M-Tech thesis

1. 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

2. (1)
calculations. 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
(1)
codes no amplification whatsoever is used. “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
(1)
considered as infinitely rigid, and the storey stiffness are of importance. However, if
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3. 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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4. 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
(2) (3)
increases produced, but not the decreases as specified in the code. 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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5. Y
4
3@7.5 3
=22.5m Xr
Cr †
Cm†
Yr 2
1
X
A B C D E
4@7.5m=30m
Fig: 1.1 Plan of an Asymmetric Building
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6. 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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7. 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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8. 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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9. 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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10. 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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11. 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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12. 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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13. 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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14. The eccentric
elevator core
r Collapse of this column due
to excessive displacement
demand initiated the
progressive collapse in the
building
Fig 2.1 Example of Structural collapse caused by torsion (Eccentric elevator core lead to
significant torsion deformation and the collapse of corner columns)
A department Store in Kobe, Japan after 1995 Earthquake
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15. 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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16. 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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17. • 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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18. - 18 -

19. 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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20. 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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21. 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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22. 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
J=1
Σm j φ² j y n + r²
J =1
Σ m j φ² j θ n
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
36 2
The calculations of torsion seismic shears as per I.S. Code 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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23. 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
- 23 -

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 hi2 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 hi2 = 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
Colu Weigh Weight Weigh Weigh Live Total weight Live Total
mn t of of slab t of t of load in in 1 to 8 load weight in
line beams in kN colum walls kN floors in kN @ roof 9th roof in
in kN n in in kN in kN kN
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
- 24 -

25. WEIGHT CALCULATION IN Y- DIRECTION
Column Weight Weight Weight Weight Live Total Live Total
line of of slab of of load in weight in load weight
beams in kN column walls kN 1 to 8 @ in 9th
in kN in kN in kN floors in roof roof in
kN in kN 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
- 25 -

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
- 26 -

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
- 27 -

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
- 28 -

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
- 29 -

30. Table 4.1 Additional Shears for the L-shaped building due to earthquake forces acting in X- direction
Tx Z K xx
Vx1 = ∴Ip = 14590.74k m4
Ip
- 30 -

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 -0.0000249
34 1 0.00177 -0.00235 -0.07052 -0.0006457 -0.0000009 -0.0000089
44 1 0.001 -0.00005 -0.07129 -0.0006252 -0.0000009 -0.0000085
47 1 0.00062 0.00239 -0.07244 -0.0006649 -0.0000009 0.0000028
49 1 0.00062 -0.00041 -0.07168 -0.0006095 -0.0000009 -0.0000146
53 1 0.00023 0.0024 -0.07168 -0.0006561 -0.0000009 0.0000064
56 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 -0.0000325
225 1 0.00547 -0.00441 -0.20801 -0.0008385 -0.0000030 -0.0000141
235 1 0.00293 -0.0001 -0.21056 -0.0008168 -0.0000030 -0.0000110
238 1 0.00166 0.00448 -0.21437 -0.0008672 -0.0000030 0.0000033
240 1 0.00166 -0.00075 -0.21183 -0.0008001 -0.0000030 -0.0000173
244 1 0.00039 0.0045 -0.21183 -0.0008545 -0.0000030 0.0000087
247 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 -0.0000342
415 1 0.00981 -0.0061 -0.36224 -0.0008615 -0.0000057 -0.0000154
425 1 0.0051 -0.00014 -0.36696 -0.0008397 -0.0000057 -0.0000114
428 1 0.00274 0.0062 -0.37404 -0.0008929 -0.0000057 0.0000037
430 1 0.00274 -0.00101 -0.36932 -0.0008232 -0.0000057 -0.0000176
434 1 0.00038 0.00621 -0.36932 -0.0008791 -0.0000057 0.0000095
437 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 -0.0000324
605 1 0.01417 -0.00741 -0.51261 -0.0008067 -0.0000083 -0.0000152
615 1 0.00723 -0.00017 -0.51955 -0.0007865 -0.0000083 -0.0000108
618 1 0.00376 0.00753 -0.52997 -0.0008372 -0.0000083 0.0000034
620 1 0.00376 -0.0012 -0.52302 -0.0007718 -0.0000083 -0.0000166
624 1 0.00029 0.00754 -0.52302 -0.0008239 -0.0000083 0.0000090
627 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 -0.0000138
805 1 0.00919 -0.00019 -0.65791 -0.0006911 -0.0000108 -0.0000096
808 1 0.00468 0.00849 -0.67143 -0.0007363 -0.0000108 0.0000028
810 1 0.00468 -0.00132 -0.66242 -0.0006787 -0.0000108 -0.0000149
814 1 0.00018 0.0085 -0.66242 -0.0007245 -0.0000108 0.0000078
817 1 0.00018 0.00812 -0.6489 -0.0007092 -0.0000108 -0.0000068
- 31 -

