Study On Elastic Critical Moment Of Continuous Steel Beams Under Combined Loads

Elastic flexural-torsional buckling is an important failure mode of the steel beams.The critical moment M_cr is an important parameter to characterize the bearing capacity of continuous steel beams with flexural-torsional buckling.The study of critical moment in current literatures are limited to biaxial symmetrical section,continuous rigid beam with equal spans or beams subjected to single load.Moreover,the formula of critical moment obtained by theoretical analysis is also complex,which is not easy to be applied and popularized in engineering.Based on previous researches,this paper divides continuous steel beams with unequal spans into simply supported beams with shear force identical to continuous steel beams.In the left and right span beams,the applied loads are exactly the same,but the left span is larger than or equal to the right span,which makes it easier to lose stability.Therefore,the left span simply supported beam is used as the control segment of the continuous steel beam,the ratio of the critical moment of the continuous steel beam from FEA to the corresponding critical moment of the control segment of the continuous steel beam from theoretical analysis is defined as the interactive coefficient C_ij.Assuming the critical moment from theoretical analysis of the continuous steel beam is equal to the one from FEA,the relationship between the critical moment of the continuous steel beam and the critical moment of the control segment of the continuous steel beam is established.The critical moment of flexural-torsional buckling of control segment of the continuous steel beam can be expressed by 3C coefficients,while the critical moment of control segment of the continuous steel beam multiplied by C_ij is the critical moment of the continuous steel beam,so the critical moment of continuous steel beam can be expressed by 4C coefficients.Utilizing LTBEAMN for finite element analysis,the critical moment of lateral-torsional buckling of continuous steel beams with 7 I-sections of continuous steel beams with different load proportional coefficient?and span ratio?is calculated.The corresponding interactive coefficient C_ij is obtained through transformation combining with the critical moment of control segment of the continuous steel beam theoretical analysis.The relationship between the interactive coefficient C_ij and the load ratio coefficient?,the adjacent span ratio?and the section parameter?are analyzed comprehensively by the control variable analysis method.The approximate formulae between C_ij and?,?and?are fitted out by multiple regression analysis.The script compiled by Python language is applied to the buckling analysis of ABAQUS,the rapid modeling of control segment of the continuous steel beam can be realized.Considering two adjacent span ratios,including 1.0:0.6 and 1.0:0.8,and three loads ratio coefficients,including 0.5,1.5 and 2.5,the theoretical analysis results are compared with the results from ABAQUS are compared.The errors between the theoretical analysis and the finite element analysis are mostly within 10%indiacating good agreement is achieved.It is shows that the formula of critical moment 4C coefficients of lateral-torsional buckling for unequal-span continuous steel beams under combined loads established by introducing the interactive coefficient C_ij has high accuracy,which can be referenced for the design of unequal-span continuous steel beams in engineering.