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

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.

Seismic Behaviour and Design of Mixed RC-URM Wall Structures

Alessandro Paparo

In several countries of central Europe, many modern residential buildings are braced by reinforced concrete (RC) and unreinforced masonry (URM) walls coupled with RC slabs. Such mixed constructions, in fact, behave better under seismic loading than buildings with URM walls alone. Similarly, the insertion of RC walls is a technique used to retrofit existing modern URM constructions that feature RC slabs, since both strength and displacement capacities of the repaired structure increase with respect to the un-retrofitted configuration. Although modern mixed RC-URM wall buildings are rather common, very little is known about their seismic behaviour and codes do not provide adequate design and assessment guidelines. Hence, the thesis focuses on four objectives: (1) to provide experimental data on the seismic behaviour of mixed RC-URM wall structures; (2) to formulate recommendations for setting up numerical models for structures with both RC and URM walls; (3) to develop a mechanical model that represents the interaction between RC and URM walls; (4) to propose a displacement-based seismic approach for the design of new mixed RC-URM wall structures and the retrofitting of URM wall buildings by adding RC walls or replacing URM walls with RC ones. An experimental investigation of two mixed RC-URM wall substructures leads to new findings with respect to the actual distribution of the reaction forces between RC and URM walls and gives insight into the displacement profile of mixed RC-URM wall structures. The results are used to validate two numerical strategies and recommendations for setting up models for structures with both RC and URM walls are formulated. A simple mechanical model, which takes into account the most important parameters influencing the seismic behaviour of mixed RC-URM wall structures, is proposed and validated. The model is based on the shear-flexure interaction as URM and RC walls display dominant shear and flexural deformations, respectively. In the last part of the thesis a displacement-based design approach for mixed RC-URM wall structures is developed. The design method is verified through inelastic time-history analyses (ITHA) of three-to-five-storey case study buildings. Comparison between the design values and the results from ITHA suggests that the design methodology controls the horizontal deflection of the structures, being almost linear over their height, and avoids concentrations of deformations in the bottom storey, a typical feature of URM wall structures. On the other hand, for the three-storey configurations, it was observed that the approach overestimates the maximum horizontal displacement.

EPFL2015

Development of a displacement-based design approach for modern mixed RC-URM wall structures

Katrin Beyer, Alessandro Paparo

The recent re-assessment of the seismic hazard in Europe led for many regions of low to moderate seismicity to an increase in the seismic demand. As a consequence, several modern unreinforced masonry (URM) buildings, constructed with reinforced concrete (RC) slabs that provide an efficient rigid diaphragm action, no longer satisfy the seismic design check and have been retrofitted by adding or replacing URM walls with RC walls. Of late, also several new construction projects have been conceived directly as buildings with both RC and URM walls. Despite the widespread use of such construction technique, very little is known about the seismic behaviour of mixed RC-URM wall structures and codes do not provide adequate support to designers. The aim of the paper is therefore to propose a displacement-based design methodology for the design of mixed RC-URM edifices and the retrofit of URM buildings by replacing or adding selected URM walls with RC ones. The article describes also two tools developed for estimating important quantities relevant for the displacement-based design of structures with both RC and URM walls. The tools are (i) a mechanical model based on the shear-flexure interaction between URM and RC walls and (ii) an elastic model for estimating the contribution of the RC slabs to the overturning moment capacity of the system. In the last part of the article the proposed design method is verified through non-linear dynamic analyses of several case studies. These results show that the proposed design approach has the ability of controlling the displacement profile of the designed structures, avoiding concentration of deformations in one single storey, a typical feature of URM wall structures.

Techno-Press2015

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.