seismic response of rc framed buildings resting on hill slopes

Available online at www.sciencedirect.com ScienceDirect Procedia Engineering 173 (2017) 1792 – 1799 11th International Symposium on Plasticity and Impact Mechanics, Implast 2016 Seismic Response of RC Framed Buildings Resting on Hill Slopes Zaid Mohammada,*, Abdul Baqib, Mohammed Arifb b a PhD Candidate, Department of Civil Engineering, IIT Roorkee, Roorkee, 247667, India Professor, Department of Civil Engineering, Aligarh Muslim University, Aligarh, 202002, India Abstract Framed structures constructed on hill slopes show different structural behavior than that on the plain ground Since these buildings are unsymmetrical in nature, hence attract large amount of shear forces and torsional moments, and show unequal distribution due to varying column lengths In present study, two different configurations of hill buildings have been modelled and analyzed using ETABS v 9.0 finite element code A parametric study has been carried out, in which hill buildings are geometrically varied in height and length In all, eighteen analytical models have been subjected to seismic forces along and across hill slope direction and analyzed by using Response Spectrum Method The dynamic parameters obtained from analyses have been discussed in terms of shear forces induced in the columns at foundation level, fundamental time periods, maximum top storey displacements, storey drifts and storey shear in buildings, and compared within the considered configurations of hill buildings At last, the suitability of different configurations of hill buildings has been suggested © Published by Elsevier Ltd This ©2017 2016The TheAuthors Authors Published by Elsevier Ltd.is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/) Peer-review under responsibility of the organizing committee of Implast 2016 Peer-review under responsibility of the organizing committee of Implast 2016 Keywords: Hill buildings, Step-back and Step-back setback, Response Spectrum method, Earthquake analysis Introduction Economic development of hill areas in the last century has led to the reconsideration of building style, optimum use of construction material and method of construction Due to scarcity of the plain land on hills, houses built on steep slopes, pose special structural and construction problems RC framed structures constructed on hill slopes show different structural behavior than on the plain ground Because of steep slopes, buildings are constructed generally in * Corresponding author Tel.: +91-9045774610 E-mail address: zaidzhcet@gmail.com 1877-7058 © 2017 The Authors Published by Elsevier Ltd This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/) Peer-review under responsibility of the organizing committee of Implast 2016 doi:10.1016/j.proeng.2016.12.221 Zaid Mohammad et al / Procedia Engineering 173 (2017) 1792 – 1799 1793 step-back configuration, though a combination of step-back and setback building configuration is also common There is a development of torsional moments due to the unsymmetrical nature of these buildings and eccentricity caused by the difference in the alignments of the center of mass and stiffness at each floor Additionally, at the location of setbacks, an increase in the stress concentration has also been reported, when the building is subjected to seismic forces Recent earthquakes, struck in hill regions viz., Nepal (2015), Sikkim (2011), Kashmir (2005), Uttarkashi (1990) and Bihar-Nepal (1988) have shown major casualties caused by design flaws and failures in RC as well as masonry structures A significant amount of research work has been done involving hill buildings Previous studies have described various problems and suggested different techniques regarding mathematical modelling formulation and lateral load analysis of step-back and setback buildings Cheung and Tso [1] incorporated the concept of compatibility analysis to subdivide the loading components (translational and torsional) in setback structures, involving the determination of center of rigidity Shahrooz and Moehle [2] presented analytical and experimental studies on influence of current static and dynamic design requirements for setback buildings, also it was found that were inadequate to prevent concentration of damage in the members near setbacks Paul [3] suggested a simplified approach for dynamic analysis of hill buildings and considered only one degree of freedom per floor in either translational direction Kumar and Paul developed a method of analysis based on transformation of stiffness and mass matrices about a vertical