抄録
The bending strength of H-shaped beam is governed by material and geometric nonlinearity. Many estimation equations of the bending strength have been proposed and are currently used for actual structural design. One problem is that they have been determined experimentally because the theoretical relationship between the bending strength and such nonlinearities has not been clarified. This prevents us from evaluating the effect of residual stress and initial deflection for the estimation of the bending strength. To overcome this problem, this study aims to understand the relationship between the bending strength and the nonlinearities using finite element models.
In the previous report, the estimation method considering only material nonlinearity is proposed and the validity of the method is investigated. In this report, the method is extended to consider the geometric nonlinearity and the method is verified in the case where only geometric nonlinearity is included and in the case both material and geometric nonlinearity is included.
Firstly, the analysis considering only geometric nonlinear is conducted. The results shows that the increase of applied bending moment becomes less and less according as out-of-plane displacement increases, though the out-of-plane displacement has little effect on the buckle strength. From this result, it can be said that the maximum strength would not be governed by the buckle strength drop due to geometric nonlinearity. Therefore, the authors assumed that the maximum strength is characterized by suppression of load increase caused by the out-of-plane displacement, which is defined as the displacement in direction of mode vector. Based on this assumption, it is possible to calculate the amount of out-of-plane deformation and to estimate the drop of the maximum strength by converting it to the buckle strength drop. By conducting analysis changing the shape and the amount of initial deflection, it is indicated that the amount of the influence of geometric nonlinearity is determined by the product of the vector representing the initial deflection and mode vector. Because the mode shape differs according to the bending moment distribution, it means that, even the shape and the amount of initial deflection is the same, the drop of the maximum bending strength due to the geometric nonlinearity is affected by the bending moment distribution.
Next, the analysis considering both material and geometric nonlinearity is conducted. The influence of the initial deflection appears as “1. Rigidity reduction due to material nonlinearity caused by the change in progress of plasticization” and “2. Rigidity reduction due to geometric nonlinearity”. In the proposed method, the former is considered as the buckle strength drop and the latter is considered as the amount of out-of-plane deformation, which is converted to the buckle strength drop, and it is confirmed that the proposed method is valid in the case where both nonlinearities are included. Moreover, by observing the buckle strength drop in detail, it is possible to investigate the degree of the influence of material (“1.”) and geometric (“2.”) nonlinearity respectively by using the proposed method. The proportion of “1.” and “2.” differs according to the value of the lateral-torsional slenderness ratio, λb, and it is shown that, in a range where λb is around 0.9, the influence of material nonlinearity (“2.”) appears first, and that of geometric nonlinearity (“2.”) appears next.
