基于选取不同剪力滞广义位移的薄壁箱梁剪力滞效应研究
Analysis on shear-lag effect of box girders based on different shear-lag generalized displacement

基于箱梁顶板、悬臂板、底板具有不同的翘曲程度,考虑各个翼板应选取不同的最大剪切转角差为剪力滞广义位移。以顶板、悬臂板和底板采用不同的最大剪切转角差和相同的最大剪切转角差2种情况,应用能量变分原理分别推导出单室箱梁受竖向对称荷载下的剪力滞效应微分方程,结合边界条件导出相应的闭合解。针对典型的简支箱梁为算例,利用数值方法和本文解析解方法,研究了满跨均布力和跨中集中力作用下跨中截面的测点应力解,对斜腹板箱梁算例而言,采用不同最大剪切转角差获得的纵向应力解和高阶样条法计算的纵向应力解的误差比较小,基本在4%以内,验证了解析解具有良好的精度;对直腹板箱梁而言,取不同最大剪切转角差的应力解析解更贴近数值解,误差比基本在6%以内,研究表明:各个翼板取不同最大剪切转角差的假设是正确合理的,能够精确的反映剪力滞规律。
It is fourd that the box girder roof, the cantilever plate and the bottom plate have different levels of warping, and each wing should select different maximum shear angle difference as the shear lag of generalized displacement. All wings utilization of different maximum shear angle difference and same maximum shear angle difference as shear-lag generalized displacement, and energy variational principle is applied to deduce respectively shear-lag differential equations of single-cell box girder under the vertical symmetrical load. Closed solutions are also derived by the use of boundary conditious. A typical example of simple box girders,using the numerical method and the analytic solution method in this paper isused to study the stress solution of measuring point in middle span under the uniform force and concentrated force.For inclined web box girder,absolute error rate of using different maximum shear angle difference to obtain the longitudinal stress solution and high step spline solution is very small,about within 4%, verify the analytical solution has good accuracy;For direct web box girder,the stress solution of the wings selection of different maximum shear angle difference is closer to analytical solution, the error ratio is lower than 6%. Research shows that: the assumption of each wing take different maximum shear angle difference as shear-lag generalized displacement is correct and reasonable, can accurately reflect the law of shear-lag