NONLINEAR STATIC SEISMIC ANALYSIS AND ITS VALIDATION USING DAMAGE DATA FROM REINFORCED-CONCRETE SCHOOL BUILDINGS

This paper introduces a simplified nonlinear static seismic analysis method that consists of a simplified procedure for push-over analysis and a procedure modified from the capacity spectrum method from ATC-40. The simplified pushover curve is obtained on the basis of assumptions for failing behavior, such as strong-beam–weak-column behavior, which is commonly observed in low-rise reinforced-concrete buildings. This limits the usage of the method but allows other merits in analysis, such as abbreviating the calculation and allowing for strength degradation or detailed consideration for the capacity curve of members. Data of 31 school buildings from a damage databank were employed to validate the method. The analytical seismic capacity was compared to the earthquake intensity that each building experienced. The proposed method produced generally conservative results with no overestimates for the seismic capacity of the buildings. Introduction Damage data of past earthquakes are especially valuable for seismic research, including seismic assessment, damage evaluation, and hazard mitigation. Since the Taiwan midlands were struck by the Chi-Chi earthquake in 1999, there have been numerous studies on the damage to building structures, most of these studies were supported by the National Center for Research on Earthquake Engineering (NCREE), Taiwan. A seismic database with a geographical information system (GIS) was also established (Hsieh et al. 2002) by integrating damage data of schools and public buildings obtained from the NCREE and apartment houses, whose data was obtained from the Taiwan Construction Research Institute. This database is very useful for hazard mitigation in a large region. However, the lack of structural details in the database limits its applicability, and thus, it cannot be used for research involving seismic assessment of individual buildings. Therefore, many years after the Chi-Chi earthquake, another databank containing more detailed data was established (Tu et al. 2009). Typical low-rise reinforced-concrete (RC) school buildings in Nantou County were chosen as subjects because of their similar structural systems and the serious damage Assistant Professor, Department of Architecture, National Cheng Kung University, Tainan 701, Taiwan Research Assistant, National Center for Research on Earthquake Engineering, Taipei 106, Taiwan Graduate Student, Department of Architecture, National Cheng Kung University, Tainan 701, Taiwan Master, Department of Architecture, National Cheng Kung University, Tainan 701, Taiwan Proceedings of the 9th U.S. National and 10th Canadian Conference on Earthquake Engineering Compte Rendu de la 9ième Conférence Nationale Américaine et 10ième Conférence Canadienne de Génie Parasismique July 25-29, 2010, Toronto, Ontario, Canada • Paper No 848 they suffered in the earthquake. The databank could not only be employed in developing the motion-damage relationship but was also useful for validating and improving detailed seismic assessment methods. This paper presents a nonlinear static seismic assessment procedure that follows the capacity spectrum method (CSM) from the ATC-40 report (ATC 1996). Data of selected buildings from the databank were compared with analytical results to validate this method. Brief Introduction of the Analytical Method Simplified push-over analysis (SPOA) is a nonlinear static seismic assessment method developed for low-rise RC buildings. It consists of two main parts: (1) obtaining a capacity/pushover curve and (2) finding the corresponding demand peak ground acceleration (PGA) for the capacity curve. To abridge the time for iterative structural analysis, the first part is performed with a simplified procedure. The second part basically follows CSM with some modifications. Basic Assumption and the Simplified Procedure for Obtaining Push-Over Curve The simplified procedure is only sustainable for buildings that agree with its basic assumptions. The procedure assumes that the structure fails through the strong-beam–weakcolumn behavior commonly observed in typical low-rise RC buildings. This behavior occurs when beams and slabs in RC buildings are cast in one piece. The beams become strengthened and more rigid than expected, which results in prior failure of the vertical members. With relatively rigid beams, the building deforms like a shear building, as illustrated in Fig. 1. In this case, the lateral capacity of each storey can be considered as the sum of the contributions of every vertical member in the storey. In order to evaluate the lateral force contribution of vertical members, the capacity curve of each member is needed. The member capacity curves can be defined analytically or obtained from structural experiments, as described on the left side of Fig. 2. Since all of the vertical members are connected to the same rigid slab, the lateral displacement of every member is considered identical to the storey drift. Therefore, storey shear can be obtained by simply superposing the lateral force in every vertical member at a given drift, as shown on the right side of Fig. 2. The concept originates from the seismic evaluation standard for RC buildings in Japan (MLIT 2001). Figure 2 shows that when a group of members fails, strength degradation or negative stiffness is exhibited in the storey force-drift curve. This is usually difficult to simulate in regular structural analysis. The procedure can also exhibit the failure sequence of members clearly. However, this assumption neglects failure in beams.