开口薄壁梁的扭转理论与应用

RESTRAINED TORSION THEORY OF OPEN THIN-WALLED BEAMS AND ITS APPLICATION

以Vlasov薄壁构件理论为基础,推导了开口薄壁构件一阶扭转理论.该理论考虑了翘曲剪应力对截面转角的影响,截面的转角分为自由翘曲转角和约束剪切转角,在约束扭转中,St.Venant扭矩仅仅与自由翘曲转角有关,而翘曲扭矩仅与约束剪切转角有关.利用半逆解方法求出了约束扭转中薄壁构件的St.Venant扭矩表达公式;依据能量方法,建立了约束剪切转角和翘曲扭矩之间的关系,并提出了翘曲剪切系数概念,给出了一阶扭转理论的微分方程.为了有效求解微分方程,给出了求解微分方程的初参数法方程和相应的影响函数矩阵;当St.Venant扭矩可以忽略时,得到与一阶弯曲理论(Timoshenko梁理论)相似的一阶扭转理论简化形式.最后利用算例证明了一阶扭转理论和简化理论的有效性.

Based on Vlasov＇s thin-walled beam theory, a first-order torsion theory of restrained torsion of open thin-walled beam is developed in consideration with the effects of shear deformation. It is assumed that the total rotation of a cross section is divided into a free warping rotation and a restrained shear rotation. In the restrained torsion, St. Venant torque is only related to the free warping rotation and the expression of St. Venant torque is derived by using a semi-inverse method. The torsion shear coefficient is derived by using the energy method. The governing equation of the restrained torsion theory is derived by using the deduced formulae. In order to solve the governing equation efficiently, the corresponding initial method is presented, and the influence function is obtained. When the St. Venant constant is negligible, an approximate analytical approach is obtained, and there exists an analogy between it and Timoshenko beam theory. To validate the new approach, an example is illustrated, and the results obtained from the current theory are compared with those of the existing theory, which demonstrate the efficiency of the current theory.