现浇混凝土空心板的正交各向异性和等效各向同性板计算方法

通过分析得到了现浇混凝土空心板正交各向异性主刚度存在着D3=D1D2~(1/2)的关系;从正交各向异性板挠曲面的偏微分方程出发,保持一个主方向尺寸不变x1=x,将另一主方向的尺寸做线性缩放y1=k-14y,并保持弹性模量与第一主方向相同E=E1,泊松比μ=μ1μ2~(1/2),将原来的正交各向异性板等效为一块各向同性板,通过分析得到:各向同性板任意点的挠度就是原正交各向异性板对应点的挠度,各对应点内力存在简单的对应关系:Mx=Mx1、My=k1/2My1、Mxy=k1/4Mx1y1。最后,通过算例验证了该方法的正确性。

ORTHOTROPIC CHARACTERS OF A CAST-IN-SITU CONCRETE HOLLOW PLATE AND THE CALCULATION METHOD OF AN EQUIVALENT ISOTROPIC PLATE

The orthotropic character of D_3=D_1D_2~(1/2) of a cast-in-situ concrete hollow slab is deduced.Based on the differential equation of the deformed surface of the orthotropic plate,one principal direction size is kept invariably,then another principal direction size is transformed linearly,maintains elasticity coefficient is kept the same as that of the first principal direction E=E_1,Poisson ratio μ=μ_1μ_2~(1/2),thus the original orthogonal plate can be equivalent to an isotropic plate.Results are obtained through analysis: the deflection of the equivalent isotropic plate is the same as that of the original orthotropic plate at the corresponding point,whose internal forces have the simple relations M_x=M_(x1),M_y=k~(1/2)M_(y1) and M_(xy)=k~(1/4)M_(x1y1).