PLAN IRREGULAR RC FRAMES: COMPARISON OF PUSHOVER WITH NONLINEAR DYNAMIC ANALYSIS

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1 ASIAN JOURNAL OF CIVIL ENGINEERING (BUILDING AND HOUSING) VOL. 12, NO. 6 (2011) PAGES PLAN IRREGULAR RC FRAMES: COMPARISON OF PUSHOVER WITH NONLINEAR DYNAMIC ANALYSIS T. Mahdi *a and V. Soltan Gharaie b a Department of Structural Engineering, Building and Housing Research Centre, Tehran, Iran b Faculty of Building and Housing, Tehran, Iran Received: 20 November 2010, Accepted: 24 February 2011 ABSTRACT In this paper, the seismic behavior of three intermediate moment-resisting concrete space frames with unsymmetrical plan in five, seven and ten stories are evaluated by using pushover analysis. In each of these frames, both projections of the structure beyond a reentrant corner are greater than 33 percent of the plan dimension of the structure in the given direction. The performance of these buildings has been investigated using the pushover analysis. Results have been compared with those obtained from non-linear dynamic analysis. Keywords: RC frames; irregular buildings; pushover analysis; nonlinear time history analysis; capacity curve; plastic hinges 1. INTRODUCTION Structural irregularities are commonly found in constructions and structures. The existence of an asymmetry in the plan is usually leading to an increase in stresses of certain elements that consequently results in a significant destruction. The analysis of the seismic response of irregular structures is complex due to nonlinear and inelastic response and more difficult than that of regular structures. Accordingly, the nonlinear dynamic analysis method is the best choice for solving these problems since they provide more realistic models of structural response to strong ground shaking and, thereby, provide more reliable assessment of earthquake performance than other methods of analysis [1]. However, such an approach is not feasible for most practical applications. Therefore, many researchers had tried to develop more rational analysis method that would achieve a satisfactory balance between required reliability and applicability for everyday design use. In recent years, a breakthrough of simplified methods for seismic analysis based on nonlinear static procedure (NSP) has occurred. This procedure; that is known as "pushover", can be effectively used as an * address of the corresponding author: mahdi@bhrc.ac.ir (T. Mahdi)

2 680 T. Mahdi and V. Soltan Gharaie evaluation method to check the acceptability of a particular structural design. Furthermore, this procedure can give information on the structural strength capacities and on the deformation demands as well as it can identify the regions potentially exposed to larger damage. The first set of NSPs comprises the Capacity Spectrum Method (CSM), introduced by Freeman et. al. [2]. In 1981, Saiidi and Sozen [3] proposed to perform nonlinear dynamic analyses on an equivalent SDOF system. Based on this idea, the N2 method has been suggested by Fajfar and Fischinger [4]. These first proposals are characterized by their simplicity and usually consider a first mode in computation of the pushover/capacity curve, and consequently have been limited to planar structural models. The first study to use pushover analysis for irregular buildings was carried out by Moghadam and Tso [5]. Later on, they extended the pushover analysis to cover plan-eccentric buildings and took the three-dimensional torsional effect into account. The procedure uses an elastic spectrum analysis of the building to obtain the target displacements and load distributions for pushover analyses [6]. Furthermore, an improved version of the extended N2 method has been presented by Fajfar et al. [7]. In this group of NSPs, the works of Chopra and Goel [8, 9] on the Modal Pushover Analysis (MPA), and Kalkan and Kunnath [10] on the Adaptive Modal Combination Procedure (AMCP), can be included. All of these works present improvements with respect to the first set of procedures. In additional to these contributions, many other papers have dealt with the practical aspects of plan asymmetric problems. Among these papers, reference is made to the work of Faella et. al. [11], Herrera and Soberón [12], Yu et. al. [13], Ambrisi et. al. [14], and Pinho et. al. [15]. In the work of Faella et. al. [11], analysis of a 6 floor reinforced concrete building with L-shape has been carried out, while the performance of Rectangular, L-shaped, U-shaped, T-shaped and square plans has been evaluated by Herrera and Soberón [12]. On the other hand, Yu et. al. has evaluated the reliability and accuracy of MPA procedure [13]. In their work, the MPA procedure was extended to assess asymmetric buildings with lateral force pattern including both lateral forces and torsional moments. Moreover, the seismic sensitivity of response of mass-asymmetrical concrete structure in plan has been assessed by Ambrisi et. al. [14]. The research of Pinho et. al. is related to application of four commonly employed NSPs (CSM, N2, MPA, and ACSM) to irregular 3D structures. The NSP's results have been compared with nonlinear dynamic analysis with the ground motions scaled for intensity levels of peak ground accelerations of 0.05, 0.1, 0.2 and 0.3g respectively. It has been concluded that from an overall viewpoint, all these procedures tend to give similar results. Furthermore, the four procedures have been found suitable to reproduce the actual dynamic response [15]. For more detailed discussions on these procedures and other aspects of the pushover analysis, reference can be made to Themelis [16]. As it can be seen from the literature review given in this paper and by others that torsional asymmetry is the most important type of plan asymmetry. However, other types of plan asymmetry need to be addressed and studied independently from the torsional effect. One type of plan irregularities is reentrant corner irregularity that is considered to exist where both plan projections of the structure beyond a reentrant corner are greater than 15% of the plan dimension of the structure in the given direction [17]. In this paper, performances of the three moment-resisting concrete buildings with reentrant corners are assessed by conducting pushover and nonlinear time history analyses.

