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CivilComp Proceedings
ISSN 17593433 CCP: 83
PROCEEDINGS OF THE EIGHTH INTERNATIONAL CONFERENCE ON COMPUTATIONAL STRUCTURES TECHNOLOGY Edited by: B.H.V. Topping, G. Montero and R. Montenegro
Paper 79
Dynamic Analysis of AgeOld Masonry Constructions S. Degl'Innocenti, C. Padovani, A. Pagni and G. Pasquinelli
Institute of Information Science and Technologies "A. Faedo", Italian National Research Council, Pisa, Italy S. Degl'Innocenti, C. Padovani, A. Pagni, G. Pasquinelli, "Dynamic Analysis of AgeOld Masonry Constructions", in B.H.V. Topping, G. Montero, R. Montenegro, (Editors), "Proceedings of the Eighth International Conference on Computational Structures Technology", CivilComp Press, Stirlingshire, UK, Paper 79, 2006. doi:10.4203/ccp.83.79
Keywords: masonry constructions, nonlinear elasticity, dynamic analysis, finite element method.
Summary
In order to perform dynamic analyses of real masonry structures many researchers
model the masonry as a linear elastic material and apply the mode superposition
method to integrate the equations of motion [1,2,3]. Alternatively, the dynamic
behaviour of very simple structures has been investigated using an elasticplastic
constitutive model imbedded into a direct integration method [4,5,6].
In this paper masonry is modelled as a nonlinear elastic material with zero tensile strength and infinite compressive strength [7,8,9]. The resulting constitutive equation, known as the equation of masonrylike or notension material, is able to account for some of masonry's peculiarities, in particular, its inability to withstand large tensile stresses. Assumptions underlying the model are that the infinitesimal strain is the sum of an elastic part and a fracture part, and that the stress, negative semidefinite, depends linearly and isotropically on the former and is orthogonal to the latter, which is positive semidefinite. Thus, the stress is a nonlinear function of the infinitesimal strain. In order to study the structural behaviour of existing masonry structures, both the static and dynamic problem can be solved via the finiteelement method [9,10]. The equation of masonrylike materials has been implemented into the finiteelement code NOSA, developed entirely at ISTICNR with the purpose of studying the behaviour of masonry solids and modelling restoration and reinforcement operations on constructions of particular architectural importance. The code has been successfully applied to the analysis of some buildings of historical interest: the S. Nicolò Motherhouse in Noto, the Medici Arsenal in Pisa, the Baptistery of the Volterra Cathedral, the Church of S. Pietro in Vinculis in Pisa, the Buti bell tower and the dome of the Church of S. Maria Maddalena in Morano Calabro. As far as numerical solution of the dynamic problem is concerned, the equations of motion must be integrated directly. In fact, due to the nonlinearity of the adopted constitutive equation, the modesuperposition method is meaningless. We instead apply the Newmark method implemented in NOSA [10] to perform the time integration of the system of ordinary differential equations obtained by discretising the structure into finite elements. In this paper, the numerical method presented in [10] is applied to ageold masonry constructions, in particular to the dome of a church located in the Calabria Region, Italy. We present the numerical method implemented in the NOSA code for the dynamic analysis of masonry structures, with particular focus on vaults and domes. Subsequently, we study the damaged dome and tambour of the Church of Santa Maria Maddalena in Morano Calabro. The structure has been discretised with shell elements and analyses performed using the NOSA code. Initially, the structure is at rest, in static equilibrium under the action of its own weight. Subsequently, the base of the tambour, which is clamped, is subjected to a cyclic horizontal acceleration acting over a given time interval, and then the construction is left to oscillate freely. The results obtained considering the masonry to be a nonlinear elastic material are compared with the results of an analogous dynamic analysis carried out on the same structure, while however assuming linear elastic material behaviour. This comparison has highlighted the profound differences between the results obtained using the two assumptions. References
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