复杂荷载作用下单向受弯简支钢梁的弹性临界弯矩

为了研究单向受弯简支钢梁的弹性弯扭屈曲理论，尤其是复杂荷载作用下的临界弯矩计算，针对端弯矩和任意集中荷载共同作用下的简支梁，首先给出了能够模拟复杂变形并满足边界条件的侧向弯曲变形函数和扭转变形函数，以及任意荷载下的构件弯矩表达式，然后采用Rayleigh-Ritz法推导出了简支梁临界弯矩及其参数的通用计算公式，临界弯矩计算公式与传统公式在形式上完全相同，便于应用。算例分析表明：该通用公式不仅适用于端弯矩、任意集中荷载、满跨均布荷载单独作用下的简支梁，也适用于端弯矩和任意集中荷载共同作用下的简支梁，具有广泛的适用性，且精度较高。

Elastic critical moment of simply-supported steel beams under unidirectional bending with complex loads

In order to study the elastic flexural-torsional buckling theory of simply-supported steel beams under unidirectional bending, especially the calculation method of critical moment under complex loads, focusing on the simply-supported beams under combined loads with end moment and any concentrated loads, the lateral bending and torsional deformation function which can simulate the complex deformation and satisfy the boundary condition were given firstly. The moment expression of beams under any loads was also presented. Then the general formula of the critical moment and its parameters of simply-supported beams were derived by Rayleigh-Ritz method. The formula of critical moment is quite similar to that of the traditional formula, and is convenient to use. A series of examples show that the general formula applies not only to simply-supported beams only under the end moment, or any concentrated loads, or full-span uniformly distributed load, but also to beams under the combined loads with end moment and any concentrated loads. It has a wide range of application, and the accuracy is very high.