INTERNATIONAL JOURNAL OF CIVIL AND STRUCTURAL ENGINEERING Volume 2, No 2, 2011

INTERNATIONAL JOURNAL OF CIVIL AND STRUCTURAL ENGINEERING Volume 2, No 2, 2011 Copyright 2010 All rights reserved Integrated Publishing services Research article ISSN 0976 4399 Solution of Shear Wall Location in Multi-Storey Building Anshuman. S 1, Dipendu Bhunia 2, Bhavin Ramjiyani 3 1- Assistant Professor, Civil Engineering Group, BITS Pilani, Rajasthan, India 2- Assistant Professor, Civil Engineering Group, BITS Pilani, Rajasthan, India. 3- Higher Degree student, Civil Engineering Group, BITS Pilani, Rajasthan, India dipendubhunia@gmail.com doi:10.6088/ijcser.00202010128 ABSTRACT Shear wall systems are one of the most commonly used lateral-load resisting systems in highrise buildings. Shear walls have very high in-plane stiffness and strength, which can be used to simultaneously resist large horizontal loads and support gravity loads, making them quite advantageous in many structural engineering applications. There are lots of literatures available to design and analyse the shear wall. However, the decision about the location of shear wall in multi-storey building is not much discussed in any literatures. In this paper, therefore, main focus is to determine the solution for shear wall location in multi-storey building based on its both elastic and elasto-plastic behaviours. An earthquake load is calculated and applied to a building of fifteen stories located in zone IV. Elastic and elasto-plastic analyses were performed using both STAAD Pro 2004 and SAP V 10.0.5 (2000) software packages. Shear forces, bending moment and story drift were computed in both the cases and location of shear wall was established based upon the above computations. Keywords: linear behaviour of shear wall, Non-linear behaviour of shear wall, seismic analysis, STAAD Pro 2004 and SAP V 10.0.5 (2000) Introduction Reinforced concrete framed buildings are adequate for resisting both the vertical and the horizontal load acting on them. However, when the buildings are tall, beam and column sizes workout quite heavy, so that there is lot of congestion at these joint and it is difficult to place and vibrate concrete at these places, which fact, does not contribute to the safety of buildings. These practical difficulties call for introduction of shear wall. The term shear wall is rather misleading as such a walls behave like flexural members. They are usually used in tall buildings and have been found to be of immense use to avoid total collapse of buildings under seismic forces. It is always advisable to incorporate them in buildings built in region likely to experienced earthquake of large intensity or high winds. The design of these shear wall for wind are design as simple concrete walls. The design of these walls for seismic forces requires special considerations as they should be safe under repeated loads. Shear walls may become imperative from the point of view of economy and control of lateral deflection. There are lots of literatures available [Cardan, B. (1961), Syngellakis et al. (1991), Wight et al. (1991), Qiusheng et al. (1994), White et al. (1995) and Rosowsky, D.V. (2002)] to design and analyse the shear wall. However, any of these literatures did not discuss much about the location of shear wall in multi-storey building. Hence, this paper has been described to determine the proper location of shear wall based on its elastic and elasto-plastic behaviours. A RCC medium rise building of 15 stories subjected to earthquake loading in Zone IV has been considered. In this regard, both STAAD Pro 2004 Received on September, 2011 Published on November 2011 493

