拱结构高跨比的优化设计

OPTIMAL DESIGN OF THE RATIO OF HEIGHT TO SPAN OF ARCH

拱结构设计中,在保证强度的基础上,拱的高跨比应取何值,才能使设计出的拱用料最省,造价最低?对这个问题,至今理论上没有明确的结论。现有的设计规范虽给出了拱的高跨比的一些推荐值,但对高跨比的最佳取值却没提出建议。本文对这个问题提出了研究,在合理拱轴线的基础上,首先分析、建立优化设计的数学模型,然后采用数值方法进行求解,最后导出了竖向均布荷载作用下的最优高跨比,并给出了高跨比的最优范围,供有关结构设计人员参考。

In design of arch,on the basis of guaranteeing strength of arch,there isn＇t clear conclusion that how to choose depth-span ratio can make the cost lowest. Although some value of depth-span ratio of the arch has been recommended in present design standard,the suggestion for the optimal value of depth-span ratio hasn＇t been given. In this paper,this question has been studied,on the basis of reasonable axis of arch,the mathematical model of optimal design has been established,and solved in a approximate method. Lastly,the optimal depth-span ratio has been derived,which affords reference to structure engineers.