基于Timoshenko梁的锚索框格结构内力与变形解析方法

Analytical Calculation Method of Internal Force and Deformation of Timoshenko Beam Suitable for Anchor Cable Frame Structure

预应力锚索框格梁广泛应用于公路岩土边坡加固。以往求解框格梁内力一般为倒梁法和弹性地基梁法,采用的梁模型多为Euler-Bernoulli梁,基本未考虑剪切变形引起梁的附加挠度以及梁体配筋对内力变形计算的影响。通过理论推导,得到了在Winkler弹性地基上于承受多处分布荷载的Timoshenko梁内布置拉、压双层钢筋时的内力与变形解析解,选取工程实例对Timoshenko梁解析解、Euler-Bernoulli梁解析解以及有限元数值仿真计算的内力与变形值进行对比,3种方法得到的内力与变形分布基本一致。Timoshenko梁解析解与数值仿真结果更为接近,Euler-Bernoulli梁解析解计算的梁体负弯矩及竖向变形值与其他方法存在一定差异。对比结果证明,提出的Timoshenko梁解析解在一定程度上提高了计算精度,计算方法较合理。

Prestressed anchor cable frame beam is widely used in strengthening projects of slopes.Generally in the past,the internal force of frame beam is solved by inverted beam method and elastic foundation beam method,and Euler-Bernoulli beam model is often used,which does not consider the additional deflection of beam caused by shear deformation and the influence of beam reinforcement on the calculation of internal force and deformation.In this paper,the analytical solution of Timoshenko beam with tension and compression double-layer reinforcement on Winkler elastic foundation subjected to multiple distributed loads is derived.Practice in projects are selected to compare the internal force and deformation calculated by Timoshenko beam,Euler Bernoulli beam analytical solution and finite element numerical simulation.The distribution of the internal force and deformation obtained by the three methods are basically the same,while the results of Timoshenko beam are closer to numerical results.The negative bending moment and vertical deformation calculated by Euler Bernoulli beam analytical solution are different from other methods.The comparison results show that the analytical solution of Timoshenko beam proposed in this paper can improve the calculation accuracy,and the rationality of the method is verified.