and SAP V 10.0.5 (2000) software packages have been considered as two tools to perform. Shear forces, bending moments and storey drifts have been calculated to find out the location of shear wall in the building. The plan of the building without shear wall as shown in Figure 1 has been considered to carry out the study. Both STAAD PRO 2004 and SAP V 10.0.5 (2000) software packages have been considered. The preliminary data as per the Table 1 is taken up for this study. Ground storey height Floor to floor height Figure 1: Plan of the Building without Shear Wall Table 1: Preliminary Data Zone IV External wall 250mm thick including Plaster 4.0m From 150mm thick Internal wall Foundation including Plaster Grade of Concrete and 3.35m steel M20 and Fe 415 Size of exterior column 300 500 mm 2 Number of storeys Shear wall thickness FIFTEEN (G+14) Size of interior column 300 300 mm 2 300 mm Size of beams in longitudinal and transverse direction 300 450 mm 2 Depth of slab 150 mm Ductility design IS:13920-1993 Loading consideration Dead Load (DL) and Live load (LL) have been taken as per IS 875 (Part 1) (1987) and IS 875 (Part 2) (1987), respectively. Seismic load calculation has been done based on the IS 1893 (Part 1) (2002) s approach. Results and Discussions It has been seen from Table 2 that the top deflection (when the seismic load direction is in the shorter dimension) has been exceeded the permissible deflection, i.e. 0.004 times the total height of the building [IS 1893 (Part 1) (2002)] in STAAD PRO 2004. It has been exceeded for the load combinations 1.5(DL+E and 0.9DL+1.5EQ, respectively. 494

Software STAAD PRO 2004 SAP V 10.0.5 (2000) Solution of Shear Wall Location in Multi-Storey Building Table 2: Maximum Deflection at the Roof without Shear Wall Load Combination Calculated Deflection 187.976 1.5(DL+E 235.725 0.9DL+1.5EQ 235.685 158.71 1.5(DL+E 198.4 0.9DL+1.5EQ 198.38 Permissible Deflection [IS 1893 (Part 1) (2002)] 203.6 Similarly, bending moment and shear force were maximum at the ground level in 1 st and 12 th frames, respectively (Table 3). Table 3: Maximum Bending Moment and Maximum Shear Force at the Ground without Shear Wall Calculated Bending Calculated Load Frame No. Software Moment Shear Force Combination (kn-m) (kn) 1 st and 12 th STAAD PRO 2004 SAP V 10.0.5 (2000) 238.041 110.49 1.5(DL+E 294.134 136.43 0.9DL+1.5EQ 288.096 133.26 236.98 113.67 1.5(DL+E 296.06 142.04 0.9DL+1.5EQ 302.65 145.26 Hence, for the above reason shear wall was provided in 1 st and 12 th frames, respectively (Figure 2). Figure 2: Plan of the Building with Shear Wall in 1st and 12th frames It has been observed from Table 4 that the roof deflection was well within the permissible limit for all cases after providing the shear wall in 1 st and 12 th frames, respectively. 495

Table 4: Maximum Roof Deflection after Providing Shear Wall in the 1 st and 12 th Frame Software STAAD PRO 2004 SAP V 10.0.5 (2000) Load Combination Calculated Deflection Without Shear Wall With Shear Wall 187.976 123.59 1.5(DL+E 235.725 154.49 0.9DL+1.5EQ 235.685 151.49 158.71 91.4 1.5(DL+E 198.4 114.29 0.9DL+1.5EQ 198.38 114.29 Permissible Deflection [IS 1893 (Part 1) (2002)] 203.6 It has also seen from Table 5 that both bending moment and shear force were increased at the ground level in 1 st and 12 th frames after providing shear wall in 1 st and 12 th frames. Table 5: Maximum Bending moment and Shear Force at the Ground after providing Shear Wall in the 1 st and 12 th Frame Software STAAD PRO 2004 SAP V 10.0.5 (2000) Load Combination Calculated Bending Moment (kn-m) Calculated Shear Force (kn) 698.24 337.97 1.5(DL+E 861.27 416.28 0.9DL+1.5EQ 854.41 412.29 630.90 308.57 1.5(DL+E 778.78 380.24 0.9DL+1.5EQ 779.73 381.03 Further, shear walls have been provided in the interior frames, i.e. 6 th and 7 th frames as per the following figure 3. Figure 3: Plan of the Building with Shear Wall in 6th and 7th frames It has been seen from the Table 6 that roof deflection was well within the permissible deflection for all cases after providing the shear wall in 6 th and 7 th frames, respectively. 496

