The Computation Of Critical Loads On Arbitrary Restrainted Thin-walled Members Using Finite Elements Method

A beam or a column often supports other members which participate in the buckling action,and significantly influence its in-plane stability and out-of-plane stability.If these elastic restraints action of buckling resistance is taken into account the critical loads of steel members may apparentely been increased and plenty of steel material is saved.As a efficiently numerical method,the finite elementes method(FEM) is especially suitable for the computation of structures consisting of bars. Using FEM, researches on the critical loads of elastic restraints thin-walled members are conducted. According to the classical theory of thin-walled members this paper presents the derivation of energy equation under restrainted conditions, and a elastic restrainted stiffness matrix of thin-walled members is derived.Continuous restrants and discrete restraints are considered in the energy equation.Euler-equation of the derived energy equation is testified.The formulation has been applied to a variety of sample problems involving bucking analysis of beam, column, and beam-column. Several numerical results of elastic restrainted thin-walled members involving bending ,torsional,and flexural-torsional elastic buckling failure modes are presented to demonstrate the accuracy,efficiency,and versatility of the method.Comparisons with published analjtical and semi-anaiftical solutions are made using some of the obtained results. All the results obtained demonstrate that restraint action may apparently increase the critical loads of all kinds of thin-walled members.