3 PLAN IRREGULAR RC FRAMES: COMPARISON OF PUSHOVER WITH DESCRIPTION OF ANALYZED BUILDING In this paper, five, seven and ten stories residential buildings are considered. In each of these three cases, plan configurations of the structure contain reentrant corners, where both projections of the structure beyond a reentrant corner are greater than 33 percent of the plan dimension of the structure in the given direction, as shown in Figure 1. However, in all these cases, the differences between center of mass and rigidity are less than 2.4% of the corresponding dimension of the building. The structural system used for these buildings is taken as concrete intermediate moment-resisting space frames (IMRSF). Soil type is considered as type two that is equivalent to type B in the USGS classification and a soil profile A spectrum according to Eurocode Classification [18]. Furthermore, the peak ground acceleration is assumed equal to 0.35g. which corresponds to that used for very high seismic zone in the Seismic Iranian Code of Practice (IS 2800) [19]. The 28-day strength of concrete, yield strength of steel, elasticity modules of concrete and elasticity modules of steel are 250, 4000, and Kg/cm 2 respectively. All the floors are considered to be subjected to dead loads equal to 570 Kg/m 2 (due to self weight, finishes and permanent partitions) and to live loads equal to 200 Kg/m 2. At the roof, loads of 580 Kg/m 2 and 150 Kg/m 2 are considered, respectively. Figure 1. A typical plan. 3. BUILDING MODELING AND SEISMIC INPUT The analyses of the three space frames have been performed using the finite element software, SAP 2000, Version 14.1 [20] based on the Capacity Spectrum Method of Freeman

4 682 T. Mahdi and V. Soltan Gharaie et. al. [2]. All these three buildings have been analyzed according to the Iranian Code of Practice for Seismic Resistant Design of Buildings (IS 2800) [19]. Each of the three structures have been designed by considering an accidental eccentricity equal to 5% of the relevant orthogonal plan dimension of the building and the sections of the structural elements have been controlled by ACI [21]. A sample of the 7-story frame is shown in Figure 2. Figure 2. Designed element of the frame in the 7-story building. The modal properties, in terms of periods and effective modal mass percentages, of the 10-story building are reported in Table 1. The results show that the main modes of the structure are transitional ones.

