## Safety Factor of Welded-Plate Beams based on Finite Element Linear Buckling Analysis

Van Ngan Lê and Henri Champliaud

### Keywords

Welded plate beams, Safety factor, Linear buckling, Load multiplier factor, Finite element method, Membrane stresses

### Abstract

Beams made of welded plates are very common thanks to the optimum combination of weight and strength of structure. One of the most important design criteria of these beams is their safety against lateral buckling and local buckling. Linear buckling analysis by Finite Element Method (FEM) quickly gives the load multiplier factor to produce elastic buckling. This factor could be considered as the safety factor against buckling if membrane compression stresses in the most critical zone remain well below yield stress up to the buckling load. Otherwise, this interpretation could become unsafe because the combined membrane plus bending stresses in critical zones, which are neglected in linear elastic analysis, could exceed the yield stress. A correction procedure must then be used and may be summarized into the following steps: (1) Carry out a linear static FEM analysis followed by a linear buckling analysis for calculating the lowest load multiplier factor « fE » to produce elastic buckling of the structure; (2) Identify the most critical zone of the buckling mode 1 and its width “b” ; (3) Check the results of static analysis and identify the value « σmeqvL » which stands for « membrane equivalent stress linearized over the buckled width »; (4) Calculate the so called « elastic buckling stress » by ScrE = fE*σmeqvL ; (5) If ScrE is low enough, accept Scr = ScrE as the critical stress or else correct the critical stress Scr by a correction procedure to be defined by considering plastic deformation due to bending across the thickness in critical zones prior to buckling; (6) Calculate the safety factor against buckling by standard formula f = ScrmeqvL. In a similar philosophy of Johnson’s empirical formulas for short columns, the summarized procedure is successfully applied in this paper to numerical examples of thin and moderately thick welded-plate beams for correcting the load multiplier factor given by FEM. Numerical example results show that the proposed correction procedure, or a similar one, is a must do step after obtaining results of linear buckling analysis by FEM, because the multiplier factor given by FEM could be unsafe or even dangerous for some welded-plate beam designs.