考虑畸变效应的梁单元刚度矩阵应用

基于势能驻值原理和广义坐标法原理推导出考虑截面畸变效应的梁单元刚度矩阵.根据此梁单元刚度矩阵,编制了计算薄壁钢箱梁结构的有限元程序,且此程序可以考虑截面畸变效应和扭转效应.运用自编程序,分析横隔板间距对薄壁钢箱梁受力性能的影响.通过数值计算,得出布置横隔板对畸变正应力的影响最大,对弯曲正应力的影响很小.畸变荷载作用下,只有当横隔板布置间距小到一定数值时,薄壁箱梁的畸变正应力才会减小.最后,引入畸变翘曲影响系数γ,简化了薄壁箱形梁纵向正应力的计算方法.当横隔板布置间距L与薄壁箱梁横截面最大尺寸H的比值小于2时,畸变翘曲影响系数γ趋于1,表明薄壁箱形梁的畸变正应力趋于零,可以忽略畸变效应的影响.

Application of stiffness matrix of a beam element considering section distortion effect

According to the stationary principle of potential energy and the generalized coordinate method, a stiffness matrix of a beam element considering distortion effects is derived. Using the stiffness matrix of the beam element, a finite element program for computing thin-walled box steel beams is developed. And the program can take the section distortion and warping effects into account. The influences of diaphragm spacing on the mechanical behavior of thin-walled box beams are analyzed by the program. The numerical analysis shows that setting diaphragms have the greatest influence on the distortion normal stress, while there is very little influence on the bending normal stress. Only when the distance of adjacent diaphragms decreases to a certain value, will the distortion normal stress in the thin-walled box beam obviously reduce under the distortion load. Finally, a distortion-warping coefficient γ is introduced for simplifying the calculation of the longitudinal normal stress of thin-walled box beams. When the ratio of diaphragms adjacent space L to the maximum section dimension H is less than 2, the distortion-warping coefficient γ tends to one, which means that the distortion normal stress of the thin-walled box beam tends to zero, and the effect of the section distortion can be ignored.