32. 980 1 0.0217 -0.0088 -0.79194 -0.0006065 -0.0000130 -0.0000240
985 1 0.0217 -0.009 -0.76492 -0.0005833 -0.0000130 -0.0000119
995 1 0.01089 -0.0002 -0.77573 -0.0005684 -0.0000130 -0.0000081
998 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 -0.0000125
1004 1 0.00008 0.00915 -0.78113 -0.0005964 -0.0000130 0.0000063
1007 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 -0.0000186
1175 1 0.02455 -0.00938 -0.85668 -0.0004415 -0.0000147 -0.0000095
1185 1 0.01228 -0.00021 -0.86895 -0.0004293 -0.0000147 -0.0000063
1188 1 0.00614 0.00953 -0.88735 -0.0004595 -0.0000147 0.0000014
1190 1 0.00614 -0.00141 -0.87508 -0.0004225 -0.0000147 -0.0000101
1194 1 0.00001 0.00953 -0.87508 -0.0004518 -0.0000147 0.0000046
1197 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 -0.0000125
1365 1 0.02669 -0.00958 -0.92243 -0.0002960 -0.0000160 -0.0000078
1375 1 0.01332 -0.00022 -0.93581 -0.0002906 -0.0000160 -0.0000045
1378 1 0.00663 0.00973 -0.95587 -0.0003093 -0.0000160 0.0000002
1380 1 0.00663 -0.00141 -0.94249 -0.0002880 -0.0000160 -0.0000063
1384 1 -0.00006 0.00973 -0.94249 -0.0003038 -0.0000160 0.0000026
1387 1 -0.00006 0.0093 -0.92243 -0.0002961 -0.0000160 -0.0000019
1550 1 0.02821 -0.00944 -1 -0.0002053 -0.0000170 -0.0000106
1555 1 0.02821 -0.00965 -0.96454 -0.0001953 -0.0000170 -0.0000039
1565 1 0.01403 -0.00022 -0.97873 -0.0001788 -0.0000170 -0.0000028
1568 1 0.00694 0.00981 -1 -0.0002051 -0.0000170 0.0000022
1570 1 0.00694 -0.00141 -0.98582 -0.0001743 -0.0000170 -0.0000084
1574 1 -0.00015 0.0098 -0.98582 -0.0002011 -0.0000170 0.0000034
1577 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 -0.0006623
34 2 0.07292 -0.0023 -0.00006 0.0000069 0.0000012 -0.0006626
44 2 0.07393 -0.00041 0.00096 0.0000082 0.0000012 -0.0006174
47 2 0.07444 0.00226 0.00249 0.0000317 0.0000012 -0.0006777
49 2 0.07444 0.00011 0.00147 0.0000033 0.0000012 -0.0006264
53 2 0.07495 0.00234 0.00147 0.0000224 0.0000012 -0.0006848
56 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 -0.0008478
225 2 0.21276 -0.00431 -0.00047 0.0000060 0.0000039 -0.0008481
235 2 0.216 -0.00077 0.00277 0.0000103 0.0000039 -0.0007987
238 2 0.21762 0.00423 0.00762 0.0000412 0.0000039 -0.0008695
240 2 0.21762 0.00021 0.00438 0.0000057 0.0000039 -0.0008101
244 2 0.21923 0.00437 0.00438 0.0000275 0.0000039 -0.0008790
247 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
- 32 -

