The use of simple models in the teaching of the essentials of masonry arch behaviour

Abstract

Traditional masonry is today an unusual material, it is alien to us at the beginning to the 21st. century. The usual assumptions for structural materials: homogeneity, isotropy, elastic constants (Young=s modulus, Poisson=s coefficient), etc., do not apply or are irrelevant in respect to masonry. Most important, though masonry presents a good strength in compression, is very weak to tension; its behaviour is >unilateral'. This fact has paramount importance in masonry behaviour. Besides, real masonry structures are cracked. A different approach is needed and it was used indeed when this type of structures were designed during the 18th. and 19th. centuries. Since the 1960=s Professor Heyman has rigorously introduced the theory of masonry structures within the frame of Limit Analysis, and has clarified many aspects of the analysis of masonry architecture. To teach a new theory (in fact a forgotten one) presents serious difficulties. Not the least is that the listeners (students, practicing architects or engineers, even professors...) must Aforget@ the usual frame of reference (elastic analysis, framed or trussed structures, etc..) and contemplate, as did for example the gothic masters, a masonry building as a "heap of stones" in equilibrium under its own weight. But, one can add to his or her knowledge, but not subtract to it. In fact, we must reconcile the intuition of the old master builders with the teachings of modern structural theory. The theory can be studied but, how to teach the intuition, this feeling of the behaviour which has a fundamental importance in structural analysis and design? After more than fifteen years of teaching masonry structural behaviour I have found the use of physical models of extraordinary help. I do not mean the complicated models of laboratory, made by skilled workmen, but very simple models that the students may replicate at home for experiment, study and reflection. I use normally only two types of models. The first is Hooke=s hanging chain. The second is a Aplane@ block (voussoir) model made of thick cardboard. It is a personal invention, an idea which occurred to me when, at the beginning of my studies of arch behaviour, I was struggling with three dimensional models. It applies to arches or masonry structures of any kind as far as its thickness in one direction could be considered uniform: barrel vaults, but also buttresses or flying buttresses, double arches, etc. The paper will present the use of this two basic models: 1) for the teaching and appreciation of the fundamental assumptions; 2) to assure a better understanding of the Fundamental Theorems of Limit Analysis applied to masonry structures; 3) to study and understand the basic crack configurations of masonry arches and vaults. But to appreciate the use of models, a brief summary of the essentials of masonry structural theory should be given beforehand