Analysis of P-Delta Effect on Multistory R.C. Building without and with Shear Wall by IJSTE

IJSTE - International Journal of Science Technology & Engineering | Volume 4 | Issue 2 | August 2017 ISSN (online): 2349-784X

Analysis of P-Delta Effect on Multistory R.C. Building without and with Shear Wall Neelapu Ramesh M. Tech Student Department of Civil Engineering Andhra University College of Engineering (A)

Shaik Yajdani Associate Professor Department of Civil Engineering Andhra University College of Engineering (A)

Abstract P-Delta effect is secondary effect on structure .it is also known as, Geometric nonlinearity effect. As number of stories increases, P-Delta effect becomes more important. If the change in displacements, overturning moments and base shear is more than 10%, P-Delta effect should be considered in design. In this study, the P-Delta effect on high rise building and the change in P-Delta effect by including shear wall in building is studied. Linear static analysis (without P-Delta effect) and nonlinear static analysis (with P-Delta effect) on high rise buildings having different number of stories is carried out. For the analysis G+4, G+9, G+14, G+19, G+24, (i.e 5, 10, 15, 20, and 25storey) R.C.C. framed buildings without shear wall and G+4, G+9, G+14, G+19, G+24, G+29 and G+34 (i.e 5, 10, 15, 20, 25, 30 and 35storey) R.C.C. framed buildings with shear wall are modelled. Earthquake load is applied on structure as per IS-18939(2002) for zone V of medium soil condition. Load combinations for analysis is set as per IS456(2000).All analysis is carried out in software ETABS. Bending moment, story displacement with and without P-Delta effect is calculated and compared for all models. Keywords: Linear static analysis, nonlinear static analysis, P-Delta, tall structures, Lateral displacement ________________________________________________________________________________________________________ I.

INTRODUCTION

Tall buildings are the most structures that requires stability because it consists a lot of frame structure with different width and height. Generally, structural designers are prone to use linear static analysis, which is also known as first order analysis, to compute design forces, moments and displacements resulting from loads acting on the structure. First order analysis is performed by assuming small deflection behavior where the resulting forces, moments and displacements take no account of the additional effect due to deformation of the structure under vertical loads prior to imposing lateral loads. In the traditional first order analysis of structures, the effects of change in the structure actions due to structure deformations are neglected. However, when a structure deforms, the applied loads may cause additional actions in the structure that are called second order or p-delta effects. In the case of first order elastic analysis, the deformations and internal forces are proportional to the applied loads. However, in some cases, the deflection of the structure can have a geometric second order effect on the behaviour of the structure, which is not evaluated by the linear first order analysis. This type of geometric non-linearity can be analysed by performing through iterative process which is only practicable by using computer programs. It is generally known as second order analysis. In this type of analysis, the deformations and internal forces are not proportional to the applied loads. P-Delta Effect: P-Delta is a non-linear second order effect that occurs in every structure where elements are subject to axial loads. It is associated with the magnitude of applied axial load (P) and displacement (∆). If a P-Delta affected member is subjected to lateral load then it will be prone to more deflection which could be computed by P-Delta analysis not the linear static analysis. The effect of P-Delta is mainly dependent on the applied load and building characteristics. In addition to this it also depends upon the height, stiffness, axial load and asymmetry of the building. The building asymmetry may be unbalanced mass, stiffness, in plane. P-delta effects can be reduce and control by using heavier members and/or stiffer frames. P-Delta effect mainly depends on:  Axial load on the structure.  Stiffness of the structure.  Slenderness ratio of the structure  Structure asymmetry. Shear Wall: Shear wall is a structural member used to resist lateral forces i.e. parallel to the plane of the wall. For slender walls where the bending deformation is more, Shear wall resists the loads due to Cantilever Action. In other words, Shear walls are vertical elements of the horizontal force resisting system. Shear walls are especially important in high-rise buildings subject to lateral wind and seismic forces.

