Deformation capacity evaluation for flat slab seismic design

In flat-slab frames, which are typically designed as secondary seismic structures, the shear failure of the slab around the column (punching failure) is typically the governing failure mode which limits the deformation capacity and can potentially lead to a progressive collapse of the structure. Existing rules to predict the capacity of flat slab frames to resist imposed lateral displacements without losing the capability to bear gravity loads have been derived empirically from the results of cyclic tests on thin members. These rules account explicitly only for the ratio between acting gravity loads and resistance against concentric punching shear (so-called Gravity Shear Ratio). Recent rational models to estimate the deformation capacity of flat slabs show that other parameters can play a major role and predict a significant size effect (reduced deformation for thick slabs). In this paper, a closed-form expression to predict the deformation capacity of internal slab-column connections as a function of the main parameters is derived from the same model that has been used to develop the punching shear formulae for the second generation of Eurocode 2 for concrete structures. This expression is compared to an existing database of isolated internal slab-column connections showing fine accuracy and allowing to resolve the shortcomings of existing rules. In addition, the results of a testing programme on a full-scale flat-slab frame with two stories and 12 columns are described. The differences between measured interstorey drifts and local slab rotations influencing their capacity to resist shear forces are presented and discussed. With respect to the observed deformation capacities, similar values are obtained as in the isolated specimens and the predictions are confirmed for the internal columns, but significant differences are observed between internal, edge and corner slab-column connections. The effects of punching shear reinforcement and of integrity reinforcement (required according to Eurocode 2 to prevent progressive collapse after punching) are also discussed.

The mechanics of shear failures in RC slabs based on refined measurements

Raffaele Cantone

Reinforced concrete planar members, as slabs and shells, are structural elements commonly used in the construction technique, which are typically designed without the arrangement of shear reinforcement. Despite the fact that this solution allows for fast and economic construction, the absence of shear reinforcement can give rise to the potential localization of strains within a critical shear crack and eventually to the shear failure of the member. In the case of redundant systems, most research on the mechanics of shear failures has been devoted to the strength of the member, neglecting in many cases the development of shear deformations due to inclined cracking as well as the redistributions of internal forces, which are instrumental for the analysis of the response of these members. The contribution to the state-of-the-art includes a series of theoretical works explaining the observed responses for a series of experimental programmes. These experimental campaigns comprise tests in tension, shear tests in one- and two-way slabs as well as punching tests. For their instrumentation, in addition to classical measurement devices, Fibre-Optic Measurements and Digital Image Correlation were intensively used.This thesis starts by revisiting the basis of the interaction between reinforcement and concrete. A series of bond tests show the stress concentrations occurring near the ribs and its complex transfer of forces with the surrounding concrete. In addition, tests on beams failing in shear show a complex interaction between bond stresses and kinking on the reinforcement due to the development of dowel action. These phenomena are normally neglected for concrete design due to the ductile nature of reinforcement, but may be relevant for fatigue and negative tension-stiffening effects.An important step in the knowledge is performed on the understanding of the shear response with respect to the characterization of the deformations in concrete members. Based on a series of test results, a complete description of the deformation field (including shear strains) is presented. On that basis, a rational model is proposed, consistent with the mechanical model of the Critical Shear Crack Theory. This model allows for a precise description of the response and also to describe the through-thickness distribution of the shear deformation.A general frame for modelling of reinforced concrete slabs is thus presented accounting for the redistribution of internal forces during propagation of the shear crack. This approach is used to investigate a testing programme performed on three wide slabs, analysing in a scientific manner the influence of the width of the member on the shear resistance. The detailed experimental data allow to capture the crack propagation and internal forces redistributions. Clear conclusions and answers are obtained, showing the influence of the shape of the failure surface and of its propagation on the load-carrying capacity.The research ends with a final investigation on the dowelling action of compression reinforcement, with an application to slabs failing in punching. Based on a large testing programme including eleven axisymmetric punching tests, an analytical approach is developed to estimate the contribution of the dowel action on the load-carrying capacity. This approach is formulated within the frame of the Critical Shear Crack Theory, and is incorporated in a consistent and efficient manner for design purposes.

