In this paper, the critical equilibrium of a simply supported compressed column on a Winkler foundation is analyzed based on Koiter’s theory. The exact expression of the potential energy functional is presented. By the Fourier series of the disturbance deflection, the second-order variation of the potential energy is expressed as a quadratic form. At critical equilibrium, the second-order variation of the potential energy is semi-positive definite, so that the stability of the critical equilibrium is determined by the sign of the fourth-order variation or sixth-order variation. It can be seen that only in two small ranges of elastic-foundation stiffness is the corresponding critical state stable and the bifurcation equilibrium upward. Then, the theoretical results of this paper are compared with previous experimental and theoretical results.
In this paper, the analysis on dynamic failure behaviors of steel double-layer cylindrical latticed shells supported by steel rectangle columns in a gymnasium with the function of earthquake victims shelter under disaster earthquake is carried out under EL-centro wave with SAP2000, and the appraisal results on their anti-failure performances are presented under strong earthquake action based on the plastic-hinge theory. In the analyses, the geometric and material nonlinear effects are considered simultaneously. The plastic development level of the rods, the deformed shape and the failure type and the ductility are estimated.The results show that Under EL earthquake wave input in the combine direction of Y+0.85X+0.65Z, the structure's elastic limitation PGA is 277gal. Its failure model is the elasto-plastic dynamic buckling and its critical PGA is 692 gal. its displacement ductility coefficient is 4.33, and the ratio of its bars with plastic hinge appearing for ultimate critical state is 26.5%. All results show the structure have good deformed capacity and energy-dissipation capacity before bucking.
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