5 PLAN IRREGULAR RC FRAMES: COMPARISON OF PUSHOVER WITH Table 1: Modal analysis of the 10-story building Modal analysis Mode number Period (sec) UX UY SumUX SumUY RZ SumRZ PUSHOVER ANALYSIS This section describes some results obtained by pushover analysis. The performance of the designed structures is assessed at a target performance level that exceeds that of the BSE-1 hazard level (Life Safety Performance Level for earthquakes with a 10% probability of exceedance in 50 years) [22]. The two gravity (vertical) loads used in this paper are as follows: GR1 = 1.1 (DL+ LL) (1) GR2 = 0.9 DL (2) For lateral seismic loads, the analysis was performed by assuming two types of lateral loads distributions. First by assuming a triangular distribution similar to that obtained by the equivalent static analysis method, and second by assuming rectangular distribution proportional to the weight of the floor. The target displacements for these buildings are calculated according to the FEMA 356 formula [22] and are given in Table 2. To obtain the capacity curves, combinations of lateral loads and gravity loads are used. Some examples of the resulting capacity curves for the three buildings are shown in Figure 3. In this figure, the locations of the first plastic hinges occurred in beams and columns are displayed. It can be seen that all curves display similar patterns of behavior. They are linear initially but start to deviate from linearity when inelastic actions start to take place. Furthermore, it can be concluded that the curves obtained for the two gravity loads are approximately similar to each other while they are more sensitive to the type of lateral loads, as shown in Figure 3. Moreover, it can be noted that the choice of a push direction has a little influence on capacity curves.

6 684 T. Mahdi and V. Soltan Gharaie Table 2: Target displacements Building 5-story 7-story 10-story Lateral load pattern Displacement (X) (Cm) Displacement (Y) (Cm) Uniform Triangular Uniform Triangular Uniform Triangular (a) (b)

7 PLAN IRREGULAR RC FRAMES: COMPARISON OF PUSHOVER WITH (c) Figure 3. The performance curves for buildings with (a) 5-story (b) 7-story (c) 10-story. On the structural level, the inter-story drift ratio is one of the important damage indicators. Sample of results of the 10-story building with both lateral load patterns are presented in Figure 4. The results obtained indicate that all the frames in both directions are within the life safety performance level. Figure 4. Performance of 10-story RC frame based on maximum inter-story drifts. From studying the distribution of hinges along the height, it has been found that the use of different lateral load patterns could lead to different results. By using a triangular pattern, the hinges are distributed more uniformly along the height of the building whereas the use of a uniform pattern, the hinges are concentrated in the lower parts of the building with some presence in the middle part. Generally, it has been found that the investigated structures in

8 686 T. Mahdi and V. Soltan Gharaie both directions subjected to any type of load combinations have remained within the life safety performance level. The formation of hinges; for the 10-story building at the life safety target displacement level along the x-axis, is shown in Figure 5. The plastic hinge pattern shows that no plastic hinges are formed in the Y-direction. This can be considered as an additional proof of the ineffectiveness of the torsional moments in these structures. Figure 5. Plastic hinges in 10-story building (uniform load pattern in X direction is used). To make detailed investigations on the effect of the plan irregularities on torsion, displacement differences between different points at the 10 th floor and the centre of mass in the 10-story building, has been calculated, as shown in Figure 6. The numbering of points is shown in Figure 1. Although some differences are observed between different points at the floor, these differences are smaller than those specified by seismic codes for torsionally irregular structures [17]. Figure 6. Displacement difference between roof joint and center of mass. Pushover analysis with uniform and triangular pattern in X direction were used.

9 PLAN IRREGULAR RC FRAMES: COMPARISON OF PUSHOVER WITH PUSHOVER ANALYSIS VERSUS NONLINEAR DYNAMIC ANALYSIS As it is well known, time histories with similar response spectra can result in very different responses when used with the nonlinear dynamic procedure. This indicates that acceleration response spectrums do not contain all the information representing structural response, a problem that is largely ignored in conventional methods. Accordingly, the appropriate choice of time history records for a given site can overcome this perceived disadvantage with nonlinear dynamic procedure. In this section, nonlinear time history analysis has been performed using two of the most critical records; Castaic-Old Ridge Route and Pacoima Kagel Canyon given in Table 3. Results of pushover analyses, using uniform and triangular pattern of loads, have been compared with the results of nonlinear time history analysis. To make such comparison, the top displacement of nonlinear dynamic analysis is equated to the target displacement given by the push-over analysis and the results obtained are compared with each other. Table 3: Records used in this paper [23] Station Component Epicentre distance (km) PGA (g) PGV (Cm/s) PGD (Cm) Pacoima Kagel Canyon PKC Castaic-Old Ridge Route ORR Maximum drifts of the three structures estimated by nonlinear static analysis are compared with those given by the nonlinear time history analysis. Percentage of the drift error for the 10 th floor of the 10-Story building using the Pacoima Kagel Canyon record is shown in Figure 7. The results of the Pacoima Kagal Canyon record show drift higher than the two percent assigned for the life safety level. Figure 7. Maximum drift comparison of 10-story building using Pacoima Kagel Canyon record.

