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Plastic mechanism analysis of circular tubes under pure bending

机译：纯弯圆管的塑性机理分析

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摘要

There are a number of solutions available to predict the response of a circular steel tube under pure bending. However, most of these solutions are based on an elasto-plastic treatment, which is complex and difficult to use in any routine design. This paper describes a theoretical treatment to predict the moment-rotation response of circular hollow steel tubes of varying D/t ratios under pure bending. The Mamalis et al. (J. Mech. Sci. 1989;203:411-7) kinematics model for a circular tube under a controlled moment gradient was modified to include the effect of ovalisation along the length of the tube. Inextensional deformation and rigid plastic material behaviour were assumed in the derivation of the deformation energy. The plasticity observed in the tests was assumed to spread linearly along the length of the tube. Two local plastic mechanisms (Star and Diamond shapes) were studied to model the behaviour observed in the tests especially during the unloading stage. The theoretical predictions are compared with the experimental results recently obtained by Elchalakani et al. (Quartral. J. Struct. Eng. 2002;3(3): 1-16). Good agreement was found between the theoretical predictions and experimental moment-rotation responses, particularly for the Star shape mechanism. A closed-form solution is presented suitable for spreadsheet programming commonly used in routine design.
机译：有许多解决方案可用来预测圆形钢管在纯弯曲下的响应。但是，这些解决方案中的大多数都是基于弹塑性处理的，这种处理很复杂并且在任何常规设计中都很难使用。本文介绍了一种理论处理方法，用于预测纯弯曲下具有不同D / t比的圆形空心钢管的弯矩-旋转响应。哺乳动物等。 （J. Mech。Sci。1989; 203：411-7）对圆形管在受控力矩梯度下的运动学模型进行了修改，以包括沿管的长度进行椭圆化的影响。在推导变形能量时，假定了无延伸变形和刚性塑性材料的行为。假设在测试中观察到的可塑性沿着管的长度线性分布。研究了两个局部塑性机制（星形和菱形），以对在测试中观察到的行为进行建模，尤其是在卸载阶段。理论预测与Elchalakani等人最近获得的实验结果进行了比较。 （Quartral.J.Struct.Eng.2002; 3（3）：1-16）。在理论预测和实验力矩-旋转响应之间发现了很好的一致性，特别是对于星形形状机理。提出了一种封闭格式的解决方案，适用于常规设计中常用的电子表格编程。

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