基于弯矩图面积法求解梁的弯曲问题

Solving the Bending Problem of Beam Based on Bending Moment Diagram Area Method

为了简化梁的平面弯曲变形计算,该文通过对梁的挠曲线近似微分方程的建模分析,推导出用弯矩图面积法求解梁的变形问题的计算公式。当梁的抗弯刚度为常量,且弯矩图面积及弯矩图形心容易得到时,利用梁上支座处的已知边界条件,无需积分即可求解梁上任意横截面的转角和挠度;与叠加法相比,也有概念清晰、计算快捷的优点。实践表明,即使在梁上作用有分布载荷使得弯矩图面积及形心不容易直接得到的情况下,稍加推广即可方便求解梁的变形问题。

In order to simplify the calculation of the plane bending deformation of the beam, this paper deduces the calculation formula of the deformation of the beam by the method of the moment diagram area. When the beam bending stiffness is constant, and the moment diagram and bending moment graph easier to obtain, the comer and the deflection of any cross section of the beam can be solved without using the integral boundary condition at the bearing on the beam. Compared with the superposition method, there are also clear concept, the advantages of quick calculation. Practice shows that even if the distribution of the load on the beam makes the bending moment area and the centroid is not easy to be obtained directly. , A little promotion can easily solve the problem of the beam deformation.