, Volume 53, Issue 7, pp 1571–1589 | Cite as

Discrete element analysis of stone cantilever stairs

New Trends in Mechanics of Masonry


Stone cantilever staircases are present in case of both new constructions and reconstructions. The aim of the present paper is to understand the mechanical behaviour of these staircases with the help of discrete element simulations, and to compare the calculated behaviour to the estimations given by the existing manual calculation methods. First a literature review is presented on the statical calculation of cantilevered staircases: manual calculation methods suggested in the 1990s for straight and spiral staircases are introduced, focusing on Heyman’s theory and its improved counterparts. Then the discrete element method is used as a tool to perform virtual experiments, in order to evaluate the mechanical behaviour of the straight and spiral staircases for selfweight, live loads and support movement. The results obtained (internal forces, stresses, deflections) are then compared with the manual calculation results. The most important conclusions are: (1) the term “cantilever stair” is misleading: significant torsion moments occur in the treads, while the bending moments are much smaller than in a free cantilever; (2) the type of the connection between wall and treads (i.e. the end of the tread is simply supported by the wall against translation and torsion, or it is also partly clamped) has a fundamental influence on the internal forces and stress distributions; (3) for simply supported treads the existing manual methods are conservative for straight stairs, but for spiral stairs they dangerously underestimate the torsional moments.


Masonry Structural mechanics 3DEC Spiral and straight stair Helicoidal stair 



This research was inspired by the discussions with Professor Santiago Huerta, Universidad Politecnica de Madrid; his generous help in exploring the literature of the subject is gratefully acknowledged. The authors express their gratitude to Itasca Consulting Group for providing the 3DEC code under the frame of the IEP program. The presented investigations were supported by the Hungarian National Research Fund under Grant No. 100770.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.


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Copyright information

© Springer Science+Business Media B.V. 2017

Authors and Affiliations

  1. 1.Budapest University of Technology and EconomicsBudapestHungary
  2. 2.Department of Structural MechanicsBudapest University of Technology and EconomicsBudapestHungary

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