Table 6: Maximum Roof Deflection after Providing Shear Wall in the 6 th and 7 th Frame Software STAAD PRO 2004 SAP V 10.0.5 (2000) Load Combination Calculated Deflection Without Shear Wall With Shear Wall 187.976 106.47 1.5(DL+E 235.725 133.08 0.9DL+1.5EQ 235.685 135.47 158.71 84.72 1.5(DL+E 198.4 105.91 0.9DL+1.5EQ 198.38 105.91 Permissible Deflection [IS 1893 (Part 1) (2002)] 203.6 It has also seen from Table 7 that both bending moment and shear force were increased at the ground level in 6 th and 7 th frames after providing shear wall in 6 th and 7 th frames. Table 7: Maximum Bending Moment and Maximum Shear Force at the Ground after providing Shear Wall in the 6 th and 7 th Frame Software STAAD PRO 2004 SAP V 10.0.5 (2000) Elasto-plastic analysis Load Combination Calculated Bending Moment (kn-m) Calculated Shear Force (kn) 665.76 324.51 1.5(DL+E 809.79 394.28 0.9DL+1.5EQ 803.14 389.25 574.87 281.61 1.5(DL+E 732.90 360.92 0.9DL+1.5EQ 729.19 358.67 Mahin and Bertero (1976) employed the wide-column frame analogy to assess the importance of the strength and stiffness of the coupling beams on the elastic and nonlinear, static, and dynamic responses of multi-story, coupled shear-wall models to severe earthquake excitation. In wide column frame analogy shear wall has been modeled as a wide column having same dimension of shear wall and shear wall is connected to frame by connecting beam. Here shear walled frame has been modeled in SAP 2000 vs. 10 in which nonlinear analysis is done by using inbuilt coefficient given by FEMA 356 (FEDERAL EMERGENCY MANAGEMENT AGENCY) provisions. According to FEMA 356 the displacement of maximum displaced column is restricted by 4% of height. Analysis is done for the design earthquake which has the probability of occurrence is 100years and obtains the performance point. Performance point gives the value of maximum displacement of column which occurs for design earth quake intensity for particular zone i.e. zone IV. Resultant base shear-displacement curve has been obtained for structure, which shows behavior of structure with respect to base shear. 497

Figure 3: Graph showing Hinge Formation s In analysis hinge formation has been also been observed. Hinge formation levels are divided as yield level (B), immediate occupancy level (IO), life safety level (LS), collapse level (CP), full collapse level (E) [Figure 3]. At the immediate occupancy level structures have no sever damage and structures can be used for further life of structure. Life safety level indicates there will not be any casualty due to earthquake but structure cannot be used for further living. At collapse level member will start to collapse and full collapse member will already collapse. The elastic analysis has been extended to elasto-plastic analysis as per the criterion discussed above. SAP2000 v10.0.5 software package has been considered to carry out this analysis. Table 8 is showing the base shear and roof displacement at the performance point. It has been observed that the performance point for both the conditions (Shear Wall provided in the 6 th and 7 th Frames and Shear Wall provided in the 1 st and 12 th Frames) is lying within the IO level. Capacity Spectrum Capacity spectrum is obtained as per IS 1893:2002 for Zone IV with medium soil. 498

Figure 4: Capacity Spectrum for shear wall in in 6 th and 7 th frame 499

Figure 5: Capacity Spectrum for shear wall in in 1 st and 12 th frame Table 8: Base shear vs. Roof displacement at the performance point Conditions Shear Wall provided in the 6 th and 7 th Frames Shear Wall provided in the 1 st and 12 th Frames Base Shear (kn) Parameters Roof Displacement 912.677 0.0434 865.357 0.326 Graph shows that in Non-linear analysis performance point is small i.e. the behaviour of the structure is within the elastic limit. Hence linear analysis is adequate for this structure. Results for Shear wall in 6 th and 7 th frames It has also seen from Table 9 that shear force was increased at the ground level in 6 th and 7 th frames after providing shear wall in 6 th and 7 th frames. 500

