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

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.