箱梁剪力滞翘曲位移函数理论推导

Theoretical derivation of shear lag warping displacement function of box girder

为研究箱梁合理的剪力滞翘曲位移函数,根据箱梁翼缘板纵向受力和变形特性,将翼缘板视为纵向平行的具有一定刚度的弹簧所连接的弹性体,建立翼缘板弹簧模型,基于能量变分原理建立了翼缘板平衡微分方程,推导出纵向位移函数为双曲函数与三角函数的线性组合。通过分析确定翘曲位移函数分别为双曲正弦函数、双曲余弦函数、正弦函数3种单一形式,并将3种函数形式代入剪力滞变分方程中,得到3种纵向位移函数的弯曲正应力方程。为验证理论推导的3种函数的合理性,将3种函数形式计算得到的翼缘板正应力与实测值、三次抛物线形式计算值、实体有限元计算值进行比较,并从函数形态分析了不同函数形式对翼缘板应力分布的影响。结果表明:文中方法推导出的函数形式中正弦函数计算值与实测值吻合度较高,与实体有限元计算值也基本吻合。另外,函数的二阶导数与翼缘板应力分布存在正相关性。

In order to study the reasonable warping displacement function of shear lag of box girder,plate flange is regarded in this paper as an elastic body connected by a spring with certain stiffness in longitudinal parallel and a flange plate spring model is established according to the longitudinal force and deformation characteristics of flange plate of box girder.And based on energy variational principle,flange plate equilibrium differential equation is established,deducing that the longitudinal displacement function is a linear combination of hyperbolic function and triangular function.The warping displacement function is determined as three single forms:hyperbolic sinusoidal function,hyperbolic cosine function and sinusoidal function.By substituting three function forms into the shear lag variational equation,the bending normal stress equations of the three longitudinal displacement functions are obtained.In order to verify the rationality of the three functions derived from the theory,the normal stress of flange plate calculated by the three functions is compared with the measured value,the calculated value in the form of cubic parabola,and the calculated value of solid finite element.The effect of different function forms on the stress distribution of flange plate is analyzed from the perspective of the function property.The results show that the calculated value of sinusoidal function is in good agreement with the measured value and the calculated value of solid finite element method.In addition,the second derivative of the function is positively correlated with the stress distribution of the flange plate.