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在辛弹性力学理论的基础上,将简支T梁的翼板简化为平面应力板,推导了简支T梁在满跨均布荷载与线性荷载作用下翼板部分的圣维南解析解,得到了闭合的关于梁长、梁宽及泊松比的多项式形式的剪力滞系数解析解表达式。以一宽翼板简支T梁为例,分别用推导出的剪力滞系数公式和有限元软件对此梁剪力滞系数进行了计算对比,验证了所推导公式的正确性。用该方法求解和验算简支T梁桥的剪力滞系数十分方便、快捷。
Based on the symplectic theory of elasticity, the wing of a simply supported T-beam is simplified as a plane stress plate, and the Saint-Venant analytical solution of the wing part of a simply supported T-beam under uniform span load and linear load is deduced. The closed analytical expressions of shear lag coefficients in the form of polynomials of beam length, beam width and Poisson’s ratio are obtained. Taking a wide-beam simple-supported T-beam as an example, the shear lag coefficient and the lag shear lag coefficient of the beam are calculated respectively by deducing the shear lag coefficient and the finite element software, which verifies the correctness of the formula. Using this method to solve and verify the shear lag coefficient of simply supported T-beam bridge is very convenient and fast.