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### Torsional response of assymetric multy story building thesis

1. 1. CHAPTER 1 INTRODUCTION1.1 GENERAL Torsion responses in structures arise from two sources: Eccentricity in the massand stiffness distributions, causing a torsion response coupled with translation response;and torsion arising from accidental causes, including uncertainties in the masses andstiffness, the differences in coupling of the structural foundation with the supporting earthor rock beneath and wave propagation effects in the earthquake motions that give atorsion input to the ground, as well as torsion motions in the earth itself during theearthquake. (1) Horizontal twisting occurs in buildings when the center of mass (CM) does notcoincide with the centre of resistance (CR). The distance between them is called theeccentricity (e). Lateral force multiplied by this (e) causes a torsion moment (T) that mustbe resisted by the structure in addition to the normal seismic force.(2) The centre ofrigidity 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 pointthrough 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 stiffnesscan 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 tothe direction of applied ground motion. A precise evaluation of the torsion response isquite complicated because the coupled lateral- torsion vibration modes of the entirestructure are to be considered by performing a two – or three dimensional response
2. 2. (1)calculations. As an approximation, the torsion moment in each storey can be obtainedby summing from the top storey the incremental torsion moments. The “static” torsion responses in each storey are then determined by computingthe 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 totaltwisting or torsion response at each floor-level.(1) Since these are “static “responses, theyshould be “amplified” for “dynamic” response using the response- spectrum amplificationfactor for the fundamental torsion frequency of the structure. However, in many design (1)codes no amplification whatsoever is used. “Accidental” torsion may arise in manyways. Most current codes (4) use accidental eccentricity value of 5% of the plan dimensionof the storey perpendicular to the direction of applied ground motion. The accidentaltorsion 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 variousstoreys; with consideration of increases in all levels or decreases in all levels to get twobounding values. The accidental torsion (or the total torsion) is computed in the same wayas the “real” torsion described above. (1)1.3 DISTRIBUTION OF SHEAR AND MOMENTS The storey shears arising from translation and from torsion response aredistributed over the height of the building in proportion to the stiffness of variouselements in the building the translational shears being affected by the translationalstiffness 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 floorsof 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 -2-
3. 3. the floor diaphragm is flexible and deforms greatly, the distribution of forces becomesmore nearly uniform than determined by the method discussed above. A simplifiedapproach is possible by considering the relative displacements of the building due totranslation and that due to rotation of each storey separately, as affected by the diaphragmor floor stiffness. The stiff nesses are determined by the forces corresponding to a unitdisplacement in either translation or torsion. Respectively, then the shears due totranslation or rotation can be distributed in proportion to these stiff nesses. The storey moments are distributed to the various frames and walls that make upthe lateral force system in a manner consistent with the distribution of storey shears. Inparticular, the shears and moments in any frame or wall should be statically consistent.Base or “overturning” moments: The flexural base moment is of importance inconnection with the foundation design. The corresponding flexural moments at each floorlevel are important in connection with the calculation of vertical stresses in the columnsand walls of the structure. These moments can be computed from modal analysis orequivalent lateral force analysis.1.4 OLD CODE PROVISIONS In 1984 version of Indian Seismic Code makes provision for the increase in shearresulting from horizontal torsion due to the eccentricity (e) between the centre of massand the centre of rigidity. The torsion moment (T) at each storey = the shear (V) in thatstorey multiplied by eccentricity (e). Since there could be quite a bit of variation in thecomputed value of e, the code recommends that the design eccentricity (ed) be taken as1.5e. Negative torsion shears shall be neglected. (3) The net effect of this torsion is to increase the shear in certain structural elementsand reduction in certain others. The code recommends that reduction in shear on account -3-
