCT SHEAR 5750.59 0.00 0.00 TOTAL ABS SHEAR 9519.85 0.00 0.00 TOTAL CSM SHEAR 5750.60 0.00 0.00 NOTE : THE BASE SHEAR (VB) FROM RESPONSE SPECTRUM IS LESS THAN THE BASE SHEAR (Vb) CALCULATED USING EMPIRICAL FORMULA FOR FUNDAMENTAL TIME PERIOD. MULTIPLYING FACTOR (Vb/VB) IS 1.0020 STATIC LOAD/REACTION/EQUILIBRIUM SUMMARY FOR CASE NO. 1 DEAD LOAD ***TOTAL APPLIED LOAD ( KN METE ) SUMMARY (LOADING 1 ) SUMMATION FORCE-X = 0.00 SUMMATION FORCE-Y = -141329.98 SUMMATION FORCE-Z = 0.00 SUMMATION OF MOMENTS AROUND THE ORIGIN- MX= 2759501.34 MY= 0.00 MZ= -3982152.50 ***TOTAL REACTION LOAD( KN METE ) SUMMARY (LOADING 1 ) SUMMATION FORCE-X = 0.00 SUMMATION FORCE-Y = 141329.98 SUMMATION FORCE-Z = 0.00 SUMMATION OF MOMENTS AROUND THE ORIGIN- MX= -2759501.34 MY= 0.00 MZ= 3982152.51 MAXIMUM DISPLACEMENTS ( CM /RADIANS) (LOADING 1) MAXIMUMS AT NODE X = 1.61965E-02 5671 Y = -1.18743E+00 6155 Z = 3.55011E-02 5653 RX= 1.63084E-03 5780 RY= 5.49876E-06 6098 RZ= -1.64138E-03 5891 STATIC LOAD/REACTION/EQUILIBRIUM SUMMARY FOR CASE NO. 2 LIVE LOAD ***TOTAL APPLIED LOAD ( KN METE ) SUMMARY (LOADING 2 )

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SUMMATION FORCE-X = 0.00 SUMMATION FORCE-Y = -68764.32 SUMMATION FORCE-Z = 0.00 SUMMATION OF MOMENTS AROUND THE ORIGIN- MX= 1336319.99 MY= 0.00 MZ= -1943738.22 ***TOTAL REACTION LOAD( KN METE ) SUMMARY (LOADING 2 ) SUMMATION FORCE-X = 0.00 SUMMATION FORCE-Y = 68764.32 SUMMATION FORCE-Z = 0.00 SUMMATION OF MOMENTS AROUND THE ORIGIN- MX= -1336320.00 MY= 0.00 MZ= 1943738.23 MAXIMUM DISPLACEMENTS ( CM /RADIANS) (LOADING 2) MAXIMUMS AT NODE X = 6.98429E-03 5671 Y = -7.89202E-01 5237 Z = 2.27731E-02 5653 RX= 1.27786E-03 5077 RY= 2.85019E-06 6098 RZ= -1.29122E-03 5188 STATIC LOAD/REACTION/EQUILIBRIUM SUMMARY FOR CASE NO. 4 SP-22 LOAD ***TOTAL APPLIED LOAD ( KN METE ) SUMMARY (LOADING 4 ) SUMMATION FORCE-X = 19112.08 SUMMATION FORCE-Y = 0.00 SUMMATION FORCE-Z = 0.00 SUMMATION OF MOMENTS AROUND THE ORIGIN- MX= 0.00 MY= 387552.13 MZ= -334521.11 ***TOTAL REACTION LOAD( KN METE ) SUMMARY (LOADING 4 ) SUMMATION FORCE-X = -19112.08 SUMMATION FORCE-Y = 0.00 SUMMATION FORCE-Z = 0.00 SUMMATION OF MOMENTS AROUND THE ORIGIN- MX= 0.00 MY= -387552.13 MZ= 334521.11 MAXIMUM DISPLACEMENTS ( CM /RADIANS) (LOADING 4) MAXIMUMS AT NODE X = 1.11679E+01 5680 Y = 6.78544E-01 1313 Z = 4.71691E-01 5671 RX= -1.12614E-03 790 RY= 1.74587E-04 5671