Storey Table 9: Shear force for Shear wall in 6 th and 7 th frames Height (m) Shear force in shear wall for load combination PUSH 2 (In kn ) Step 0 Step 1 Shear wall 1 Shear wall 2 Shear wall 1 Shear wall 2 14 th Roof level 52.40-6.608-6.608-36.369-49.586 14 th 49.05 + 6.608 + 6.608 + 36.369 + 49.586 13 th 14 th 49.05-6.104-6.104-85.000-97.207 13 th 45.70 + 6.104 + 6.104 + 85.000 + 97.207 12 th 13 th 45.70-6.714-6.714-132.821-146.249 12 th 42.35 + 6.714 + 6.714 + 132.821 +146.249 11 th 12 th 42.35-6.983-6.983-181.334-195.299 11 th 39.00 + 6.983 + 6.983 + 181.334 + 195.299 10 th 11 th 39.00-7.208-7.208-230.157-244.574 10 th 35.65 + 7.208 + 7.208 + 230.157 + 244.574 9 th 10 th 35.65-7.383-7.383-279.180-293.948 9 th 32.30 + 7.383 + 7.383 + 279.180 + 293.948 8 th 9 th 32.30-7.523-7.523-328.266-343.312 8 th 28.95 + 7.523 + 7.523 + 328.266 + 343.312 7 th 8 th 28.95-7.625-7.625-377.267-392.516 7 th 25.60 + 7.625 + 7.625 + 377.267 + 392.516 6 th 7 th 25.60-7.676-7.676-426 - 441.358 6 th 22.25 + 7.676 + 7.676 + 426 + 441.358 5 th 6 th 22.25-7.651-7.651-474.242-489.544 5 th 18.90 + 7.651 + 7.651 + 474.242 + 489.544 4 th 5 th 18.90-7.509-7.509-521.617-536.635 4 th 15.55 + 7.509 + 7.509 + 521.617 + 536.635 3 rd 4 th 15.55-7.187-7.187-567.604-581.977 3 rd 12.20 + 7.187 + 7.187 + 567.604 + 581.977 2 nd 3 rd 12.20-6.563-6.563-611.447-624.572 2 nd 8.85 + 6.563 + 6.563 + 611.447 + 624.572 1 st 2 nd 8.85-5.666-5.666-651.843-663.174 1 st 5.50 + 5.666 + 5.666 + 651.843 + 663.174 1 st 5.50-2.261-2.261-689.286-693.808 Ground Ground 1.50 + 2.261 + 2.261 + 689.286 + 693.808 Ground 1.50-2.158-2.158-727.732-732.047 0 + 2.158 + 2.158 + 727.732 + 732.047 It has also seen from Table 10 that bending moment was increased at the ground level in 6 th and 7 th frames after providing shear wall in 6 th and 7 th frames. Storey Table 10: Bending moment for Shear wall in 6 th and 7 th frames Height (m) Bending Moment in shear wall for load combination PUSH 2 (In kn ) Step 0 Step 1 Shear wall Shear wall Shear wall 1 Shear wall 2 501

