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

Abstract

Even for the doubly symmetric I-beams under linear distributed moment, the design formulas given by codes of different countries are quite different. This paper will derive a dimensionless analytical solution via linear stability theory and propose a new design formula of the critical moment of the lateral-torsional buckling (LTB) of the simply supported I-beams under linear distributed moment. Firstly, the assumptions of linear stability theory are reviewed, the dispute concerning the LTB energy equation is introduced, and then the thinking of Plate-Beam Theory, which can be used to fully resolve the challenge presented by Ojalvo, is presented briefly; secondly, by introducing the new dimensionless coefficient of lateral deflection, the new dimensionless critical moment and Wagner's coefficient are derived naturally from the total potential energy. With these independent parameters, the new dimensionless analytical buckling equation is obtained; thirdly, the convergence performance of the dimensionless analytical solution is discussed by numerical solutions and its correctness is verified by the numerical results given by ANSYS; finally, a new trilinear mathematical model is proposed as the benchmark of formulating the design formula and, with the help of 1stOpt software, the four coefficients used in the proposed dimensionless design formula are determined.

Lateral–Torsional Buckling of Cantilever Steel Beams under 2 Types of Complex Loads

“…If it can also meet the mechanical boundary conditions, the accuracy will be higher. Based on the above situation, the following trigonometric series are used to describe the lateral deflection u(z) and twist angle ϕ(z) of cantilever steel beams [4,12].…”

“…Many scholars have studied C 1 , C 2 and C 3 factors of lateral-torsional buckling of simply supported beams. Zhang et al [4] studied the general formula of M cr under linear distributed moment. The study used dimensionless parameters and infinite series to calculate M cr and fitted the specific values of C 1 , C 2 and C 3 .…”

Analytical Solution for Lateral‐Torsional Buckling of Concrete‐Filled Tubular Flange Girders with Torsional Bracing

“…We then define the dimensionless parameters, which are given as follows [16,[24][25][26][27][28][29]:…”

Discussion of “Out-Plane Elastic-Plastic Buckling Strength of High-Strength Steel Arches” by Mark Andrew Bradford, Yong-Lin Pi, and Airong Liu

“…However, the discussers take a different view from the authors on the influence of D=b f on buckling strength of HSS arches. In the next section, the discussers will demonstrate that the D=b f has almost no influence on buckling strength of HSS arches based on a simplified mechanical model and the plate-beam theory (Zhang 2015a(Zhang , b, c, d, 2016(Zhang , 2018aZhang et al 2017Zhang et al , 2018.…”

“…It can be shown that for the simplified mechanical model shown in Fig. 1, the following analytical expression for the geometrical properties of the cross section can be easily derived (Zhang 2018b;Zhang et al 2017Zhang et al , 2018:…”