Investigation and evaluation of parameters affecting the elastic critical moment value of structural steel beams

In this study, lateral torsional buckling behavior of I cross-section structural steel beams was investigated. The elastic critical moment Mcr value of the simple supported beam, where applied from both ends in opposite direction a moment of equal magnitude is easily calculated analytically and the reference elastic critical moment is called Mcr,ref. Analytical calculation of Mcr is difficult in different support and loading cases. Numerical methods are inevitable for this. Therefore, for loading cases other than the reference loading case, it is recommended that the Mcr,ref be multiplied by the equivalent uniform moment factor (C1 or Cb). There are different formulas for the calculation of C1. The main purpose of this study is to derivation an expression that gives more accurate results for equivalent uniform moment factor C1. For the different loading cases, the moments MA, MB, MC respectively at distances L/4, L/2 and 3L/4 along the beam and the maximum moment Mmax at any point was calculated. In this process, Mmax was expressed as unit moment and other moment values are scaled at the same ratio as Mmax. For the same loading cases, Mcr values were found by using LTBeam software, and C1 coefficients calculated by ratioing them to Mcr,ref values were determined. The aim is to write the equivalent uniform moment factor C1 as a function of MA, MB, MC and Mmax. The design variables in this function were obtained by a code written using one of the metaheuristic optimization methods Gray Wolf Optimization (GWO) in Matlab program, and a new expression for C1 was derivation. When the formula derived from the study is compared with the other formulas, it can be seen from the graphs and error amounts that our study has achieved its purpose. It is concluded that the proposed formula can be used safely in lateral torsional buckling problems.