EFFECT OF COLUMN LOCATION ON PLAN OF MULTI- STORY BUILDING ON SHEAR LAG PHENOMENON

Transcription

1 The Eighth Asia-Pacific Conference on Wind Engineering, December 10 14, 2013, Chennai, India EFFECT OF COLUMN LOCATION ON PLAN OF MULTI- STORY BUILDING ON SHEAR LAG PHENOMENON G.J.Singh 1, S.Mandal 2 and R.Kumar 3 1 Ph.D.Scholar, Structural Engineering, IIT (BHU) Varanasi, India, gyani963d@gmail.com 2 Associate Professor, Civil Engineering, IIT (BHU) Varanasi, India, smandal.civ@iitbhu.ac.in 3 Associate Professor, Civil Engineering, IIT (BHU) Varanasi, India, rajesh8223@yahoo.co.in ABSTRACT Additional corner columns, if provided in tubular multi-storied buildings, may stiffen the buildings as a whole and this serve many other functional requirements. The objective of the present study is to investigate the effect of such additional corner columns on shear lag effect. The variations of axial forces at the column base and lateral deflections of the buildings with varying plans are calculated for the two different wind loading conditions, viz., IS 875- (Part3) 1987 and 120kN/m uniform loading. It is concluded that these additional corner columns, though small in number, are capable to significantly increase overall rigidity against wind load and results into reduction of shear lag effect. Keywords: Plan, Wind loading, Base reactions, Shear lag Introduction Shear lag problem has long been recognized in the tubular buildings subjected to lateral load [Reissner (1945), Coull and Bose (1975), Coull and Ahmed (1978), Ha et al. (1978), Foutch and Chang (1982), Kwan (1994)]. Under the symmetrical flexure without torsion, the distributions of bending stress across the flanges of the tube cross section are not uniform. In this case, simple bending theory is violated and hence uniform flexural stress variation along flange is not actuated. Similarly, in web the expected triangular variation of flexural stresses, as observed in simple bending theory of hollow beams is not obtained. The stresses and the axial forces in the corner column are much higher than the central column in flange. This phenomenon is usually known as positive shear lag. At higher height near tip of the building, the bending stresses, thus the axial force, in the corner column is much smaller than the central column. This result is opposite to the positive shear lag and is called negative shear lag as explained in detail by Shushkewich (1991). In this study, only the positive shear lag effect in base of the building is considered. Case 1 Case 2 Case 3 Proc. of the 8th Asia-Pacific Conference on Wind Engineering Nagesh R. Iyer, Prem Krishna, S. Selvi Rajan and P. Harikrishna (eds) Copyright c 2013 APCWE-VIII. All rights reserved. Published by Research Publishing, Singapore. ISBN: doi: /

2 Case 4 Case 5 Fig. 1 : Five plan variations of the building adopted in the study Input Data Given In STAAD Pro.V8i A 40-storey reinforced concrete framed tube building is chosen for analysis. The plan dimension of the tube is 35 m in flange and 30 m in web. All the beam and column members are of size 0.8 m 0.8 m. The height of each story is 3m, and the center-to-center spacing of the columns is 2.5 m. The young s modulus and Poisson s ratio are 20 GPa and 0.15 respectively (Haji Kazemi and Company, 2002). The present study uses STAAD Pro.V8i software for analyzing the buildings. Wind Load Cases Used Two wind load cases have been considered such as uniform loading = kn/m 2 (Haji-Kazemi and Company, 2002), and IS 875 (part 3) For estimation of wind load following constants have been adopted as k 1 (Risk coefficient) = 1.08, k 2 (Terrain, height and structure height factor) as per category 3, k 3 (Topography factor) =1, V b (Basic wind speed) = 55 m/s, C pe and C pi are taken as 0.8 and ±0.5 respectively. The face of length 35 m or the longer faces are subjected to wind loads. The direction of wind load (same for all cases) is as shown in case 1 of Fig.1. Validation of Results Table 1 : Validation of the STAAD. Pro results Axial force (kn) distribution in flange and web columns at the base of the structure analyzed by different methods Spacing of column from corner (m) STAAD Pro.V8i ( 2007) Matrix method (Ha et al., 1978) Haji- Kazemi & Company (2002) Kwan (1994) Coull and Bose (1975)