Analysis of P-Delta Effect on Multistory R.C. Building without and with Shear Wall (IJSTE/ Volume 4 / Issue 2 / 005)

Location of Shear Wall Shear walls should create a box structure. Shear walls can provide at corners, sides, and in the interior space, but the location of shear wall at the corners give more strength and stiffness compared to other cases. ď&#x20AC; To be effective, shear walls should be equal length and placed symmetrically on all four exterior walls of the building. ď&#x20AC;

II. OBJECTIVES OF STUDY 1) To determine in what way the P-delta analysis influence the variation of responses of the structure such as bending moments, displacements and base shear forces against linear static analysis. 2) To determine the effect of shear wall on the parameters base shear, displacement, moment and torsion 3) To find the height of building from which it is necessary to include the effect of P-delta by performing analysis on R.C.C. buildings of different heights starting from 5 stories in every 5 story intervals. 4) To find the effect of stiffness on the same structure by including shear wall at the corners of the structure. 5) After comparing the performance of RC structure with respect to displacement, base shear and moment between two analyses mentioned above, necessity of P-delta analysis over linear static analysis will be understood clearly. III. METHODOLOGY For the study seven three dimensional building models are used as the basic models in the study. The buildings have 5, 10, 15, 20, 25 stories without shear wall and 5, 10, 15, 20, 25, 30 and 35 stories with shear wall. Plot area of each building is 28.423x36.043m with openings (28.423m along X-direction and 36.043m along Y direction. The floors are assumed rigid in their plane. 1) Case I: buildings without shear wall Model type 1: five bare frame models with G+4, G+9, G+14, G+19, G+24 stories without considering P-Delta effect. Model type 2: five bare frame models with G+4, G+9, G+14, G+19, G+24 stories with P-Delta effect. 2) Case II: buildings without shear wall Model type 3: seven models with G+4, G+9, G+14, G+19, G+24, G+29, G+34 stories with shear wall of size 3m along X and Y directions without considering P-Delta effect. Model type 4: five models with G+4, G+9, G+14, G+19, G+24, G+29, G+34 stories with shear wall of size 3m along X and Y directions at each corner with P-Delta effect. Loading: Dead loads of respective members. Concrete density: 25kN/m3. Finishes: Floor finish=1kN/m2 on all floors. Live loads= 2kN/m2 on all floors except roof. =3kN/m2 on balconies and corridors. Lateral loads: Earthquake load as per IS 1893(Part 1): 2002. Zone factor (Z) =0.36 (zone V). Importance factor (I) =1 (Residential building). Response Reduction Factor =5 (special moment resisting frame, SMRF). Damping ratio: 5%. Material Properties: Concrete grade: M25 for beams and slabs.M30 for columns and shear wall. Steel grade: Fe415. Modulus of elasticity of steel (Es)= 2x105 MPa Modulus of elasticity of concrete (Ec) =5000â&#x2C6;&#x161;đ?&#x2018;&#x201C;đ?&#x2018;?đ?&#x2018;&#x2DC; =25000MPa for M25 =27386.127MPa for M30 Assumed Element Dimensions: Columns: 230x610mm and 310x610mm. Beams: 230x420mm and 230x 620mm. Floor and Roof slabs: 125mm. Shear Wall: 3m along X and Y directions with 150mm thickness. Story height: Typical floor height= 4m. Remaining floors height= 3m.

Analysis of P-Delta Effect on Multistory R.C. Building without and with Shear Wall (IJSTE/ Volume 4 / Issue 2 / 005)

Drawing:

Fig. 3.1: Plan of the building for all type of models

IV. RESULTS AND DISCUSSIONS Comparison of Lateral Displacements without and with P-Delta Effect in Top Story for the Buildings without and with Shear Wall: G+19 Story Building: S.No.

