任意连续梁内力包络图的自动绘制法

根据内力包络图设计梁的断面，可以保证满足安全和经济两方面的要求。但是按传统方法绘制梁的内力包络图手续十分繁琐，对于连续梁之类的多跨梁尤其如此。介绍一种利用奇异函数对连续梁进行力学分析的新方法及其智能分析软件。该方法利用奇异函数与拉普拉斯变换相结合的方法导出连续梁变形和内力的普遍表达式，利用变形和内力的边界条件确定约束反力，然后再在内力普遍表达式的基础上建立一种内力包络图的自动绘制方法。该方法和程序对承受任意恒载和活载、具有任意跨数的连续梁具有普遍的适用性。

New Method to Draw the Internal Force Envelope Diagrams of Arbitrary Continuous Beams

The section of beam designed according to the internal force envelope diagrams can meet demands of security and economy. But the process of drawing the internal force envelope diagrams of the beams using the classical mechanics methods is overelaborate, especially multispan beams such as continuous beams. So, a new method for arbitrary continuous beam analysis and its intelligent software with singularity functions are introduced. The general expressions of the continuous beams deformation and the internal force are developed, using a method combining singularity functions with Laplace transformations, and binding reactions are determined by boundary conditions and deformation conditions of the beams, then an automatic method to draw the internal force envelope diagrams of arbitrary continuous beams is established on the basis of the general expressions of the internal forces. The method and its corresponding computer program can be universally used for arbitrary multispan continuous beams that bear different kinds of dead loads and live loads: concentrated force, concentrated moment and uniform load.