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Civil-Comp Proceedings
ISSN 1759-3433 CCP: 81
PROCEEDINGS OF THE TENTH INTERNATIONAL CONFERENCE ON CIVIL, STRUCTURAL AND ENVIRONMENTAL ENGINEERING COMPUTING Edited by: B.H.V. Topping
Paper 192
Stability of No-Tension Masonry Walls having a Non-Linear Constitutive Law I. Mura
Department of Structural Engineering, University of Cagliari, Italy Full Bibliographic Reference for this paper
I. Mura, "Stability of No-Tension Masonry Walls having a Non-Linear Constitutive Law", in B.H.V. Topping, (Editor), "Proceedings of the Tenth International Conference on Civil, Structural and Environmental Engineering Computing", Civil-Comp Press, Stirlingshire, UK, Paper 192, 2005. doi:10.4203/ccp.81.192
Keywords: masonry, instability, brick walls, nonlinear constitutive law, no-tension material, eccentric loads, finite differences method.
Summary
The adoption of a nonlinear elastic models in the description of the stress-strain
constitutive law of masonry represents a step forward compared to the use of the
linear elastic model since it allows better approximation of the material's
experimental curve. As a consequence, in the case of the study of elastic instability
phenomena one arrives at theoretical results that describe the real behaviour of
structures with excellent approximation. The various proposals that have thus far
been formulated and adopted in theoretical studies differ to a certain extent
(Frish-Fay [1,3], Powell et al [2], Priestley et al [4], Mura [5], La Mendola et al [6],
Eurocode 2 [7]). Such studies call for the adoption of quite different constitutive
laws. The dispersion of experimental results and the deformation curves
subsequently adopted derive from an objective factor: they are essentially attributed
to the dispersion of the characteristics of the different kinds of masonry involved.
One model describing the realistic material behaviour for concrete is given in a
standardised material law in [7]. In general, two barriers can be set: linear-elastic material behaviour (theory of elasticity) as the lower limit; or rigid-plastic material behaviour (theory of plasticity) as the upper limit.
The actual
material behaviour of brickwork is nonlinear and lies within these two barriers for
all masonry unit and mortar combinations. The schematization of the constitutive
law with a second-degree parabolic trend and the vertex corresponding to the
maximum strength value appears to be the most generalized one. Such a
schematization indeed describes the behaviour of brick walls and concrete walls (see [2,4]).
Examined herein is the behaviour of load-bearing masonry walls or piers with
no reinforcement subject to eccentric loads, made of a no-tension material and
whose stress-strain law is nonlinear (a second-degree parabolic trend). For a fixed
free-ended column subject to axial load with constant initial eccentricity along the
axis, the complete critical path is predicted by a computer program.
As a preliminary step, the stress and strain distribution is derived for a rectangular
section of width
Then the differential equations governing the problem of equilibrium stability are
formulated. Since analytic integration of this type of nonlinear differential equations turn
out to be quite complex, the recourse is to program the automatic calculation
optimized for the purpose of performing numerical integration with the finite
difference method. The results of the numerical investigation will be illustrated in
detail, both through examination of the load-deflection curves obtained directly and
through illustration of the diagram deduced from them, which supplies the reduction
coefficient of the load by eccentricity and slenderness
References
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