Abstract
Based on nonlinear inelastic dynamic analysis of Single Degree Of Freedom systems (SDOF), this work investigates the effect of different parameters on the seismic response of these systems. Generalized SDOF systems that present both short and long period structures are subjected to two sets of synthetic ground motions according to the site condition; stiff rock site and stiff soil one, each contains three records. The structural period vary from (0.1 to 2) seconds and the post yielding stiffness ratios vary from (0.0 to 0.2) with two hysteresis models. Modified Clough and Bilinear models have been utilized in the analysis to illustrate the effect of stiffness degradation. The relationship between the force modification factor (R) and the global ductility demand (μ) tends to be more affected under different post yielding stiffness ratios in the structures of short period more than long period structures, where the effect is negligible. Furthermore, while the post yielding stiffness ratio increases, the ductility demand of the structure decreases under all different periods and models. The effect of hysteresis models at all ranges of period is observed while the modified Clough model shows a higher ductility demand than the force modification factor in comparison with the bilinear model. The site condition influence indicates that short period structures have higher ductility demand in stiff soil sites. However, long period structures have higher ductility demand in stiff rock sites.
Highlights
Designing a structure to remain in the elastic range during earthquake excitation will acquire a very large elastic restoring force to overcome the cyclic action, this large force means large or additional structural elements, which is neither economical nor practical
C parameter is related to seismic demand of the structure; when C is higher the ductility demand ratio μ is larger than the force modification factor and when C is lower the ductility demand ratio is lower than the response modification factor
It was found that in short period the hard rock soils have greater spectral acceleration than the stiff soils and for long periods the stiff soils have a greater spectral acceleration than the hard rock soils. To relate this with seismic demands of Single Degree Of Freedom (SDOF) system (R and μ), it is important to illustrate the relationship between the spectral acceleration and the ductility demand ratio; while; when the spectral acceleration increases the ductility demand ratio decreases. These results provide a clear distinction between the stiff soils and the hard rock, while it is observed that for short period systems, the stiff soil sites have larger C-values which means higher ductility demand and lower spectral acceleration, since in long period systems the stiff soil sites have the smaller C-values which means lower ductility demand and higher spectral acceleration; the rock sites are critical case in flexible systems, while stiff soils are critical case in rigid systems regardless to the post yielding stiffness ratio and the type of the model
Summary
Designing a structure to remain in the elastic range during earthquake excitation will acquire a very large elastic restoring force to overcome the cyclic action, this large force means large or additional structural elements, which is neither economical nor practical. In order to achieve the objectives of the parametric study; an inelastic dynamic analysis is carried out by changing the hysteresis model, post yielding stiffness ratios, structural period, soil condition and the intensity of earthquake excitation. The parameters variation includes; six periods (0.1, 0.2, 0.3, 0.5, 1 and 2 sec), five levels of Peak Ground Acceleration (PGA), four post yielding stiffness ratios (0, 0.05, 0.1 and 0.2), two hysteresis models (Bilinear and modified Clough) and six synthetic records with constant damping ratio of 5%. Nassar and Krawinkler (N&K) did a comprehensive study on SDOF systems with typical damping ratio 5%, N&K have proposed a general form that relates R, μ and the structural period, as indicated in Equation 5 and 6: R. where, C is nonlinear regression parameter, a and b are nonlinear regression constants depends on the post yielding stiffness ratio of the bilinear model. C parameter is related to seismic demand of the structure; when C is higher the ductility demand ratio μ is larger than the force modification factor and when C is lower the ductility demand ratio is lower than the response modification factor
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