宽翼缘T梁温差应力的弹性力学解法

ELASTICITY SOLUTION TO TEMPERATURE DIFFERENCE STRESS IN TEE BEAM WITH WIDE FLANGE

为了充分反映宽翼缘梁的温差自应力分布特点,克服按梁理论计算温差自应力时的不足,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差应力.根据翼缘板与腹板连接处的变形协调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,导出翼缘板与腹板的温差应力及位移的解析式.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.

In order to obtain the distribution of the temperature self-stress in beams with wide flanges and improve the conventional method of self-stress analysis,a refined analytical method is presented based on elasticity.The flange and web plates are considered to be in a state of plane stress under temperature difference conditions.The condition of the deformation compatibility and equilibrium at the connection of the flange and web plates is used to establish additional equations by which the constants of integration in the Airy stress function are evaluated.The analytical expression of the temperature difference stress and displacement in the flange and web plates is derived.Numerical results of a tee beam with wide flanges show that the self-stress in the flange plate under temperature difference with respect to web plate 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 distribution feature of the temperature self-stress is not explained by the conventional analytical method based on the beam theory.