Study On Out-Plane Elastic-Plastic Stability Of Monosymmetrical Steel I-Beam

I-beams are widely used in industrial plants,and out-of-plane bending and torsional instability is the main mode of instability for thin-walled components,which is much more complicated than torsional and bending instability alone..In this paper,Finite element software is used to study the out-of-plane stability of monosymmetrical steel I-beam,and the initial defects and residual stress are considered.The analysis mainly involves the following three aspects:(1)Firstly,two definitions of the stability coefficient are provided according to the previous domestic and foreign codes.A finite element model was established to calculate the stability factors of different section sizes under the action of the mid-span concentrated load.The values of the stability coefficients of the elastic and elastoplastic sections were studied.The maximum value of the stability coefficient of members with different width-thickness ratios in the elastoplastic section is obtained.In the past,the stability coefficient formula did not consider monosymmetrical sections.In this paper,stability coefficient curves with different cross-section sizes were obtained by fitting.The formula includes the influencing factors that reflect the aspect ratio of the section,the uniaxial symmetry ratio,and the height of the load.The validity of the formula is verified by changing the size of the finite element model;(2)The stability of the crane beam under two-point wheel pressure is studied.First,the critical moments of two-point moving loads with different positions and track lengths were obtained by the energy method,and the two-point symmetrical loads at the mid-span were determined as the most unfavorable positions during the load moving process.The calculation theory of the equivalent bending moment coefficient was established by using the calculation formula of the critical bending moment for torsional buckling under the combined load,and the expression of the critical bending moment under two-point load with symmetrically distributed midspan was obtained.Based on the previous chapter,the overall stability of steel beams under two-point loads is studied.The parameter to express the two-point load and the mid-center concentrated load in a unified form is defined,and this parameter is reflected in the calculation formula of the stability coefficient.Finite element models are established to compare the results of the finite element calculation with the results of the formula in the previous chapter,and verifying that the stability factor formula is also applicable to two-point load conditions;(3)In actual working conditions,steel beams are subjected to bending moments in both directions and torque due to eccentric load.To solve this problem,the current steel structure design code does not have relevant calculation formulas.This paper addresses this issue.The equilibrium differential equation of steel beams under bidirectional bending is established.By solving differential equations,the exact solution of the bending moment amplification factor considering the second-order effect is given.The Galerkin method is used to obtain the approximate solution of the bending moment magnification factor including the second-order effect when the torque is involved.By introducing amplification factors into the bending moment term in the y-axis direction,the stability check formulas of I-beams under two-way bending without considering the torque and considering the torque are constructed,and a finite element model is established to verify the validity of the formula.Checking formulas are applicable to sections with different load point heights,diferent aspect ratios,and uniaxial symmetry ratios which can be considered as a reference for engineering practice and related research.