reference axis and, results obtained have been compared with the IS Code method 1893 (1984) [4 & 5] Kumar [6] and Kumar and Paul [7 & 8] illustrated a simplified three dimensional approach for elastic seismic analysis of irregular and asymmetrical hill structures, incorporating rigid floor diaphragm action and compared with the rigorous method of analysis considering complete flexibility of floor in all the directions and found similar results from the two methods Birajdar and Nalawade [9 & 10] studied various configurations of step-back and setback buildings, and observed that in step-back buildings shorter frame on the uphill side attracts more base-shear force than the other frames of the building Singh et al [11] applied different seismic analysis approaches viz., Response Spectrum Method of analysis, Linear and Non-linear Time History analysis and compared dynamic properties at across and along slope of step-back and buildings at vertical steep/cut slopes The results obtained in the study were corroborated by the damage pattern of hill buildings observed in Sikkim earthquake in 2011 Murty et al [12] described the adequacy of translational fixidity of column foundations under lateral loads in step-back buildings, and commented on the suitability of the plan size of the buildings to be built on steep slope Although, the researches carried out in past have provided a better view of structural behavior of hill buildings but the performance of the hill building in different configurations has not been studied thoroughly Also, IS 1893 (1984) and IS 1893 (Part 1): 2002; recommend that buildings with geometrical irregularity and or having irregular distribution of mass and stiffness should be analyzed by modal analysis and torsional shear should be accounted separately, but fails to capture the true response of the structure Thus, in order to get the realistic behavior of hill buildings subjected to seismic load, a three dimensional modelling of structure is required, considering real structural behavior of beams/columns, rigid slabs, infill masonry walls and RC shear walls, etc Also, to incorporate the inelastic behavior of hill buildings, linear and non-linear dynamic analysis should be carried out In the present study three dimensional modelling of two different configurations of hill buildings has been undertaken and the effect of plan aspect ratio has been parametrically studied by varying plan dimensions and height of the models Results have been discussed in terms of static and dynamic properties of buildings such as shear forces induced in the columns at foundation level, fundamental time period, maximum top storey displacements, storey drifts and storey shear in buildings and compared with in the considered configurations of hill buildings Method of Analysis Three dimensional space frame analyses of two configurations of hill buildings involving the effect of plan aspect ratio have been carried out by parametrically varying plan and height of the models The seismic analysis is carried out by using equivalent static approach and response spectrum method using finite element code ETABS v 9.0, and seismic parameters such fundamental time period, maximum top story displacement, story shear, story drift and column shear at ground level in each direction, i.e along slope and across slope of hill, are determined using SRSS modal combination and compared within the considered configurations Concrete, as constituent material, is assumed to be homogenous, isotropic and elastic in nature with modulus of elasticity and Poisson’s ratio of concrete as 25000 1794 Zaid Mohammad et al / Procedia Engineering 173 (2017) 1792 – 1799 N/mm2 and value of Poisson’s ratio is 0.2 The yield stress of reinforcement steel is taken as 415 MPa For seismic analysis, the floor system in the all the configurations is modelled as rigid frame diaphragm and beam and column members modelled as two node beam elements The foundation in all the models is assumed to be fixed support system The torsional effects and accidental eccentricity is considered in the analysis as per recommendations of Indian code IS 1893 (Part 1): 2002 2.1 Geometrical properties All the models have same geometrical and material properties, and rest on the same inclination of ground which is 26o (Fig 1) The geometrical properties of the structural elements in the models with designation of different model types are given in Table The inter-storey height is taken as meters and foundation depth is 1.5 m in all the buildings The thickness of the slab at all floors in all the models is considered