In-Plane Elastic-Plastic Stability Design of Pin-Ended Circular Spoke Arches

Due to the pulling effect of cables to the arch rib, the stability problem of spoke arches is more complex than that of steel arches, which is influenced by arch rib slenderness ratio, rise-to-span ratio, cable disk height, cable number, cable area and the prestressing in cables. At present, the studies on spoke arches are limited to the qualitative analysis of elastic stability, while the elasto-plastic stability and design method are lacking. By using finite element analyses, the paper dealt with the in-plane elasto-plastic buckling performance of pin-ended circular spoke arches under full-span and half-span uniformly distributed loading, and proposed the optimized parameter ranges for design and the calculation formulas for the ultimate buckling strength. Firstly, the inerative method of applying intial strain was aclopted, the prestressing in spoke arches was applied by stretching the two cables connected to the arch ends, and the effects of prestressing on the inner forces, deformation and ultimate buckling strength were investigated. Next, the influence of a single parameter on the buckling strength was analyzed individually, including the slenderness ratio, rise-to-span ratio, cable number and cable area ratio. According to the load-carrying efficiency, the optimized range of the parameters was suggested. Then the response surface method was used to create 30 representative examples of spoke arches, and the buckling strength ratios to the corresponding pure steel arches were obtained. With 4 key parameters namely the rise-to-span ratio, slenderness ratio, arch-to-cable area ratio and the number of cables, the fitting equations for in-plane buckling strength of spoke arches were established and the accuracy and applicability were verified. The results showed that:1) The presence of prestressing had little effect on the ultimate load-carrying capacity of the spoke arch. In actual engineering, the spoke arch could be designed without prestressing, or the prestressing could be applied according to the requirement of the arch thrust adjustment. 2) In design, the optimal value range of cable disk height was 1/2 of the sagittal height, number of cable was 8~20, arch-to-cable area ratio was 10~30, rise-to-span ratio was 0. 20~0. 50, which covered the common application range. 3) From the results of the response surface method, the influence of the rise-span ratio on the buckling strength was the most significant, followed by the slenderness ratio, while the influence of the arch cable area ratio and the number of cables was relatively small. 4) The proposed equations for the in-plane elasto-plastic buckling strength of spoke arches had the accuracy within 5%, the simplified formula was conservative, most of the errors were within 15%, and it was suitable for different steel strength, which could be used to safely predict the buckling strength of spoke arches in practical design.