4. 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 seismicresisting system with due consideration given to the relative stiff nesses of the verticalcomponents 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 followingsteps 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 takenat the left corner of the building Fig. 1.1. If x and y are the coordinates of variouselements and Kx and Ky their stiff nesses in the two directions, the coordinates (Xr,Yr) ofthe 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 isgiven by Ip = Σ(KxY2 + KyX2) …… 3 If the torsional moment T= Ved …… 4Where 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 IpWhere Kxx, Kyy are the total stiff nesses of the column line under consideration and X andY are coordinates w.r.t the centre of rigidity Cr. -4-
5. 5. Y 43@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 -5-
6. 6. CHAPTER 2 LITERATURE SURVEY2.1 GENERAL It has been observed repeatedly in strong earthquakes that the presence ofasymmetry in the plan of a structure makes it more vulnerable to seismic damages. Thereare reports of extensive damages to buildings that are attributed to excessive torsionresponses caused by asymmetry in earthquakes such as the 1972 Managua earthquake(Pomares Calero5 1995), the 1985 Michanocan earthquake (Esteva6 1987) and the 1989Loma Prieta earthquake (Mitchell et al7 (1990)). Fig. 2.1 shows damages in a multi-storeybuilding after the 1995 Hyogoken-Nanbu earthquake in Kobe, probably caused byexcessive torsion responses because its core was eccentrically located in plan. Asymmetry in plan causes torsion in a building because the centre of mass and thecentre of rigidity do not coincide. The distance between the two centers is termedstructural eccentricity and the magnitude of this eccentricity can be estimated. Torsioncan also arise in a building due to other sources for which estimating their magnitude isdifficult. Some examples of these sources for the so-called accidental torsion are therotational components in the ground motion, an unfavorable distribution of live load, andthe 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 thatleads to non-uniform distribution of in-plan floor displacement. This results in unevendemands on the lateral resisting elements at different locations of the system. -6-
7. 7. Although torsion has long been recognized as a major reason for poor seismicperformance of multi-story buildings and many studies have been done on the seismictorsion responses of single story buildings, the analytical and experimental studies on theinelastic seismic response of multi-story buildings do not have a long history. The reasonas explained by De la Llera & Chopra8 (1995c) is that "most researchers have beendiscouraged to look into the multi-story case in light of the already complex response ofsingle storey asymmetric buildings". In most of the available studies on the seismic torsion response of multi-storeybuildings, simple building models such as shear walls are used and the conclusions of thestudies are based on the responses of buildings subjected to a limited number ofearthquake ground motions. Currently, there is no general agreement on how the torsioneffect should be allowed for in seismic design. These observations provided themotivation for the study by A.S. Moghadam9 in order to provide a better understandingof the problem of seismic damages caused by torsion in multi-storey reinforced concreteframe buildings. Those investigations on torsion response that involve using the recordeddata in buildings during earthquakes are explained. Then experimental research is carriedout, 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. Toobtain 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 recordedmotions of some instrumented buildings in earthquakes can provide valuable informationabout the seismic performance of such buildings. Safak and Celebi10 (1990) introduced amethod 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 -7-
8. 8. Hall11 (1992) studied the data from two low-rise, extensively instrumented buildings in the1987 Whittier Narrows Earthquake. Their study involved the investigation of responses ofbuildings, responding in the elastic and marginally inelastic range, by comparing thebehavior of the buildings with computer simulations. Both buildings were modeled asframe structures using a shear wall idealization. The recorded data at the basements wereused as the ground motion input for the models. The results from unidirectional groundmotion input were found to provide a reasonably close match of the actual responses duringthe earthquake. Using bi-directional ground motion inputs gave an even better match to themeasurements. Sedarat et al.12 (1994) studied the torsion response characteristics of threeregular buildings in California, by analyzing the strong motions recorded in thesebuildings during three recent earthquakes: the 1989 Loma Prieta earthquake, the 1986 Mt.Lewis earthquake, and the 1984 Morgan Hill earthquake. The responses of the buildingswere 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 toaccount for the torsion responses of these buildings.2.3 EXPERIMENTAL STUDIES Some experiments on scaled models are reported in the literature. Bourahla andBlakeborough13 (1994) examined the performance of knee braces in asymmetric framebuildings by designing and testing a one-twelfth-scale building model using a shakingtable. 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 changesin 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 framebuildings is less significant compared with other sources of asymmetry. The energydissipation capacities of the frames were also studied. Based on the experimental results, -8-
