Keywords: cantilevered, stone, stairs, assessment, static, Weibull, load capacity.

This paper presents a methodology for assessing the safe load capacity of cantilevered stone stairs. Cantilevered stone stairs were constructed widely between the sixteenth and early twentieth century. The term cantilevered stone stairs is a misnomer: such stairs are constructed using monolithic stone treads but they usually do not carry their loads as cantilevers. Instead, each tread is supports the tread above and rests on the tread below. The resulting torsional forces are resisted by the wall supporting the stairs and, if the treads are rebated, by a couple which is the result of the horizontal contact forces between treads.

Although cantilevered stone stairs are generally robust, they do fail occasionally and their mode of failure tends to be a sudden failure without prior warning. In addition, these stairs frequently comprise the fire escape route for historic public buildings. For these reasons it is very important to be able to quantify their safe load capacity.

The principal structural behaviour of a cantilever stone stairs can be discerned from the equations of statics. Previous authors have presented analyses for unrebated stairs. This paper presents a method for rebated stairs, and provides a theoretical justification for assuming that the peak stresses in a rebated stairs are approximately half those of an unrebated stairs. The analysis presented in the paper explicitly identifies the assumptions on which this result is based. The validity of the static analysis is supported by the results of a parametric finite element analysis, which showed that the static analysis method presented in the paper is valid over a wide range of flight lengths, tread sections and support conditions.

The static analyses can be used to determine the peak torsional force in the treads and hence the peak stresses. The paper proposes the use of a probabilistic Weibull brittle-failure criterion. This is a more rational approach that the simple Mohr's failure criterion that is often used. This approach acknowledges the size effect that is ignored by Mohr's criterion and facilitates a Bayesian approach that takes account of the previous load history.

The paper acknowledges that stone is a natural material and structural engineers must be cautious in making assumptions that stone is a homogeneous material. There are many situations in which the only responsible course of action is to perform a full scale load test.

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