33. 415 2 0.36806 -0.00595 -0.00114 0.0000050 0.0000070 -0.0008647
425 2 0.37393 -0.00106 0.00473 0.0000103 0.0000070 -0.0008150
428 2 0.37687 0.00584 0.01354 0.0000428 0.0000070 -0.0008877
430 2 0.37687 0.0003 0.00767 0.0000057 0.0000070 -0.0008269
434 2 0.37981 0.00603 0.00767 0.0000278 0.0000070 -0.0008977
437 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 -0.0008057
605 2 0.51859 -0.00721 -0.00194 0.0000039 0.0000102 -0.0008060
615 2 0.52712 -0.00127 0.00659 0.0000094 0.0000102 -0.0007602
618 2 0.53138 0.00708 0.01939 0.0000401 0.0000102 -0.0008280
620 2 0.53138 0.00037 0.01086 0.0000051 0.0000102 -0.0007714
624 2 0.53565 0.0073 0.01086 0.0000255 0.0000102 -0.0008376
627 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 -0.0007059
795 2 0.6545 -0.00813 -0.00276 0.0000028 0.0000132 -0.0007061
805 2 0.66549 -0.00143 0.00823 0.0000080 0.0000132 -0.0006659
808 2 0.67098 0.00797 0.02471 0.0000352 0.0000132 -0.0007258
810 2 0.67098 0.00043 0.01372 0.0000040 0.0000132 -0.0006758
814 2 0.67648 0.00821 0.01372 0.0000218 0.0000132 -0.0007343
817 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 -0.0005789
985 2 0.76986 -0.00874 -0.00354 0.0000017 0.0000157 -0.0005791
995 2 0.78297 -0.00153 0.00957 0.0000063 0.0000157 -0.0005462
998 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 -0.0005543
1004 2 0.79608 0.00882 0.01613 0.0000172 0.0000157 -0.0006027
1007 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 -0.0004360
1175 2 0.86074 -0.00911 -0.00425 0.0000006 0.0000178 -0.0004362
1185 2 0.87557 -0.00159 0.01058 0.0000044 0.0000178 -0.0004105
1188 2 0.88299 0.00893 0.03282 0.0000217 0.0000178 -0.0004489
1190 2 0.88299 0.0005 0.01799 0.0000014 0.0000178 -0.0004167
1194 2 0.8904 0.00918 0.01799 0.0000123 0.0000178 -0.0004545
1197 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 -0.0002883
1365 2 0.92537 -0.00929 -0.00489 -0.0000012 0.0000193 -0.0002884
1375 2 0.94148 -0.00162 0.01122 0.0000025 0.0000193 -0.0002756
1378 2 0.94954 0.00912 0.03539 0.0000140 0.0000193 -0.0002976
1380 2 0.94954 0.00052 0.01928 0.0000012 0.0000193 -0.0002794
1384 2 0.95759 0.00936 0.01928 0.0000071 0.0000193 -0.0003014
1387 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 -0.0001872
1555 2 0.96595 -0.00936 -0.00547 0.0000002 0.0000204 -0.0001873
1565 2 0.98297 -0.00163 0.01155 0.0000014 0.0000204 -0.0001613
- 33 -

