两铰圆弧车辐钢拱平面内弹塑性稳定设计

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

车辐式钢拱的稳定问题相对纯拱来说更为复杂,除长细比、矢跨比之外,还受索盘高度、拉索数量、拉索面积及预应力水平的影响。目前钢拱平面内稳定性及承载力设计方法已经成熟,但对车辐拱的研究仅限于弹性稳定性能的定性分析,尚未有弹塑性稳定承载力的设计计算方法,导致设计人员在初步设计时对于车辐拱各几何参数的取值以及稳定承载力的估算无章可循。针对工程中常见的两铰圆弧车辐拱,采用有限元参数分析,深入研究了其在全跨和半跨均布荷载下的平面内弹塑性稳定性能和主要参数影响规律,提出了关键参数的优化取值范围,并建立了稳定承载力的计算式。首先在有限元模型中采用施加初应变的迭代法,张拉连接索盘和拱脚的两根拉索使其达到目标张拉力,为车辐拱施加不同水平预应力,考察预应力对车辐拱的内力、变形和极限承载力的影响。随后,研究了主要结构参数如长细比、矢跨比、拉索数量、拱索面积比等单因素变化对车辐拱平面内弹塑性稳定承载性能的影响,以稳定承载力效率为标准,提出了各参数的优化设计取值范围,涵盖了工程常用范围。在参数建议取值范围的基础上,采用响应面法设计了30组代表性算例,选择拱索面积比、拉索数量、矢跨比、长细比为4个关键考察因素,以相同条件下对应纯拱的弹塑性稳定承载力为基准值,建立了其平面内弹塑性稳定承载力计算式,并对其精度和适用性进行了分析验证。结果表明:1)预应力的存在对车辐拱的受力性能影响不大,实际施工中拉索可不施加预应力而以张紧为宜,或根据调整拱脚推力的需要进行确定;2)设计中建议索盘高度为1/2矢高,拉索数量为8~20根,拱索面积比为10~30,矢跨比为0.20~0.50,各参数的优化取值范围涵盖了工程常用范围;3)从方差分析的结果来看,矢跨比对平面内弹塑性稳定承载力的影响最为显著,长细比次之,而拱索面积比和拉索数量的影响相对较小;4)响应面法给出的精确算式误差小于5%,简化算式偏于保守,大多数误差在15%之内,且对不同强度的钢材均适用,可以安全地估计车辐拱的平面内弹塑性稳定承载力,供初步设计时采用。

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.