用有限积分改进混凝土构件的挠度计算

TO IMPROVE CALCULATION OF DEFLECTION FOR CONCRETE STRUCTURAL MEMBER BY FINITE INTEGRAL METHOD

我国混凝土结构设计规范给出的混凝土构件挠度计算方法是一种近似方法,其他一些国家的混凝土结构规范或者标准也给出类似的方法。这类方法的研究路线有两阶段,一是依据弯矩得到曲率(x),二是使用力学办法由曲率得到挠度。使用力学办法由曲率得到挠度是不合理的。由曲率计算挠度已经是几何问题,应该使用积分的方法。因此,基于有限积分法给出的挠度z(x)与挠度的一、二阶导数间的数值关系,通过矩阵运算推导得到了挠曲矩阵,通过引入转换式(x)=-z″(x)得到了曲率挠度关系式,就几种常见边界条件讨论了具体的曲率挠度关系,提出了混凝土构件挠度计算的公式和方法。计算表明,引用有限积分法改进混凝土构件挠度计算是简便的,精度明显提高。

The calculation of deflection for concrete structural member that was put forward in ＂Code for Design of Concrete Structures＂ was an approximate method.Similar methods were also put forward in some foreign codes or standards for concrete structures.The mentality for this kind of approximation calculation consisted of two steps.Firstly,curvature was calculated with bending moment.Secondly,deflection was calculated by curvature with the help of mechanics.It was unreasonable to calculate deflection by curvature with the help of mechanics.Essentially,the calculation of deflection by curvature was a geometric problem,and integral method should be used to resolve this problem.Based on the numerical equation between the deflection and its derivative or the relation between the derivatwe and the second derivative of deflection in finite integral solution,deflection-curvature matrix was derived by matrix operation,and the curvature-deflection equation was derived with functional relation （x）=-z″（x）.The curvature-deflection equations for some kinds of common boundary conditions were discussed.The methods and formulae of deflection calculation for concrete structural member were put forward.Calculation showed that it was convenient to improve the approximation calculation of deflection for concrete element by finite integral method.The accuracy of calculation was greatly improved.