1 2 Roof 14 th 52.40 + 11.782 + 11.782 + 63.369 + 86.932 level 14 th 49.05-10.356-10.356-58.467-79.179 13 th 14 th 49.05 + 9.929 + 9.929 + 145.893 + 165.751 13 th 45.70-10.520-10.520-138.854-159.894 12 th 13 th 45.70 + 11.171 + 11.171 + 225.789 + 248.131 12 th 42.35-11.321-11.321-219.162-241.805 11 th 12 th 42.35 + 11.623 + 11.623 + 306.858 + 330.104 11 th 39.00-11.769-11.769-300.612-324.151 10 th 11 th 39.00 + 12.018 + 12.018 + 388.278 + 412.315 10 th 35.65-12.128-12.128-382.753-407.007 9 th 10 th 35.65 + 12.322 + 12.322 + 469.905 + 494.549 9 th 32.30-12.412-12.412-465.355-490.178 8 th 9 th 32.30 +12.566 +12.566 + 551.499 + 576.631 8 th 28.95-12.636-12.636-548.193-573.465 7 th 8 th 28.95 + 12.748 + 12.748 + 632.814 + 656.311 7 th 25.60-12.795-12.795-631.029-656.618 6 th 7 th 25.60 + 12.851 + 12.851 + 713.536 + 739.237 6 th 22.25-12.863-12.863-713.585-739.312 5 th 6 th 22.25 + 12.835 + 12.835 + 793.225 + 818.896 5 th 18.90-12.796-12.796-795.485-821.077 4 th 5 th 18.90 + 12.638 + 12.638 + 871.226 + 896.502 4 th 15.55-12.517-12.517-876.193-901.227 3 rd 4 th 15.55 + 12.159 + 12.159 + 946.551 + 970.869 3 rd 12.20-11.916-11.916-954.922-978.754 2 nd 3 rd 12.20 + 11.227 + 11.227 + 1017.803 + 1040.258 2 nd 8.85-10.757-10.757-1030.546-1052.061 1 st 2 nd 8.85 + 9.732 + 9.732 + 1084.901 + 1104.372 1 st 5.50-9.248-9.248-1098.766-1117.263 1 st 5.50 + 5.567 + 5.567 + 1354.254 + 1365.388 Ground Ground 1.50-3.475-3.475-1402.894-1409.844 Ground 1.50 + 2.215 + 2.215 + 457.035 + 461.465 0-1.021-1.021-634.563-636.606 It has been seen from the Table 11 that roof deflection was well within the permissible deflection for all cases after providing the shear wall in 6 th and 7 th frames, respectively. Table 11: Storey drift of shear wall in 6 th and 7 th frames STOREY NO. Height ( m ) Storey Drift of shear wall for load combination PUSH 2 502

Step 0 Step 1 ROOF 52.40 0.0030 194 14 TH 49.05 0.0002 170 13 TH 45.70 0.0002 139.8 12 TH 42.35 0.0001 134 11 TH 39.00 0.0000 127..4 10 TH 25.65 0.0000 119.9 9 TH 32.30 0.0000 111.6 8 TH 28.95 0.0000 102.6 7 TH 25.60 0.0000 92.7 6 TH 22.25 0.0000 82.2 5 TH 18.90 0.0000 70.9 4 TH 15.55 0.0000 59.1 3 RD 12.20 0.0000 46.9 2 ND 8.85 0.0000 34.2 1 ST 5.50 0.0000 21.3 GROUND 1.50 0.0000 1.5 Results for Shear wall in 1 st and 12 th frames It has also seen from Table 12 that shear force was increased at the ground level in 1 st and 12 th frames after providing shear wall in 1 st and 12 th frames. Storey Table 12: Shear force for shear wall in 1 st and 12 th frame Height (m) Shear force in shear wall for load combination PUSH 2 (In kn ) Step 0 Step 1 Shear wall 1 Shear wall 2 Shear wall 1 Shear wall 2 14 th Roof level 52.40-6.179-6.179-22.726-35.795 14 th 49.05 + 6.179 + 6.179 + 22.726 + 35.795 13 th 14 th 49.05-2.129-2.129-59.632-63.918 13 th 45.70 + 2.129 + 2.129 + 59.632 + 63.918 12 th 13 th 45.70-2.705-2.705-91.758-91.173 12 th 42.35 + 2.705 + 2.705 + 91.758 + 91.173 11 th 12 th 42.35-2.799-2.799-124.576-130.178 11 th 39.00 + 2.799 + 2.799 + 124.576 + 130.178 10 th 11 th 39.00-2.935-2.935-157.513-163.380 10 th 35.65 + 2.935 + 2.935 + 157.513 + 163.380 9 th 10 th 35.65-3.055-3.055-190.516-196.623 9 th 32.30 + 3.055 + 3.055 + 190.516 + 196.623 8 th 9 th 32.30-3.165-3.165-223.456-229.782 8 th 28.95 + 3.165 + 3.165 + 223.456 + 229.782 7 th 8 th 28.95-3.256-3.256-256.192-262.701 7 th 25.60 + 3.256 + 3.256 + 256.192 + 262.701 6 th 7 th 25.60-3.316-3.316-288.553-295.182 6 th 22.25 + 3.316 + 3.316 + 288.553 + 295.182 5 th 6 th 22.25-3.325-3.325-320.312-326.960 5 th 18.90 + 3.325 + 3.325 + 320.312 + 326.960 503

