Second order analysis of space frame considering height of the structure effects

In recent years, structures for economic and aesthetic reasons have been growing larger and thinner and this subject leading to non - linear behavior of structures. Therefore, the application of different methods for considering the effects of second order analysis in evaluation of the behavior of structures has always been considered by the designers. in this study to investigate the P-Δ effects, analyze the nonlinear behavior of multi - storey space structures. in order to estimate the effects of second order analysis in this study, methods of Stiffness Matrix, Stability Functions and Assume lateral load method have been used. in present study, in addition to comparing the accuracy of the proposed methods, examine the effect of the parameter height on the accuracy of the second order analysis. the accuracy of the second order analysis methods is investigated by comparing the results of the existing research. In the first part of the present study, after presenting the formulation of three methods of second-order analysis of stiffness matrix, stability functions and assume lateral load method, for beam-column element of a portal frame, a two-story regular structure and finally an irregular six-story structure, that studied by previous researchers, the most accurate second-order analysis is introduced by comparing the load-deformation curves. In the second part, in order to investigate the effect of height of structure on the accuracy of second-order analysis methods, similar structures of three, five, and seven floors were analyzed in two longitudinal and transverse directions and the final load coefficients obtained from the second-order analysis with The first-order analysis of the structures is compared. The analysis of three, five and seven-story structures was performed in two assume lateral load and stiffness matrix methods in OpenSees software as well as stability function analysis using Paap software.the accuracy of second-order analysis methods has decreased and this reduction is more pronounced in the transverse direction of the structure. As the height of the structure increases, the accuracy of the stiffness matrix methods, stability functions and the Assume lateral load method in the second-order analysis of the transverse direction are reduced by 15.5%, 10% and 7.2%, respectively. It is observed in more than three storeys, the accuracy of the Assume lateral load method in estimating the P - Δ effects is greatly reduced and the highest correlation with the height of the structure is observed in this method. also among the second - order analysis methods in tall structures, the highest accuracy is related to the method of Stiffness Matrix.