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Abstract: The present work is aimed at deriving assessment and design formulae for determining the elastic–plastic response and the ultimate compressive strength of circular concrete columns confined by Fiber Reinforced Polymers (FRP). To achieve this, a constructive method for obtaining closed-form elastic and post-elastic solutions for Functionally Graded Material Cylinders (FGMCs), constituted by an isotropic central core and arbitrary cylindrically orthotropic hollow phases, is proposed. In the first part of the paper, under the hypotheses of axis-symmetrical boundary conditions, elasticity and perfect bond between the phases, new analytical solutions for self-equilibrated axial forces applied at the extremities of the object are derived. In particular, the rather general mathematical approach has been based on a strategy already proposed by some of the authors in a previous work, and here extended to anisotropic hollow phases. The key of the involved method is to reduce the differential Boundary Value Problem (BVP) to the equivalent linear algebraic one, by means of a special matrix-like arrangement of the governing equations and invoking the Complex Potential Theory for anisotropic materials. The obtained general solution has been then easily particularized to the two phase FGMC representing the circular concrete column confined by FRP sheets. In the second part of the paper, the above mentioned solutions for the concrete column are “moved” within the post-elastic range and we investigate the evolution of the stress field in the solid components when the concrete core is characterized by an Intrinsic Curve or Schleicher-like elastic–plastic behavior endowed with associate flow rule, and the FRP cylindrically orthotropic hollow phases obey to an elastic–brittle Tsai–Hill anisotropic yield criterion. At the end, the elastic and post-elastic response of the overall solid and predictive formulae for estimating the failure mechanism, in terms of concrete ultimate compressive strength, confining pressure and strain at failure, are derived. The obtained results are finally compared with several experimental literature data, highlighting the very good agreement between the analytical predictions and experimental tests. [Copyright &y& Elsevier]

The proposal of the present work is to furnish a general approach to construct exact elastic solutions for FGM cylinders, made of a central core and n arbitrary cylindrical hollow homogeneous and isotropic phases. The hypothesis of axis-symmetrical boundary conditions is here assumed in order to analyze a class of elastic problems which present no-decaying of selected mechanical quantities and in particular of the axial strains ε33 in the radial direction, being x3 the axis of the laminated cylinder. To construct a robust mathematical procedure for obtaining exact elastic solutions for axis-symmetrical n-plies-Functionally Graded Material Cylinders (n-FGMCs), a theorem is first given for qualifying the space of the solutions and then their mathematical form is identified, when the object exhibits no-decaying of the axial strain. By starting from the classical Boussinesq-Somigliana-Galerkin vector and specializing it to torsionless composite cylinders characterized by no-decaying of the axial strain, a special form of the bi-harmonic Love's function χ (i)(r, x3) is finally obtained. It is then demonstrated that the differential boundary value problem (BVP) always can be translated in an equivalent linear algebraic one, first solving an in cascade one-dimensional Euler-like differential system (field equations) and then writing the boundary conditions by means an algebraic system ruled by a (6n + 4)-order square matrix P. At the end, constructive and existence theorems are formulated and proved, showing examples in comparison with literature data. [ABSTRACT FROM AUTHOR]