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力学与实践 ›› 2010, Vol. 32 ›› Issue (2): 60-64.doi: 10.6052/1000-0879-2009-172

• 应用研究 • 上一篇    下一篇

宽翼缘梁非线性温差自应力级数解

张元海   

  1. 兰州交通大学
  • 收稿日期:2009-04-20 修回日期:2009-06-10 出版日期:2010-04-08 发布日期:2010-04-08

Series solution for the self-stresses in beams with wide flanges due to nonlinear thermal differential

  • Received:2009-04-20 Revised:2009-06-10 Online:2010-04-08 Published:2010-04-08

摘要: 为了客观反映宽翼缘梁在非线性温差作用下的自应力分布特点,克服按梁理论计算温度自应力时的不足,本文从弹性力学的分析方法入手,按平面应力状态分析翼缘板和腹板的温度应力。通过翼缘板与腹板连接处的变形协调条件及平衡条件建立补充方程,求解艾瑞应力函数中的积分常数,推导了翼缘板与腹板的纵、横向正应力、剪应力及位移分量解析式。导出的翼缘板纵向正应力公式可自动考虑宽翼缘梁沿横截面宽度自应力不均匀分布的特点。对一宽翼缘T梁的计算表明,当翼缘板相对于腹板发生温差变化时,沿其宽度的纵向温度自应力分布很不均匀,在翼缘板根部自应力较大而在悬臂端则显著减小。按通常基于梁理论的温度自应力计算方法,无法反映这种应力分布规律。

关键词: 非线性温差, 温度应力, 平面应力问题, 级数解, 宽翼缘梁, 应力函数, 自应力

Abstract: In order to reveal fully the characteristic of thermal self-stress distribution in beams with wide flange under nonlinear thermal differential and improve the currently used thermal self-stress analysis method, a refined analytical method is presented which is based on the mechanics of elasticity. The flange and web plates are considered to be in a state of plane stress under nonlinear thermal differential. The conditions of deformation compatibility and equilibrium at the connection of flange and web plates are used to establish additional equations by which the constants of integration in Airy stress function can be evaluated. The analytical expressions of stresses and displacements in flange and web plates are derived. In the normal stress formula of flange, non-uniform distribution of thermal differential self-stress is taken into account automatically. Numerical results of a tee beam with wide flange show that, the self-stress in flange plate under thermal differential is distributed very non-uniformly along its width. Greater compression stress occurs near the fixed edge while much smaller stress at the free edge in the flange plate. This characteristic of thermal self-stress can’t be revealed by using the common analytical method.

Key words: nonlinear thermal differential, thermal stress, plane stress problem, series solution, beams with wide flange, stress function, self-stress