Keywords: plates, limit analysis, collapse load, rigid-perfectly plastic media, reinforced concrete, orthotropic reinforcement.

Limit analysis solutions for plates with free edges are found to be more difficult to obtain than for plates with supports. In [1] the authors supply an interval of variation in the collapse load for a rectangular plate having one edge free and the other three simply supported or fixed. In [2] the limit load for a rectangular plate simply supported at the corners is in all cases exactly identified. In [3] the collapse load for the plate supported on one side and on the opposite corners is in all cases exactly identified. In [4] the solution for the plate fixed on one side and simply supported on the opposite corners is partly exact and partly approximate (but with a high level of precision).

The study [1] on the orthotropic rectangular plate with a single free edge is not to be considered conclusive. In this work a new solution is provided for the problem of calculating the collapse load of the orthotropic rectangular reinforced concrete plate, supported on three edges and free on the fourth edge, subjected to a uniformly distributed load. Firstly, the upper and lower bounds of the collapse load are obtained by applying the kinematic and static theorems of limit analysis. The calculated upper and lower bound values agree remarkably well and the collapse load is defined with sufficient precision for technical purposes. The proposed solution represents a step forward compared to the best solution found previously [1], since the limitation of the free edge having to be "short" is removed and the numerical evaluation of collapse load p_c is more accurate.

The solution given can be used in optimizing the coefficient of orthotropy k, for the purpose of arriving at the determination of the minimum weight of reinforcement of the plate under study. Moreover, the solution obtained may represent the starting point for the study of other plate arrangements with a free edge.

1

K.S. Subba Rao, N. Rangaiah, B.V. Ranganatham, "Limit Analysis of Slabs with Free Edge", Journal of the Structural Division, ASCE, 105(11), 2419-2431, 1979.

2

I. Mura, "Calcolo a rottura della piastra rettangolare ortotropa in C.A. appoggiata negli angoli e soggetta a carico uniformemente distribuito sulla superficie", Atti della Facoltà di Ingegneria, Università di Cagliari, Vol. 13, 31-52, 1980.

3

I. Mura, "Limit analysis of R.C. rectangular slabs constrained at one edge and simply supported at the opposite corners", in Nonsmooth/Nonconvex Mechanics with Applications in Engineering-II.NNMAE, C.C. Baniotopoulos, Editor, 237-244, Editions ZITI, Thessaloniki, Greece, 2006.

4

I. Mura, "Limit Analysis of Reinforced Concrete Rectangular Slabs with Free Edges", in Proceedings of the Eighth International Conference on Computational Structures Technology, B.H.V. Topping and G.Montero and R. Montenegro, Editors, paper 129, Civil-Comp Press, Stirlingshire, UK, 2006. doi:10.4203/ccp.83.129

purchase the full-text of this paper (price £20)

go to the previous paper
go to the next paper
return to the table of contents
return to the book description
purchase this book (price £120 +P&P)