Elastic buckling analysis of rectangular longitudinally profiled (LP) steel plates under uniform compression

摘要

Longitudinally profiled (LP) steel plates are plates rolled to variable thickness along the rolling direction in order to suit practical loading distributions in construction applications. The elastic buckling load of LP steel plates is different to normal flat plates due to the change in thickness and it is hard to find analytical solutions to the governing equation. In this paper, the elastic buckling coefficients of rectangular LP plates were calculated using the Galerkin and Rayleigh-Ritz method (GRM). The plates were under uniform compression and four typical boundary conditions were considered. The element expression of the feature matrix was obtained by theoretical derivation and the elastic buckling coefficients were obtained by calculating the eigenvalues of the feature matrix numerically with MATLAB. Numerical models of LP plates were developed to validate the derivation. Upon validation it was further found that the elastic buckling coefficients of LP plates can be approximately expressed by those of constant thickness steel plates together with variable thickness coefficients. A series of approximation formulae of elastic buckling coefficients of LP rectangular steel plates were proposed. Simplified design formulae of elastic buckling coefficients of LP plates were proposed for the first time to promote the application of LP plates in engineering practice.