SEISMIC ANALYSIS OF REINFORCED CONCRETE STRUCTURES CONSIDERING DUCTILITY EFFECTS

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1 SEISMIC ANALYSIS OF REINFORCED CONCRETE STRUCTURES CONSIDERING DUCTILITY EFFECTS Hima Elizabeth Koshy 1 and Remya V 2 1,2 Assistant Professor, Department of Civil Engineering, Mount Zion College of Engineering, Kadammantta, Pathanamthitta, Kerala Abstract This study is conducted to review the methods proposed by Indian Standard codes in order to take account of the concept of ductility of structural elements. Ductility is the most important factor for evaluating a structure's capacity to resist seismic actions. In this study, 2D moment resisting frames are considered for analysis. Reinforced concrete building structures having moment resisting frames or mixed (frames and shear wall), are analysed for their responses to lateral loading by applying the static nonlinear push-over analysis using SAP2000. These structures are assumed to be located in a region of medium seismicity and are subject to lateral loads deducted from the Indian seismic codes and are designed with the Indian standard code. The results of this study show the importance of the ductility and their ability to resist horizontal loads caused by earthquakes. The results also showed that frame with shear wall have more ductility than regular frame and irregular frame. Keywords Ductility, moment resisting frames, 2D analysis, SAP2000, nonlinear push-over analysis, shear wall I. INTRODUCTION Seismic analysis is a subset of structural analysis and is the calculation of the response of a building (or non-building) structure to earthquakes. It is part of the process of structural design, earthquake engineering or structural assessment and retrofit in regions where earthquakes are prevalent. Apart from gravity loads, the structure will experience dominant lateral forces of considerable magnitude during earthquake shaking. It is essential to estimate and specify these lateral forces on the structure in order to design the structure to resist an earthquake. It is impossible to exactly determine the earthquake induced lateral forces that are expected to act on the structure during its lifetime. However, considering the consequential effects of earthquake due to eventual failure of the structure, it is important to estimate these forces in a rational and realistic manner. Past experience and observations of building behaviour following severe earthquakes has shown that ductility plays a very important role in protecting buildings from collapse so that a building gets more flexibility. Ductility can be defined as the ability of material to undergo large deformations without rupture before failure. Ductility in concrete is defined by the percentage of steel reinforcement within it. This is explained by the presence of such structures with significant reserve strength not accounted for in design. In the literature, several studies have been carried out in order to evaluate the effect of the ductility on the seismic response of reinforced concrete (R/C) and steel moment-resisting framed buildings. These studies have shown that the ductility depends on different factors which the most important of them is member ductility factor. Recently, a study was conducted to investigate the ductility factor of reinforced concrete frame irregular in elevation. According to this study it is found that the geometry and ductility supply of the frames affect significantly the ductility factor. The objective of this work tries to evaluate the ductility factor of the R/C structures, having different geometric form in elevation and lateral force resisting structural system, through their seismic behaviour by nonlinear static pushover analysis using SAP2000. Structural irregularities are commonly found in constructions and structures. DOI: /IJMTER BKZ 179

