任意复杂截面梁的扭转中心

TORSIONAL CENTER OF BEAMS OF ARBITRARY COMPLEX CROSS-SECTION

为了计算任意复杂非圆截面梁横截面扭转中心的位置,用节线法将其约束受扭后所有横截面面外变形的形状用一族包含节线未知函数的曲面表示,建立梁约束受扭时的控制方程后,再用常微分方程求解器分别求出单纯扭矩与横向载荷单独作用时节线未知函数的数值解,最后用刚度等效原理导出复杂截面梁横截面扭转中心的位置。算例计算结果表明:该方法是合理的、有效的,是计算任意复杂非圆截面梁横截面扭转中心位置的可靠方法。

In order to determine the position of the torsional center of a beam of arbitrary complex non-circular section,the shape of all the out-of-plane deformation of the beam of non-circular section caused by non-uniform torsion is expressed by the nodal-line method as a family of surfaces containing unknown functions of the nodal lines.After establishing the governing equations of the beam caused by its non-uniform torsion,the numerical solutions of these unknown functions are obtained by using an ODE(ordinary differential equation)solver for a torque and a transverse load separately.Finally,the position of the torsional center of the beam of a complex cross section is derived by using the principle of stiffness equivalence.The computational results of examples show that the method is reliable for computing the torsional center position of a beam of arbitrary complex non-circular section.