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周平槐，張群力，楊學(xué)林

（浙江省建筑設(shè)計(jì)研究院， 杭州 310006）

 

［摘要］建筑中經(jīng)常出現(xiàn)曲線型旋轉(zhuǎn)樓梯，其內(nèi)力分析較為復(fù)雜，國(guó)內(nèi)少見(jiàn)這種樓梯的計(jì)算理論。結(jié)合實(shí)際工程，利用微分幾何等數(shù)學(xué)方法，建立了橢圓旋轉(zhuǎn)樓梯中心線為橢圓螺旋線、樓梯內(nèi)外邊線則為中心線主法矢上的等距線的數(shù)學(xué)模型的空間曲梁模型?；跇翘莸那汉?jiǎn)化計(jì)算模型，同時(shí)選用了接近于實(shí)際作用的荷載等效作用曲線，推導(dǎo)出在單位力和均布荷載作用下梯梁上任一點(diǎn)的內(nèi)力計(jì)算公式,并與有限元分析結(jié)果作了比較。分析表明，空間曲梁模型能較好地描述橢圓旋轉(zhuǎn)樓梯的幾何性質(zhì)，公式推導(dǎo)和有限元分析所得的內(nèi)力十分接近。其他旋轉(zhuǎn)形式的樓梯，也可參考上述方法建立與其形狀一致的數(shù)學(xué)模型以及內(nèi)力分析，為設(shè)計(jì)提供依據(jù)。

［關(guān)鍵詞］橢圓旋轉(zhuǎn)樓梯;空間曲梁;橢圓螺旋線;等距線;微分幾何

中圖分類(lèi)號(hào)：TU 323-3文獻(xiàn)標(biāo)識(shí)碼：A文章編號(hào)：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

作者簡(jiǎn)介：周平槐，工程師，Email: anji18@126.om。

 

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