位移法计算简支梁任意截面的位移

DISPLACEMENT OF ANY SECTION OF A SIMPLY SUPPORTED BEAM BY DISPLACEMENT METHOD

  • 摘要: 为了更加便捷地求解简支梁任意截面的位移。借用位移法的求解思想,将简支梁从待求位移的截面处截开后转化成两个一端固定、一端简支的超静定梁,再利用弯矩相等和剪力相等的关系给出了建立关于待求截面角位移和线位移的二元一次方程组的3种做法。算例表明,利用位移法求解简支梁任意截面的位移比其他方法更加便捷,尤其是载荷种类和分布复杂时位移法的优势更加明显。

     

    Abstract: In order to solve for the displacement of any section of a simply supported beam more conveniently. Borrowing the idea of the displacement method, the simply supported beam is transformed into two statically indeterminate beams fixed at one end and simply supported at the other end after being cut off from the cross-section to be dislocated, and then the relationship of equal bending moments and equal shear forces is utilized to give the three ways of establishing a system of binary equations on the angular displacement of the cross-section to be dislocated and the linear displacement. Examples show that the displacement method is more convenient than other methods for solving the displacement of any cross-section of a simply supported beam, especially when the type and distribution of loads are complex, the advantages of the displacement method are more obvious.

     

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