Optimization of modal load pattern for pushover analysis in double-layer barrel vault roof with vertical double-layer walls

Nonlinear time history analysis (NL-THA) is the most accurate method to estimate the seismic demand of structures and predict their failure. To that end, extensive efforts have been made to develop fast and convenient methods to carry out nonlinear static analyses. In recent years, pushover methods have been widely used as a suitable tool to evalute the seismic performance of structures. Also, various advanced pushover procedures have been proposed to take into account the effect of higher modes and the change in the dynamic properties of structures in the nonlinear phase. Therefore, different pushover procedures have been further developed for this purpose. The nonlinear static analysis  has been widely employed to evaluate the nonlinear behavior of structures. The pushover analysis was first expanded in a number of studies to investigate buildings. Not many studies have been conducted on the seismic demand of latticed space structures. In the present work, therefore, an optimization procedure has been employed to refine the performance of the pushover analysis in estimating the seismic response of double-layer barrel vault roofs with vertical double-layer walls. In the  method proposed herein, the coefficients of the modal load combinations of the studied structures have been optimized using the simplex algorithm to find the optimum load pattern. Fifteen models with various rise-to-span and height-to-span ratios were considered to assess the accuracy of the proposed method in predicting the seismic demand of these structures. The models were analyzed using the OpenSees software. In order to model the buckling behavior of the members, each member was divided into two nonlinear beam-column elements with an initial imperfection of 0.1% at its mid-node.  The models were designed with the dead, snow, temperature, and earthquake loads having been considered. All of the mentioned loads, with the exception of snow load, were applied to the structures as concentrated nodal loads. The snow load, by contrast, was applied to the structures in two symmetric and asymmetric patterns in accordance with the sixth volume of the Iranian national code of buildings. For earthquake loads, the 4th edition of the Iranian code of practice for seismic resistant design of buildings was used. It should be noted that the seismic mass of the roof of each model was calculated by considering the entirety of the dead load in addition to 40% of the snow load. In the design process of each model, the dead, snow, temperature, and earthquake load combinations were formulated based on the AISC-ASD89 standard. The sections of the members of the structures were chosen from hollow tubular sections, with  their slenderness ratios limited to 100. Afterwards, pushover analyses were performed using the optimized load pattern. The obtained results were compared to those of the incremental dynamic analyses (IDA) and two other well-known pushover methods, namely the MPA and the conventional first-mode pushover analysis. The results revealed that the proposed pushover method can provide a good estimation of the base shear and intial stiffness of the structures when compared to dynamic analyses. In addition, an increase in the rise-to-span ratio of the roof causes an improvement in the accuracy of the proposed pushover method. Also, in comparison with the  MPA and conventional pushover procedures, the responses produced by the proposed method are closer to those generated by dynamic analyses. In addition, a comparison of the obtained drift patterns reveals that the results of both the pushover and incremental dynamic analyses along the longitudinal direction of the wall are quite close to each other. Another advantage of the proposed pushover method is that it also produces acceptable results on the nodes on the roof of the space structure. Also, along the transverse direction, the proposed method yields better results.