EPFL2021

Seismic behaviour of slab-column connections without transverse reinforcement

Ioannis Sokratis Drakatos

Reinforced concrete (RC) flat slabs supported by slender columns are often used as gravity load resisting system for buildings in regions of moderate and high seismicity. Such buildings are typically braced by RC walls, which carry the largest portion of the horizontal loads generated during earthquakes. Therefore, the slab-column system does not contribute significantly to the lateral stiffness and strength of the structure, but each slab-column connection must be able to accommodate the seismically induced drifts of the building while maintaining its capacity to transfer vertical loads from the slab to the columns. Otherwise, brittle punching failure of the slab occurs and the deformation capacity of the entire building is limited by the deformation capacity of the slab-column connection if the building is not designed to resist progressive collapse. The first part of this work presents an experimental investigation on 13 full-scale internal slab-column connections without transverse reinforcement. The objective of the test campaign is to assess the influence of the loading history (monotonic vs. reversed cyclic) for different gravity loads and reinforcement ratios. The study shows that cyclic loading leads, in particular for slabs subjected to low gravity loads, to significant moment strength and deformation capacity reduction when compared to results obtained from monotonic loading tests. The effect of cyclic loading is more pronounced for slabs with low reinforcement content. In the second part, a mechanical model is presented for predicting the moment-rotation relationship of interior slab-column connections without transverse reinforcement when subjected to seismically induced drifts. The model accounts explicitly for the three load transfer mechanisms between slab and column contributing to the unbalanced moment resistance, i.e., eccentric shear, flexure and torsion. The moment resistance and deformation capacity are deduced from the intersection of the moment-rotation curve with a failure criterion that is based on the Critical Shear Crack Theory and distinguishes between monotonic and cyclic loading conditions. The model predicts well the moment strength and the deformation capacity of slabs tested within this research and reported in the literature. The third part of this thesis proposes an extension of the mechanical model for the moment-rotation relationship presented earlier to account for the hysteretic behaviour and cumulative damage effects on slab-column connections subjected to cyclic loading. A hysteretic moment-curvature relationship is proposed for the radial direction, based on local deformation measurements from the cyclic tests. Cyclic damage is considered by adopting a damage index proposed by a previous study. The extended model predicts more accurately the response of cyclic tests than the simplified approach based on the monotonic model. Finally, based on the theoretical investigation of the two previous parts, two methods are proposed for the numerical analysis of flat slab buildings to simulate the column deformation and the slab deformation until midspan. First, an Effective Beam Width method is presented and compared to test results of flat slab buildings with over-hangs. Then, a simplified method is proposed for the analysis of slab-column connections not part of the lateral force-resisting system. This method allows estimating the contribution of column and slab deformation to the interstorey drift.

EPFL2016

The Deformation Capacity of Lap Splices in RC Walls: From Experimental Testing to Numerical Modelling

Danilo Tarquini

Field observations as well as experimental tests have shown that both the strength and displacement capacity of reinforced concrete (RC) members might be significantly reduced by the presence of lap splices. This degradation applies in particular if the longitudinal reinforcement is spliced in regions where inelastic deformations concentrate, which is frequently the case for RC building walls or bridge piers. In fact, these members often feature lap splices above the foundation level, where seismic demands are largest and damage is likely to occur. In performance-based earthquake engineering (PBEE), which now sets the standards for seismic assessment, deformation rather than force capacities are compared to the demand; however, past experimental studies on spliced members have focused on the characterization of the strength rather than the deformation capacity of lap splices. Further-more, these tests were primarily performed on spliced RC beam and column specimens, typically subjected to mono-tonic loading. Experimental investigations on the deformation capacity of members with lap splices under cyclic loading are underrepresented. This applies in particular to walls, despite the fact that splicing of longitudinal reinforcement in their plastic hinge regions is common construction practice. In line with the available experimental work, most of the developed empirical and analytical expressions aim solely at quantifying the force capacity of lap splices. The preceding observations have motivated the following objectives of the present work: (i) investigate the displacement capacity of spliced RC walls through experimental tests; (ii) propose expressions characterizing the deformation capacity of lap splices subjected to monotonic and cyclic loading; and (iii) develop numerical and mechanical models suitable for practicing engineers to simulate the behaviour of RC members with lap splices. Existing experimental programmes on spliced RC walls, including the cyclic test of two units recently carried out at the structural laboratory of EPFL, are first reviewed and collected in a database. The review of the experimental data shows that the failure of the outermost lap splices, located in the boundary element, typically triggers the failure of the RC wall. Moreover, the main parameters influencing the deformation capacity of lap splices are identified. Building on these findings, an experimental programme on spliced RC wall boundary elements is designed using lapsplice length, confining reinforcement, and loading history as variable parameters. From the obtained results, an empirical expression for the lap-splice strain capacity is derived. A 2D shell element model is first developed to simulate the global force-displacement response of the walls in the aforementioned database. The lap splice response is considered through a new equivalent uniaxial steel stress-strain law. Secondly, an axially equilibrated displacement-based beam element model is proposed in which the lap splice response can be included by using the derived strain limit expression. Finally, a novel mechanical model describing the behaviour of spliced RC wall boundary elements is presented. It extends the tension chord model by accounting for anchorage slip and the presence of lap splices.

EPFL2019