9. 9. it is concluded that the magnitude of the eccentricity in itself is meaningless, but it is theability 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 elasticand inelastic behavior of buildings. Study of a seven-storey frame-wall structure (Sedaratand Bertero 1990a14, 1990b15) demonstrated that linear dynamic analysis mightsignificantly underestimate the effect of torsion on the inelastic dynamic response of thestructure. On the other hand, the study of a thirteen storey regular space frame structureBoroschek and Mahin16 (1992) showed that the effects of torsion were more severe if thebuilding is modeled as an elastic structure instead of an inelastic one, and the results werefound 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 beensettled. Teramoto et al.17 (1992) presented some results of dynamic analyses of anasymmetric 10-storey shear beam building. They used one earthquake record as the inputmotion. A conclusion of this study is that mass eccentric and stiffness eccentric systemsbehave differently. When mass eccentricity exists at upper floors only, the eccentricitywill also have some effects on the lower floors. However, stiffness eccentricity onlyaffects the floors where eccentricity exists. Cruz and Cominetti18 (1992) used a five storey-building model in their study andconcluded that the overall ductility and the fundamental period of the building are theparameters that most strongly affect the responses of the building. In a study by De la Llera and Chopra19 (1996) they concluded that increasing thetorsion capacity of the building by introducing resisting planes in the orthogonal -9-
10. 10. direction, and modifying the stiffness and strength distribution to localise yielding inselected resisting planes, are the two most important corrective measures for asymmetricbuildings.2.5 DESIGN PROCEDURES Several issues related to the design of multi-storey buildings and evaluation ofbuilding codes have been studied in the literature. Bertero20 (1992) developed formulaewith the objective of considering the elastic and inelastic torsion in the preliminary designof tall buildings. Bertero21 (1995) used the classical theorems of plastic analysis toestimate 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 inthe seismic design of buildings. Ozaki et al.23 (1988) proposed a seismic design methodfor multi-storey asymmetric buildings. Azuhata and Ozaki24 (1992) proposed a methodfor safety evaluation of shear-type asymmetric multi-storey buildings. In both of thesestudies, the damage potential due to torsion is evaluated based on the shear and torsionstrength capacity and the design shear force and torsion moment for each storey of thebuilding. In a study by Duan and Chandler25 (1993) on an asymmetric multi-storey framebuilding model, they concluded that application of the static torsion provisions of somebuilding 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 theeffectiveness 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 andinelastic properties of a representative model of an asymmetric multi-storey building is - 10 -
11. 11. enormous. Therefore, all studies that have been reported in the literature involved usingsimple models for the building and the conclusions are drawn based on a limited numberof earthquake records as ground motions input. In almost all these studies, the multi-storey frame buildings are modelled as shearbuildings. The shear building model is not a good representative of the frame buildings ina seismic zone because a shear building model has strong beams, which causes the plastichinges to occur at the columns. This is in contradiction to the strong column-weak beamphilosophy 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 importantdesign parameters. Rutenberg and De Stefano28 (1997) have pointed out that some of thedifference between the results of modeling a building as a shear building versus a ductilemoment resisting frame building in the study by Moghadam and Tso27 (1996b) might bedue to differences in the periods of the two compared models. Modeling of a building as ashear building involves changing the stiffness of beams to very high values. This in turncauses the period of the shear beam model to change. Therefore; modeling a ductile framebuilding as a shear building will cause changes in not only the mode of failure, but also thenatural periods of the building. Thus, the relevance of observations of studies using shearbeam modeling to actual ductile moment resisting frame structures in seismic activeregions is questionable.2.7 SIMPLIFIED METHODS Some simplified approaches have been developed in the literature to estimate theinelastic 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 storeyof the building is represented by a single super-element in the simplified model. The use ofstorey shear and storey torque interaction surface (Kan and Chopra29 (1981), Palazzo and - 11 -