4 th 5 th 18.90-3.257-3.257-351.159-357.670 4 th 15.55 + 3.257 + 3.257 + 351.159 + 357.670 3 rd 4 th 15.55-3.074-3.074-380.655-386.802 3 rd 12.20 + 3.074 + 3.074 + 380.655 + 386.802 2 nd 3 rd 12.20-2.702-2.702-408.206-413.608 2 nd 8.85 + 2.702 + 2.702 + 408.206 + 413.608 1 st 2 nd 8.85-2.234-2.234-432.798-736.366 1 st 5.50 + 2.234 + 2.234 + 432.798 + 736.366 1 st 5.50-0.388-0.388-454.607-455.384 Ground Ground 1.50 + 0.388 + 0.388 + 454.607 + 455.384 Ground 1.50-1.632-1.632-477.792-474.527 0 + 1.632 + 1.632 + 477.792 + 474.527 It has also seen from Table 13 that bending moment was increased at the ground level in 1 st and 12 th frames after providing shear wall in 1 st and 12 th frames. Storey Table 13: Bending moment for shear wall in 1 st and 12 th frame Height (m) Bending Moment in shear wall for load combination PUSH 2 (In kn ) Step 0 Step 1 Shear wall 1 Shear wall 2 Shear wall 1 Shear wall 2 14 th Roof level 52.40 + 13.361 + 13.361 + 37.465 + 65.808 14 th 49.05-7.338-7.338-38.668-54.107 13 th 14 th 49.05 + 3.144 + 3.144 + 102.956-109.291 13 th 45.70-3.989-3.989-96.811-104.835 12 th 13 th 45.70 + 4.529 + 4.529 + 156.377-165.444 12 th 42.35-4.531-4.531-151.013-160.086 11 th 12 th 42.35 + 4.646 + 4.646 + 211.267 +220.565 11 th 39.00-4.731-4.731-206.064-215.529 10 th 11 th 39.00 + 4.880 + 4.880 + 266.199 + 275.958 10 th 35.65-4.951-4.951-261.487-271.367 9 th 10 th 35.65 + 5.084 + 5.084 + 321.148 + 331.311 9 th 32.30-5.151-5.151-317.079-327.376 8 th 9 th 32.30 + 5.272 + 5.272 + 375.891-386.428 8 th 28.95-5.331-5.331-372,689-383.342 7 th 8 th 28.95 + 5.431 + 5.431 + 430.188 + 441.045 7 th 25.60-5.476-5.476-428.056-439.004 6 th 7 th 25.60 + 5.542 + 5.542 + 483.739 + 494.819 6 th 22.25-5.566-5.566-482.914-494.040 5 th 6 th 22.25 + 5.575 + 5.575 + 536.142 + 547.288 5 th 18.90-5.564-5.564-536.905-548.028 4 th 5 th 18.90 + 5.487 + 5.487 + 586.833 + 597.804 4 th 15.55-5.422-5.422-589.551-600.392 3 rd 4 th 15.55 + 5.219 + 5.219 + 635.012 + 645.447 3 rd 12.20-5.079-5.079-640.183-650.338 2 nd 3 rd 12.20 + 4.669 + 4.669 + 679.624 + 688.962 2 nd 8.85-4.381-4.381-687.866-696.626 504

