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A linear elastic model constituted by two interacting concentric arches is developed. The sensitivity of the behaviour of the system to its mechanical and geometrical parameters is studied to individuate the fundamental ones. The analysis is extended to the nonlinear field by means of computational finite element models. Another objective of the research is to specifically analyse the interaction between the two arches when there is a large difference in stiffness. A practical case is represented by the retrofitting of a masonry vault with a single curvature (barrel vaults) with a reinforcing concrete layer that, in several cases, resulted in the detachment of some masonry blocks. Finally, on the basis of the results of the nonlinear analyses, which qualitatively confirmed the results of the linear ones, a slightly innovative approach to the use of the reinforcing layers is proposed. [ABSTRACT FROM AUTHOR]

A linear elastic analytical model of curved beam with constant curvature coupled with curved strings has been developed. To model the connections between the strings and the beam, a continuous distribution of tangential and orthogonal linear elastic springs have been introduced. To evaluate the behavior of the system, a numerical integration of the field equations has been performed. A parametric analysis, capable of pointing out the influence on the behavior of the system of both the stiffness of the tangential connection between strings and beam and of the geometrical characteristic of the beam, has been performed. The results of the proposed model have been compared with those obtained from a finite element model. They show that the strings, in some cases, do not work as expected. [ABSTRACT FROM AUTHOR]

The nonlinear elastic problem for planar frames, made of rectilinear beams subjected to thermal loadings, is resolved here. The basic element is an Euler–Bernoulli beam, whose elongation is a nonlinear function of the displacements. The elastic law accounts for thermal deformations and for temperature-dependence of the elastic modulus. The elastic problem is formulated in a mixed equilibrium-compatibility form and an ‘exact’ finite element is derived. Assembling the element relations, the governing equations for the frame are recast in a discrete form. The nonlinear algebraic problem is solved numerically and results are compared with those provided by a FE software. [ABSTRACT FROM AUTHOR]

Highlights: [•] A numerical-perturbation method for analyzing nonlinear planar frames is illustrated. [•] The displacement fields are obtained by asymptotic integration of the field equations. [•] Calculations are rearranged in a way they can be made by a computer. [•] Modeling is carried out in the context of the mixed formulation of elasticity. [•] The semi-analytical results are in excellent agreement with FEM analyses. [ABSTRACT FROM AUTHOR]