as 125 mm Since, the models are varied in length along and across the slope, their heights will also be varied accordingly, variation in length of stepback and step-back setback configurations along the slope is carried out from four bays (6 m each) to eight bays with an increment of one bays at each step by keeping width of building constant to one bay across slope (Fig 2) Further, the length of both building types, across the slope is altered from one bay (5 m each) to five bays of same length at one bay at a time by keeping the same number of bays along slope and number of storeys in the structure (Fig 3) Fig Terrain properties of hill slope Table Geometrical properties of different configurations of hill buildings Building Configuration Step-back Step-back setback Parametric variation Designation of models to bays STEPALS to bays to bays to bays STEPACS SETALS SETACS Column size (mm) up to 5: 400×400 from to 8: 450×450 all: 400×400 all: 400×400 all: 400×400 Beam size (mm) along slope: 300×500 across slope: 300×450 2.2 Seismic parameters and loads The seismic parameters considered in dynamic analysis of all the models are assumed as per IS 1893 (Part 1): 2002 The hill buildings are assumed to be in Zone V with the peak ground acceleration value of 0.36g The importance factor, I is taken as 1.5 (for important building) Also, the response reduction factor R taken as for SMRF system of the buildings The soil strata beneath the foundation is assumed as medium soil The gravity and imposed loads are taken as per IS 875 (Part and 2): 1987, self-weight of the structure is calculated and imposed load is assumed to be kN/m2 for a typical residential building Since, the lateral load due to earth pressure on foundation columns does not take part in the seismic weight of the structure, thus its effect is neglected in the analysis to observe only the effect of lateral forces due to seismic loads However, for design purposes, the effect of lateral earth pressure should be considered All the models of both building configurations are analyzed, designed and checked for any failure of members and hence the size of the columns are varied accordingly as the height of the structure increases (Table 1) Zaid Mohammad et al / Procedia Engineering 173 (2017) 1792 – 1799 Fig Variation in length (bays) along slope direction; (a) Step-back buildings, (b) Step-back setback buildings Fig Variation in length (bays) across slope direction; (a) Step-back buildings, (b) Step-back setback buildings 1795 1796 Zaid Mohammad et al / Procedia Engineering 173 (2017) 1792 – 1799 Discussion of results In this study, geometrical variations in the structure of step-back and step-back setback configurations are performed by varying height and length of the buildings in along and across slope direction In all, eighteen models of different lengths and widths have been analyzed for earthquake loads and accidental eccentricity as per codal provisions The hill buildings are subjected to seismic loads independently in either direction viz., along and across slope of the hill The results obtained in the analyses are discussed in terms of seismic parameters such as storey drift, fundamental time period (FTP), top storey displacement, storey shear and normalized base shear in columns at ground level and compared within the considered effects on hill buildings 3.1 Configurations with variation in length along hill slope The dynamic parameters of both configurations viz., step-back and step-back setback buildings along and across hill slopes are shown in Table and Table In step-back buildings, marginal difference is observed in the values of time period obtained by empirical relation as per code and RSA The top storey displacement is found to be varying from 4.29 mm to 6.64 mm as the length is increased Further, the values of shear force in columns at ground level increased significantly in frame A (Fig 4a) On the other hand, in the step-back setback buildings, the values of time period obtained in the dynamic analysis are found to be same (Table 3) Whereas, the values calculated by empirical formula are similar to the values of step-back buildings The top storey displacements are found to be less due to less storey weight as compared to that of step-back buildings The shear force at ground level found to be substantially less which is about 55.2 % (in SETALS 8) of the previous value at frame ‘A’ in STEPALS (Fig 5a) This reduction in the base shear is mainly due to less seismic weight of step-back setback building in their respective models Step-back buildings have shown significant