3 Owing to the symmetry, results for only half length of flange and web panels are shown in Table 1. For relative comparison purpose, the axial forces for each case have been compared with the matrix method analysis results of Ha et al. (1978). The percentage deviation for each case, have been computed with respect to the axial force values of Ha et al. (1978). The maximum percentage deviation varies up to 22.9, 6.6, 24.09, and 24.09% for cases of STAAD Pro.V8i (2007), Haji-Kazemi and Company (2002), Kwan (1996), Coull and Bose (1975) respectively. The deviation in magnitude of axial forces obtained in the present study is 22.9%, which is lesser than that of Kwan (1996), Coull and Bose (1975). Thus, it can be considered that the variability of results from STAAD analysis are within an acceptable range. The probable reasons in the variability in axial force values from different studies may be attributed to the adopted assumptions in respective methods. Variation of axial force in flange and web columns Fig. 2(a) :Wind load case 1 Fig. 2(b) : Wind load case 2 Fig. 2 : Variation of axial forces in the flange of the base of the buildings 122

4 As evident from Fig.1, the additional number of columns, i.e., 1, 3 & 5 respectively have been provided at each corner and in each direction of flange and web to strengthen the web and flange panel simultaneously. Interestingly, it could be noted that the provision of these additional corner columns, though small in number, are capable to provide significant rigidity and result into reduction of shear lag effect (ref. Fig.2). The axial force in the web column of the building is also calculated for all different five plan cases of building for load case 1 and load case2 (ref. Fig.3). As the extra column is added along the flange and web respectively, it is observed that the variation is similar to the flange and decrease respectively and significantly. The axial force in the web columns in plan case 4 become equivalent as in plan case 1 and in plan case 5 axial forces in the web columns are lesser than the plan case 1. Fig. 3(a): Wind load case 1 Fig. 3(b): Wind load case 2 Fig. 3: Variation of axial forces in the web of the base of the buildings Lateral deflection of the Building Fig. (a): Wind load case 1 Fig. (b): Wind load case 2 Fig. 4 : Variation of lateral deflection (mm) with height 123

5 The lateral deflections of the five plan cases of the buildings have been calculated and analyzed. As evident from the fig 4, lateral deflection decreases after adding the additional corner columns along flange and web direction at each corner. Lateral deflection in plan case 2 and plan case case3 are nearly equivalent. Further, in plan case 4 and plan case 5 it reduces significantly and lesser in plan case 5 in comparison with other plan case 2, 3 and 4. It is evidence that the additional corner columns in the direction of flange and web at each corner provide significant stiffness to the buildings. Variation of Base Bending Moment in flange and web columns Base bending moment of the flange and web columns for all five plan cases of the buildings have been calculated for wind load case 1 and wind load case 2 and presented in tabular form in this paper (ref. Table 2 and 3). For wind load case 1, base bending moment in the middle columns of the web are increasing up to the plan case 2 after then it decrease for the plan case 3, 4 and 5. In the opposite corner column (in the direction of load), base bending moment increases up the plan case 5 and in column same side to the loading base bending moment increases up to the plan case 4 and then decreases respectively (ref. table 2). In the central column of the web the base bending moment increases up to the plan case 2 after then decreases for plan case 3, 4 and 5. Also, the base bending moments in the middle column of the flange increase up to the plan case 2 and then decrease for plan case 3, 4 and 5 except corner column in which base bending moment increases up to the plan case 4 and then decreases respectively for plan case 5. And in the two columns flange adjacent to the corner columns, the base bending moment increases up to the plan case 3 and then decreases. For wind load case 2, the variation of the base bending moments in the web and flange columns are similar as it is in wind load case 1 except the base bending moment in the corner column of the flange which is increase up to the plan case 3 and further decrease for plan case 4 and 5 (ref. table 3) The variation observed in the base bending moments is due to the increment in the total lateral load as the flange area increasing from plan case 2 to 5. This variation is not due to P- effect as the deflection decreases along with the increment in the total load. The additional bending moment may be an expected cause of the variation of the base bending moments of the web and flange columns of the selected tubular structures. 124

