不同模量理论弹性支承连续梁及框架

THE ELASTIC SUPPORTED CONTINUOUS BEAM AND FRAME OF DIFFERENT MODULUS

弹性支承连续梁及框架结构的内力不仅与各杆件的刚度有关,而且与支承结构的刚度有关。当引入拉压不同模量后,各杆件的抗弯刚度EI不再为常数(与经典力学不同),而是内力的函数,使结构内力计算成为非线性问题。用分段积分法推导出不同模量弹性支承连续梁及框架的中性轴公式和内力计算表达式并编制非线性内力计算迭代程序。通过实例计算对比分析不同模量与经典力学相同模量两种方法计算结果的差异,最后提出对该类结构计算的合理建议以及利用不同模量对结构进行优化的结论。

For the elastic supported continuous beam and frame, its internal forces are related not only to the stiffness of each member, but also to the stiffness of the supported structure. With a different tension and compression modulus, the flexural rigidity of each member is not constant any more (as is different from that of classic mechanics), but is a function of the internal force, that is, the calculation for the internal force is a nonlinear problem. In this paper, the formulas of neutral axis and internal force for the elastic supported continuous beam and frame are derived by using the phased integration method, and an iterative program for nonlinear internal force is developed, an example is calculated and analyzed. In the end, the author proposes a suggestion for the calculation of structure, and concludes that the structure can be optimized by using the different modulus theory.