Wind strength of Gothic Cathedrals

• The wind strength of Gothic Cathedrals is examined with the kinematic theorem of the Limit Analysis.
• The collapse load is evaluated adopting a rigid no-tension constitutive model with no sliding.
• Local and global collapse mechanisms are considered.

Aim of the paper is the evaluation of the wind strength of one of the most amazing structural typology of the Middle Age, the Gothic Cathedral. Among his most significant structural problems, wisely solved by the ancient builders, there was the need to realize structures with high lateral resistance, in order to counteract the action of the wind. Deformations of the cathedral under the wind action are negligible, both in longitudinal and in transverse direction, owing the high stiffness of the structure. Wind action is therefore essentially static and it can be represented by a suitable distribution of horizontal forces. In this framework the paper evaluates the collapse wind load according to the kinematic approach of the Limit Analysis considering various failure mechanisms as, among them, the semi-global mechanism, involving only the leeward side and the global, interesting both sides of the structure. The analysis is performed making reference to a cathedral modulus similar to that of the Cathedral of Notre-Dame of Amiens, one of the most important examples of Gothic Cathedrals. The paper shows that the stone skeleton of these cathedrals is able to sustain the action of fierce winds whose intensities are larger than those prescribed by actual codes.