34. 1568 2 0.99149 0.00918 0.03709 0.0000111 0.0000204 -0.0001940
1570 2 0.99149 0.00053 0.02007 -0.0000042 0.0000204 -0.0001652
1574 2 1 0.00942 0.02007 0.0000040 0.0000204 -0.0001974
1577 2 1 -0.00957 -0.00547 -0.0000061 0.0000204 -0.0001961
29 3 -0.05381 0.00068 0.07502 0.0006895 0.0000685 0.0004976
34 3 -0.05381 -0.00044 -0.0679 -0.0006235 0.0000685 0.0004968
44 3 0.00336 -0.00003 -0.01073 -0.0000937 0.0000685 -0.0000284
47 3 0.03194 -0.00135 0.07502 0.0006871 0.0000685 -0.0002996
49 3 0.03194 0.00013 0.01785 0.0001481 0.0000685 -0.0002685
53 3 0.06052 0.00136 0.01785 0.0001697 0.0000685 -0.0005556
56 3 0.06052 0.00021 -0.0679 -0.0006242 0.0000685 -0.0005590
57 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 0.0006365
225 3 -0.15722 -0.00083 -0.1984 -0.0007983 0.0002004 0.0006356
235 3 0.01005 -0.00005 -0.03113 -0.0001194 0.0002004 -0.0000380
238 3 0.09369 -0.00254 0.21977 0.0008832 0.0002004 -0.0003846
240 3 0.09369 0.00025 0.0525 0.0001933 0.0002004 -0.0003486
244 3 0.17732 0.00255 0.0525 0.0002181 0.0002004 -0.0007140
247 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 0.0006486
415 3 -0.27208 -0.00114 -0.34337 -0.0008135 0.0003471 0.0006476
425 3 0.01765 -0.00007 -0.05364 -0.0001210 0.0003471 -0.0000394
428 3 0.16252 -0.0035 0.38096 0.0009017 0.0003471 -0.0003929
430 3 0.16252 0.00034 0.09123 0.0001977 0.0003471 -0.0003561
434 3 0.30739 0.00351 0.09123 0.0002231 0.0003471 -0.0007291
437 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 0.0006036
605 3 -0.38332 -0.00138 -0.48378 -0.0007572 0.0004893 0.0006027
615 3 0.02511 -0.00008 -0.07535 -0.0001122 0.0004893 -0.0000370
618 3 0.22933 -0.00425 0.53729 0.0008403 0.0004893 -0.0003661
620 3 0.22933 0.00041 0.12886 0.0001844 0.0004893 -0.0003319
624 3 0.43354 0.00425 0.12886 0.0002079 0.0004893 -0.0006795
627 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 0.0005275
795 3 -0.48359 -0.00156 -0.61036 -0.0006618 0.0006176 0.0005267
805 3 0.0319 -0.00009 -0.09487 -0.0000978 0.0006176 -0.0000326
808 3 0.28964 -0.00478 0.67836 0.0007351 0.0006176 -0.0003203
810 3 0.28964 0.00046 0.16287 0.0001613 0.0006176 -0.0002902
814 3 0.54739 0.00478 0.16287 0.0001818 0.0006176 -0.0005944
817 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 0.0004310
985 3 -0.56848 -0.00167 -0.71753 -0.0005409 0.0007263 0.0004303
995 3 0.03768 -0.0001 -0.11136 -0.0000797 0.0007263 -0.0000269
- 34 -

35. 998 3 0.34076 -0.00514 0.79788 0.0006013 0.0007263 -0.0002619
1000 3 0.34076 0.00049 0.19172 0.0001319 0.0007263 -0.0002373
1004 3 0.64384 0.00513 0.19172 0.0001486 0.0007263 -0.0004863
1007 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 0.0003228
1175 3 -0.63511 -0.00174 -0.80165 -0.0004053 0.0008116 0.0003224
1185 3 0.04226 -0.0001 -0.12427 -0.0000593 0.0008116 -0.0000203
1188 3 0.38095 -0.00536 0.89179 0.0004512 0.0008116 -0.0001965
1190 3 0.38095 0.00051 0.21442 0.0000985 0.0008116 -0.0001775
1194 3 0.71964 0.00534 0.21442 0.0001113 0.0008116 -0.0003649
1197 3 0.71964 0.00084 -0.80165 -0.0004057 0.0008116 -0.0003665
1360 3 -0.68221 0.00277 0.95831 0.0002977 0.0008720 0.0002113
1365 3 -0.68221 -0.00178 -0.86112 -0.0002657 0.0008720 0.0002110
1375 3 0.04556 -0.0001 -0.13335 -0.0000388 0.0008720 -0.0000140
1378 3 0.40945 -0.00546 0.95831 0.0002971 0.0008720 -0.0001291
1380 3 0.40945 0.00052 0.23054 0.0000662 0.0008720 -0.0001184
1384 3 0.77333 0.00544 0.23054 0.0000731 0.0008720 -0.0002402
1387 3 0.77333 0.00085 -0.86112 -0.0002659 0.0008720 -0.0002410
1550 3 -0.71156 0.00279 1 0.0001934 0.0009097 0.0001372
1555 3 -0.71156 -0.00179 -0.89821 -0.0001719 0.0009097 0.0001368
1565 3 0.04772 -0.0001 -0.13892 -0.0000230 0.0009097 -0.0000084
1568 3 0.42736 -0.0055 1 0.0001926 0.0009097 -0.0000847
1570 3 0.42736 0.00052 0.24072 0.0000366 0.0009097 -0.0000685
1574 3 0.807 0.00548 0.24072 0.0000470 0.0009097 -0.0001562
1577 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
- 35 -

