Modelling of the Cyclic Response of an Unreinforced Masonry Wall through a Force Based Beam Element

The seismic assessment of existing masonry buildings is based on the prediction of their nonlinear response under lateral loading. This requires a reliable estimation of the force and displacement demand. For this purpose, modelling strategies using structural component elements are widely applied both in research and in engineering practice, since they can provide a satisfactory description of the cyclic behaviour of a masonry building with a limited computational cost. One of such modelling strategies are equivalent frame models, in which beam elements describe the response of piers and spandrels. This paper proposes the use of two-node, force-based beam elements with distributed inelasticity to model the in-plane response of modern unreinforced brick masonry panels. The nonlinearity of the response is described through the use of numerically integrated fibre sections and a suitable material model, implemented for this scope in the open-source platform “OpenSees”, describing a coupling at the local level between axial and shear response. Experimental results from a shear and compression test are used to validate the approach and justify some details of the proposed modelling strategy. Since the experimental data included also local displacement measures, the comparison of the numerical and experimental results is extended to curvatures and shear strains. The good agreement between numerical and experimental response confirms the applicability of the proposed approach for modelling the cyclic response of unreinforced brick masonry walls.

Punching shear strength and behaviour of compact reinforced concrete footings

Miguel Fernández Ruiz, Aurelio Muttoni, João Tiago Ramos Bernardo de Santa Rita Simões

concrete footings with and without transverse reinforcement. Even though that punching shear failures have already been deeply investigated, there is still scanty experimental information on full-scale reinforced concrete footings failing in punching shear. The results of an experimental programme addressed to this issue (punching of reinforced concrete footings with and without shear reinforced) are presented in this paper. A total number of 5 square specimens were tested with a nominal thickness of 550 mm, where the influence of the side length of the footings, the column size (and thus shear slenderness) and the presence of top and transverse reinforcement were investigated. The experimental results show that punching strength increases with the increase of the column size and with the decrease of the size of the footing. It also results as experimental evidence that a significant flexural-shear interaction might occur for high shear loads, leading to much lower flexural strengths than those calculated according to yield-line theory. Limit analysis might be a consistent tool to investigate the failure of concrete struts provided that cracking is properly accounted for, particularly with reference to the effective concrete compressive strength as a function of the state of deformations. In this sense, the kinematical theorem of limit analysis is used to investigate on the governing failure mechanisms and to calculate failure loads. The theoretical results show that an important flexural-shear interaction occurs, leading to a smooth transition between the flexural and punching shear failures. The experimental results are analysed based on theoretical considerations resulting from the application of limit analysis. It is shown that a consistent agreement can be found between such theoretical approach and the experimental evidences.

11th fib International PhD Symposium in Civil Engineering2016

Influence of load history on the force-displacement response of in-plane loaded unreinforced masonry walls

Katrin Beyer, Kiarash Mohtasham Dolatshahi, Bastian Valentin Wilding

Empirical drift capacity models for in-plane loaded unreinforced masonry (URM) walls are derived from results of quasi-static cyclic shear-compression tests. The experimentally determined drift capacities are, however, dependent on the applied demand, i.e., on the loading protocol that is used in the test. These loading protocols differ between test campaigns. The loading protocols applied in tests are also different from the displacement histories to which URM walls are subjected in real earthquakes. In the absence of experimental studies on the effect of loading histories on the wall response, this article presents numerical simulations of modern unreinforced clay block masonry walls that are subjected to different loading protocols. The study shows that the force capacity is not very sensitive to the loading protocol. The drift capacity of walls failing in shear is, however, rather sensitive to the loading history while the drift capacity of walls failing in flexure is not. The largest difference in drift capacity of up to 100% is observed between monotonic and cyclic loading for shear controlled walls under double-fixed boundary conditions and low axial load ratios.

2017

Stiffness, force and drift capacity of in-plane loaded modern unreinforced brick masonry walls

Bastian Valentin Wilding

In countries of low to moderate seismicity, such as Switzerland, unreinforced masonry (URM) is mainly used in residential buildings due to its good insulation capacity and fire resistance along with a fair compressive strength. URM walls however show a limited horizontal in-plane deformation capacity, which can lead to an unfavorable seismic response. To predict this response, at least the walls' effective stiffness, shear force and drift capacity are required. While mechanics-based models for the force capacity are well established, such approaches are largely lacking for the effective stiffness and the drift capacity. The mostly empirical code equations for the two latter parameters lead to unsatisfactory and, in the case of drift capacities, often unconservative predictions when compared to tests. To address the issue, this thesis introduces an analytical model describing the monotonic force-displacement response of in-plane loaded URM walls. Based on a Timoshenko beam, the influence of diagonal shear and horizontal flexural cracking is captured by mechanical models, leading to an analytical description of the pre-peak force-displacement response. The shear force capacity is determined using local stress criteria and the ultimate drift capacity is estimated with a plastic zone approach evaluating a crushed region of high curvatures at the wall toe at ultimate failure. A comparison with experiments indicates that the model yields reliable predictions of stiffness, strength and drift capacity. Moreover, the monotonic model is extended to capture the full cyclic response including stiffness degradation and residual displacements. Furthermore, an existing numerical mesoscale approach is used to conduct parametric studies. The wall is modelled with solid elements, capturing brick crushing, and interface elements, simulating sliding and flexural uplift in the bed-joints. A study of the load history influence shows that for walls failing in shear, the drift capacity can reduce to half from monotonic to reversed-cyclic loading. The second study simulates different test setups used in the literature to impose double-fixed support conditions. While there appears to be hardly any difference between the force and the mixed-controlled mode, simulating the double-fixed wall as a cantilever with half its original height leads in many cases to a strong overestimation of force and drift capacities. The final investigation concerns a change in axial force during horizontal loading. The force and drift capacities of walls under changing normal force appear to be very similar to those of walls under a constant normal force that corresponds to the changing axial load towards ultimate failure. In addition, a database of shear-compression tests is extended and analysed for trends in stiffness and drift capacity. Both, the initial and the effective stiffness increase with increasing axial load, while the ratio of effective-to-initial stiffness is rather constant and lies around 0.75. As for the drift capacity, an upward trend with increasing shear span ratio and a downward trend with increasing axial load are observed. Concluding, simple mechanics-based formulations for the effective stiffness, the force and the drift capacity to be used in design are proposed. A validation with the database shows that the new formulations are more accurate in predicting effective stiffness and drift capacity than currently used code equations.