A simple formula for predicting the horizontal capacity of masonry portal frames

In this paper, a simple formula for predicting the horizontal capacity of masonry portals is proposed and discussed. Moving from the approach firstly introduced by J. Heyman in his keystone paper The Stone Skeleton [Heyman J. The stone skeleton. International Journal of Solids and Structures 1966;2:249–79], the principle of virtual works for olonomic systems is applied to derive expressions for the collapse multiplier of a chosen load distribution. With this goal, four collapse mechanisms have been selected on account of mechanical and engineering considerations, and closed form expressions for the multipliers for each of them has been derived. Those expressions have allowed us to perform extensive parametric analyses, varying the geometrical ratios that determine the portal configuration. As a result, the ranges of the main geometrical ratios, in which one or another mechanism may prevail have been derived. An abacus is also provided to evaluate the collapse multiplier of any portal, once its geometrical characteristics are known. Finally, a simplified expression is proposed, whose results show scatters from the exact solution almost always below 6%. Such an expression may turn out valuable for designers from the point of view of seismic vulnerability assessment.