Geometry,Construction and Structural Analysis of the Crossed-Arch Vault of the Chapel of Villaviciosa,in the Mosque of Córdoba

The vault of Villaviciosa is one of the oldest existing examples of a true ribbed vault, and is the first of the crossed-arch type. Although its perfection suggests earlier trials, none has been found so far. It predates the oldest Romanesque ribbed vaults by more than a century. Notwithstanding its importance, no construction and structural study has ever been done; neither has an accurate survey been published. The purpose of this article is to fill this gap in the history of vault construction. A detailed survey has been made, providing the first accurate drawings of the vault. A close inspection of the extrados, completed with a visual inspection of interior damages, has allowed ascertaining the main construction features. With the geometry and the material data a structural analysis has been carried out. This analysis explains the fundamental structural behavior of the vault and throws new light into some historical issues; for example, it leads to discarding the widespread belief that the ribs are decorative: they are supporting the weight of the vault.     

A Procedure to Investigate the Collapse Behavior of Masonry Domes: Some Meaningful Cases

Masonry domes represent an important part of the architectural heritage. However, the literature about domes analysis seems less consistent than that referred to other masonry structures. The collapses that have happened in recent years as a consequence of seismic actions or lack of maintenance show the need for detailed studies. Here a limit analysis to evaluate the masonry domes behavior is presented. An algorithm based on the kinematic approach has been developed to evaluate the geometric position of the hinges that determine the minimum collapse load multiplier. The proposed procedure is validated by a comparison with some meaningful cases—the collapse of Anime Sante Church in L’Aquila, the collapse of San Nicolò Cathedral in Noto, the crack pattern of San Carlo Alle Quattro Fontane Church in Rome, and the analysis developed on Hagia Sofia in Istanbul. The comparison with real cases shows a good agreement between the model results and the phenomenological crack patterns.     

Rapid Diagnosis of Crack Patterns of Masonry Buildings Subjected to Landslide-Induced Settlements by Using the Load Path Method

One of the main difficulties, when dealing with landslide structural vulnerability, is the diagnosis of the causes of the crack pattern. This is also due to the excessive complexity of models based on classical structural mechanics that makes them inappropriate especially when there is the necessity to perform a rapid vulnerability assessment at the territorial scale. This is why in this article a new approach for the rapid diagnosis of crack patterns of masonry buildings subjected to landslide-induced settlements is proposed. This approach is based on the Load Path Method, recently applied to the interpretation of the behavior of masonry buildings subjected to landslide-induced settlements.     

Effectiveness of FRCM Reinforcement Applied to Masonry Walls Subject to Axial Force and Out-Of-Plane Loads Evaluated by Experimental and Numerical Studies

ABSTRACT

An experimental campaign and a numerical analysis devoted to the investigation of the out-of-plane behavior of masonry walls reinforced with Fiber Reinforced Cementitious Matrix (FRCM) are presented here. The main goal of this study is to analyze and evaluate the effectiveness of the strengthening system, by discussing failure modes and capacity of strengthened masonry walls, in order to assess their behavior under out-of-plane horizontal actions, such as, for example, seismic actions. A purposely designed experimental set-up, able to separately and independently apply an axial force and out-of-plane horizontal actions on masonry walls, was used. Experimental results are discussed and compared with the outcomes of nonlinear analyses performed on simplified finite element models of the walls. A proper evaluation of the flexural capacity of FRCM strengthened walls is the first step of the ongoing process of drawing reliable code guidelines leading to a safe design of strengthened masonry structures.     

A Fully Graphical Approach for Limit State Analysis of Existing Structures: Application to Plane Elastic-Plastic Bended Structures and to Plane Masonry Arches

ABSTRACT

When classical elastic analysis fails to model correctly the structural behavior of historical masonry structures because of the brittle, rigid, anisotropic, and inhomogeneous characteristics of their building material, equilibrium-based limit state analysis constitutes an efficient alternative for their structural assessment. The lack of knowledge about the history of loading makes the actual state of stresses impossible to determine for these statically indeterminate structures. However, Plastic Theory provides a powerful theoretical framework that defines in a rather simple way the structural safety level. The lower-bound theorem of plasticity can be applied using graphic statics because it ensures that equilibrium and yield conditions are respected when applying specific constraints to the nodes of the reciprocal diagrams.

This article focuses on limit stat analysis of statically indeterminate structures by means of geometrical considerations using graphic statics reciprocal diagrams. For linear-bended structures, we show that: (1) the conditions of stability can be defined graphically by constructing safety domains; (2) collapse modes can be identified and related to specific reciprocal polygons; and (3) the exact value of the collapse load factor can be deduced graphically from the diagrams. Finally, we extend these results to plane masonry arches in relation with the classical thrust line approach.     

