Equivalent uniform moment factors for lateral–torsional buckling of steel members

Effect of End Connection Restraints on the Stability of Steel Beams in Bending

“…In this analysis the end supports of the beam are assumed to be fixed for out of plane deflection, 0 v = and twist rotation, 0 The reason is that the EC3 ENV formula assumes that coefficient 1 C does not vary with end support conditions for equal end moments. However, using finite differences approach, Miguel A. Serna [7] shows that for the case of equal end moments, the values of 1 C for beams with prevented lateral bending at supports ( z k =0.5) are higher than those for simply supported beams, which confirms the difference found in this study between the numerical and analytical results of cr M for the case of restrained end supports against lateral bending ( z k =0,5). Following the difference between the FEM results and those obtained analytically by EC3 ENV formula, for z k =0,5 it is recommended that the value of 1 C be taken as 1,05 which is the value suggested in [14].…”

“…The beam simultaneously exhibits lateral displacements v in the y direction (bending about the minor axis of the cross-section) and twist rotation θ about its longitudinal axis x. [4], where (x-x) is the axis along the member, (y-y) is the major axis of cross-section and (z-z) is the minor axis of the cross-section, the governing differential equation for the lateral torsional buckling is [7]:…”

“…The elastic critical moment is directly dependent on the following factors [7]: material properties such as the modulus of elasticity and shear modulus; geometric properties of the cross-section such as the torsion constant, warping constant, and moment of inertia about the minor axis; properties of the beam such as length, and lateral bending and warping conditions at supports; and finally loading, since lateral-torsional buckling is greatly dependent on moment diagram and loading position with respect to the section shear centre. The bending moment diagram is taken into account by means of the equivalent uniform moment factor 1 C .…”

Dimensionless Analytical Solution and New Design Formula for Lateral‐Torsional Buckling of I‐Beams under Linear Distributed Moment via Linear Stability Theory

“…More recently, Suryoatmono and Ho [9] and Serna et al [10] have reported the results of elastic LTB load analysis using finite difference technique to solve the governing differential equation; Lim et al [11] have conducted an extensive investigation into the elastic LTB of I-beams using both the Bubnov-Galerkin approach [1] and the finite element method [8]. In their papers, Vlasov's differential equation governing [1] for lateraltorsional buckling of beams was used; Park et al [12] use the finite element program developed by Lim et al [11] to perform parametric studies to investigate the lateral-torsional buckling behavior of singly symmetric I-beams, in which Ibeams are modeled by the beam element with two nodes per element and seven nodal degrees of freedom; Greiner and Lindner [13], Greiner et al [14], and Mohri et al [15] also use finite element method to present a quite complete numerical study on lateral-torsional buckling of beams; Kim et al [16] adopt the variation of the total potential energy to derive the stability equations for the lateral buckling analysis of an arbitrarily laminated thin-walled composite beam, and the exact analytical stiffness matrix is presented based on power series expansions.…”

“…The authors have found that shell elements could consider local buckling, section distortion, and the local effects of concentrated loads and boundary conditions, which were all ignored in the beam element theory; Dolamune Kankanamge and Mahendran [19] use ABAQUS [18] to investigate the LTB behavior of simply supported cold-formed steel lipped channel beams subjected to uniform bending. The authors have found that European design rules are conservative, while Australian/North American design rules are unconservative; Tong [20] uses ANSYS [21] to regress the design formula for the singly symmetric I-beams under linear distributed moment; Sweedan [22] adopts ANSYS to numerically investigate the lateral stability of cellular steel beams subjected to equal end moments, midspan concentrated loads, and uniformly distributed loads; Serna et al [10] use Cosmos/M27 [23] to simulate the lateraltorsional buckling of the I-beams.…”