10 688 T. Mahdi and V. Soltan Gharaie Other results used to assess the pushover method are those related to the variations of displacements along the height of the buildings. Results of the displacement shape derived from uniform and triangular pushover analysis for the 10-story building are represented in Figure 8. These results are compared with those obtained by the Castaic Old Ridge Route record. It can be seen that the differences between the two methods are quite noticeable. Figure 8. Displacement comparison for 10-story building between uniform and triangular pushover with nonlinear time history analysis. To have further assessment of the pushover analysis, base shears for the three types of buildings are calculated. For the five story building, the pushover analysis with a uniform pattern load has shown better results than the triangular one. However, for the seven and ten story buildings, and as shown in Figure 9, the pushover analysis with a triangular pattern load gives closer results. Figure 9. Base shear- comparison of pushover and nonlinear time history analyses

11 PLAN IRREGULAR RC FRAMES: COMPARISON OF PUSHOVER WITH CONCLUSION In this paper, the applicability of the 3D pushover analysis for predicting the seismic response of intermediate moment-resisting frame structures with plan irregularity has been investigated. The results from push-over analyses have been compared to those from nonlinear dynamic analyses for two selected earthquake records, each scaled to achieve predetermined values of roof drift. The results obtained show that: The results of pushover analyses confirm the validity of designs based on IS2800. However, for irregular buildings similar to those tested in this paper, additional nonlinear time history analysis need to be performed. Since the first two periods of vibration are predominantly translational, the investigated buildings can be classified as torsionally stiff buildings The results obtained for the three frames show that pushover techniques still require further refinement in order to provide reliable estimates of the dynamic response of 3D asymmetrical structures. Although nonlinear dynamic procedures are more accurate than conventional methods, care must be taken in the selection of an appropriate time history record for a given site. REFERENCES 1. Deierlein GG, Reinhorn AM, Willford MR. Nonlinear Structural Analysis for Seismic Design, A Guide for Practicing Engineers. NEHRP Seismic Design Technical Brief No. 4, NIST GCR , Freeman SA, Nicoletti JP, Tyrell JV. Evaluation of existing buildings for seismic risk a case study of Puget Sound Naval Shipyard, Bremerton, Washington, Proceedings of U.S. National Conference on Earthquake Engineering, Berkley, USA., 1975, pp Saiidi M, Sozen MA. Simple nonlinear analysis of RC structures, ASCE, Structural Division, 107(1981) Fajfar P, Fischinger M. N2-A method for non-linear seismic analysis of regular buildings, The Ninth World Conference in Earthquake Engineering, Tokyo-Kyoto, Japan, Vol. 5, 1988, pp Moghadam AS, Tso WK. Damage Assessment of eccentric multistory buildings using 3-D pushover analysis. The 11th World Conference on Earthquake Engineering, Mexico, 1996, Paper No Moghadam AS, Tso WK. Pushover analysis for asymmetric and set-back multi-story buildings. The 12th World Conference on Earthquake Engineering, Auckland, New Zealand, 2000, Paper No Fajfar P, Marusic D, Perus I. Torsional effects in the pushover-based seismic analysis of buildings, Journal of Earthquake Engineering, 9(2005) Chopra AK, Goel RK. A modal pushover analysis procedure for estimating seismic demands for buildings, Earthquake Engineering and Structural Dynamics, 31(2002)

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