12. 12. Fraternali30 (1988), De la Llera and Chopra31 (1995b)) is an important component of thismethod. The storey shear and torque (SST) surface is basically the yield surface of thestorey due to the interaction between storey shear and torque. Each point inside thesurface represents a combination of storey shear and torque that the storey remainselastic. On the other hand, each point on the surface represent a combination of shear andtorque that leads to the yielding of the storey. It is shown that the SST surfaces can beused for single storey systems and multi-storey shear buildings. One major assumptionembedded in the method is that the stories of a multi-storey building are considered asindependent single storey systems. In other words, the floor diaphragms are assumedrigid, both in-plane and out-of-plane. This assumption of out-of-plane rigid diaphragmsis equivalent to assuming rigid beams in the building. How realistic is such a model torepresent the behavior of ductile frame buildings in seismic regions is a subject thatrequires further investigation. In the performance based design codes and in the guidelines for retrofitting ofbuildings, 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 theacceptability of any proposed design, or to assess the damage vulnerability of existingbuildings. Moghadam and Tso32 (1996a) extended the application of the pushoveranalysis to asymmetrical buildings by using a 3-D inelastic program. Kilar and Fajfar33(1997) developed a simple method to conduct pushover analysis for asymmetric buildingsby modeling the building as a collection of planar macro-elements. Another methodproposed by Tso and Moghadam34 (1997) incorporates the results of elastic dynamicanalyses of the building in the pushover procedure. A further simplification is achievedby requiring only a two-dimensional inelastic analysis program to perform the pushoveranalysis on asymmetrical multi-storey buildings (Tso and Moghadam34 1997, Moghadam - 12 -
13. 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 pushoverand inelastic dynamic analyses. - 13 -
14. 14. The eccentric elevator core r Collapse of this column due to excessive displacement demand initiated the progressive collapse in the buildingFig 2.1 Example of Structural collapse caused by torsion (Eccentric elevator core lead tosignificant torsion deformation and the collapse of corner columns)A department Store in Kobe, Japan after 1995 Earthquake - 14 -
15. 15. CHAPTER 3 STRUCTURAL MODEL, LOADINGS & RESPONSE PARAMETERS OF INTEREST3.1 INTRODUCTION The study in this work is based on the analyses of a family of structural modelsrepresenting multi-story asymmetrical buildings. These models are subjected to bothcritical and lateral loadings expected on buildings during an earthquake. A set of responseparameters 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 utilizedin this work. The different building configurations are introduced first. Then the methodsand the loadings used in the analyses are discussed. Finally the chosen responseparameters are outlined. The material presented in this chapter prepares the backgroundinformation 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 featuresexpected from multi-story buildings subjected to seismic loading. The assumed plan ofbuilding is shown in Fig. 3.1. It has an L-shape floor plan of dimensions 42.4 m by 53.0m, and a uniform floor height of 4.2 m Fig. 3.2. The plan considered is asymmetric. Forconvenience, the X-direction is referred to as the main direction and the Y-direction isreferred to as the transverse direction. To resist the lateral loads, there are 28 RC columnssupporting to flat slab. The flat slab is of thickness 0.25 m with column caps 3.6x3.6x0.5m with (post tensioned) edge beams of size 0.6x0.5 m are provided through out thebuilding in all floors. All the columns are placed at strategic locations with spacing of - 15 -
16. 16. 10.6x10.6 m, having 5 bays in X direction & 4 bays in Y direction. The grids are markedas 1 to 6 in X direction and A to E in Y direction as shown in Fig. 3.1. The Seismicanalysis is carried out as per the latest IS-1893-2002 code by the Response Spectrumtechnique. The buildings are assumed to be located in zone-II, zone-V and located onthree types of soils (Hard, Medium; Soft soils). The Response quantities consideredincludes axial forces, moments in X & Y directions, twisting moments, %steel, steel areaetc. for the columns; further both ordinary moment resisting frame (OMRF) and specialmoment resisting frame (SMRF) are considered.3.3 COMPUTER SOFTWARE STAAD.Pro 2006 The static and dynamic behavior of the multi-story asymmetric buildings in theelastic range is the main focus of the study reported in this work. Therefore computerprogram with the ability of performing 3-D elastic static and dynamic analysis wasnecessary. The program STAAD.Pro-2006 has been chosen as the base computersoftware in performing the analyses. To have a clear understanding of the analysis a studyhas been carried out to evaluate this program by comparing its results with the responsesderived 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. - 16 -
