| In order to improve the accuracy and the scope of application for the practical equations of equivalent uniform moment factor,the historical research on the critical moment of steel beams subjected to combined loading is reviewed and summarized.This paper presents the complete transverse concentrated load terms of the flexural-torsional buckling equilibrium differential equations derived from the complete potential energy equation of flexural-torsional buckling for steel members via variation.The influence of Rayleigh-Ritz method and Galerkin method on theoretical derivation is studied,and it is pointed out that there is no essential difference between the two methods in the application.Using the two approximation methods to solve the potential energy equation,the simultaneous torsion displacement function and lateral displacement function will improve the accuracy of the calculation formula of the two methods.The equivalent uniform moment factor,which plays a key role on the accuracy of the critical moment,is the most important factor in determining Mcr.Based on the calculation theory of equivalent uniform moment Cb and parameterζy,the torsional parameter K considering geometric effect is introduced.Four closed-form formulae are proposed for determining the equivalent uniform moment factor on the basis of its theoretical expression,by employing more accurate C1 confidence in Mcr.The proposed Cb formulae are compared with current“quarter-point”e-quations of equivalent uniform moment factor within-1≤ψ≤1.The accuracy of the proposed formulae is checked and the criterion on Cb formulae is proposed.The criterion on Cb formulae is valid by numerical examples.Compared with FEA results,it is shown that the proposed formulae of Cb are accurate within their scopes when the end moment ratio is-1≤ψ≤1.Accurate critical moments of steel beams with flexural-torsional buckling can be obtained on the basis of the proposed Cb formulae. |
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