increase in the FTP obtained in RSA (ranging from 0.575 sec to 1.089 sec) in across slope direction (Table 2) A linear increase in values of top storey displacements is observed Unlike the behavior in along slope direction, the values of shear force at ground level have shown marginal increase with length In case of step-back setback buildings (Table 3), the variation in the values of time period obtained from dynamic analysis are varied from 0.575 sec to 0.695 sec, which are different from the values calculated from the empirical relation as from 0.543 sec to 1.026 sec The top-storey displacement vary from 28.37 mm to 15.57 mm, this variation is opposite to the step-back buildings subjected to lateral loads across slope The values of shear force in columns at ground are not much significant, ranging from minimum of 18.89 kN to 105.24 kN as maximum value, and shows same variation as in the step-back building configurations (Figs 4b & 5b) A significant amount of difference in storey drift is observed between step-back and step-back setback configurations, as the length of the models is increased The reduction in storey drift ranges from 10.48% to 49.8% in along slope direction and 25.29% to 46.26% in across slope direction at their maximum difference Further, it is observed that step-back setback buildings induce less shear force than step-back buildings at each story levels The difference at that level in along slope direction is found to be 10.19% (STEPALS and SETALS 5) and increases to 51.54% (STEPALS and SETALS 8) However, values of storey shear obtained in analysis of hill buildings in across slope direction, show that the maximum shear built up is at the middle heights of the structure models Further, as the length of the models is increased, more difference in the shear force is observed between step-back and setback buildings In case of buildings with five bays in length (across slope), there is a reduction of 164.13 kN at maximum and the difference increases up to 299.92 kN in case of SETALS (51.63% of STEPALS 8) Table Dynamic response of step-back building along and across hill slope (STEPALS) Designation No of Bays Height (m) STEPALS STEPALS STEPALS STEPALS STEPALS 8 13.5 16.5 19.5 22.5 25.5 FTP by RSA (sec) Along Across 0.252 0.575 0.267 0.708 0.281 0.833 0.294 0.961 0.306 1.089 FTP as per IS 1893 (sec) Along Across 0.248 0.543 0.271 0.664 0.293 0.785 0.312 0.906 0.331 1.026 Max Top storey displacement (mm) Along Across 4.29 28.37 4.81 32.49 5.46 35.12 6.05 39.02 6.64 42.88 Base Shear ratio (λ) Along Across 1.338 1.457 1.312 1.324 1.330 1.256 1.335 1.205 1.339 1.158 1797 Zaid Mohammad et al / Procedia Engineering 173 (2017) 1792 – 1799 500 bays bays bays bays 120 a 400 300 200 100 bays bays bays bays bays 100 Shear Force in kN Shear Force in kN bays b 80 60 40 20 0 Frame Frame Frame Frame Frame Frame Frame Frame Frame A B C D E F G H I Frame Frame Frame Frame Frame Frame Frame Frame Frame A B C D E F G H I Fig Base shear distribution in step-back configuration; (a) along hill slope direction, (b) across hill slope direction Table Dynamic response of step-back setback building along and across hill slope (SETALS) Shear Force in kN SETALS SETALS SETALS SETALS SETALS 250 No of Bays Height (m) 13.5 16.5 19.5 22.5 25.5 bays bays bays FTP by RSA (sec) Along Across 0.252 0.575 0.253 0.632 0.253 0.663 0.253 0.683 0.253 0.695 bays bays FTP as per IS 1893 (sec) Along Across 0.248 0.543 0.271 0.664 0.293 0.785 0.312 0.906 0.331 1.026 120 a 200 150 100 50 100 Shear Force in kN Designation Max Top storey displacement (mm) Along Across 4.29 28.37 4.62 23.66 4.82 20.43 4.84 18.11 4.78 15.57 bays bays bays bays Base Shear ratio (λ) Along Across 1.338 1.457 1.326 1.240 1.311 1.100 1.280 1.025 1.249 0.923 bays b 80 60 40 20 0 Frame Frame Frame Frame Frame Frame Frame Frame Frame A B C D E F G H I Frame Frame Frame Frame Frame Frame Frame Frame Frame A B C D E F G H I Fig Base shear distribution in step-back setback configuration; (a) along hill slope direction, (b) across hill slope direction 3.2 Configurations with variation in length across hill slope As it is observed in the previous geometrical variations, seismic parameters obtained in across the hill slope direction show different variation than in along slope direction Thus, analyzing the models with only one bay length in across slope direction will not suffice the analysis and the seismic response in that direction Hence, in this section, by keeping the length and height of the models fixed at five bays and five storey, both the configurations are varied in length across