Load case

1 2 3 4 5 6 7 8 9 10 11 12 13

1.5[DL+LL] 1.2[DL+LL+EQX] 1.2[DL+LL-EQX] 1.2[DL+LL+EQY] 1.2[DL+LL-EQY] 1.5[DL+EQX] 1.5[DL-EQX] 1.5[DL+EQY] 1.5[DL-EQY] 0.9DL+1.5EQX 0.9DL-1.5EQX 0.9DL+1.5EQY 0.9DL-1.5EQY

WITHOUT SHEAR WALL With Without P-Delta % Difference P-Delta 10.865 11.494 5.789% 78.483 80.114 2.078% 77.983 79.382 1.795% 122.165 132.675 8.603% 113.737 123.484 8.570% 102.000 103.660 1.628% 99.136 100.928 1.808% 151.997 165.071 8.601% 142.880 155.128 8.572% 99.943 101.554 1.613% 98.696 100.475 1.802% 150.174 163.082 8.596% 144.704 157.117 8.578%

WITH SHEAR WALL With Without P-Delta % Difference P-Delta 7.285 7.456 2.347% 71.858 72.913 1.468% 62.562 63.357 1.271% 94.743 97.224 2.619% 90.589 92.807 2.448% 88.096 89.374 1.450% 79.168 80.185 1.284% 117.457 120.508 2.598% 114.207 117.029 2.471% 85.873 87.098 1.427% 79.532 80.560 1.293% 116.807 119.812 2.573% 114.857 117.725 2.497%

WITHOUT SHEAR WALL With Without P-Delta % Difference P-Delta 15.213 16.398 7.789% 112.472 115.052 2.293% 99.371 101.668 2.312% 202.60 226.142 11.618% 193.214 215.440 11.503% 136.491 139.547 2.239% 127.737 130.734 2.347%

WITH SHEAR WALL With Without P-Delta % Difference P-Delta 10.614 10.970 3.354% 94.073 95.977 2.024% 80.461 81.848 1.724% 126.931 131.764 3.808% 120.793 125.087 3.555% 115.077 117.372 1.994% 102.861 104.666 1.755%

G+24 story building: S.No.

Load case

1 2 3 4 5 6 7

1.5[DL+LL] 1.2[DL+LL+EQX] 1.2[DL+LL-EQX] 1.2[DL+LL+EQY] 1.2[DL+LL-EQY] 1.5[DL+EQX] 1.5[DL-EQX]

Analysis of P-Delta Effect on Multistory R.C. Building without and with Shear Wall (IJSTE/ Volume 4 / Issue 2 / 005)

8 9 10 11 12 13

1.5[DL+EQY] 1.5[DL-EQY] 0.9DL+1.5EQX 0.9DL-1.5EQX 0.9DL+1.5EQY 0.9DL-1.5EQY

252.208 242.564 132.260 127.368 250.279 244.493

281.517 270.461 135.166 130.344 279.306 272.672

11.621% 11.501% 2.198% 2.336% 11.598% 11.525%

156.929 152.725 111.837 103.617 156.088 153.566

162.854 158.210 114.023 105.447 161.925 159.139

3.776% 3.591% 1.955% 1.766% 3.739% 3.629%

Comparison of Lateral Displacements without and with P-Delta Effect in Top Story for G+29 And G+34 Story Buildings With Shear Wall: Sr.No.

Load case

1 2 3 4 5 6 7 8 9 10 11 12 13

1.5[DL+LL] 1.2[DL+LL+EQX] 1.2[DL+LL-EQX] 1.2[DL+LL+EQY] 1.2[DL+LL-EQY] 1.5[DL+EQX] 1.5[DL-EQX] 1.5[DL+EQY] 1.5[DL-EQY] 0.9DL+1.5EQX 0.9DL-1.5EQX 0.9DL+1.5EQY 0.9DL-1.5EQY

G+29 With Without P-Delta P-Delta 14.527 15.178 117.672 120.781 98.636 100.825 193.999 212.768 185.990 203.83 143.633 147.369 127.634 130.549 239.817 263.549 235.169 258.198 139.205 142.740 128.975 131.939 238.888 262.479 236.099 259.269