2 II. RELATION BETWEEN DUCTILITY AND DESIGN STRENGTH Ductility, which is specified as member or structural capacity, is usually defined using ductility factor, which may be defined as the ratio of maximum base shear in actual behaviour to first significant yield strength in structure. Figure 1 presents a typical relationship between base shear and top displacement of a structure. The terms used in the figure are: Ve : elastic base shear, Vy : yield base shear, V 1 : base shear at first plastic hinge and Vd : design base shear. Table 1. Dimension Details Sl. No. Structural Element Size in mm 1 Longitudinal Beam 250x500 2 Transverse Beam 350x700 3 Corner Column 600x650 4 Interior Column 500x700 5 Exterior Column 600x800 Figure 1. Definition of non-linear parameters III. MAIN SOURCES OF DUCTILITY The main sources of ductility are reviewed in other researches. These include: (1) the difference between the actual and the design material strength; (2) conservatism of the design procedure and ductility requirements; (3) load factors and multiple load cases; (4) accidental torsion consideration; (5) serviceability limit state provisions; (6) participation of non-structural elements; (7) effect of structural elements not considered in predicting the lateral load capacity (e.g. actual slab width); (8) minimum reinforcement and member sizes that exceed the design requirements; (9) Redundancy of the structure and redistribution of forces (stresses) between structural members; (10) strain hardening; (11) actual confinement effect; and (12) utilizing the elastic period to obtain the design forces. IV. DESCRIPTION OF MODEL STRUCTURES In this study three 6-storey moment resisting frame structures (regular and irregular in elevation) and one 6-storey frame-wall structure are assessed. The structures are designed and detailed in accordance with the Indian code (IS ) for seismic loads, Indian code for concrete structures (IS ) and Indian code (IS ) for ductility detailing. The considered geometrical configurations are depicted in figure 3.1. The span length and the inter-storey height for all structures are equal to 5.0 m and 3.3 m, respectively. The member dimension is provided in Table 1. The specified 28-day concrete compressive strength is 20 N/mm 2 and the specified yield stress of the steel is 415 N/mm 2. The analysis of structures was carried out All rights Reserved 180

3 SAP2000 software, which is a structural analysis program for static and dynamic analyses of structures. The weights of the systems were assumed to consist of total dead load, Gk plus 20% of live load, Qk. Moment Resisting Frames STR1 Regular Frame STR2 Regular Frame with shear wall STR3 Irregular Frame 1 STR4 - Irregular Frame 2 Shear wall thickness = 150mm Slab thickness = 120mm Storey Height = 6 bays of 3.3m = 19.8m Length of transverse beam = 3 bays of 5m = 15m Length of longitudinal beam = 4 bays of 7m = 28m Grade of concrete, fck = 20 N/mm 2 Grade of steel, fy = 415 N/mm 2 Live Load = 3 kn/m 2 Figu. 2. Building Models V. STATIC PUSHOVER ANALYSIS Static pushover analysis was performed to evaluate the ductility factor of the structures under investigated. The four structures were subjected to an incremental static pushover analysis for the gravity and earthquake forces tributary to them. The gravity loads are held constant at their full value. The earthquake forces are assumed to be distributed along the height according to the provisions of Indian Standards. The lateral forces were increased in suitable increments until a mechanism forms, or an interstorey displacements goes past the design limit of 2% of the storey height. In the analysis, it is assumed that the plastic hinges form only at the ends of the members. The moment- rotation relationship for a potential hinge is taken to be bilinear or elasto-plastic. The analysis includes an elastic and inelastic range. Inelastic range starts at the stage of first plastic hinge formation and ends when the mechanism is formed. The objective was to estimate the capacity curves and the ductility All rights Reserved 181

4 VI. RESULTS OF PUSHOVER ANALYSIS The capacity curves (pushover curves), in terms of top displacement-base shear for all frames, is shown in figure 3. In this study, analyses have been performed using SAP2000 computer program. Maximum base shear in actual behaviour, Vy, base shear relevant to formation of first plastic hinge, V1 and ductility factor, µ, for all structures under investigation are listed in Table 2. Displacement ductility is defined in terms of maximum structural drift and the displacement corresponding to the idealized yield strength. The ductility factor was found to be in the range of to Also, member ductility factors for all the frames were plotted against calculated ductility factors for all structures separately and are illustrated in figure 4. To plot the comparison between ductility factors for all the frames, it can be possible to obtain the ductility factor directly using the software. Fig. 3. Comparison of Base Shear and Displacement for all frames Table 2. Ductility Factors for all frames Frame Ductility Factor STR STR STR STR Figure. 4. Comparison of Ductility Factor for all frames VII. DISCUSSION OF RESULTS Based on the results obtained above, the following conclusions were taken: 1) The displacement ductility, μ of the structures increases as the structural stability All rights Reserved 182