the slope from one bay to five bays in length of m each Table and Table show the dynamic properties of step-back and step-back setback buildings in along and across hill slope direction Due to similar height and length, the fundamental time period obtained from empirical relations in that direction is 0.271 seconds Whereas, in the RSA, values of time period are recorded, ranging from 0.267 to 0.303 sec, showing a marginal change in the results Also, top storey displacements are minimum (4.81 mm to 5.78 mm) and there is insignificant increase in base shear ratio is observed A marginal increase in shear force is observed from 228.87 kN to 262.56 kN in frame ‘A’ (Fig 6a) However, in case of step-back setback buildings, the fundamental time period is found to be less (0.253 sec to 0.288 sec) as compared to step-back buildings There is also a marginal difference in the top storey displacements and base shear ratio Further, shear force in column at ground level experience a small decrease in all respective frames, ranging from 205.80 kN at frame ‘A’ in SETACS to 238.60 kN in SETACS (Fig 7a) 1798 Zaid Mohammad et al / Procedia Engineering 173 (2017) 1792 – 1799 In across slope direction the response of step-back models (Table 4) show reduction in the time period Also, top storey displacement is reduced from 32.39 mm to 19.95 mm However, due to increase in the seismic weight of the structure, there is a linear increase in the base shear The larger value of shear force in the columns at foundation level is obtained in mid-frames (B, C and D) of the structure and this increases in the shear force is get shifted to frame ‘A’ and ‘B’ (95.63 kN in STEPACS to 182.37 kN in STEPACS 5) as the length of the bays from one bay to five bays across hill slope (Fig 6b) In the case of step-back setback configuration, all the seismic parameters obtained in the dynamic analysis are found to be reduced The value of fundamental time period lies between 0.632 sec and 0.415 second Whereas, values of displacement at top storey and base shear ratio are found to be varying from 23.66 mm to 15.22 mm and 1.240 to 1.652, respectively (Table 5) Also, the maximum values of shear force in columns at ground level are coming to be 93.33 kN in frame ‘C’ of SETACS and 169.32 kN in frame ‘B’ of SETACS Thus, stepback setback buildings develop lesser amount of torsion and induce less shear forces as compared to step-back buildings (Fig 7b) The storey drift values obtained in along and across hill slope direction show marginal difference in step-back and step-back setback configuration The storey shear distribution show similar pattern as in the previous geometrical variation In along slope direction, the storey shear is found to be higher at second last storey The difference in the values of storey shear between STEPACS and SETACS varies from 36.1 kN to 185.52 kN On the other hand, in across hill slope direction, the maximum storey shear response is found in the mid-height of the models However, as the number of bays are increased, the position of larger shear force get changed to second last storey The maximum value of storey shear ranges from 576.82 kN to 1985.57 kN and from 551.89 kN to 2061.9 kN in along and across slope direction respectively Also, the difference in the storey shear values of step-back and step-back setback buildings in across slope direction varies from 64.74 kN to 231.09 kN at maximum difference levels 300 bay bays bays bays bays 200 a bay bays bays bays bays b Shear Force in kN Shear Force in kN 250 200 150 100 150 100 50 50 0 Frame A Frame B Frame C Frame D Frame E Frame F Frame A Frame B Frame C Frame D Frame E Frame F Fig Base shear distribution in step-back configuration; (a) along hill slope direction, (b) across hill slope direction Table Dynamic response of step-back building along and across hill slope (STEPACS) Designation No of Bays Height (m) STEPACS STEPACS STEPACS STEPACS STEPACS 5 16.5 16.5 16.5 16.5 16.5 FTP by RSA (sec) Along Across 0.267 0.708 0.285 0.605 0.294 0.539 0.299 0.495 0.303 0.462 FTP as per IS 1893 (sec) Along Across 0.271 0.664 0.271 0.469 0.271 0.383 0.271 0.332 0.271 0.297 Max Top storey displacement (mm) Along Across 4.81 32.39 5.3 32.68 5.53 27.32 5.69 23.53 5.78 19.95 Base Shear ratio (λ) Along Across 1.312 1.323 1.320 1.592 1.324 1.570 1.326 1.646 1.326 1.685 Table Dynamic response of step-back setback building along and across hill slope (SETACS) Designation No of Bays Height (m) SETACS SETACS SETACS SETACS SETACS 5 16.5 16.5 16.5 16.5 16.5 FTP by RSA (sec) Along Across 0.253 0.632 0.271 0.540 0.307 0.502 0.285 0.443 