% Difference 4.481% 2.642% 2.219% 9.675% 9.592% 2.601% 2.284% 9.896% 9.792% 2.540% 2.298% 9.875% 9.814%

G+34 With Without P-Delta P-Delta 19.192 20.291 150.312 160.197 124.392 132.711 287.846 328.464 278.262 317.461 183.269 195.384 162.723 173.506 356.040 406.411 351.596 400.994 177.440 189.212 164.872 175.747 355.151 405.328 352.485 402.078

% Difference 5.726% 6.577% 6.687% 14.111% 14.087% 6.610% 6.627% 14.148% 14.050% 6.634% 6.596% 14.128% 14.070%

Variation in Percentage Difference of Lateral Displacement for G+4, G+9, G+14, G+19 and G+24 Story Buildings without Shear Wall: Sr.No. 1 2 3 4 5 6 7 8 9 10 11 12 13

LOAD CASE 1.5[DL+LL] 1.2[DL+LL+EQX] 1.2[DL+LL-EQX] 1.2[DL+LL+EQY] 1.2[DL+LL-EQY] 1.5[DL+EQX] 1.5[DL-EQX] 1.5[DL+EQY] 1.5[DL-EQY] 0.9DL+1.5EQX 0.9DL-1.5EQX 0.9DL+1.5EQY 0.9DL-1.5EQY

G+4 1.092% 0.430% 0.446% 0.821% 0.932% 0.430% 0.445% 0.817% 0.795% 0.433% 0.442% 0.813% 0.800%

G+9 2.540% 0.870% 0.872% 1.733% 1.609% 0.870% 0.872% 1.723% 1.620% 0.871% 0.871% 1.704% 1.642%

G+14 4.066% 1.128% 1.318% 2.771% 2.533% 1.103% 1.321% 2.754% 2.551% 1.312% 1.318% 2.716% 2.594%

G+19 5.789% 2.078% 1.795% 8.603% 8.570% 1.628% 1.808% 8.601% 8.572% 1.613% 1.802% 8.596% 8.578%

G+24 7.789% 2.293% 2.312% 11.618% 11.503% 2.239% 2.347% 11.621% 11.501% 2.198% 2.336% 11.598% 11.525%

Fig. 1: Variation In Percentage Difference of Lateral Displacement For G+4, G+9, G+14, G+19 and G+24 Story Buildings Without Shear Wall among all load cases

Analysis of P-Delta Effect on Multistory R.C. Building without and with Shear Wall (IJSTE/ Volume 4 / Issue 2 / 005)

Variation In Percentage Difference of Displacement for G+4, G+9, G+14, G+19, G+24, G+29 and G+34 Story Buildings with Shear Wall: S.No. 1 2 3 4 5 6 7 8 9 10 11 12 13

LOAD CASE 1.5[DL+LL] 1.2[DL+LL+EQX] 1.2[DL+LL-EQX] 1.2[DL+LL+EQY] 1.2[DL+LL-EQY] 1.5[DL+EQX] 1.5[DL-EQX] 1.5[DL+EQY] 1.5[DL-EQY] 0.9DL+1.5EQX 0.9DL-1.5EQX 0.9DL+1.5EQY 0.9DL-1.5EQY

