恒载效应对梁变形影响的数值分析法

The Numerical Analysis Method of Dead Loads Effect on Static Deformation of Beams

应用势能驻值原理,推导了梁考虑恒载效应的静力分析数值公式,得到了荷载影响刚度矩阵.分析了不同边界支撑条件下恒载对梁挠度的影响.计算结果表明:数值分析方法与解析解的结果吻合良好,具有较高的精度.同时由于采用了矩阵形式,不仅便于编制计算机程序,且有更广泛的适用性和灵活性,可更方便地用于各种不同的构造和边界条件的实际结构.

Based on the principle of resident potential energy, the numerical analysis expressions of static beams with the nonlinear effect of dead loads are derived and the element stiffness matrix including the nonlinear effect of dead loads is obtained. The nonlinear effects of dead loads on the deflection are analyzed by the numerical analysis method for both simply supported and fixed beam. It is found that the results are in good agreement with the analytical solutions, which shows that they have a high precision. The proposed method is applicable to practical structures under various conditions due to its advantages.