Elastic Lateral-torsional Buckling Of Lateral Restrained Beams

In order to improve the overall stability of simply-supported steel I-beam,elastic or rigid restraints can be set on the compression flange of the beam span to restrict the lateral displacement,thus forming lateral restrained beams.The lateral restrained beam is commonly used in roof beam with purlin,and purlin can be regarded as lateral restraints.Because the lateral-torsional buckling critical moment is an important parameter of lateral restrained beams,it has been widely concerned by scholars at home and abroad.For steel beams with equidistant rigid restraints in the span,according to the number of restraints n,the equivalent uniform moment factorβ_b for calculating the critical moment is given in the current national standards GB 50017-2017 and GB50018-2002 according to n=1 and n≥2.For n≥2,the unified coefficientβ_b may reduce the calculation accuracy.In addition,there is no provisions of restraint stiffness in the code.Therefore,according to total potential energy equation of lateral restrained beams,the formula of the critical moment for lateral restrained beams is derived by using the Rayleigh-Ritz method,then the practical formula of the critical moment of the lateral restrained beams is proposed.The accuracy and applicability of the practical formula are verified by comparing the experimental data and the FEA data.Firstly,the restraint potential energy term is introduced into the total potential energy equation of simply-supported I-beams,based on the total potential energy equation,sin(πz/L)and sin[(n+1)πz/L]are selected respectively as the primary deformation functions of simply-surpported beam with a elastic restraint in the middle span or n rigid restraints in the span.Then,by using Rayleigh-Ritz method,the expressions of the critical moment of the above two kinds of restrained beams are derived.The formula of the former is proposed in this thesis,which is similar to Clark and Hill’s"3C"formula,and can be reduced to"3C"formula when the stiffness is zero;the formula of the latter is exactly the same as"3C"formula.Whether u andφare coupled or not does not affect the form of"3C"formula,but only affects the value of"3C"coefficient,in addition,the accuracy of the coefficient is higher in the case of coupling.Owing to selected deformation function can not fully simulate the actual deformation of the steel beam,the formula only has high accuracy in a limited range.It can be seen from the numerical verification that the formula of the beam with a elastic restraint in the middle span has high accuracy only when the restraint stiffness K is small,and the calculation error increases with the increase of the stiffness;while the formula of the beam with n rigid restraint in the span is close to the FEA data when n=1,and the calculation error increases with the increase of n.In order to improve the accuracy of the two formulae,this thesis carries out the FEA numerical analysis of the critical moment based on the software LTBeam N,adjusts the value of the original"3C"coefficient in the formula,and the practical formula of the critical moment proposed in this thesis.For the beams with a elastic restraint in the middle span,the practical formula of the critical moment in this thesis is compared with the experimental data,and the calculated values in this thesis are in good agreement with the experimental data,and are safe;for the beams with n rigid restraint in the span,the calculated values in this thesis and the Chinese and American codes are compared with the FEA respectively,which shows that the calculated values in this thesis not only have high,but also have a wide range of application.