钢-超高性能混凝土组合梁剪力滞分析的有限梁段法

在选定的剪力滞翘曲位移函数的基础上,钢-超高性能混凝土(UHPC)组合梁剪力滞控制微分方程以及相应边界条件可基于能量变分法推导得到。将钢-UHPC组合梁离散为若干梁段,通过剪力滞控制微分方程的常数求解,可得到用于求解钢-UHPC梁段单元剪力滞效应的系数矩阵和广义荷载列阵,从而建立梁段单元各结点具有2个剪力滞未知量的有限梁段法。以余弦函数作为钢-UHPC组合梁的翘曲位移函数,运用有限梁段法研究以矮肋式UHPC桥面板作为桥面系的轻型组合梁的剪力滞效应。为了验证有限梁段法求解等截面钢-UHPC组合梁剪力滞效应的正确性,比较不同边界条件下钢-UHPC组合梁在施加均布荷载和集中荷载时的剪力滞系数与由变分法得到的组合梁剪力滞一般解,吻合度较好。应用于钢-UHPC组合梁剪力滞分析的有限梁段法简单实用,计算公式简洁,也可以将其应用于变截面钢-UHPC组合梁的剪力滞效应的求解。

Finite segment method of shear lag analysis for steel-UHPC composite beams

Based on the selected warping displacement function of shear lag and the energy variational principle,the governing differential equations for shear lag of the steel-UHPC composite beam and the corresponding boundary conditions were derived.After the beam segment was divided into several elements,the formulations of shear lag coefficient matrix and generalized load vector for the finite segment method including 2 degrees of freedom of the shear lag at each node,which was corresponding to beam element for analyzing shear lag effect,were established by the solution of the constants of the governing differential equations.In the present study,the cosine function was chosen as the warping displacement function to study the shear lag effect of the proposed light-weight composite beam composed of the short-ribbed UHPC slab in the bridge deck system.The shear lag effect was analyzed for both simply supported and cantilever composite beam under uniform load and concentrated load and the results obtained from the finite segment procedure accurately agree with the closed-form solutions from the variational analysis method.The effectiveness and reliability of the present method was verified.This method is simple and practical,so it also can be easily applied to calculation for the shear lag effect of the steel-UHPC composite beam with varying depths.