G+4 0.224% 0.390% 0.389% 0.531% 0.525% 0.391% 0.390% 0.530% 0.525% 0.393% 0.391% 0.529% 0.526%

G+9 0.750% 0.544% 0.495% 0.836% 0.797% 0.541% 0.498% 0.831% 0.801% 0.537% 0.524% 0.825% 0.807%

G+14 1.484% 0.974% 0.860% 1.627% 1.530% 0.965% 0.866% 1.616% 1.542% 0.953% 0.917% 1.601% 1.557%

G+19 2.347% 1.468% 1.271% 2.619% 2.448% 1.450% 1.284% 2.598% 2.471% 1.427% 1.293% 2.573% 2.497%

G+24 3.354% 2.024% 1.724% 3.808% 3.555% 1.994% 1.755% 3.776% 3.591% 1.955% 1.766% 3.739% 3.629%

G+29 4.481% 2.642% 2.219% 9.674% 9.591% 2.601% 2.284% 9.895% 9.792% 2.540% 2.298% 9.875% 9.813%

G+34 5.726% 6.577% 6.687% 14.111% 14.087% 6.610% 6.627% 14.148% 14.050% 6.634% 6.596% 14.128% 14.070%

Fig. 2: Variation In Percentage Difference of Lateral Displacement For G+4, G+9, G+14, G+19, G+24, G+29 and G+34 Story Buildings With Shear Wall among all load cases

Comparison of Bending Moment In Columns Subjected to Maximum B.M for Bottom Five Stories of Buildings without and with Shear Wall: G+19 Story building: Story

Column Number

5 4 3 2 1

1692 542 827 1113 1396

Without shear wall With Without P-Delta % Difference P-Delta 239.6852 258.2987 7.766% 244.4768 264.6127 8.236% 248.1266 269.5531 8.635% 259.3355 282.1938 8.814% 309.0711 336.429 8.852%

Without P-Delta 142.226 133.028 118.789 101.802 73.088

With shear wall With % Difference P-Delta 145.518 2.315% 135.840 2.114% 120.886 1.765% 103.014 1.191% 73.333 0.335%

G+24 Story building: Without shear wall Story

Column Number

5 4 3 2 1

1692 542 827 1113 1396

With shear wall

Without P-Delta

With P-Delta

% Difference

Without P-Delta

With P-Delta

% Difference

278.2794 285.1408 291.1773 306.1102 389.7976

310.2125 318.9958 326.5856 343.2698 441.3788

11.475% 11.873% 12.160% 12.139% 13.233%

135.852 126.716 112.946 96.780 69.234

140.158 130.247 115.448 98.088 69.490

3.170% 2.786% 2.215% 1.352% 0.370%

Analysis of P-Delta Effect on Multistory R.C. Building without and with Shear Wall (IJSTE/ Volume 4 / Issue 2 / 005)

Comparison of bending moment in columns subjected to maximum B.M for bottom five stories of buildings with shear wall: G+29 Story Building: STORY

COLUMN NUMBER

WITHOUT P-DELTA

WITH P-DELTA

% DIFFERENCE

5 4 3 2 1

1692 542 827 1113 1396

149.652 139.170 123.547 105.016 60.611

162.275 149.926 131.861 110.456 61.682

8.435% 7.728% 6.730% 5.180% 1.767%

STORY

COLUMN NUMBER

WITHOUT P-DELTA

WITH P-DELTA

% DIFFERENCE

5 4 3 2 1

1692 542 827 1113 1396

167.340 155.257 137.335 115.814 64.865

185.967 170.942 149.297 123.468 66.223

11.131% 10.102% 8.710% 6.608% 2.094%

G+34 Story Building:

Discussions         

Lateral displacement after applying P-Delta effect continuously increasing as number of stories increases. Percentage difference in lateral displacement increased slowly from G+4 to G+14 and increased suddenly for G+19 (from 2.771% to 8.603%) in buildings without shear wall and it increased slowly from G+4 to G+24 and increased suddenly for G+29 (3.802% to 9.675%) in buildings with shear wall. Percentage difference in lateral displacement crossed the limit 10% for G+24 building without shear wall and for G+34 building with shear wall. The percentage difference is more for the load cases 1.2[DL+LL+EQY], 1.2[DL+LL-EQY], 1.5[DL+EQY], 1.5[DL-EQY], 0.9DL+1.5EQY, 0.9DL-1.5EQY. Percentage difference in overturning moment is very less for all load cases in all models considered. The overturning moment due to P-Delta effect increased for load cases 1.5[DL+LL], 1.2[DL+LL+EQX],1.2[DL+LL+EQY],1.5[DL+EQX],1.5[DL+EQY], 0.9DL+1.5EQX, 0.9DL+1.5EQY and decreased for load cases 1.2[DL+LL-EQX],1.2[DL+LL-EQY], 1.5[DL-EQX],1.5[DL-EQY],0.9DL1.5EQX, 0.9DL-1.5EQY. The base shear value after applying P-Delta decreased for all load cases. In addition, the percentage difference is very less. The bending moment in columns increased after applying P-Delta effect and the percentage difference between the bending moments before and after applying P-Delta effect is more than 10% in G+24 story building without shear wall and in G+34 story building with shear wall. The percentage difference between shear force in columns is less than 10%. The percentage difference between bending moment and shear force in beams is less than 10% for all models considered. V. CONCLUSIONS

