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本文提出了计算变截面梁(轴)变形的平均弯矩数值解法。应用该法,可求出任一截面的挠度、转角、极值点坐标及最大挠度的近似解或精确解。亦可用于求解静不定梁的变形。便于在工程中应用,适于电算。变截面梁(轴)在机械、建筑工程中获得广泛应用,计算变截面梁(轴)变形的方法,目前推荐采用的有虚用法、初参数法、等效(当量)直径法、叠加法、有限差分法等。其中有的方法计算准确度高、但求解过程较烦,有的则误差较大,且不能估算出误差大小,因此在一定程度上限制其应用。 本文提出一种简便的变截面梁(轴)变形的数值解法——平均弯矩法。具有计算公式和计算过程简单,适于电算,并且可事先计算出误差值等优点,可求解梁上任一截面的挠度、转角、极值点坐标及最大挠度的近似解或精确解。亦可求解静不定梁的变形。
This paper presents a numerical method for calculating the mean bending moment of a deformed beam (shaft). Using this method, the approximate solution or exact solution of deflection, rotation angle, extreme point coordinates and maximum deflection of any section can be obtained. Can also be used to solve static deformation of beam. Easy to use in engineering, suitable for computing. Variable cross-section beam (shaft) is widely used in machinery and construction. The method of calculating the deformation of the beam with variable cross-section is currently recommended. There are two methods: virtual method, initial parameter method, equivalent diameter method, Finite difference method and so on. Some methods have high computational accuracy, but the solution process is more annoying, while others have larger error, and can not estimate the size of the error, so it limits its application to a certain extent. In this paper, a simple numerical method of deformation of beam with variable cross section (average shaft bending moment) is proposed. The utility model has the advantages of simple calculation formula and calculation process, suitable for computer calculation, error value calculation in advance, etc., and can solve the approximate solution or the exact solution of deflection, rotation angle, extreme point coordinate and maximum deflection of any section on the beam. Can also solve the static deformation of the beam.