Static and Dynamic Nonlinear Analysis of Space Frame

Abstract

Space Frame Structures are widely adopted for important structures like high-rise buildings, industrial structures, oil and gas platforms etc which require higher safety and accuracy in design. To understand actual behavior of structure, it should be analyzed rigorously by considering structural nonlinearities. The present study is concerned with the analysis of space frame structure. The linear and nonlinear analysis for static and dynamic loading conditions are carried out. Main focus of analysis is on e ects of geometric nonlinearity on behavior of space frame structure. Space frame elements with six degrees of freedom (three translations and three rotations) at each node are considered. Single element per member is assumed. Linear static analysis is performed using direct sti ness method. Natural frequencies and mode shapes are calculated using free vibration analysis. Wilson-Theta method is used for time stepped analysis of space frame and as a result time history plots are developed. These methods are extended for nonlinear analysis. Mostly, space frames are consisting of slender sections which can have large deformations. Due to large deformations, second-order e ects are developed which can be included in analysis by updating sti ness matrix. In present study, geometric sti ness matrix which is depending on deformed geometry is considered. Di erent solution methods for nonlinear equilibrium equations are also discussed in brief. For static nonlinear analysis, combined incremental and iterative method is adopted. Nonlinear response can be evaluated by updating geometric sti ness matrix at the end of each incremental step. To consider large strain and large deformation condition, both geometric sti ness as well as geometry of structure are updated at the end of each incremental step. Unbalanced forces are calculated at the end of each incremental step and are recovered by performing iterations. Same incremental-iteration method is used for time stepped method. In nonlinear dynamic analysis, incremental forces are depended on time dependent forces. Combination of Wilson-Theta method and Newton-Raphson method is adopted for nonlinear dynamic analysis. Detail procedures of linear and nonlinear analysis for both static and dynamic conditions are presented. Computer programs are developed based on these procedures. Computer programs are capable of nding linear and nonlinear response. Single bay single storey as well as multi storey frames are analyzed for static and dynamic loading conditions for both linear and nonlinear case. Space frame building with plan dimension of (15m 20m) with varying number of storeys from 6 storey to 30 storey with storey height of 5m are analyzed to understand the e ects of height on nonlinear behavior of space frame. Loading conditions are kept same for all types of multi-storey frames to compare results. In static loading condition, equivalent static earthquake loads based on IS:1893-2002 are considered for multi storey frames and for dynamic case, time dependent lateral forces are applied at top storey of each frame. Results of linear analysis are compared with ETABS results for validation. Nonlinear analysis results are compared with nite element analysis results to validate procedure of nonlinear analysis. Load displacement curves and time history curves are plotted based on results obtained from developed programs.