1) The effect of P-Delta is always increase as the slenderness ratio of the building increases which means as the number of stories of the building increase effect of P-Delta also increases. 2) From the study, it is inferred that the effect of P-Delta should be considered after 20 stories (61m) for the buildings without shear wall. 3) The construction of shear wall in the building increase the stiffness of the structure which results in decrease of lateral displacement of the building and also decrease in bending moment, shear force of the individual columns and beams. 4) 4. It is also inferred that as we include shear walls in a building, we can increase the P-Delta consideration further to 20 stories. For example in this study, by the inclusion of a shear wall of thickness 150mm it is allowed to consider the P-Delta effect after 30th story. 5) The base shear and torsion values of buildings without and with shear wall are become reduced after applying P-Delta effect and the percentage difference is very less for all models. 6) The percentage change in overturning moment is very less and it is negative for some load cases 1.2[DL+LL-EQX], 1.2[DL+LL-EQY], 1.5[DL-EQX], 0.9DL-1.5EQX, 0.9DL-1.5EQY for all buildings. VI. FUTURE SCOPE OF THE WORK 1) In this study the stiffness of the building changed by inserting a shear wall of length 3m in both X and Y axis of thickness 150mm. further study can be carried out to know how the P-Delta effect changes by changing the stiffness of shear wall i.e. by increasing length and thickness.

Analysis of P-Delta Effect on Multistory R.C. Building without and with Shear Wall (IJSTE/ Volume 4 / Issue 2 / 005)

2) In this work the stiffness of building is increased by including the shear wall, further study can be carried for the remaining concepts i.e. by including X-bracing or brick infill panels for achieving economical design. REFERENCES J Sullivan, T.H Pham and G.M Calvi“P-delta effects on tall rc frame-wall buildings” the 14th world conference on earthquake engineering October 2008, Beijing, China. [2] Yousuf dinar,Nazzim uddin rahi,Pronob Das,”Variation of deflection of steel High-Rise structure Due to P-delta effect considering Global Slenderness Ratio”. [3] Michael R.Lindeburg, PE with Majid Baradar, PE “Seismic Design of Building Structures” a professional’s introduction to Earthquake forces and design details. [4] Wilson, E.L., Eeri, M. and Habibullah, A. “Static and Dynamic Analysis of Multi Story Building Including P-Delta Effects”, Earthquake spectra, 3, 2 (1987). [5] Bungale S. Taranath “Structural Analysis and Design of Tall Buildings” [6] Yousuf dinar,Nazzim uddin rahi,Pronob Das,”Variation of deflection of steel High-Rise structure Due to P-delta effect considering Global Slenderness Ratio” [7] Pushparaj j.Dhawale, G.N.Narule “analysis of p-delta effect on high rise buildings” Issue 4, July-August, 2016 ISSN 2091-2730 [8] Prashant Dhadve, Alok Rao, Atul Rupanvar, Deokate K., Admile P.R, Dr. Nemade. P. D. “ [9] Assessment of P-Delta Effect on High Rise Buildings” Volume: 3 Issue: 5 ISSN: 2321-8169 [10] ETABS 2016 Analysis reference manual and ETABS videos. [1]