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RZ= -4.86347E-03 759 ************ END OF DATA FROM INTERNAL STORAGE ************ 5111. PRINT CG CENTER OF GRAVITY OF THE STRUCTURE IS LOCATED AT: (METE UNIT) X = 28.18 Y = 20.68 Z = 19.53 TOTAL SELF WEIGHT = 141324.719 (KN UNIT) 5112. PRINT MODE SHAPES MODE SHAPES ----------- JOINT MODE X-TRANS Y-TRANS Z-TRANS X-ROTAN Y-ROTAN Z-ROTAN 1 1 0.00000 0.00000 0.00000 0.000E+00 0.000E+00 0.000E+00 2 1 0.00000 0.00000 0.00000 0.000E+00 0.000E+00 0.000E+00 3 1 0.00000 0.00000 0.00000 0.000E+00 0.000E+00 0.000E+00 4 1 0.00000 0.00000 0.00000 0.000E+00 0.000E+00 0.000E+00 5 1 0.00000 0.00000 0.00000 0.000E+00 0.000E+00 0.000E+00 6 1 0.00000 0.00000 0.00000 0.000E+00 0.000E+00 0.000E+00 7 1 0.00000 0.00000 0.00000 0.000E+00 0.000E+00 0.000E+00 8 1 0.00000 0.00000 0.00000 0.000E+00 0.000E+00 0.000E+00 9 1 0.00000 0.00000 0.00000 0.000E+00 0.000E+00 0.000E+00 10 1 0.00000 0.00000 0.00000 0.000E+00 0.000E+00 0.000E+00 11 1 0.00000 0.00000 0.00000 0.000E+00 0.000E+00 0.000E+00 12 1 0.00000 0.00000 0.00000 0.000E+00 0.000E+00 0.000E+00 13 1 0.00000 0.00000 0.00000 0.000E+00 0.000E+00 0.000E+00 14 1 0.00000 0.00000 0.00000 0.000E+00 0.000E+00 0.000E+00 15 1 0.00000 0.00000 0.00000 0.000E+00 0.000E+00 0.000E+00 16 1 0.00000 0.00000 0.00000 0.000E+00 0.000E+00 0.000E+00 17 1 0.00000 0.00000 0.00000 0.000E+00 0.000E+00 0.000E+00 18 1 0.00000 0.00000 0.00000 0.000E+00 0.000E+00 0.000E+00 19 1 0.00000 0.00000 0.00000 0.000E+00 0.000E+00 0.000E+00 20 1 0.00000 0.00000 0.00000 0.000E+00 0.000E+00 0.000E+00 21 1 0.00000 0.00000 0.00000 0.000E+00 0.000E+00 0.000E+00 22 1 0.00000 0.00000 0.00000 0.000E+00 0.000E+00 0.000E+00 23 1 0.00000 0.00000 0.00000 0.000E+00 0.000E+00 0.000E+00 24 1 0.00000 0.00000 0.00000 0.000E+00 0.000E+00 0.000E+00 25 1 0.00000 0.00000 0.00000 0.000E+00 0.000E+00 0.000E+00 26 1 0.00000 0.00000 0.00000 0.000E+00 0.000E+00 0.000E+00 27 1 0.00000 0.00000 0.00000 0.000E+00 0.000E+00 0.000E+00 28 1 0.00000 0.00000 0.00000 0.000E+00 0.000E+00 0.000E+00 29 1 -0.00304 0.00189 0.06760 6.423E-04 1.535E-06 3.413E-05 30 1 -0.00311 0.00155 0.06652 6.429E-04 2.986E-06 2.727E-05 31 1 -0.00308 0.00149 0.06546 6.334E-04 2.874E-06 2.754E-05 32 1 -0.00305 0.00147 0.06446 6.234E-04 2.777E-06 2.744E-05 33 1 -0.00302 0.00146 0.06352 6.132E-04 2.665E-06 2.759E-05 34 1 -0.00308 0.00192 0.06257 5.929E-04 4.178E-06 2.517E-05 35 1 -0.00206 -0.00013 0.06781 5.974E-04 3.404E-06 1.936E-05 36 1 -0.00206 -0.00008 0.06665 6.090E-04 3.274E-06 1.898E-05

