In this work, a macroelement for the cyclic analysis of masonry structures is presented. The proposed model is based on the equivalent frame method to represent the structure, in which each masonry pier or spandrel is schematised by a beam-type macroelement containing two flexural nonlinear springs at both ends, a shear nonlinear spring in the middle and two Euler-Bernoulli elastic beams connecting them. Each springs have a length conventionally chosen by the user in percentage of the macroelement height, and their characteristics are calculated automatically. The springs exhibit a cyclic behaviour, different for flexure and shear. Stiffness and strength degradation are implemented in both hysteretic laws; moreover, the strength is calculated during the analysis as a function of the axial compressive load. All parameters governing degradations and hysteretic cycles are obtained on the base of the results of experimental tests on masonry piers. The macroelement, implemented as User Element (UEL) in the general FE code Abaqus is formulated using the static condensation method, and it supplies the tangent stiffness matrix and the force vector as output. The force vector is obtained assembling the contribution of each element and performing some simple Newton-Raphson iterations to ensure the internal equilibrium. To validate the proposed cyclic behaviour, two cyclic experimental tests on masonry piers have been reproduced numerically. It is shown that the macroelement is able to change the amount of dissipated energy on the base of the slenderness of the masonry wall thanks to the stiffness ratios of the non-linear springs. For a slender pier, which mostly has a flexural collapse, the rotational springs will mainly influence the whole response, while for a squat wall, that presents a shear failure, the shear spring will be more stressed. A comparison between experimental and numerical results is also performed on a 2-storey perforated façade subjected to a cyclic test, evidencing the validity of the presented approach in real models.
A macroelement for the cyclic analysis of masonry structures
Rinaldin, G.
;Amadio, C.
2015-01-01
Abstract
In this work, a macroelement for the cyclic analysis of masonry structures is presented. The proposed model is based on the equivalent frame method to represent the structure, in which each masonry pier or spandrel is schematised by a beam-type macroelement containing two flexural nonlinear springs at both ends, a shear nonlinear spring in the middle and two Euler-Bernoulli elastic beams connecting them. Each springs have a length conventionally chosen by the user in percentage of the macroelement height, and their characteristics are calculated automatically. The springs exhibit a cyclic behaviour, different for flexure and shear. Stiffness and strength degradation are implemented in both hysteretic laws; moreover, the strength is calculated during the analysis as a function of the axial compressive load. All parameters governing degradations and hysteretic cycles are obtained on the base of the results of experimental tests on masonry piers. The macroelement, implemented as User Element (UEL) in the general FE code Abaqus is formulated using the static condensation method, and it supplies the tangent stiffness matrix and the force vector as output. The force vector is obtained assembling the contribution of each element and performing some simple Newton-Raphson iterations to ensure the internal equilibrium. To validate the proposed cyclic behaviour, two cyclic experimental tests on masonry piers have been reproduced numerically. It is shown that the macroelement is able to change the amount of dissipated energy on the base of the slenderness of the masonry wall thanks to the stiffness ratios of the non-linear springs. For a slender pier, which mostly has a flexural collapse, the rotational springs will mainly influence the whole response, while for a squat wall, that presents a shear failure, the shear spring will be more stressed. A comparison between experimental and numerical results is also performed on a 2-storey perforated façade subjected to a cyclic test, evidencing the validity of the presented approach in real models.Pubblicazioni consigliate
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