Most international design codes consider the nonlinear seismic performance of a structure by the concept of reduction/modification factor (R). Then, an elastic static force-based method can be normally used for seismic design to create earthquake resistant RC buildings. The response modification factor (R) is sensitive to many aspects such as overall ductility, over-strength, damping, and redundancy levels. Indeed, these factors are severely affected by geometric irregularity of the structural system. So, R-value does not become a constant number for the all types of structures with the same lateral load resisting system, as many standard codes noted. It depends on types, combination, and degrees of geometric vertical irregularity. This research assesses the actual values of R for regular and familiar vertical irregularity cases in RC buildings with moment-resisting frames (MRF) systems. Also, it takes into account the reduction percent that may occurs in R-value due to these studied vertical irregularities. The vertical irregularity cases, such as set-back and soft story, are essentially needed to be studied greater than ever due to the wide propagation of these types of buildings in Egypt, recently. In addition, the potential analytical methods that may be used to calculate R-value in comparison with Egyptian code’s value. Nonlinear static pushover analysis is carried out using ETABS via three-dimensional numerical models. The findings prove that vertical irregular models have poor seismic capacities, in comparison with regular one, due to their sudden change in lateral stiffness than that with regular aspect. So, the response modification factor (R) must be re-calculated or even scaled-down before design stage with 15% and 25% for single and combined vertical irregularity, respectively. In addition, this investigation derives a vital equation between R values with vertical irregularity ratios in each studied model. This equation shall be a guide for seismic design codes, structural design engineers, and researchers. Accordingly, the response modification factor R does not become a fixed value regardless vertical irregularity aspects of the buildings, but it has a variable value that depend on their inelastic seismic performance of the lateral load resisting systems.
Pushover analysis has been recommended as a reliable tool to estimate the seismic capacity of the structures. Vertical irregular structures are highly vulnerable during earthquakes due to stiffness irregularity in their elevations. Hence, seismic capacities of these types of structures need to be re-estimated during structural design stage. So, in this paper, an attempt has been made to assess the actual seismic performance of buildings with two common types of vertical irregularities such as; soft story and setback in comparison with regular (reference) building. These types of vertical irregularities are studied in individual cases, combined in one story, and combined in two different stories of the building models, while most previous studies satisfy with individual type of vertical irregularity case in the studied model. In addition, combined vertical irregularity generates extra weak points, which alter the seismic capacities, failure mode mechanism, and performance point location. Three-dimensional numerical models are created to find out significant response demand such as; the variation in periods of vibration, lateral displacement, inter-story drift, pushover curve, and plastic hinges formation. The results showed that vertical irregular buildings are subjected to early damages and have less seismic capacity than regular one. The fundamental time period becomes misleading term in seismic force calculation for vertical geometric irregular buildings and needs to be re-considered. In addition, extra lateral displacement and inter-story drift are passively generated in the vertical irregular buildings due to sudden change in stiffness. Significant negative variation in the pushover curves, ductility ratios, and plastic hinges' formation is observed when combinations of pre-mentioned vertical irregularity cases occur. Buildings with open soft ground story with asymmetric setback should have additional precautions from international codes during structural design stage according to their irregularity ratio. Therefore, response modification/reduction factor (R) may be scaled-down to adapt these negative variation in seismic capacities.
Most design codes assume the nonlinear seismic performance of structures using response reduction/modification factor (R). The R factor is sensitive to a variety of factors in terms of overall ductility and over-strength. This research assesses the actual R factor for vertical irregularity cases for RC bare buildings with moment-resisting frames (MRF) systems. Also, this research derives a significant relationship between R values and identified vertical irregularity index calculated from relative stiffness between adjacent stories. Three-dimensional numerical models are carried out for the soft story and setback irregularity scenarios using ETABS. Modal pushover analysis (MPA) is selected to obtain the inelastic seismic capacity. The obtained results demonstrate that vertical irregular buildings have weak inelastic seismic capacities compared to regular one. So, the response modification factor (R) should be scaled down before the design stage by 15% to 40% for single and combined vertical irregularity scenarios. Structures with a combined asymmetric setback with a soft ground story experience the worst R factor. Also, R factors are sensitive to the identified vertical irregularity index (Vtm) that has 80% regression percent. So, it may be used to specify the allowable vertical irregularity ratio, location, and combination for each seismic zone.
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