Funicularity in elastic domes: Coupled effects of shape and thickness

An historical overview is presented concerning the theory of shell structures and thin domes. Early conjectures proposed, among others, by French, German, and Russian Authors are discussed. Static and kinematic matrix operator equations are formulated explicitly in the case of shells of revolution and thin domes. It is realized how the static and kinematic matrix operators are one the adjoint of the other, and, on the other hand, it can be rigorously demonstrated through the definition of stiffness matrix and the application of virtual work principle. In this context, any possible omission present in the previous approaches becomes evident. As regards thin shells of revolution (thin domes), the elastic problem results to be internally statically-determinate, in analogy to the case of curved beams, being characterized by a system of two equilibrium equations in two unknowns. Thus, the elastic solution can be obtained just based on the equilibrium equations and independently of the shape of the membrane itself. The same cannot be affirmed for the unidimensional elements without flexural stiffness (ropes). Generally speaking, the static problem of elastic domes is governed by two parameters, the constraint reactions being assumed to be tangential to meridians at the dome edges: the shallowness ratio and the thickness of the dome. On the other hand, when the dome thickness tends to zero, the funicularity emerges and prevails, independently of the shallowness ratio or the shape of the dome. When the thickness is finite, an optimal shape is demonstrated to exist, which minimizes the flexural regime if compared to the membrane one

Scale effects in the post-cracking behaviour of fibre-reinforced concrete beams

The scale effects on the global structural response of fibre-reinforced concrete (FRC) beams subjected to bending are discussed in the framework of Fracture Mechanics by means of the Updated Bridged Crack Model (UBCM). This model predicts different post-cracking regimes depending on two dimensionless numbers: the reinforcement brittleness number, NP, which is related to the fibre volume fraction, Vf; and the pull-out brittleness number, Nw, which is related to the fibre embedment length, wc. Both these dimensionless numbers depend on the beam depth, h, which, keeping the other variables to be constant, drives a ductile-to-brittle transition in the post-cracking regime of the composite. The critical value of the reinforcement brittleness number, NPC, allows for prediction of the minimum (critical) specimen size, hmin, which, analogously to the minimum fibre volume fraction, Vf,min, is required to achieve a stable post-cracking response. Numerical simulations are compared to experimental results reported in the scientific literature, in which FRC specimens, characterized by the same fibre volume fraction but different sizes, are tested in bending

Scale-dependent maximum reinforcement percentage in reinforced concrete beams

The Cohesive/Overlapping Crack Model is able to describe the transition between cracking and crushing failures occurring in reinforced concrete beams by increasing beam depth and/or steel percentage. Within this Nonlinear Fracture Mechanics model, the tensile and compressive ultimate behaviors of the concrete matrix are modeled through two different process zones that advance independently one of another. Moreover, this model is able to investigate local mechanical instabilities occurring in the structural behavior of reinforced concrete structures: tensile snap-back and snap-through, which are due to concrete cracking or steel fracture, and the compressive snap-back occurring at the end of the plastic plateau, which is generated by the unstable growth of the crushing zone. In this context, the application of the Cohesive/Overlapping Crack Model highlights that the ductility, which is represented by the plastic rotation capacity of a reinforced concrete element subjected to bending, decreases as reinforcement percentage and/or beam depth increase. Thus, a scale-dependent maximum reinforcement percentage beyond which concrete crushing occurs prior to steel yielding is demonstrated to exist. In particular, the maximum steel percentage results to be inversely proportional to h0.25, h being the beam depth. In this way, a rational and quantitative definition of over-reinforcement is provided as a steel percentage depending on the beam depth

A review on acoustic emission monitoring for damage detection in masonry structures

Acoustic emission monitoring is widely used for damage detection in materials research and for site monitoring. Its use for masonry structures is however challenging due to the highly heterogenic nature of masonry and rapid signal attenuation. However, the non-invasive nature and high sensitivity of the technique also provide interesting opportunities, especially for historical masonry structures, to locate damage, identify severity of damage and rate of deterioration. Aim of this paper is to provide an extensive literature review on the application of the acoustic emission technique for masonry structures, addressing specific challenges and recent findings. AE-based methods for damage assessment in masonry are discussed in view of monitoring approaches, wave propagation, source location and crack development under static, fatigue and creep loading. Site applications are discussed for identifying crack location and crack propagation in historical masonry towers, buildings and masonry arch bridges. The paper concludes with future challenges identified in this research field