周平槐，张群力，杨学林

（浙江省建筑设计研究院， 杭州 310006）

 

［摘要］建筑中经常出现曲线型旋转楼梯，其内力分析较为复杂，国内少见这种楼梯的计算理论。结合实际工程，利用微分几何等数学方法，建立了椭圆旋转楼梯中心线为椭圆螺旋线、楼梯内外边线则为中心线主法矢上的等距线的数学模型的空间曲梁模型。基于楼梯的曲梁简化计算模型，同时选用了接近于实际作用的荷载等效作用曲线，推导出在单位力和均布荷载作用下梯梁上任一点的内力计算公式,并与有限元分析结果作了比较。分析表明，空间曲梁模型能较好地描述椭圆旋转楼梯的几何性质，公式推导和有限元分析所得的内力十分接近。其他旋转形式的楼梯，也可参考上述方法建立与其形状一致的数学模型以及内力分析，为设计提供依据。

［关键词］椭圆旋转楼梯;空间曲梁;椭圆螺旋线;等距线;微分几何

中图分类号：TU 323-3文献标识码：A文章编号：1002-848X(2012)08-0137-05

 

Zhou Pinghuai, Zhang Qunli, Yang Xuelin

(Zhejiang Province Institute of Architectural Design and Research, Hangzhou 310006, China)

 

Abstract: There are many curve spiral stairs which inner forces are hard to analyze in buildings, and theories and methods of these stairs are rare domestically. Under the background of the project, the spatial curve beam differential model is established by mathematical method such as differential geometry and so on, which the center curve as elliptical helix, and the inside and outside edges as offset curves on the main normal vector of the center curve. The curve beam is modeled simply. After the equal load-curve is adopted, calculation formulas of inner forces under unit load and under vertical uniform load are obtained. Compared with the results of finite element methods(FEM), it shows that mathematical modeling is in agreement with elliptical spiral stairs, the inner forces from formulations and FEM are similar. It can be reference for spiral stairs to establish the mathematical model and then analyze inner forces for-design these stairs.

Keywords: elliptical spiral stair;spatial curve beam;elliptical helix;offset curve;differential geometry

作者简介：周平槐，工程师，Email: anji18@126.om。

 

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