Riccardo Barsotti

Equilibrium of Pointed, Circular, and Elliptical Masonry Arches Bearing Vertical Walls

AbstractThis paper addresses the long-standing problem of the equilibrium of the circular, pointed, and elliptical arches commonly found in historical masonry buildings and bridges that are subjected to their own weight and the weight of superimposed masonry walls. The equilibrium problem is studied by applying two different complementary methods: the first is a simple extension and analytical re-reading of the Durand-Claye stability area method; the second is based on the application of a nonlinear elastic one-dimensional model, already used by the authors in previous studies. It is assumed that the arch’s constituent material has limited compressive strength and null tensile strength. In addition, the load transferred to the arch by the wall is determined under the common assumption that each vertical strip of wall bears directly down on the underlying arch element. The study focuses on the maximum height that the superimposed wall can reach under equilibrium conditions while maintaining acceptable valu...

The web bridge

Abstract Optimal cable arrangements for tensile structures, for bridges in particular, are determined by drawing inspiration from the wrinkling behavior of flat elastic membranes stretched in their plane. The underlying rationale for the approach consists in the fact that wrinkle patterns naturally develop according to a “maximum-stiffness” criterion. By way of illustration, a two-dimensional theory is proposed to model the wrinkling phenomenon in membranes subjected to general in plane loading, and an iterative procedure is then presented for solving numerically the governing set of non-linear equilibrium equations in a finite-element framework. The numerical results show good agreement with experiments performed on thin polyethylene sheets. An idealized web bridge is then conceived of, in which the deck is regarded as being sustained by an elastic membrane. A simple criterion is then used to pass from the continuous natural wrinkled equilibrium configuration of the membrane to a discrete layout, formed by a cable net, exploitable in the design of a real bridge. By changing the parameters controlling the shape of the web, various “optimal” cable arrangements are determined. These turn out to resemble classical cable-stayed bridges or mixed suspended and cable-stayed “hybrid” solutions.

Notes on Limit and Nonlinear Elastic Analyses of Masonry Arches

This chapter is a critical presentation of studies over the last 10 years on the mechanical response of masonry arches and vaults. More precisely, we focus on a study of masonry arches conducted in parallel via both nonlinear elastic and limit analyses. The one-dimensional elastic model for masonry arches incorporates a simple but effective nonlinear constitutive law. In turn, collapse analysis is performed by the so-called ‘method of stability areas’, originally proposed by Durand-Claye in 1867. Rather than offering two alternative paths, the approaches may be considered complementary points of view on the same problem. A reasoned illustration of the concepts in question is furnished by the topics addressed: an analysis of the possible failure mechanisms of a pointed arch subject to its own weight; the search for explicit solutions to the equilibrium problem of a depressed arch subject to a uniformly distributed load; the study of arches of different shapes subject to their own weight and the weight of a superimposed wall.

A knowledge-based approach for the structural assessment of cultural heritage, a case study: La Sapienza Palace in Pisa

The full knowledge of the morphological evolution of an historical masonry building, defined more as ‘structural aggregate’ than as ‘single construction’, together with the analysis of the architectural, structural, geological and geotechnical aspects, allow the assessment of the static safety and seismic vulnerability of the complex and the design of retrofit interventions. In the present paper, a Knowledge-Based-Approach is applied to the historical building ‘Palazzo La Sapienza’ in Pisa, allowing to provide reliable results concerning the actual structural condition of the building avoiding the strong computational effort usually associated to the execution of refined numerical analyses. In case of complex buildings, characterized by a high heterogeneity of materials, structural typologies, geometries and so on, the adoption of a global model is not always useful to represent the effective structural behaviour. The proposed approach shows how a deep multidisciplinary knowledge of the construction can limit the use of cumbersome numerical modelling and analysis, however reaching reliable and accurate results usable also in the current practice.

Analysis of rotational and sliding collapse modes of masonry arches via Durand-Claye’s method

In this paper the mechanical behavior of circular and pointed masonry arches subject to their own weight is examined in order to determine their collapse modes. Different arch’s shapes and thicknesses are considered; the influence of the friction coefficient on the arch collapse is analyzed as well. The safety level of arches is investigated by suitably reworking in semi-analytical form the stability area graphical method proposed by a renowned 19th century French scholar, Durand-Claye. Our analysis enables accounting for any given eccentricity of the thrust at the crown; furthermore, also the strength of masonry is taken into account. According to Durand-Claye’s method, the arch is safe if along any given joint both the bending moment and the shear force do not exceed some given limit values. It is shown that attainment of a limit condition according to Durand-Claye corresponds to the onset of a collapse mechanism characterized by either relative rotation or sliding between masonry units. All possible sy...

A Simple Mechanical Model for a Wiper Blade Sliding and Sticking Over a Windscreen

From the mechanical standpoint, wiper blades may be thought of as belonging to a category of systems in which some components are forced to slide with friction over each other or over some rough surface. Such systems, which are in widespread use in all areas of modern engineering, exhibit complex dynamic behavior, even when only a small number of degrees of freedom are involved. In this paper we reconsider a well-known, simple mechanical model in which a rigid block connected to a linear spring is free to slide over a rough surface. The surface moves according to a prescribed sinusoidal law. The model, despite its apparent simplicity, proves to be quite useful for studying the main dynamic features of such systems. In particular, herein the equations of motion are solved analytically and the exact sequence of sticking and sliding phases found. The influence on the solution of three dimensionless parameters chosen to describe the system is investigated, and some early indications provided on the set of possible long-term system responses. Lastly, a first evaluation of the different limit cycles for the block’s motion is illustrated.

Characterisation of the mechanical behaviour of the bell tower of the Cathedral of San Miniato (Pisa)

This paper reports the results of a wide-ranging study performed on the Tower of Matilde, the masonry bell tower of the Cathedral of San Miniato (Pisa, Italy). The structure, dating back to the XII century, has been subjected to various modifications over the centuries: from military fortification, to the bell tower incorporated into the church. The research followed a multidisciplinary approach to studying the tower, combining static and dynamic experimental analyses, structural FE modelling and updating through a suitable methodology seldom used in practice on masonry constructions. The aim was to achieve accurate characterization of the overall behaviour of whole masonry construction and the mechanical properties of its constituent materials.