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
SHEAR- SHEAR-
MEMBER LOAD JT AXIAL Y 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
- 36 -

37. 34 -4945.51 -685.13 -117.83 8.38 -265.85 40.32
7 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 43.19
9 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 15.8
10 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 22.71
11 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 13.58
12 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 38.43
15 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 9.07
16 5 16 10499.42 209.56 9.3 1.54 34.78 917.31
44 - 207.38 5 1.59 -7.71 71.87
- 37 -

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 12.42
17 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 1.52
18 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 7.14
24 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
- 38 -

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
- 39 -

40. Table 4.4 Column forces, moments in X & Y direction , twisting moments &
reinforcement for Zone II, Type-I soil, OMRF, R=3
Column -
For- Groups 9thfloor 8thfloor 7thfloor 6thfloor 5thfloor 4thfloor 3rdfloor 2ndfloor 1stfloor
ces
Central Col 1247 2719 4190 5662 7132 8603 10073 11541 13008
E1 Column 444 944 1430 1905 2369 2826 3277 3811 4336
B1 Column 443 942 1426 1900 2363 2819 3269 3861 4384
P B3 Column 1022 2207 3397 4589 5784 6984 8187 9641 11004
A3 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
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
Mx 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
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
My 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
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
Mz 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
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
Steel A3 Column 5016 1037 748 996 1238 1475 1709 2021 2334
area A6 Column 5977 1868 1297 1095 1385 1675 1965 2251 2621
E6 Column 6028 1871 1299 1096 1387 1678 1967 2253 2564
- 40 -

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%
% of B3 Column 0.22% 0.17% 0.22% 0.3% 0.39% 0.45% 0.56% 0.62% 0.73%
Steel 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%
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
- 41 -

42. Column -
For- Groups 9thfloo 8thfloo 7thfloo 6thfloo 5thfloo 4thfloo 3rdfloo 2ndfloor 1stfloor
ces
Central Col 1247 2719 4191 5661 7132 8602 10072 11541 13007
E1 Column 440 931 1404 1863 2310 2746 3176 3691 4201
B1 Column 438 928 1400 1858 2303 2739 3169 3741 4250
P B3 Column 1023 2208 3398 4593 5291 6993 8198 9656 11021
A3 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
Central Col 0.24 0.24 0.25 0.27 0.26 0.24 0.17 0.019 0.075
E1 Column 0.24 0.24 0.25 0.27 0.26 0.24 0.17 0.019 0.075
B1 Column 0.24 0.24 0.25 0.27 0.26 0.24 0.17 0.019 0.075
M x B3 Column 0.24 0.24 0.25 0.27 0.26 0.24 0.17 0.019 0.075
A3 Column 0.24 0.24 0.25 0.27 0.26 0.24 0.17 0.019 0.075
A6 Column 0.24 0.24 0.25 0.27 0.26 0.24 0.17 0.019 0.075
E6 Column 0.24 0.24 0.25 0.27 0.26 0.24 0.17 0.019 0.075
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
My 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
Central Col 183 264 319 347 361 359 382 464 670
E1 Column 363 247 202 144 101 42 63 182 555
B1 Column 360 245 200 142 99 39 63 183 558
M z B3 Column 215 101 113 157 177 178 269 357 631
A3 Column 357 243 197 140 93 48 46 126 547
A6 Column 574 451 521 521 444 504 502 698 258
E6 Column 573 449 520 519 517 502 510 637 733
Central Col 640 1393 2148 2901 3655 4409 512 5914 9072
E1 Column 4574 859 720 955 1184 1407 1628 1892 2153
B1 Column 4520 856 717 952 1180 1404 1624 1917 2178
B3 Column 1201 1132 1742 2354 2968 3584 4202 4949 5648
Steel A3 Column 4823 974 735 975 1208 1436 1659 1962 2267
area A6 Column 6195 2235 1785 1116 1415 1716 2016 2313 2289
E6 Column 6248 2239 1788 1118 1417 1716 2019 2314 2633
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%
% of B3 Column 0.17% 0.17% 0.22% 0.3% 0.4% 0.45% 0.56% 0.61% 0.73%
Steel 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%
E6 Column 0.78% 0.28% 0.22% 0.17% 0.22% 0.22% 0.28% 0.3% 0.34%
- 42 -

