薄壁构件弯扭失稳的一般理论

在薄壁构件的弯扭失稳问题上近20年以来存在着传统的和较新的两种不同的理论,这两种理论的并存使得一些国家的规范和一些著作出现不一致,例如我国的(GB50017—2003)和N.S.Trahair的著作犤17犦仍然采用传统理论的结果,而(GB50018—2003)、ISO的钢结构材料标准和美国的金属结构稳定设计解说却采用较新理论的结果。作者发现被忽视的横向正应力也是影响薄壁构件稳定的重要因素。本文在考虑非线性横向应变能的基础上,导出了薄壁构件的总势能方程。从板的理论出发,全面考虑微元上各种应力以及外荷载的影响,用假想荷载法导出了薄壁构件的弯扭失稳平衡微分方程。这组平衡微分方程和本文提出能量法的是一致的,这进一步证实了本文提出理论的正确性。

A general theory about flexural-torsional buckling of thin-walled members

There exist two different theories about the flexural torsional instability of the thin walled members, and very different results of beam elastic buckling are obtained from them. In this paper, a new theory is presented to solve the inconsistency between the two different theories. In this new theory, the transverse stress is introduced as an important factor for member stability in addition to the longitudinal and shear stresses and strains already considered in existing theories. Two classical methods, the energy method and the fictitious load method, are used to derive the general theory respectively. In the energy method, the nonlinear potential energy of the external loads is excluded according to the variational principles. By use of the fictious load method, the equilibrium differential equation is derived in consideration of the effects of all stresses and external loads acting on minute element. The same set of equilibrium differential equations is obtained using these two methods, which confirmed with each other.