Analytical Solution For Postbuckling Of Uniform Nonlinear Masonry Piers
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In this paper the stability condition of uniform cantilevered masonry piers, subjected to eccentric concentrated load, is investigated, considering materials with nonlinear (parabolic) stress-strain law under compression. The analytical solution is obtained by integrating the nonlinear differential equation of the deflection curve using the Taylor series method. Depending on load intensity, on the height-to-depth ratio and initial eccentricity of the applied load, a column can fail owing to elastic instability or because the masonry at the fixed section has attained, or exceeded, the allowable compressive or tensile stress. Keywords: masonry, piers, instability, nonlinear constitutive law, Taylor series. 1 Introduction The stability study of panels and columns under eccentric compression requires an accurate knowledge of the material’s constitutive law, which is generally nonlinear. The experimental results reported in the literature (Powell and Hodgkinson , Priestley and Elder , Naraine and Sinha , Pume , Mojsilović ) and the various deformation curves that have thus far been adopted in theoretical studies of instability (Frish-Fay , Sawko and Rouf , La Mendola and Papia , Mura [10, 11]) differ to a certain extent. One model realistically describing the behaviour for concrete is given in a standardised material law in Eurocode2 . This law simulates two behaviour limits for the material: elastic and rigid-plastic. Schematising the constitutive law with a second-degree parabolic trend, where the vertex corresponds to the maximum strength value, appears to be the most generalized approach. Indeed this schematization describes the behaviour of brick and concrete walls [1, 2] and will thus be used in the present study.
masonry, piers, instability, nonlinear constitutive law, Taylor series.