1 st 2 nd 8.85 + 3.840 + 3.840 + 720.792 + 728.471 1 st 5.50-3.643-3.643-729.081-736.366 1 st 5.50 + 1.519 + 1.519 + 891.424 + 894.463 Ground Ground 1.50-0.035-0.035-927.003-927.073 Ground 1.50 + 1.861 + 1.861 + 288.393 + 284.671 0-0.587-0.587-428.294-427.119 It has been seen from the Table 14 that roof deflection was well within the permissible deflection for all cases after providing the shear wall in 1 st and 12 th frames, respectively. Table 14: Storey drift of shear wall in 1 st and 12 th frame STOREY NO. Height ( m ) Storey Drift of shear wall for load combination PUSH 2 Conclusions Step 0 Step 1 ROOF 52.40 0.0031 102.9 14 TH 49.05 0.0017 100.1 13 TH 45.70 0.0004 96.7 12 TH 42.35 0.0000 92.7 11 TH 39.00 0.0000 88.1 10 TH 25.65 0.0000 83.0 9 TH 32.30 0.0000 77.2 8 TH 28.95 0.0000 70.9 7 TH 25.60 0.0000 64.0 6 TH 22.25 0.0000 56.7 5 TH 18.90 0.0000 48.8 4 TH 15.55 0.0000 40.6 3 RD 12.20 0.0000 32.1 2 ND 8.85 0.0000 23.4 1 ST 5.50 0.0000 14.5 GROUND 1.50 0.0000 1.0 The above study shows the idea about the location for providing the shear wall which was based on the elastic and inelastic analyses in this paper. It has been observed that the top deflection was reduced and reached within the permissible deflection after providing the shear wall in any of the 6 th & 7 th frames and 1 st and 12 th frames in the shorter direction. 505

It has been also observed that the both bending moment and shear force in the 1 st and 12 th frame were reduced after providing the shear wall in any of the 6 th & 7 th frames and 1 st and 12 th frames in the shorter direction. It has been observed that the in inelastic analysis performance point was small and within the elastic limit. Thus result obtained using elastic analyses are adequate. Hence, it can be said that shear wall can be provided in 6 th and 7 th frames or 1 st and 12 th frames in the shorter direction. References 1. Bureau of Indian Standards: IS-875, part 1 (1987), dead loads on buildings and Structures, New Delhi, India. 2. Bureau of Indian Standards: IS-875, part 2 (1987), live loads on buildings and Structures, New Delhi, India. 3. Bureau of Indian Standards: IS-1893, part 1 (2002), Criteria for Earthquake Resistant Design of Structures: Part 1 General provisions and Buildings, New Delhi, India. 4. Bernhard Cardan (September 1961), Concrete Shear Walls Combined with Rigid Frames in Multistory Buildings Subject to Lateral Loads, Journal of American Concrete Institute, 58, pp 299-316, 5. Li Qiusheng, Cao hong and Li Guiqing analysis of free vibrations of tall buildings ASCE. 6. David V. Rosowsky (November 2002), Reliability-based seismic design of wood shear walls Journal of Structural Engineering ASCE. 7. SAP2000: Advanced 10.0.5 (2006), static and Dynamic Finite Element Analysis of Structures, Computers and Structures Inc., Berkeley, CA. 8. Stavros Syngellakis' and Idris A. Akintilo (1991), nonlinear dynamics of coupled shear walls using transfer matrices ASCE. 9. Maurice W. White and J. Daniel Dolan (1995), Nonlinear shear wall analysis Technical Notes, Journal of Structural Engineering ASCE. 10. John Bolander Jr. and James K. Wight (1991), Finite element modeling of shearwall- dominant buildings ASCE. 506