A Novel Procedure for Simplified Nonlinear Numerical Modeling of Structural Units in Masonry Aggregates

ABSTRACT

Historical centers are always composed of masonry building aggregates often designed without respecting seismic design criteria. The current seismic Italian code does not foresee a clear calculation method to predict their static nonlinear behavior. For this reason, in this article the seismic response of structural units into masonry aggregates has been predicted through a simplified modeling approach. The implemented procedure has been calibrated on the results of a numerical model performed by using the Equivalent Frame Method (EFM), implemented within a Finite Element Method (FEM) calculation program, used to investigate a basic building compound representative of the constructive techniques developed in the past decades in the Southern Italy.

First, the whole aggregate has been modeled and analyzed in the nonlinear static field in order to evaluate the seismic behavior of both intermediate and head structural units.

Later on, the seismic response of these structural units, considered as isolated structures, has been assessed by considering in simplified way their position in the aggregate, as well as the influence of other constructions.

Finally, the achieved results on the above single analysis cases have been compared with those deriving from the investigation of the whole building compound, allowing to confirm the effectiveness of the proposed novel analysis procedure.     

In-Situ Destructive Testing of Ancient Strengthened Masonry Vaults

ABSTRCT

Developing suitable tools to assess the actual structural performance and designing and executing interventions to improve that performance is a key issue in the field of conservation and enhancement of architectural heritage. This article presents the results of five full-scale destructive tests performed on the Castello di San Pietro in Verona (North-East Italy), a building set on a hill above the city and going back to the 19th century under the Habsburg Empire. It evaluates the behavior of the barrel vaults of 5.6 m span, 1.1 m rise, and 27 cm thickness in the original building. Although experimental work is common in the relevant literature, the testing program described here was not performed on reconstructed vaults but on original elements, which can reveal their real behavior more clearly. Four strengthening solutions were also evaluated, in which organic and inorganic fibers were applied to both types of matrix.     

Effect of stereotomy on the lower bound value of minimum thickness of semi-circular masonry arches

Constructing structural systems with the minimal required cross section of its members was a strong motivation for progress whole along the history of building. This article investigates the effect of stereotomy on the minimum thickness value of a semi-circular arch made of masonry: a material with negligible tensile strength. The arch is modeled with its center line to which the loading is assigned according to arch length. Here, instead of some scalar parameters such as the rupture angle and the location of the middle hinge on the intrados, the geometry of the stereotomy is associated with a continuous function. Stereotomy-related constraints are introduced to keep the results feasible from an engineering point of view, and it is also demonstrated that they are essential for a well-posed constrained optimization problem. The necessary condition for a non-vanishing lower bound of minimum thickness values is derived analytically considering the assumptions of limit state analysis, infinite friction, and a no-tension material model. The lower bound thickness to radius ratio (t/R) is found to be t/R = 0.0819. A numerical method is introduced to demonstrate the existence of a valid stereotomy at the lower bound. Multiple admissible stereotomy patterns are presented at various minimum thickness values (higher than the lower bound) to demonstrate that suitable stereotomy for a fixed (t/R) ratio is far not unique—in general even the location of the middle hinge and the rupture angle might vary.     

Masonry Italian Code-Conforming Buildings. Part 2: Nonlinear Modelling and Time-History Analysis

ABSTRACT

The unreinforced masonry (URM) buildings designed to be conforming with the Italian building code, as illustrated in the companion paper, were analyzed by performing time-history analyses on models realized using an equivalent frame approach and by adopting two different constitutive laws. Both the effect of record-to-record variability and of epistemic and aleatory uncertainties in modelling were explored. The achieved results constitute the basis for the evaluation of the risk level implicit in Italian code-conforming buildings. Two main performance conditions are considered, namely usability-preventing damage and global collapse limit states.     

SIGNIFICANT GROUND MOTION PARAMETERS FOR EVALUATION OF THE SEISMIC PERFORMANCE OF SLENDER MASONRY TOWERS

The evaluation of seismic risk of masonry monuments requires to study the combination of vulnerability and hazard. In the present work, the global seismic response of slender masonry towers has been studied by means of a specific 3-D fibre model. Accounting for the particular behaviour of such structures, the hazard should also be described by a suitable measure of intensity of the seismic action. A variety of different parameters relating with the ground acceleration recordings have been investigated for what regards their correlation with the damage indicators of the model. The combination of the peak ground velocity of the horizontal component and of the significant duration is an effective measure of intensity. This measure can be improved by considering the accord of the frequency content of the ground motion with the dynamical characteristics of the tower. Since in some cases the effect of the vertical component proved to be important, a further improvement can be obtained by taking into account also the vertical ground motion intensity.