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。 Curved spiral staircase often appear in buildings, its internal force analysis is more complicated, and the calculation theory of this staircase is rare in China. According to the actual project, the mathematical model of differential geometry is used to establish the elliptical spiral curve of the elliptical spiral staircase. The inner and outer lines of the staircase are the space curved beam model of the mathematical model of the equidistant line on the principal normal of the centerline. Based on the simplified calculation model of curved curved beam based on stairway and selecting the equivalent curve of load acting close to the actual effect, the internal force formula at any point on the ladder beam under the unit force and uniform load is deduced and compared with the finite element analysis A The analysis shows that the space curved beam model can well describe the geometric properties of an elliptical spiral staircase. The internal forces derived from the formula derivation and finite element analysis are very close. Other rotating forms of stairs, but also can refer to the above method to establish its mathematical model consistent with its shape and internal force analysis, provide the basis for the design.