纤维增强聚合物布加固木梁的非线性弯曲分析

Nonlinear Bending Analysis of Timber Beam Strengthened with Fiber Reinforced Polymer

考虑纤维增强聚合物(fiber reinforced polymer,FRP)布加固层拉伸与压缩时的不同弹性模量以及木梁非线性弯曲的二阶变形和轴向拉伸效应,利用摄动法研究均布横向荷载作用下简支FRP布加固木梁的非线性弯曲问题,得到加固木梁的挠度和弯矩等渐近解析表达式,并给出数值分析.结果表明:FRP加固木梁非线性弯曲的挠度和弯矩小于线性弯曲的挠度和弯矩,并且当无量纲荷载小于5时,FRP加固木梁非线性弯曲和线性弯曲的挠度和弯矩几乎相等,没有明显差别;但随着载荷的增大,二者相差逐渐增大;当无量纲载荷大于20时,非线性弯曲效应十分显著,必须选用FRP加固木梁的非线性弯曲模型进行分析.

Taking into account the effects of bi-modulus for tension and compression of fiber reinforced polymer （FRP） layers and second order deformation and axial tension of the nonlinear bending of a timber beam, nonlinear bending of simply-supported FRP-strengthened timber beams under a uniform transversal load is investigated with the perturbation method. Asymptotic expressions of deflection and bending moments of the FRP-strengthened timber beam are obtained, and numerical results are presented. It is revealed that deflections and bending moments of nonlinear bending of the FRP-strengthened timber beam are smaller than those of linear bending. When the dimensionless load is less than 5, deflections and bending moments of nonlinear and linear bending are almost equal to each others, and there are no distinct differences. The difference between them increases when the load is increased. When the dimensionless load is greater than 20, the effect of nonlinear bending is remarkable, and a model of nonlinear bending of the FRP-strengthened timber beam should be used.