43. Table 4.6 for Zone II, Type-III soil, OMRF, R=3
Column -
For- Groups 9thfloor 8thfloor 7thfloor 6thfloor 5thfloor 4thfloor 3rdfloor 2ndfloor 1stfloor
ces
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
P 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
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
M x 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
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
M y 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
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
M z 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
Central Col. 639 1393 2147 2901 3655 4409 5162 5914 10368
E1 Column 4392 848 708 937 1157 1372 1584 1839 2094
B1 Column 4339 798 706 934 1154 1369 1584 1865 2119
B3 Column 913 1132 1743 2355 2970 3588 4207 4955 5656
Steel A3 Column 4641 963 724 958 1183 1402 1616 1910 2209
area A6 Column 6386 2557 2126 1134 1441 1751 2060 2365 2749
E6 Column 6440 2612 2130 1136 1444 1751 2063 2367 2694
Central Col. 0.17% 0.22% 0.28% 0.4% 0.46% 0.56% 0.7% 0.8% 1.3%
- 43 -

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%
% of B3 Column 0.17% 0.17% 0.22% 0.3% 0.4% 0.45% 0.56% 0.61% 0.73%
Steel 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%
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
Column -
For- Groups 9thfloor 8thfloor 7thfloor 6thfloor 5thfloor 4thfloor 3rdfloor 2ndfloor 1stfloor
ces
Central Col 1247 2719 4190 5661 7131 8601 10071 11539 13005
E1 Column 408 847 1244 1605 1938 2251 2553 2947 3364
B1 Column 406 844 1240 1599 1932 2244 2547 2997 3413
P B3 Column 1023 2213 3411 4617 5830 7049 8273 9748 1127
A3 Column 418 872 1282 1657 2001 2323 2633 3103 3606
A6 Column 509 1116 1759 2434 3132 3842 4555 5255 6084
E6 Column 510 1119 1763 2440 3139 3850 4564 5263 5978
Central Col 0.53 0.53 0.57 0.62 0.64 0.6 0.45 0.14 0.12
E1 Column 0.53 0.53 0.57 0.62 0.64 0.6 0.45 0.14 0.12
B1 Column 0.53 0.53 0.57 0.62 0.64 0.6 0.45 0.14 0.12
M x B3 Column 0.53 0.53 0.57 0.62 0.64 0.6 0.45 0.14 0.12
A3 Column 0.53 0.53 0.57 0.62 0.64 0.6 0.45 0.14 0.12
A6 Column 0.53 0.53 0.57 0.62 0.64 0.6 0.45 0.14 0.12
E6 Column 0.53 0.53 0.57 0.62 0.64 0.6 0.45 0.14 0.12
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
M y 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
Central Col 481 699 844 920 775 888 1008 1226 1777
E1 Column 415 299 317 366 371 359 373 646 1612
B1 Column 410 302 321 370 374 362 376 653 1607
M z B3 Column 179 546 681 780 828 830 955 1171 1752
A3 Column 407 303 325 375 380 364 438 674 1601
A6 Column 753 788 901 921 921 893 932 1289 1812
E6 Column 749 787 898 918 918 890 936 1223 1790
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
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45. Stee A3 Column 4029 1574 921 849 1026 1191 1349 1590 5175
area A6 Column 7579 4705 4548 3251 1718 1969 2334 2693 5612
E6 Column 7645 4717 4646 3259 1721 1973 2339 2697 5208
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%
% of B3 Column 0.22% 0.17% 0.22% 0.3% 0.39% 0.45% 0.56% 0.62% 1.7%
Stee 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%
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