5 2) Structures with uniform profile in elevation (or regular) have more lateral load capacity compared to structures with non-uniform profile in elevation (or with setbacks). In other words, the structures with vertical geometric irregularity have lower demands than regular structures. 3) The ductility factor in the beams is lower than that in columns. Hence, the columns are more flexible or ductile. 4) A comparison of ductility developed in the members show that ductility in moment-resisting frames are smaller than the corresponding ones in the frame-wall. In other words, the most rigid structures have the higher ductility. 5) A comparison of ductility developed in the members show that ductility in moment-resisting frames are smaller than the corresponding ones in the frame-wall. In other words, the most rigid structures have the higher ductility. VIII. CONCLUSION In the present work, the assessment of the performance of four reinforced concrete structures, with six stories and three bays, has been investigated through static non-linear (pushover) analyses. Two of these structures have irregularities in elevation. The results obtained from the pushover analyses leads to the following main conclusions: - The ductility factor depends on structural stability and rigidity. - The decrease in strength of the structure results in a decrease in ductility. - The structures with vertical geometric irregularity have lower demands than regular structures. As for future works, there are many parameters that can be changed to increase the ductility. Studies on change in parameters according to the need is yet to be done so that building can be built with considering seismic effects and also without much expense thereby making it a common construction methods. REFERENCES [1] D. Dubina, Ductility and seismic performance of thin-walled cold-formed steel structures, Steel structures, vol. 4, pp , [2] Baris Binici, Design of FRPs in circular bridge column retrofits for ductility enhancement, Engineering Structures 30, pp 766 to 776, [3] Ioana Olteanu, Ioan-petru Ciongradi, Mihaela Anechitei and M. Budescu, Ductile design concept for seismic actions in miscellaneous design codes, BULETINUL INSTITUTULUI POLITEHNIC DIN IAŞI, pp 55 to 62, [4] C. D. Annan, M. A. Youssef, and M. H. El Naggar, Seismic Overstrength in Braced Frames of Modular Steel Buildings, in Journal of Earthquake Engineering, Vol. 13, pp. 1-21, [5] Juraj Králik, Juraj Králik Jr, Seismic analysis of reinforced concrete frame-wall systems considering ductility effects in accordance to Eurocode, Engineering Structures 31, pp 2865 to 2872, [6] M. Mahmoudi, M. Zaree, Evaluating the overstrength of concentrically braced steel frame systems considering members post-buckling strength, in International Journal of Civil Engineering, Vol. 9, No. 1, pp , March [7] Haijuan Duan a, Mary Beth D. Hueste, Seismic performance of a reinforced concrete frame building in China, Engineering Structures 41, pp 77 to 89, [8] M. Shahria Alam, M. Moni, S. Tesfamariam, Seismic overstrength and ductility of concrete buildings reinforced with superelastic shape memory alloy rebar, Engineering Structures 34, pp 8 to 20, [9] Z. A. M. Z. Mohd, R. Debbie, S. Fatehah, An Evaluation of Overstrength Factor Of Seismic Designed Low Rise RC Buildings, in Procedia Engineering, Elsevier, Vol. 53, pp , [10] Branci Taïeb, Bourada Sofiane, Accounting for ductility and overstrength in seismic design of reinforced concrete structures, Proceedings of the 9th International Conference on Structural Dynamics, Portugal, pp 311 to 314, [11] SAP-2000 (v12), Computer and structures, inc. Berkeley, California, USA. [12] Jing Zhou, Fangping He, Tian Liu, Curvature ductility of columns and structural displacement ductility in RC frame structures subjected to ground motions, Soil Dynamics and Earthquake Engineering 63, pp 174 to 183, [13] Stojadinovic, Seismic behavior of slender reinforced concrete walls, Engineering Structures 80, pp 377 to 388, All rights Reserved 183