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37 1 -0.00205 -0.00008 0.06559 5.997E-04 3.383E-06 1.896E-05 38 1 -0.00204 -0.00008 0.06460 5.903E-04 3.393E-06 1.895E-05 39 1 -0.00204 -0.00008 0.06365 5.806E-04 3.211E-06 1.886E-05 40 1 -0.00203 -0.00002 0.06278 5.517E-04 2.298E-06 2.054E-05 41 1 -0.00101 0.00006 0.06781 5.977E-04 3.373E-06 1.062E-05 42 1 -0.00101 0.00008 0.06666 6.097E-04 3.260E-06 9.337E-06 43 1 -0.00103 0.00003 0.06562 6.017E-04 3.427E-06 9.207E-06 44 1 -0.00104 0.00003 0.06463 5.922E-04 3.517E-06 9.587E-06 45 1 -0.00105 0.00003 0.06368 5.825E-04 3.356E-06 9.527E-06 46 1 -0.00105 0.00004 0.06282 5.536E-04 2.365E-06 9.964E-06 47 1 -0.00005 -0.00199 0.06760 6.420E-04 1.550E-06 -4.615E-06 48 1 0.00001 -0.00148 0.06654 6.427E-04 2.895E-06 5.111E-07 49 1 -0.00001 0.00047 0.06564 5.882E-04 2.899E-06 5.885E-06 ............................................................................... Due to Large size input data such as mode shape coefficient was Skip the input data for minimizing the information. ............................................................................. 5113. LOAD LIST 5 6 5114. PRINT STORY DRIFT STORY HEIGHT LOAD AVG. DISP(CM ) DRIFT(CM ) RATIO ----------------------------------------------------------------------------- (METE) X Z X Z BASE= 0.00 5 0.0000 0.0000 0.0000 0.0000 L /999999 6 0.0000 0.0000 0.0000 0.0000 L /999999 5 0.3504 0.0164 0.3504 0.0164 L / 1198 6 1.0885 0.0019 1.0885 0.0019 L / 386 5 1.0367 0.0499 0.6863 0.0335 L / 612 6 3.0930 0.0062 2.0045 0.0043 L / 209 5 1.7944 0.0884 0.7577 0.0385 L / 554 6 5.1509 0.0108 2.0579 0.0046 L / 204 5 2.5174 0.1265 0.7230 0.0380 L / 581 6 6.9462 0.0151 1.7953 0.0043 L / 234 5 3.1646 0.1616 0.6472 0.0352 L / 649 6 8.3758 0.0188 1.4295 0.0037 L / 294 STORY HEIGHT LOAD AVG. DISP(CM ) DRIFT(CM ) RATIO ----------------------------------------------------------------------------- (METE) X Z X Z BASE= 0.00 5 3.7190 0.1917 0.5544 0.0301 L / 757 6 9.4264 0.0221 1.0507 0.0032 L / 400 5 4.1703 0.2167 0.4513 0.0250 L / 931 6 10.1304 0.0249 0.7040 0.0029 L / 596 5 4.5103 0.2382 0.3400 0.0214 L / 1235 6 10.5516 0.0275 0.4212 0.0025 L / 997 5 4.7433 0.2546 0.2330 0.0164 L / 1802 6 10.7835 0.0299 0.2319 0.0025 L / 1811 5115. PRINT MEMBER FORCES LIST 1 TO 28 856 TO 883 1640 TO 1667 2424 TO 2451 3208 - 5116. 3209 TO 3235 3992 TO 4019 4776 TO 4803 5560 TO 5587 6344 TO 6371

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APPENDIX – B

Torsional response of assymetric multy story building thesis

Design

Transcript of Torsional response of assymetric multy story building thesis