Multi-angle Capacity Spectrum Method Research Based On Pushover Analysis

ABSTRACT:Due to the randomness and complexity of seismic motion, it is difficult to determine the seismic input direction accurately, however, the Capacity method based on Pushover analysis at present mostly aims at two-dimension major axis, the researches about Pushover analysis of directions in different angle are very few, however, the response is different when push in different angle for anisotropy structure. Hence, it makes total sense for achieving variation trend of Capacity spectrum curve, Demand spectrum curve and performance point of structure which is subjected to earthquake to establish the multi-angle Capacity method of structure subjected to earthquake in different angles, so that we can protect structure from damage by targeted repair.This paper gain the Capacity spectrum curves in0°,10°,20°,30°,40°,50°,60°,70°,80°,90°ased on Capacity spectrum method, then on this basis, plot the three-dimension Capacity spectrum surface; Corresponding with each Capacity spectrum curve we can get elastic-plastic Demand spectrum curves based on strength reduction factor method, and plot the three-dimension elastic-plastic Demand spectrum surface; then utilize the Capacity spectrum method to get performance points of each angle to plot the property curves. Through the analysis of Capacity spectrum curves and surface, elastic-plastic Demand spectrum curves and surface research, performance points and property curves, the following conclusions are reached:(1) With the direction of pushover changed from0degree to90degree, the spectrum acceleration of Capacity spectrum curves of round-ended pier and rectangle pier increased at the same spectrum displacement, and keep the same value when closed to90degree, the limit spectrum displacement first decreases then increases a little; the spectrum acceleration of Capacity spectrum curves of square pier keep almost the same at the same spectrum displacement, the limit spectrum displacement decreases at first and then increases, the values are symmetrical about45degree. The change of stiffness is the key factor of the variation of Capacity spectrum curves, and the ratio of principal axis stiffness is major influential factor of the change slope of Capacity spectrum curve in different angles.(2) There is little change of elastic-plastic Demand spectrum when push in different angles. Compared with other directions elastic-plastic Demand spectrum changed larger when the push direction closed to principal axis (the included angle of principal is within20degree) the elastic-plastic Demand spectrum keep the same when the push direction keep away from principal axis (he included angle of principal is out20degree), we may use the same elastic-plastic Demand spectrum in these directions.(3) With the direction of pushover change from0degree to90degree, the performance points of round-ended pier change monotonously, the spectrum acceleration increases gradually while the spectrum displacement decreases gradually; spectrum acceleration of rectangle pier increases gradually and keep almost the same when closed to90degree, the spectrum displacement decreases first then increases. The spectrum acceleration of performance points of square pier change little while the spectrum displacement decreases first then increases, the values are symmetrical about45degree. The variation of performance points are in direction proportional to the ratio of principal axis stiffness, so it is necessary to push in multi-angle.(4) There is biggest spectrum displacement and minimum spectrum acceleration when push in weak-axis, thus the pier need more ductility in direction closed to weak-axis; there is larger spectrum acceleration and smaller spectrum displacement when push closed to strong-axis, and the biggest spectrum acceleration occurres more closed to strong-axis when the ratio of principal axis stiffness is bigger, thus the structure need more strength in direction closed to strong-axis.