A fibre flexure

Abstract

Existing sophisticated numerical micro- and macro models have already proven to be capable of simulating typical masonry behaviour. However, assessing the global response of masonry buildings using brick-to-brick micro modelling or even simplified macro modelling, in which masonry is regarded as a continuum material, takes such an amount of time that these methods cannot be considered as cost-effective. For the last two decades it has been recognized that, for the global structural behaviour of masonry buildings, simplifications have to be made. The idealization of a masonry wall as an assemblage of numerically integrated (or fibre) beam elements could considerably reduce the computational burden and therefore this study addresses the following research question:
To what extent are numerically integrated beam elements applicable for assessing the global response of masonry structures?
Whereas existing equivalent frame methods are usually based on lumped plasticity models, the approach discussed here considers the entire member (e.g pier or spandrel) as an inelastic element in which the sectional response is evaluated via a fibre discretization in which each fibre (or integration point over the depth) may follow a material uniaxial nonlinear stress-strain relation. Initially the shear response is kept linear, automatically idealizing the structural response as purely flexural. The proposed model will be hereinafter named FFM (Fibre Flexure Model). Additionally, an extension of the FFM has been proposed, describing the shearing behaviour by means of a structural nodal interface element. Adopting the nodal interface element, placed between two nodes of adjacent beam elements, the axial and bending behaviour is described with the fibre-section discretization and the shear behaviour is modelled via an equivalent Coulomb-type criterion describing the shear force limit. The proposed model will be hereinafter named FF-LSM (Fibre Flexure – Lumped Shear model) because it lumps shearing nonlinearities in one single interface element located in the centre of the structural component, whereas flexural and crushing behaviour is evaluated via smeared crack beam elements.
To validate the numerical models, two different types of benchmarks have been investigated, respectively representing the behaviour of either a single structural component (masonry pier) or a composite façade. All numerical models have been subjected to static nonlinear (pushover) analyses and results have been compared with experimental and numerical data through the use of a reference continuum model.
First, it has been demonstrated that the FFM, idealizing the structural response as purely flexural, is capable of simulating the rocking failure mode of unreinforced masonry walls, whereas it fails to simulate typical masonry shearing modes such as diagonal cracking and sliding. The use of the model for squat members that are characterized by shear failure leads to significant overpredictions, making the model not applicable for the analysis of masonry structures containing relatively squat structural components, having shear span to depth ratios less than approximately 1.
Second, the shortcoming of the FFM regarding the shearing failure mode has been overcome by combining the numerically integrated beam elements with a structural nodal interface element describing the shear behaviour. The FF-LSM including the nodal interface is able to correctly predict the shear capacity of both slender and squat walls, although the observed level of accuracy depends largely on the adopted shear failure criterion. Various shear force criteria (Coulomb friction based) have been considered: the Mann and Muller (1982) criterion, the correction proposed by Magenes and Calvi (1997) and the modification according to Abrams (1992). Generally it was observed that the criteria developed by Abrams (1992) was the most accurate and that especially for a decreasing shear ratio the criterion developed by Magenes and Calvi (1997) appeared to be less precise.
Third, analysing a composite façade, with respect to the reference continuum model the FFM and FF-LSM significantly reduce the number of elements, nodes and integration points, consequently minimizing the computational effort and maximizing the computational robustness. In comparison with the corresponding continuum model the computational time decreases by a factor of approximately 10. Despite the limitations of the FFM regarding the shearing failure mode, the model shows an acceptable accuracy in terms of initial stiffness, stiffness reduction and peak strength. Adopting the FF-LSM the numerical model predictions were significantly enhanced and both flexural and shearing failure modes (in piers and spandrels) were detected correctly. Therefore, the result of the investigation has proved to be very promising as with the FF-LSM an acceptable balance between computational cost and accuracy is found, applicable to the global analysis of two dimensional masonry structures constituting slender as well as squat walls. As many problems in engineering practice require solutions in three-dimensional space, a fully three-dimensional extension of the FF-LSM is highly recommended.