Keywords: masonry, buckling, collocation method, nonlinear constitutive law, combined load, different end conditions.

In this study the stability of unreinforced load-bearing masonry walls or piers with different support conditions subject to a combined load consisting of a vertical uniformly distributed axial load and a concentrated load at the top end is examined. The stability of members subjected only to a concentrated load at the top is the most intensively studied case. The case of members under gravity loads has also been investigated. Only a few papers addressed the stability of members under simultaneous vertical concentrated load at the top and distributed axial load (gravity loads or its own weight) [1,2].

The adoption of a nonlinear elastic model for the description of the stress-strain constitutive law of masonry marked a move forward with respect to the use of the linear elastic model, in that it makes it possible to approximate the experimental curve of the material more accurately. As a consequence the theoretical results obtained in the study of phenomena in the field of elastic instability give an optimal approximation of the realistic behaviour of the structure.

The study of buckling conditions of masonry walls or piers presents different causes of nonlinearity. The nonlinearity of a geometric nature deriving from second-order effects and the nonlinearity deriving from the constitutive law of the material (the stiffness of the material is reduced with the increase in the intensity of the acting compressive stress) must be considered.

In the present paper the constitutive law of masonry is assumed to be of a nonlinear elastic type and is represented by a second-degree parabola. The differential problem is formulated extremely carefully and then solved numerically. The solution to both the differential problem and the determination of unknown parameters (instability load, redundant moment and forces at the supported extremities) is reached by using the collocation method.

Matlab® provides some functions (bvp4c, bvp5c and bvp6c) to solve two-point boundary value problems with the collocation method with the possibility of determining the unknown parameters of the physical problem (like the stability load, redundant forces or moments at the support extremities etc.) by the simple addition of surrounding conditions to those derived from the differential problem.

The accuracy of the results obtained is assessed by comparison with the results derived by the use of other methods of solution. It concludes that different support conditions have an important influence on the load carrying capacity of walls and that the collocation method makes it possible to the solve the problem in simply and precisely within a period of time.

1

I. Mura, "Stability of nonlinear masonry members under combined load", Computers & Structures, 86(15-16): 1579-1953, 2008. doi:10.1016/j.compstruc.2008.01.003

2

I. Mura, "Stability of Double-Hinged Nonlinear Masonry Members under Combined Load", in B.H.V. Topping, M. Papadrakakis, (Editors), "Proceedings of the Ninth International Conference on Computational Structures Technology", Civil-Comp Press, Stirlingshire, UK, Paper 240, 2008. doi:10.4203/ccp.88.240

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