Analytical solution for ductile and FRC plates on elastic ground loaded on a small circular area

Abstract

The problem of an infinite FRC slab resting on a Winkler-type elastic foundation and subject to a transversal load distributed over a small circular area is investigated in the present work. The mechanical behavior is described by the Kirchhoff theory of elastic-perfectly plastic plates obeying Johansen’s yield condition and associative flow rule. The governing equations within both the inner elastic-plastic circular region near to the loaded area and the outer elastic region are found in terms of the transversal displacement and solved in closed form. After the formation of radial positive yield lines, namely cracks at the bottom side of the slab, the onset of a circumferential crack at the top of the slab defines its load-carrying capacity. Two possible configurations are envisaged, depending on whether the circumferential crack occurs within the inner elastic-plastic region, where radial cracks take place on the bottom side, or the outer uncracked elastic region. The ratio between the subgrade modulus and flexural rigidity of the plate allows introducing a characteristic length. The influence of both material and geometrical parameters on the ultimate load is then investigated. Based on the analytical results, a simplified method for the calculation of the load-carrying capacity of FRC slabs on grade is also proposed and compared with previously developed models

Failure mechanism of FRC slabs on non-local ground

“…Comparison between the results provided by the present study and that reported in[24] for n ? 0 and a/ L = 0.1…”

“…n ? 0, then the results provided by Radi and Di Maida [24] are retrieved. Indeed, in that case, the foundation resembles a Winkler-type subgrade, and the corresponding values of the radii of the elastic and plastic regions and the ultimate carrying capacity are recovered (see Table 2).…”

“…Therefore, the positive moment-carrying capacity for FRC slabs can be assessed by adding the post-cracking bending moment capacity (5) to the admissible positive bending moment capacity of plain concrete, thus providing the positive bending moment capacity (c.f. eqn (41) reported in [24])…”

“…An exact solution for an infinite FRC slab resting on a Winkler foundation subjected to a uniform load applied on a circular area has been recently found by Radi and Di Maida [24]. These Authors assumed the Johansen failure criterion and associative flow rule for the plate and calculated the ultimate bearing capacity of the system varying the size of the loaded area, the plate bending stiffness and the stiffness modulus of subgrade.…”

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“…Recently, the problem of an infinite elastic-plastic plate resting on an elastic Winkler-type subgrade and uniformly loaded on a circular area has been solved by Radi and Di Maida [2014] by assuming the Johansen yield criterion for the plate [Johansen 1962] and associative flow rule. In that work, the exact ultimate bearing capacity of the system has been assessed varying the radius of the loaded region.…”