0.288 0.415 FTP as per IS 1893 (sec) Along Across 0.271 0.664 0.271 0.470 0.271 0.383 0.271 0.332 0.271 0.297 Max Top storey displacement (mm) Along Across 4.62 23.66 5.12 23.67 6.08 21.91 5.50 17.24 5.61 15.22 Base Shear ratio (λ) Along Across 1.326 1.240 1.336 1.499 1.351 1.579 1.344 1.617 1.345 1.652 1799 Zaid Mohammad et al / Procedia Engineering 173 (2017) 1792 – 1799 bay bays bays bays bays 200 a Shear Force in kN Shear Force in kN 300 200 100 Frame A Frame B Frame C Frame D Frame E Frame F bay bays bays bays bays b 150 100 50 Frame A Frame B Frame C Frame D Frame E Frame F Fig Base shear distribution in step-back setback configuration; (a) along hill slope direction, (b) across hill slope direction Conclusions The present study discusses the behavior of hill buildings under seismic load conditions Two common configurations of hill buildings are parametrically investigated by altering their plan dimensions All the models are geometrically modelled and analyzed with a finite element code incorporating equivalent static and response spectrum method The results obtained in the analyses are discussed in terms of seismic parameters such as storey drift, fundamental time period (FTP), top storey displacement, storey shear and base shear in columns at ground level and compared within the considered effects on hill buildings The performance of step-back and step-back setback configurations is significantly unlike when compared to each other and entirely different than a building resting on plain ground The empirical relations given in IS 1893 (Part 1): 2002 (Clause 7.6) are unable to depict the correct values of time period in along and across slope direction Since, the parameters involved in equivalent static method are entirely depend on the time period value, thus this method should not be used to design a hill building Instead response spectrum analysis of a three dimensional model of complex structures like hill buildings should be carried out to ascertain true behavior The step-back setback configurations experience less torsional moments and seismic forces as compared with stepback buildings due to less seismic weight of the structure Around 45 % reduction in base shear value is observed in case of step-back setback buildings when compared to step-back configurations Also, step-back buildings show higher storey drift and storey shear, making the structures more vulnerable to earthquake forces Hence it can be stated that the step-back setback buildings perform better than step-back configuration when subjected to seismic loads Further, maximum storey shear in both the configurations is observed in top most stories thus, structural members experiencing high shear forces and moments under lateral loads should be designed accordingly References [1] [2] [3] [4] V.W.T Cheung and W.K Tso, Lateral load analysis for buildings with setbacks J ASCE Structural Divison 113 (1987) (2), 209-227 B.M Shahrooz and J.P Moehle, Seismic response and design of setback buildings J of Structural Engg ASCE, 116 (1990) (5), 1423-1439 D.K Paul, Simplified seismic analysis of buildings on hill slopes Bull Indian Society of Earthquake Technology 30 (1993) (4), 113-124 S Kumar and D.K Paul, 3-D analysis of irregular buildings with rigid floor diaphragm Bull Indian Society of Earthquake Technology 31(1994a) (3), 141-154 [5] S Kumar and D.K Paul, Dynamic analysis of step-back and setback buildings Proc Tenth Symposium on Earthquake Engineering, 1(1994b), 341-350 [6] S Kumar, Seismic analysis of step-back and setback buildings Thesis(1996), Earthquake engineering, University of Roorkee, Roorkee [7] S Kumar and D.K Paul, A simplified method for elastic seismic analysis of hill buildings Journal of Earthquake Engineering, 2(1998)(2), 241-266 [8] S Kumar and D.K Paul, Hill buildings configuration from seismic consideration Journal of Structural Engineering, 26(1999) (3), 179-185 [9] S.S Nalawade, Seismic Analysis of Buildings on Sloping Ground Dissertation (2003), University of Pune, Pune [10]B.G Birajdar and S S Nalawade, Seismic analysis of buildings resting on sloping ground In Thirteenth World Conference on Earthquake Engineering (13WCEE), 2004, Vancouver, Canada [11]Y Singh, P Gade, D.H Lang and E Erduran, Seismic behaviour of buildings located on slopes: An analytical study and some observations from Sikkim earthquake of September 18, 2011 15 WCEE, Lisbon, Portugal [12]A.R.V Narayanan, R Goswami and C.V.R Murty, Performance of RC buildings along hill slopes of Himalayas during 2011 Sikkim earthquake 15 WCEE, Lisbon, Portugal, WCEE Online Proceedings, 2012