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Civil-Comp Proceedings
ISSN 1759-3433
CCP: 108
Edited by: J. Kruis, Y. Tsompanakis and B.H.V. Topping
Paper 77

A Macroelement for the Cyclic Analysis of Masonry Structures

G. Rinaldin and C. Amadio

Department of Engineering and Architecture, University of Trieste, Italy

Full Bibliographic Reference for this paper
G. Rinaldin, C. Amadio, "A Macroelement for the Cyclic Analysis of Masonry Structures", in J. Kruis, Y. Tsompanakis, B.H.V. Topping, (Editors), "Proceedings of the Fifteenth International Conference on Civil, Structural and Environmental Engineering Computing", Civil-Comp Press, Stirlingshire, UK, Paper 77, 2015. doi:10.4203/ccp.108.77
Keywords: macroelement, masonry wall, cyclic analysis, hysteretic law, non-linear spring.

In this paper, 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 idealised 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 spring must have a length conventionally chosen by the user as a 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 basis of the results of experimental tests on masonry piers.

The macroelement, implemented as a User Element (UEL) in the general finite element 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 basis of the slenderness of the masonry wall as a result of the stiffness ratios of the non-linear springs. For a slender pier, which mostly exhibits 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 two-storey perforated façade subjected to a cyclic test, demostrating the validity of the presented approach in real models.

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