Shear strength of URM walls retrofitted using FRP

This paper compares different models currently used to calculate the shear strength of unreinforced masonry (URM) walls retrofitted using fiber reinforced polymers (URM-FRP). The shear strengths of six recently tested URM-FRP walls were compared to shear strengths predicted by the models herein. Four of these specimens were tested under constant gravity load and incrementally increasing in-plane loading cycles. The other two specimens were tested on a uniaxial earthquake simulator. The specimens were subjected to synthetic earthquake motions with increasing intensity. Each specimen was retrofitted on the entire surface of a single side using FRP with different axial rigidities. One of the shear strength models compared in this study has been recently developed by the authors: The model was explicitly developed to predict the shear strength of unreinforced masonry walls retrofitted using FRP. The model idealized masonry, epoxy, and FRP in a URM-FRP as. different layers of isotropic homogeneous elastic materials. Then, using principles of the theory of elasticity, the governing differential equation of the system is formulated and linearly solved. Then, the material nonlinearity was implemented via a step-by-step degradation in the layer stiffness; after each step the equations were resolved linearly. In most cases, failure occurred in either the masonry or the epoxy and in no case did FRP reach its ultimate load. Comparisons between the different shear models showed that the authors' model is more conservative than the other existing models. In addition, for a small FRP axial rigidity, the difference between the models was insignificant. However, with increasing FRP axial rigidity the differences between the models became more significant. This paper highlighted the advantages and disadvantages of each model. It was found that the authors' model offered several advantages over the other available models. However, the authors' model also has its own disadvantages and limitations. One of these limitations is that it does not explicitly take into consideration the out-of-plane normal stresses. Finally, additional experimental verification of the authors' model is recommended. (c) 2006 Elsevier Ltd. All rights reserved.

Force–displacement response of in-plane loaded unreinforced brick masonry walls: the Critical Diagonal Crack model

Katrin Beyer, Bastian Valentin Wilding

This article introduces an analytical model to compute the monotonic force–displacement response of in-plane loaded unreinforced brick masonry walls accounting for walls failing in shear or ﬂexure. The masonry wall is modelled as elastic in compression with zero tensile strength using a Timoshenko beam element. Its cross-section properties (moment of inertia and area) are continuously updated to capture the non-linearity that results from ﬂexural and shear cracking. For this purpose, diagonal cracking of shear critical walls is represented by one Critical Diagonal Crack. The ultimate drift capacity of the wall is determined based on an approach evaluating a plastic zone at the wall toe. Validation against results of cyclic full-scale tests of unreinforced masonry walls made with vertically perforated clay units shows that the presented formulation is capable of accurately predicting the effective stiffness, the maximum strength and the ultimate drift capacity of the wall. It outperforms current empirical code equations with regard to stiffness and ultimate drift capacity estimates and yields similar results concerning strength prediction.

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.

EPFL2018

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

Bastian Valentin Wilding

EPFL2018