Column -
For- Groups 9thfloor 8thfloor 7thfloor 6thfloor 5thfloor 4thfloor 3rdfloor 2ndfloor 1stfloor
ces
Central Col. 1247 2718 4189 5660 7130 8600 10069 11537 13004
E1 Column 389 799 1151 1456 1724 1965 2194 2516 2880
B1 Column 388 795 1146 1450 1717 1958 2186 2566 2928
P B3 Column 1023 2215 3419 4632 5853 7081 8316 9801 11188
A3 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
Central Col. 0.7 0.7 0.76 0.83 0.85 0.8 0.62 0.21 0.15
E1 Column 0.7 0.7 0.76 0.83 0.85 0.8 0.62 0.21 0.15
B1 Column 0.7 0.7 0.76 0.83 0.85 0.8 0.62 0.21 0.15
Mx B3 Column 0.7 0.7 0.76 0.83 0.85 0.8 0.62 0.21 0.15
A3 Column 0.7 0.7 0.76 0.83 0.85 0.8 0.62 0.21 0.15
A6 Column 0.7 0.7 0.76 0.83 0.85 0.8 0.62 0.21 0.15
E6 Column 0.7 0.7 0.76 0.83 0.85 0.8 0.62 0.21 0.15
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
My 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
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
Mz 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
E6 Column 850 982 1116 1149 1150 1114 1183 1563 2403
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46. Central Col. 1667 1393 2147 2901 3654 4408 6709 13600 25272
E1 Column 3954 2816 2349 1827 1176 1007 1124 2321 12101
Steel B1 Column 3918 2840 2447 1959 1254 1003 1121 2499 12077
area B3 Column 3269 2620 1879 2374 3000 3629 4262 9042 20642
A3 Column 4239 3044 2673 2124 1314 1049 1170 3164 11724
A6 Column 8424 6198 6339 5121 3510 2116 2519 4953 12453
E6 Column 8498 6217 6358 5136 3519 2121 2524 3794 12257
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%
% of B1 Column 0.5% 0.39% 0.34% 0.28% 0.17% 0.17% 0.17% 0.34% 1.50%
Steel 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%
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
Column -
For- Groups 9thfloor 8thfloor 7thfloor 6thfloor 5thfloor 4thfloor 3rdfloor 2ndfloor 1st floor
ces
Central Col. 1247 2718 4189 5660 7130 8600 10069 11537 13003
E1 Column 374 757 1071 1327 1539 1719 1883 2145 2462
B1 Column 372 754 1066 1321 1532 1711 1876 2196 2511
B3 Column 1023 2218 3425 4644 5873 7109 8353 9847 11241
P A3 Column 387 789 1119 1391 1617 1809 1982 2323 2727
A6 Column 542 1206 1932 2711 3530 4374 5224 6056 6984
E6 Column 544 1210 1937 2719 3540 7385 5237 6067 6883
Central Col. 0.85 0.85 0.92 1.00 1.04 0.98 0.75 0.27 0.17
E1 Column 0.85 0.85 0.92 1.00 1.04 0.98 0.75 0.27 0.17
B1 Column 0.85 0.85 0.92 1.00 1.04 0.98 0.75 0.27 0.17
M x B3 Column 0.85 0.85 0.92 1.00 1.04 0.98 0.75 0.27 0.17
A3 Column 0.85 0.85 0.92 1.00 1.04 0.98 0.75 0.27 0.17
A6 Column 0.85 0.85 0.92 1.00 1.04 0.98 0.75 0.27 0.17
E6 Column 0.85 0.85 0.92 1.00 1.04 0.98 0.75 0.27 0.17
Central Col. 5.6 4.4 4.4 4.2 4.0 4.2 2.0 2.2 0.96
E1 Column 285 211 210 178 162 147 141 174 140
B1 Column 287 209 213 173 168 148 213 199 111
M y B3 Column 492 346 374 380 385 388 290 254 178
A3 Column 345 256 259 223 195 179 205 272 200
A6 Column 508 329 361 370 376 381 345 438 349
E6 Column 526 338 373 381 388 391 377 392 265
Central Col. 803 1169 1409 1536 1595 1587 1682 2047 2969
E1 Column 471 662 723 796 803 776 831 1277 2751
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