Flexural deformations of URM piers: Comparison of analytical models with experiments

Despite the fact that displacement-based methods are now frequently applied when assessing the seismic performance of unreinforced masonry (URM) structures, the displacement capacity of in-plane loaded URM piers is still estimated from empirical rather than mechanical relationships. One idea for estimating a pier’s force-displacement curve including its displacement capacity that has been put forward in the past is based on the double integration of the curvature profile. The curvature is derived assuming a bilinear stress-strain relationship in the compression domain and neglecting the tensile strength of the masonry. We tested several identical URM piers under different constant axial load and shear span ratios while applying quasi-static horizontal cyclic in-plane loading. During testing, we tracked with a set of cameras the displacement of four LEDs on each full brick of the masonry piers. Therefore, we were able to determine the local deformations, e.g. average strains in the bricks and deformations of the joints. In this paper we will present experimentally determined local and global deformation quantities of one pier dominated by flexural deformations and compare these to the estimates from the analytical model. Differences between model and experiment will be discussed and first estimates of performance limits describing local deformations will be proposed.

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.

EPFL2015

Modelling shear–flexure interaction in equivalent frame models of slender reinforced concrete walls

Katrin Beyer, Panagiotis Mergos

Quasi-static cyclic tests on reinforced concrete (RC) walls have shown that shear deformations can constitute a significant ratio of the total deformations when the wall is loaded beyond the elastic regime. For slender RC walls that form a stable flexural mechanism the ratio of shear to flexural deformations remains approximately constant over the entire range of imposed displacement ductilities. This paper proposes a method for incorporating shear-flexure interaction effects in equivalent frame models of slender RC walls by coupling the shear force-shear strain relationship to the curvature and axial strain in the member. The suggested methodology is incorporated in a finite element consisting of two interacting spread inelasticity sub-elements representing flexural and shear response, respectively. The element is implemented in the general finite element code IDARC and validated against experimental results of RC cantilever walls. In a second step, it is applied in inelastic static and dynamic analyses of tall wall and wall-frame systems. It is shown that ignoring shear-flexure interaction may lead to erroneous predictions in particular of local ductility and storey drift demands.

2014

Cyclic test data of six unreinforced masonry walls with different boundary conditions

Katrin Beyer, Sarah Petry

Previous test data on unreinforced masonry walls focused on the global response of the wall. A new data set (Petry and Beyer 2014a; D01:10.5281/zenodo.8443) on six wall tests, which is publicly available, allows for linking global to local deformations of masonry walls, which can be useful for advancing performance-based design and assessment methods for unreinforced masonry buildings. This data paper presents the results of a test series on six identical unreinforced masonry walls that were constructed using hollow clay brick units and standard cement-based mortar. The test units were subjected to quasi-static cycles of increasing drift demands and the tests differed with regard to the applied axial load and the moment restraint applied at the top of the walls. The walls were tested up to failure. Throughout the loading the deformations of the walls were recorded using a digital photogrammetric measurement system tracking the movement of 312 points per test unit.

Earthquake Engineering Research Inst2015

Force-displacement response of unreinforced masonry walls for seismic design

Sarah Petry

EPFL2015