圆弧钢拱破坏荷载的理论计算

拱结构经常在桥梁、屋顶等大跨结构中使用。尽管这些结构构件容易出现各种失稳现象,但其中短粗拱或细长拱的侧向水平连接失效是由塑性破坏而非平面内或平面外屈曲引起的。通过极限荷载方法分析塑性破坏荷载,以最大限度地发挥截面的塑性能力和出现塑性铰后的内力重分布能力。描述了竖向荷载下圆弧钢拱塑性破坏荷载的计算方法。使用塑性力学中的上限法、下限法和位移协调法来计算塑性破坏荷载,压力致使拱截面的容许塑性力矩减小。确定外荷载与容许塑性力矩之间的非线性关系后,使用迭代法得到塑性破坏荷载。利用有限元方法对分析结果进行检验,二者的分析结果相吻合。最后基于迭代法绘制设计图。

A Theoretical Method for Calculating the Collapse Load of Steel Circular Arches

Arches are frequently used in large span structures like bridges and roofs. Although these structural elements may be prone to various instability phenomena, stocky arches or slender arches with sufficient lateral bracing fail due to plastic collapse instead of in-plane buckling or out-of-plane buckling. The plastic collapse load can be obtained through limit load analyses, making full use of the plastic capacity of the cross-section and possible redistribution of internal forces after formation of the first hinge. This paper describes an analytical approach to obtain the plastic collapse load of circular steel arches subjected to vertical loading. The upper-bound theorem, lower-bound theorem and kinematic admissibility rules of plastic theory were employed to arrive at a plastic collapse load. Reduction of the full plastic moment capacity of the arch cross-section due to the presence of compressive forces was accounted for. An iterative procedure was found necessary to obtain the plastic collapse load since a non-linear relationship was observed between the acting loads and the reduced plastic moment capacity. Finite element analyses were performed to verify analytical results. Good agreement between the suggested iterative procedure and finite element computations was found. Design graphs were developed based on the iterative procedure.