基于变分原理的改进型波形钢腹板箱梁的挠度计算

Deflection Calculation of Improved Corrugated Steel Web Box Girder Based on Variational Principle

针对钢底板-波形钢腹板箱梁的挠度计算方法进行研究,将组合截面的广义位移细分为顶板、翼缘和底板,以精确模拟组合截面的纵向位移特征。同时,引入两种材料模量参数进行修正,以余弦能量变分原理,建立广义位移矩阵方程组,并求解。通过以上修正计算,得到结论如下:修正解≥有限元解≥试验值≥未修正解≥初等梁理论解。参照有限元值对比后,修正解的偏差率为(1.2~1.5)%,偏安全。未修正解为(-4.3~-9.3)%,初等梁理论解为(-7.4~-14.5)%。表明除了剪切变形外,有效面积减小以及钢、砼的材料模量差异对主梁挠曲有影响。

A study was conducted on the deflection calculation method of steel bottom plate-corrugated steel web box beams.The generalized displacement of the composite section was subdivided into top plate,flange,and bottom plate to accurately simulate the longitudinal displacement characteristics of the composite section.Two types of material modulus parameters for correction were introduced,while a matrix equation system for generalized displacement was established based on the energy-variational principle of cosine,so as to obtain the solution.Through the above correction calculations,a conclusion could be made as follows:Corrected solution≥Finite element solution≥Experimental value≥Uncorrected solution≥Elementary beam theoretical solution.After comparing with the finite element values,the deviation rate of the corrected solution is(1.2~1.5)%,which has been proved to be relatively safe.The uncorrected solution is(-4.3~-9.3)%,and the theoretical solution for elementary beams is(-7.4~-14.5)%.This indicates that apart from shear deformation,the reduction of effective area and the difference in material modulus between steel and concrete have an impact on the deflection of the main beam.