17. 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. Inthis study an edge beam element with flat slab having and a column element are used tomodel the elements of the frames in the buildings. - 17 -
18. 18. - 18 -
19. 19. CHAPTER 4 ANALYSIS & DESIGN OF ASYMMETRICAL MULTI- STOREY BUILDINGS INCORPORATING TORSIONAL PROVISIONS4.1 INTRODUCTION In a symmetric building, all the lateral load-resisting elements at differentlocations in plan experience the same lateral displacement when subjected tounidirectional forces. As a result, the force induced in each element is proportional to itslateral stiffness. This observation leads to a guideline that calls for assigning the designstrength of the lateral load-resisting elements according to their stiffness. In anasymmetric building, however, the location of a lateral load-resisting element affects theshare of load that it should resist because the loadings on the rigid floors of thesebuildings are accompanied by torques caused by the structural eccentricity in thebuilding. The force induced in each element from the floor torques is proportional to itscontribution to the torsion stiffness of the building. The torque-induced force in anelement is called the torsion shear. The location of an element not only determines themagnitude, but also the direction of the torsion shear. Depending on the direction of thetorque, the torsion shear should be added to or subtracted from the forces induced in thatelement by the translational displacement of the floors. To compensate the torsion effect on the performance of a building, differentapproaches have been suggested to replace the rule of distribution of strength among theelements proportional to their lateral stiffness. These approaches can collectively be referred toas torsion provisions. The goal of this chapter is to evaluate the effectiveness of a few torsionprovisions to improve the seismic performance of asymmetric multistory buildings. - 19 -
20. 20. The first approach that is studied here is distribution of the strength based on staticequilibrium consideration. Then the static torsion provisions based on the Indian seismiccode (IS: 1893-2002) are studied. Finally, the application of response spectrum analysis toproportion the design strength of the elements is considered.4.2 TORSIONAL PROVISIONS Torsion provisions are incorporated in most building codes to redistribute thestrength among elements to minimize the torsion effects. Codes usually divide thebuildings into regular and irregular buildings and consider that static torsion provisions willbe 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 tobe included in the determination of the design forces. The product of the lateral force andthe design eccentricity determines the value of the torsion moment. The designeccentricity can be different from the structural eccentricity in a building. To protect theelements on both side of the building, codes require two separate load cases to beconsidered involving two design eccentricities. The magnitudes of the two designeccentricities 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 resistingthe torsion moments (torsion shears) should be combined with the shear fromtranslational loading. - 20 -
21. 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 Thenature of a mode can be identified using the modal mass information derived from thefree vibration analysis. The first two mode shapes of the buildings and also the effectivemodal masses of the first 12 modes of the buildings are presented. The mode shapes ofthe buildings are given in two formats. In one format, the displacements and rotations atCM of the floors are given for each mode. In the second format, the lateral displacementsof the five frames are shown for each mode. Based on structural dynamics, it can be shown that translation predominant modesin general have larger modal masses than torsion predominant modes.1 In the figures, theeffective modal masses are shown in figure: against the natural periods of the building. Itcan 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 largemodal masses associated with the second mode for Y-direction of the building. In thecase of third mode purely torsion predominant, where as in first and second modes alsovery less torsion values will be appearing, but predominant case is translational. A parameter defined here as effective modal moment of inertia provides aquantitative way of identifying the contribution of different modes to the displacements ofedge 1 and edge 6 of a building.1 Depending on the sign of this parameter one can showwhether the effects of the rotational and translational components of a coupled mode areadditive or subtractive on each edge of the building. The effective modal moment ofinertia for the nth mode is defined as I*On (Chopra 1995, where this parameter is calledmodal static response for base torque)1: - 21 -
