基于二阶理论的2端弹性约束压弯梁的稳定性分析和最大弯矩计算

Stability analysis and maximum bending moment calculation of free beam with elastic constraints at both ends based on second-order theory

运用二阶理论对2端弹性约束压弯梁的稳定性进行了分析,通过求解其挠曲微分方程得到其变形及临界载荷的精确表达式,随后给出了方便工程应用的高精度实用近似计算式。推导了弹性约束简支压弯梁在各种横向载荷作用下的跨中最大弯矩的精确计算式,进而讨论了GB/T13752—1992《塔式起重机设计规范》中的非弹性约束压弯梁的最大弯矩近似计算公式对计算弹性约束简支压弯梁的跨中弯矩的适用性问题。通过分析推导证明:在加入了必要的修正项之后,规范中的最大弯矩近似计算式仍可用于弹性约束简支压弯梁的跨中弯矩的计算,从而为规范的补充修订提供了理论依据。

The paper analyzes stability of free beam with elastic constraints at both ends by means of second - order theory, and derives precise math expression for calculating critical load and deformation from deflection differential equations. It gives practical approximate calculating formula for engineering application, and derives precise formula for calcu- lating maximum bending moment of the free beam with elastic constraints while lateral force loaded at middle of beam span. Furthermore it discusses applicability of the approximate formulas for both calculating maximum bending moment of free beam with non - elastic constraints from GB/T 13752--1992 and calculating maximum bending moment of free beam with elastic constraints while lateral force loaded at middle of beam span. The analysis and derivation indicates that the formula from GB/T 13752--1992 can be applicable to bending moment calculation of free beam if adding revised items to it. It provides a theoretical basis for revising GB/T 13752--1992.