The static behavior of historical vaults and cupolas

Journal of Heritage Conservation (Wiadomosci Konserwatorskie), volume 32/2012, pp. 65-81, 2012

ABSTRACT After discussing the problem of roofing empty spaces by ancient masonry builders, it is found out that curvature and horizontal thrust are the basic elements for masonry to get over long spans. Basic properties of masonry do not allow to rely on tensile strength, and beam behaviour cannot be trusted on. Nevertheless in 2D walls and in double curvature vaults, a particular organization of the vault apparatus can in some instances, through the action of compression and friction, give place to a equilibrium pattern including tension, which explains the unexpected good performance of some walls and cupolas. Anyway, it is recognized that, apart from a few cases, the No-Tension assumption yields a effective model for structural assessment. The theory is briefly illustrated, and its application to vaults is explained in detail, leading to a Monge-Ampere equation ruling the static regime through a membrane stress surface.

Open Journal of Civil Engineering, 2018

This paper reports a validation study involving sixth scale masonry model to replicate prototype tests carried out on five unit high masonry prisms. In order to test the applicability of small masonry models to real life problems, an investigation into masonry behaviour relevant to the serviceability requirement of masonry arch bridges was chosen as prototype test to validate the small scale masonry tests. Only representative masonry specimens were considered in the study; this corresponded to parts of an arch ring in a complete masonry arch. Two mortar designations; designation iv and designation v were used. These weak mortars tend to conform better to existing old structures. Loads were applied at four eccentricities of 0, 5, 9, and 14 mm from the centre of the specimens. This corresponds to e/d ratios of 0, 0.14, 0.25, and 0.39, where e is the eccentricity of the load and d the length of the transverse section of the specimens. The result shows that validation study corresponds with prototype study for low eccentricities; therefore, strength enhancement is seen over the concentric compressive strength. However, this does not apply at higher eccentricities as specimens were noticed to fail by elastic instability characterised by tension debonding of the top mortar joint.

International Journal of Architectural Heritage, 2020

Free access: https://www.tandfonline.com/eprint/5MJBQWVBWIQGHDYUYMHK/full?target=10.1080/15583058.2019.1648586 The purpose of this paper aims at critically examining Monasterio’s unpublished manuscript, found by Santiago Huerta in the Library of the Escuela de Ingenieros de Caminos, Canales y Puertos of the Universidad Politécnica de Madrid and entitled Nueva teórica sobre el empuje de bóvedas. The manuscript has a relevant role within the historical development of pre-elastic theories on vaulted structures since for the first time the topic concerning non-symmetric masonry arches is investigated. Thus, first of entering into the detailed analysis of the manuscript, a brief account of the historical literature concerning the pre-elastic theories on vaulted structures will be given by identifying two significant research lines, namely the kinematic and static approach, the last one first introduced by Coulomb in his Essai of 1773. In line with the historical kinematic approach, Monasterio a priori identifies the various collapse mechanisms through the permutation criterion of the minimum number of possible relative displacements between voussoirs; then, through an analysis technique extremely succinct and precise, he gives the conditions required for activating the collapse modes by him identified of non-symmetric arches. Although Monasterio’s criterion adopted to find the collapse conditions has only a local and not a global validity, it will be demonstrated that the Scholar is conscious of the critical role of the most important geometric and mechanical parameters. In this respect, with reference to the simple case study of a semi-circular arch of constant thickness, a comparison between Monasterio’s approach and Coulomb’s method is provided. It will be quoted that Coulomb’s method is in full agreement with the plastic theory for standard behavior, and also that its appropriate use, even in the presence of finite friction, allows to obtain a general and complete chart related to the activation of the various collapse modes of symmetric arches, as a function of geometric and mechanical parameters. The examination of the case study shows that also the basic assumptions of the Monasterio’s analysis are fully in agreement with the modern limit analysis, according to a kinematic approach somehow analogous to Virtual Work Principle. Moreover, also his approach allows the construction of a chart to assess overall stability of symmetric arches, through a comparison between the different mechanisms and by providing a relationship between limit friction and arch’s thickness.

2001

1997

In this paper a constitutive equation for masonry arches is defined and its main properties are proven;

"Theory and practice of constructions: knowledge, means and models. Didactis and research experiences". Fondazione Flaminia, Ravenna, Italia, pp. 747-761. ISBN 888990003 2, 2005

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 1960s 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 "forget" 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 "plane" 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.

In this paper, we revisit the limit equilibrium analysis of masonry arches. Firstly, the major contributions during the last three centuries associated with geometric and energy formulations are discussed, and subsequently, the paper explains that the problem of determining the minimum thickness of a masonry arch capable to support its own weight has multiple solutions. The infinite many neighboring solutions for the minimum thickness of a masonry arch result from the infinite many possible directions of rupturing that an arch with finite thickness may develop when becoming a mechanism. Given this infinite number of physically admissible rupturing directions, the energy approach expressed with the principle of stationary potential energy emerges as the most powerful tool to analyze masonry arches at their limit equilibrium state. The paper concludes that vertical rupturing is the most critical rupturing direction since it results to the largest value of the minimum thickness that an elliptical arch needs to support its own weight. For the common case where there is an intrados layer of voussoirs with physical joints perpendicular to the intrados, the initial rupture has to first follow the physical joint; therefore, the broken rupture pattern reported by Lamé and Clapeyron in 1823 corresponds to the larger value of the minimum allowable thickness.

Acta Mechanica, 2014

ABSTRACT In the paper, one presents the theoretical set-up of an original formulation aimed at accounting for the contribution of the fill to the structural strength of masonry vaults and arches and at providing an evaluation about its skill of cooperating to stress absorption with the main vaulted resisting structure. Usually the action of components ordinarily regarded as non-structural members is often neglected in static analyses. Actually, it is a common practice to assume a number of elements of vaulted or arched constructions, such as the fill and the buttress, as completely unable to exert any structural action, rather than trying to evaluate their contribution; therefore, those are usually assumed to be a dead weight, unable to contribute to the bearing capacity of the vault. Starting from the consideration that the fill is somehow subject to some pre-compression because of the permanent load, an approach is proposed where the fill is considered to be able to provide a partial absorption of the variable loads with a reduced load transmission onto the main structural members. The procedure leads to more realistic evaluations about the safety assessment of vaulted structures, which are in major agreement with their real behaviour.

International Journal of Mechanical Sciences, 1986

This paper presents a calculation procedure for assessing the structural integrity of a masonry arch with non-horizontal springing settlement. By applying the Principle of Virtual Work (PVW) to the deformed arch system, the procedure proposed herein details the reaction forces and thrust lines for each step of imposed settlement of the support. The procedure can also be used estimate the final displacement that causes complete failure of arch structural capacity. The results of the analysis procedure were compared against those obtained by experimental testing so as to validate the proposed calculation method.