22. 22. NI*On = Σ r2 Γ n m j φj θn J=1 This equation is developed for an asymmetric building with eccentricity in onedirection 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= massradius of gyration, m = mass of floor, φj θn= the rotational element on the jth floor in then-th vibration mode shape.Γn is defined as: N Σ m j φj y n J=1Γn = -------------------------------------------------------- (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. Theeffective 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 ofinertia to expand the effective force vector of a structure.4.5 TORSIONAL ANALYSIS OF AN L-SHAPED BUILDING 36 2The calculations of torsion seismic shears as per I.S. Code is illustrated for the L-shape building shown in Fig. 3.1Imposed load floor 39 = 4kN/m²; Imposed load roof 39= 1.5 kN/m²Grade of concrete M35 and density 37 = 25 kN/m³, E 37 = 29.580 kN/m²Floor finishes 38 = 60mm of 20 kN/m³ - 22 -
23. 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/m²Note: - 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. 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 = 121663873CENTRE 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- DIRECTIONColu 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 inline beams in kN colum walls kN floors in kN @ roof 9th roof in in kN n in in kN in kN kN kN1-1 145.8 1255.60 340.2 534.24 337.80 2612.92 - 2275.842-2 291.6 2511.20 340.2 178.08 674.16 3995.24 - 3321.083-3 340.2 2929.70 425.30 534.24 786.52 5013.96 - 4227.444-4 388.8 3348.30 425.30 356.16 898.88 5417.44 - 4518.565-5 388.8 3348.30 425.30 356.16 898.88 5417.44 - 4518.566-6 194.4 1674.20 425.30 890.4 449.44 3633.74 - 3184.30 ΣW=26090.74 ΣW=22045.78 - 24 -
25. 25. WEIGHT CALCULATION IN Y- DIRECTIONColumn 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 kNA-A 145.8 1255.60 340.2 534.24 337.08 2612.92 - 2275.84B-B 388.8 3348.33 510.3 534.24 896.76 5678.43 - 4781.67C-C 486.0 4185.4 510.3 356.16 1123.6 6661.46 - 5537.86D-D 486.0 4185.4 510.3 356.16 1123.6 6661.46 - 5537.86E-E 243.0 2092.7 510.3 890.4 561.8 4298.20 - 3736.40 ΣW=25912.47 kN ΣW=21869.63kNCENTRE OF MASS IN X- DIRECTIONTaking 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 26090.74Cmx (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 22045.78CENTRE OF MASS IN Y – DIRECTIONTaking 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. 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 21869.63CENTRE OF RIGIDITY IN X – DIRECTIONLateral stiffness of column k = 12EI L3For a square column (0.9x0.9 mts) (having) (using)M35 grade of “E” value same and also “L” are constant; kx = ky = kxr = 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 28kCENTRE OF RIGIDITY IN Y– DIRECTIONZr= 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 28kEccentricity:-For 1st, 2nd, 3rd, 4th, 5th, 6th, 7th, 8th floorsex = | Cmx - xr| = | 28.48 – 28.014| = 0.466 mez = | Cmz - Zr| = | 22.981 – 22.714| = 0.267 mFor 9th (roof) storeyex = | Cmx - xr | = | 28.53 – 28.014| = 0.516 m - 26 -
27. 27. ez = | Cmz - Zr | = | 22.983 – 22.714| = 0.269 mTORSIONAL STIFFNESSIp = 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 m4Σ 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 m4Ip = Σ (kX. Z2 + kY. X 2 )Ip = (5778.51 + 8812.23) = 14590.74k m4ADDITIONAL MOMENTS DUE TO SESMIC FORCE IN X- DIRECTION(b = 42.4 mts)1st floorT1a = Vx (1.5 ez +0.05b) = 9507.3(1.5 x 0.267+ 0.05 x 42.4) T1a = 23963.15 kNmT1b = Vx (ez - 0.05b) = 9507.3 (0.267 - 0.05 x 42.4) T1b = - 17617 kNm2nd floorT2a = 9471.3(1.5 x 0.267+0.05 x 42.4 T2a = 23872.4 kNmT2b = 9471.3 (- 1.853) = -17550.3 kNm - 27 -
28. 28. 3rd floorT3a = 9327.3 (2.5205) = 23509.5 kNmT3b = 9327.3 (- 1.853) = -17283.5 kNm4th floorT4a = 9003.6 (2.5205) = 22693.6 kNmT4b = 9003.6 (- 1.853) = -16683.7 kNm5th floorT5a = 8428.1 (2.5205) = 21243.03 kNmT5b = 8428.1 (- 1.853) = -15617.3 kNm6th floorT6a = 7528.9 (2.5205) = 18976.6 kNmT6b = 7528.9 (- 1.853) = -13951.05 kNm7th floorT7a = 6233.9 (2.5205) = 15712.5 kNmT7b = 6233.9 (- 1.853) = -11551.4 kNm8th floorT8a = 4471.5 (2.5205) = 11270.4 kNmT8b = 4471.5 (- 1.853) = -8285.7 kNm9th floor (roof)T9a (roof) = 2169.8 (1.5 x 0.269 + 0.05 x 42.4) = 5475.5 kNmT9b (roof) = Vx ( ez -0.05b) 2169.8 (0.269 – 2.12) = -4016.3kNm - 28 -
29. 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 kNmT1b = Vz (ex - 0.05b) = 9507.3 (0.466- 0.05*53) T1b = - 20763.9 kNmT2a = 9471.3 (3.349) = 31719.4 kNmT2b = 9471.3 (- 2.184) = -20685.3 kNmT3a = 9327.3 (3.349) = 31237.13 kNmT3b = 9327.3 (- 2.184) = -20370.8 kNmT4a = 9003.6 (3.349) = 30153.06 kNmT4b = 9003.6(-2.184) = -19663.9 kNmT5a = 8428.1(3.349) = 28225.7 kNmT5b = 8428.1 (-2.184) = -18406.9 kNmT6a = 7528.9 (3.349) = 25214.3 kNmT6b = 7528.9 (- 2.184) = -16443.12 kNmT7a = 6233.9 (3.349) = 20877.3 kNmT7b = 6233.9 (- 2.184) = -13614.8 kNmT8a = 4471.5 (3.349) = 14975.05 kNmT8b = 4471.5 (- 2.184) = -9765.7 kNmT9a (roof) = Vz (1.5 ex + 0.05b) = 2169.8(1.5 x 0.516 + 0.05 x 53 = 7429.4 kNmT9b (roof) = Vz (ez - 0.05b) = 2169.8(0.516-0.05 x 53) = -4630.4 kNm - 29 -
