基于等效梁长法的组合深梁临界预紧力计算模型

Calculation Model of Critical Preload of Prestressed Composite Deep Beam Based on the Method of Equivalent-beam-length

为确定合理的临界预紧力,保证预紧组合结构横梁的整体性,提出采用等效梁长法修正传统Airy应力函数计算结果,从而得到更准确的临界预紧力。基于平面应变理论,建立临界预紧力的理论计算模型,通过叠加原理,分别得到弯曲模型和压缩模型中间截面x方向应力的傅里叶三角级数形式解,分析误差原因;采用等效梁长法进一步修正,结合临界开缝判据,得到临界预紧力理论计算公式。试验结果表明:等效梁长法修正的临界预紧力理论计算结果与试验结果最小误差为10.1%,最大误差为13.5%,与试验结果吻合较好,能够为大型成形设备的预紧组合结构横梁的设计提供理论依据。

To determine a reasonable critical preload and ensure the integration of prestressed composite deep beam, the method of equivalent-beam-length is proposed to revise the traditional theoretical results of airy stress function. Then a more accurate critical preload is obtained. Firstly, the theoretical calculation model of critical preload is established based on the plane strain theory. Secondly, based on the principle of superposition, the stress in the direction ofx in the middle section of bending model and prestressed model are deduced and were presented in the way of Fourier series. The reasons for error are analyzed. Then, it is further revised with the method of equivalent-beam-length. Finally the theoretical formula of critical preload is derivedcombined with the critical criterion. Experimental results show that the minimum error between theoretical results of critical preload revised with the method of equivalent-beam-length and experimental results is 10.1%, while the maximum error is 13.5%. The theoretical results are in good agreement with the experimental results. It is able to provide theoretical basis for the design of prestressed composite beams in large mechanical equipments.