地基上混凝土梁的温度应力

Thermal stresses in concrete beams on elastic foundations

地基上混凝土梁常需控制温度应力以避免裂缝。本文首先简要介绍马斯洛夫应力解,然后用弹性力学方法给出地基对梁的温度变形的抗力系数,从而得到地基上梁的温度应力的一套完整解法。根据地基弹性模量及梁的长高比,对梁所受到的地基约束作用分为4类:(a)弯曲变形完全约束,水平变形部分约束;(b)弯曲变形完全约束,水平变形无约束;(c)弯曲变形部分约束,水平变形无约束;(d)水平变形和弯曲变形均无约束。对于每类约束情况分别给出了简洁的温度应力计算公式,使计算得到简化。给出了混凝土弹性模量和温度随龄期而变化时的计算方法。指出了目前工程界采用的地基上梁温度应力计算方法的不足之处。

It is necessary to control thermal stresses and prevent cracks in concrete beams on elastic foundations. The solutions proposed by Maslof for thermal stresses in beams on Winkler foundation have not found applications in engineering, because there are no formulas for the coefficients of foundation restraint involved in the solutions. In this paper, formulas for coefficient of foundation restraint are obtained by using the theory of elasticity. The thermal stresses are categorized into four types by referring to the relative stiffness of beam and foundation： （a） full restraint on bending and partial restraint on horizontal displacement; （b） full restraint on bending and no restraint on horizontal displacement; （c） partial restraint on bending and no restraint on horizontal displacement; （d） no restraint on both bending and horizontal displacement. Practical, simple yet accurate formulas are provided for each type of beams.