Vol. 9, No. 3, 2014

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ISSN: 1559-3959
Analytical solution for ductile and FRC plates on elastic ground loaded on a small circular area

Enrico Radi and Pietro Di Maida

Vol. 9 (2014), No. 3, 313–331
Abstract

The problem of a large 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 criterion 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, under the hypothesis of proportional loading. After the formation of positive yield lines, namely radial cracks at the bottom side of the plate, the onset of a negative yield line, namely a circumferential crack at the upper side of the, defines the load-carrying capacity of the slab on grade. 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 thus activating a plastic mechanism, or within 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 load-carrying capacity of the plate 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.

Keywords
Kirchhoff plate theory, Winkler elastic subgrade, load-carrying capacity, yield lines, elastic-perfectly plastic material, Johansen's yield criterion, fiber reinforced concrete
Milestones
Received: 11 December 2013
Revised: 21 February 2014
Accepted: 10 March 2014
Published: 4 October 2014
Authors
Enrico Radi
Dipartimento di Scienze e Metodi dell’Ingegneria
Università di Modena e Reggio Emilia
Via Amendola 2
I-2 42122 Reggio Emilia
Italy
Pietro Di Maida
Dipartimento di Scienze e Metodi dell’Ingegneria
Università di Modena e Reggio Emilia
Via Amendola 2
I-2 42122 Reggio Emilia
Italy