Limit states of modern unreinforced clay brick masonry walls subjected to in-plane loading

Recent research showed that the in-plane horizontal displacement capacity of unreinforced masonry (URM) walls depends on numerous factors that are not yet captured by current empirical drift capacity models; e.g., axial stress, shear span, geometry of the walls and the material used. In order to improve the performance-based assessment of URM wall buildings, future research should aim at developing numerical and mechanical models that link the global force-displacement response of URM walls to local deformation measures such as strains. This paper addresses the behaviour of modern clay brick masonry and makes first contributions to such an endeavour by the evaluation of experimental results: first, two sets of limit states are proposed that link local damage limit states to characteristic points of the global force-displacement response of the URM wall. The two sets define limit states for walls developing a shear or a flexural mechanism respectively. Second, local deformation measures deemed suitable for the characterisation of these limit states are evaluated from optical measurement data of quasi-static cyclic wall tests. These include strains, compression zone depth and the ratio of shear to flexural deformations.

Structural Response of R-UHPFRC - RC Composite Members Subjected to Combined Bending and Shear

Talayeh Noshiravani

The addition of a thin overlay of Ultra-High Performance Fibre Reinforced Concrete (UHPFRC) to Reinforced Concrete (RC) members is an emerging technique to strengthen and protect existing structures and to design durable new structures. Combining UHPFRC with closely spaced, small-diameter steel rebars in Reinforced UHPFRC (R-UHPFRC) layers improves the UHPFRC's strain hardening behaviour. For reasons of practicality, R-UHPFRC layers are cast or glued (in the case of prefabricated elements) on top of RC members, thus changing the latter into R-UHPFRC - RC composite members. The high strength and deformation capacity of R-UHPFRC elements make them a suitable external flexural reinforcement for RC members over intermediate supports, e.g., bridge decks and slabs or beams in buildings. Over reinforcement of RC beams and slabs with tensile flexural reinforcement can result in their shear failure at either a lower resistance or deformation than the associated values for member failure in flexure. A comprehensive experimental program was conducted to study the flexure-shear behaviour of R-UHPFRC - RC composite beams. The program comprises two test series on cantilever beams and continuous beams. The test parameters include shear span-depth ratio (a/d), the amount of transverse reinforcement ( ρν), the amount of longitudinal reinforcement, and the strength and bond condition of the R-UHPFRC rebars. The experimental results reveal the different failure modes of R-UHPFRC - RC composite members and the contribution of the R-UHPFRC elements to the member resistance, ductility and capacity to redistribute the internal stress. It was shown that in R-UHPFRC - RC beams with ribbed rebars and a shear span to depth ratio greater than 2.5 the stresses are carried by beam action. Depending on the degree of longitudinal reinforcement, all but two of the beams with 3.0≤a/d≤3.4 and ρν≤0.17 had a flexure-shear failure; the rest failed in flexure. The flexure-shear failure of the composite beams was at an approximately equal rotation level as their RC reference beam but at a resistance 2.3 times that of the RC beam. This is due to (1) the debonding interface zone between the elements that allows the R-UHPFRC - RC beams to rotate more freely and (2) the out-of-plane resistance of the R-UHPFRC element that contributes to the shear resistance. The internal flow of forces and the structural response of composite members strongly depend on the bond condition between the R-UHPFRC and RC, the UHPFRC and its rebars, as well as the concrete and its rebars. Cracking of the concrete along the interface zone causes bond reduction, i.e., softening of the shear connection, between the two elements. In presence of high shear stresses and diagonal flexure-shear cracks, interface zone softening is observed between the elements prior to the maximum resistance, while UHPFRC is strain hardening. The cause of this softening behaviour is the prying action due to the relative rotational movement of the RC rigid bodies separated by the flexure-shear cracks. Static and kinematic solutions of the theory of plasticity for RC beams are extended to predict the collapse load of R-UHPFRC - RC composite beams at the ultimate limit state. A mechanical model for predicting the structural response of composite beams is proposed. In combination with truss models, the concept of an R-UHPFRC - RC plastic hinge is introduced to calculate the force-displacement response of composite beams. The failure criterion based on the collapse mechanisms (kinematic solutions) sets the limit of the force-displacement response. The model is corroborated by the experimental results. This model provides a tool for analysis of RC members reinforced with an added tensile R-UHPFRC element.