30. 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. 31. 4.6 MODE SHAPES The mode shape coefficients outputted from STAAD are listed in Table-4.2 for theMaster joints. The first few mode shapes are shown in Figures 4.1 to 4.8 for 3D buildingFig 4.9 shows the top floor displacements in plan illustrating the torsionmode # 3Table 4.2 Mode shape coefficients for Master slave jointsJoint 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 -0.0000079790 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. 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 0.00000211000 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 -0.00000541170 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 -0.00000411360 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 -0.00000191550 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 -0.0006623 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 -0.0006823220 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 -0.0008762410 2 0.36806 0.00614 0.01354 0.0000241 0.0000070 -0.0008644 - 32 -
33. 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 -0.0008948600 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 -0.0008349790 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 -0.0005789 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 -0.00059551000 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 -0.00060071170 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 -0.00045301360 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 -0.00030061550 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 - 33 -
34. 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 0.0004976 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 0.0001155220 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 -0.0007179410 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 -0.0007329600 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 -0.0006829790 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 -0.0005974980 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 - 34 -
35. 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 -0.00015704.7 MEMBER END FORCES The axial forces, shear forces, bending moments and twisting moments obtainedfor the Ground floor columns are given in Table 4.3. The same are illustrated in Fig. 4.10to 4.13 The member end forces for different columns (central, edge, corners) consideringOrdinary 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 Figs4.14 for the L- shaped building without considering torsion effects; with are regarded totorsion effects the increased values are shown in Fig. 4.15. The relative displacements in - 35 -
36. 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. 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 15.810 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 9.22 144.7413 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 -726.3914 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 - 37 -
38. 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 -5.38 127.6119 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 -432.4420 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 6.17 414.25 240.0421 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 -71.4822 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 25.1323 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 -12.75 129.6225 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 -433.0726 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 5.05 438.28 228.527 5 27 6370.28 235.54 -148.13 1.36 240.35 958.32 - 38 -
39. 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 14.42Due to large size input data such as member (Column) forcesare skip the input data for minimizing the information - 39 -
40. 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 1stfloorces 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 5639Steel A3 Column 5016 1037 748 996 1238 1475 1709 2021 2334area A6 Column 5977 1868 1297 1095 1385 1675 1965 2251 2621 E6 Column 6028 1871 1299 1096 1387 1678 1967 2253 2564 - 40 -
41. 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. 42. Column -For- Groups 9thfloo 8thfloo 7thfloo 6thfloo 5thfloo 4thfloo 3rdfloo 2ndfloor 1stfloorces 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 5648Steel A3 Column 4823 974 735 975 1208 1436 1659 1962 2267area 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. 43. Table 4.6 for Zone II, Type-III soil, OMRF, R=3 Column -For- Groups 9thfloor 8thfloor 7thfloor 6thfloor 5thfloor 4thfloor 3rdfloor 2ndfloor 1stfloorces 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 5656Steel A3 Column 4641 963 724 958 1183 1402 1616 1910 2209area 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. 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 1stfloorces 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 3413P 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 0.12M 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 141M 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 1607M 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 - 44 -
45. 45. Stee A3 Column 4029 1574 921 849 1026 1191 1349 1590 5175area 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 1stfloorces 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 2928P 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 0.15Mx 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 125My 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 2217Mz 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 - 45 -