（同济大学建筑设计研究院（集团）有限公司， 上海 200092）

［摘要］对于钢筋混凝土板式楼梯考虑踏步作用的现有研究，均是建立在理想匀质弹性材料的基础上，其适用性尚缺乏全面的非线性有限元分析验证。以踏步单元为研究对象，根据应力扩散假定及应变能等效原则，推导了梯板等效厚度理论公式。利用ABAQUS软件进行了非线性有限元分析，验证了等效厚度理论公式对于钢筋混凝土材料是适用的。经与有限元计算结果对比，表明理论公式具有很高的精度并略偏于安全。实际工程中，可以利用该公式进行挠度计算，使楼梯设计更为合理。

［关键词］板式楼梯；  应力扩散；  应变能；  等效厚度； 跨厚比

中图分类号：TU375-2文献标识码：A文章编号：1002-848X(2020)13-0030-08

Deflection calculation and design suggestions for reinforced concrete slab stairs considering the effect of steps

XU Xiaoliang

(Tongji Architectural Design (Group) Co., Ltd., Shanghai 200092, China)

Abstract:The existing researches on reinforced concrete slab stairs taking the effect of steps into account are based on the assumption of the ideal homogeneous elastic materials, but these studies have not been verified comprehensively by nonlinear finite element analysis. Taking the step elements as the object of study, a theoretical formula of equivalent thickness was deduced on the basis of the stress dispersion hypothesis and the strain energy equivalence principle. It is demonstrated that the formula is applicable to the reinforced concrete materials by nonlinear finite element analysis using ABAQUS program. The comparisons between the results of theoretical formula and finite element analysis  show that the proposed formula of equivalent thickness is of high precision and the results of the formula are lean to security. The deflection can be calculated easily with the formula, resulting in a more reasonable design of slab stairs in practical engineerings.

Keywords:slab stairs; stress dispersion; strain energy; equivalent thickness; span to thickness ratio

作者简介：许晓梁，硕士，高级工程师，一级注册结构工程师，Email:12XXL@tjad.cn。