EPFL2012

Review and improvement of simple mechanical models for predicting the force-displacement response of URM walls subjected to in-plane loading

Katrin Beyer, Sarah Petry

In performance-based seismic design the global displacement capacity of structures is predicted on the basis of local engineering demand parameters and mechanical models that link local and global deformation quantities. Although unreinforced masonry (URM) is one of the most used construction materials for residential structures all over the world, the displacement capacity of in-plane loaded URM walls is still mainly estimated from empirical drift capacity models rather than mechanical relationships between local and global deformation capacities. In this article, we present an analytical model which links the top displacement of an URM wall to the applied in-plane shear load. In order to verify the model, we compare the predicted results to global and local deformation quantities from own URM wall tests. Comparison of global deformation quantities shows that we are able to predict the initial stiffness of the walls with the simple assumption of a no-tension material and a linear-elastic material in compression. For walls developing a diagonal shear failure or hybrid failure, the predicted force-displacement curve starts diverging from the experimental envelope with the formation of the first diagonal cracks. With comparison of local deformation quantities, e.g. curvature profiles and shear strain profiles, we show that this is due to the formation of a significant diagonal shear crack.

2014

Force-displacement response of unreinforced masonry walls for seismic design

Sarah Petry

In regions with low to moderate seismicity, unreinforced masonry (URM) is commonly used for the construction of low to mid-rise buildings. When these structures are subjected to seismic loading, the stiff URM walls attract considerable part of the lateral forces and need therefore to be considered in seismic design and assessment. Nevertheless, the response of URM walls subjected to lateral in-plane loading is not yet fully understood and given estimates for some of the crucial design parameters are unsatisfactory (the displacement capacity and the effective stiffness). Two series of URM walls tested under lateral in-plane loading are presented. First series was built at full-scale using a typical Swiss hollow clay brick and a commercially available standard cement-based mortar. Second series represented the same walls at half-scale. During all tests, the walls were subjected to quasi-static cycles of increasing drift demands, while controlling the boundary conditions (axial load and moment restraint at the top of the walls) such to simulate the typical loading of a ground floor wall in an URM building. From the experiments several new insights on the kinematics of URM walls are drawn. For instance, it is identified that once several diagonal cracks develop in the walls, the deformation capacity of the walls is governed by the separation of the rectangular wall into two triangles. From comparison between both test series at different scales, new recommendations for the correct scaling of hollow core masonry are derived and proposed. In order to compare our own results to other existing wall tests, an existing dataset of URM walls is extended and reanalyzed. Finally, a dataset of 64 quasi-static tests on modern URM walls of different heights and masonry types is presented. The evaluation of the dataset confirms the influence of the boundary conditions on the drift capacity. Moreover, it reveals the presence of a strong size effect and an empirical equation is proposed to estimate the ultimate drift capacity while accounting for these factors. Throughout the wall tests, an optical measurement system is used to track the displacement field of the walls. This measurement was synchronized with the force measurement such that global and local engineering demand parameters of the walls could be linked. This point was crucial for the following contributions of this thesis: (i) proposition of two sets of limit states (LSs) that link local damage states to characteristic points of the global force-displacement curve of URM walls; (ii) the study of different deformation parameters for the validation of mechanical and numerical models at local level. A new mechanical model is proposed which describes the nonlinear force-displacement response of flexural dominated URM walls. For this, first, an analytical part is derived based on the plane section hypothesis and a non-tension material with a linear-elastic constitutive material law in compression. It assumes that only the compressed part of the wall contributes to the wall resistance and accounts for a softening due to the reduction of the effective area. In a second step, new criteria are developed which predict the occurrence of the previous proposed local LSs, which are then incorporated in the analytical model. The new complete mechanical model is validated through the comparison with experimental evidence yielding to good estimates for the effective stiffness and the displacement capacity.