Collision safety and lightweight vehicle structures are key components in the development process of new vehicles. A method is needed to estimate the structural strength accurately so that designers can consider the response to high-speed collisions in their initial design process. In this study, we carried out bending analyses of thin-shell square cylinders to simulate automotive frame members using the finite element method (FEM) to investigate the effective width. The accuracies of conventional formulas, Karman's formula and the formula of Noma et al. were verified in the case of 270-MPa to 1500-MPa materials.
In this study, the estimated effective width using Karman’s formula was larger than the results of FEM analyses under all conditions. In addition, the discrepancy between Noma’s formula and the FEM results is large for higher-strength materials. Thus, the conventional formulas lack the accuracy to estimate recently developed higher-strength materials.
Therefore, we proposed a new high-precision formula based on these FEM results. The proposed formula is more accurate than the conventional formulas, even for 1500-MPa material. This new formula improves the efficiency of car body development.
However, frame members of car body have holes for air conditioning ducts, parts positioning, and other purposes. The effect of these holes on the stress state and effective width are not clear. In this study, we clarified the effect on strength of a hole located in a planar portion of the member. Then, we found a way to compensate for the effect of the hole using flanges.