6 Table 2 (a) :Variation of base bending moment for wind load case 1 in web, Mx Spacing of column Base bending moment in web, Mx (knm) from center Case 1 Care 2 Case 3 Case 4 Case 5 (m) Table 2(b) : Variation of base bending moment for wind load case 1 in flange, Mx Spacing of Base bending moment in flange, Mx, (knm) column from center Case 1 Case 2 Case 3 Case 4 Case 5 (m))

7 Table 3(a) : Variation of base bending moment for wind load case 2 in web, Mx Spacing of column Base bending moment in web, Mx (knm) from center (m)) Case 1 Case 2 Case 3 Case 4 Case Table 3(b): Variation of base bending moment for wind load case 2 in flange, Mx Spacing of Base bending moment in flange, Mx, (knm) column from center Case 1 Case 2 Case 3 Case 4 Case 5 (m)

8 Conclusions Although the STAAD Pro.V8i is design software, the deviation in magnitude of axial forces calculated using this software is of similar order when compared with other approaches. It is observed that the provision of very few additional columns in the direction of flange and web column respectively increases the stiffness of the structure significantly and the axial forces in flange and web columns decrease considerably. In plan case 5, total lateral load is more than the other four plan cases for both the wind load cases. In spite that, the shear lag phenomenon (positive) is lesser in plan case 5 and the structure responds similar to a rigid hollow tube subjected to simple bending. Thus to avoid the shear lag phenomenon the flange configuration of plan case 5 proposed in this study is quite efficient. To emphasize, the axial forces reduce very significantly and structure may be considered as stiff as in case 1, although, the number of additional columns provided, totals to only 40 in case 5, compared to that of 143 in case 1. Thus, structural efficiency against wind load increases significantly with additional corner columns when provided in the manner proposed in the present study. This observation may be quite useful in recommending an economic foundation system and an architectural planning, which is structurally efficient, especially for tubular multi-storied buildings to effectively reduce the shear lag phenomenon. References Coull, A. and Subedi, N. K. (1971), Framed-Tube Structures for High-Rise Buildings. J. Struct. Div., ASCE, 104(9), Coull, A. and Bose, B. (1975), Simplified Analysis of Frame Tube Structures. J. Struct. Div., ASCE, 101(11), Coull, A. and Bose, B. (1976), Torsion of Frame Tube Structures. J. Struct. Div., ASCE, 102(12), Coull, A. and Ahmed, A. A. (1978), Deflections of Frame-Tube Structures. J. Struct. Div., ASCE, 104(5), Foutch, D. A. and Chang, P. C. (1982), A Shear Lag Anomaly. J. Struct. Eng., 108(7), ASCE,108(7), Haji Kazemi, H. and Compani, M. (2002), Exact method of analysis of shear lag in framed tube structures. The structural design of tall buildings, 11, Ha, K. H., Fazio, P. and Moselhi, O. (1978), Orthotropic Membrane for Tall Building Analysis. J. Struct. Div., ASCE, 104(9), IS 875 (part 3) 1987, Indian standard code of practice for design loads (other than earthquake) for building and structures, part 3. Bureau of Indian Standards, New Delhi. 127

9 Kwan, A. K. H., (1994), Simple method for approximate analysis of framed tube structures. J.of Struct. Eng., ASCE, 120(4), Reissner, E. (1945), Analysis of shear lag in box beam by the principle of minimum potential energy. Quarterly Applied Mathematics, 4(3), Shushkewich, K. W. (1991), Negative shear lag explained. J. of Struct. Eng., ASCE, 117(11), Singh, G. J., (2012), Relative influence of beam and column stiffness on shear lag phenomenon in high rise structures. M. Tech. Dissertation, Dept. of Civil Eng., IIT (BHU), Varanasi. 128