Experimental and numerical analysis of tensile membrane action in reinforced concrete slabs in the framework of structural robustness

摘要

As a consequence of several structural failures in the last decades, the European Standard EN 1990 (2002) ‘Basis of structural design’ incorporated the following requirement with respect to robustness: “A structure shall be designed and executed in such a way that it will not be damaged by events such as explosion, impact and the consequence of human errors to an extent disproportionate to the original cause”. In addition, the European Standard EN 1991-1-7 (2006) ‘Actions on structures – Part 1-7: Accidental actions’ points to strategies to enhance structural robustness, emphasising amongst others the favourable contribution of developing alternate load paths in case of abnormal loading events. The investigations reported in the present thesis aim for a better understanding of the alternate load path provided by the transition from a flexural to a tensile load transfer. In particular, the load transfer provided by tensile membrane action developing at very large displacements after a support removal scenario and, subsequently, excessive loading is investigated. It is widely appreciated that this tensile membrane behaviour has a positive effect on the structural behaviour. The ultimate limit state behaviour for tensile membrane action developing in slabs, however, is largely unknown due to the limited amount of experimental largescale investigations.Based on an extensive literature review, an experimental program has been elaborated in order to investigate tensile membrane action developing in a restrained one-way concrete slab. A unique test set-up has been developed allowing a loading test on a four-span reinforced concrete slab strip under longitudinal elongation restraint into the region of large deflections. The tested slabs were 140 mm or 160 mm thick and 1800 mm wide with a geometric reinforcement ratio of about 0.5 %. The total length of each specimen was 14.3 m, whereas the distance between the inner supports and the central support was 4 m. These spans changed to one span of 8 m between the inner supports after the controlled removal of the central support, thus simulating an accidental event.Further, also a testing procedure was elaborated, consisting of 3 phases (i.e. loading until an arbitrary preloading level, removal of the central support and loading until failure). During the first phase, the load was gradually increased up to the preloading level for the situation where the central support was still present.Subsequently, the slab was unloaded. In a second phase, the central support of the specimens was gradually removed in order to simulate a failure of the support and to obtain valuable data regarding the robustness of the specimens. Accordingly, the two inner spans of 4 m each, changed to a single span of 8 m. The specimens were allowed to bend progressively in the central span of the slab, resulting in a redistribution of stresses and the development of an alternate load path distributing the emerging forces to the remaining supports. Finally, in the third phase, the load was applied again by two line loads in a displacement controlled manner until failure. With increasing vertical deflections of the specimens the slabs’ ends started to move inwards provoking a significant increase in the loadcarrying capacity due to emerging tensile membrane forces established by a horizontal restraining system. In total three different tests on slab strips with horizontal restraint were performed. In case of slab 1, the longitudinal top and bottom flexural reinforcement was continuous over the entire length of the specimen. Hence, no reinforcement curtailing was applied. Further, a second specimen featuring a realistic reinforcement curtailment was tested. In case of slab 3 the longitudinal flexural reinforcement was curtailed similar to slab 2, but the thickness of the slab was reduced from 160 mm to 140 mm. In all three tests, tensile membrane action was activated during the third phase of testing, significantly increasing the load carrying capacity of the specimen under investigation. During the tests, manual measurements were executed after each successive increase of the load or displacement, comprising dial gauges, crack widths measurements and DEMEC measurements. Further, around 60 digital channels were recording the digital measurements comprising displacements, horizontal (membrane) and vertical (reaction) load cell forces and strain measurements with stirrups.Each tested slab strip was exposed to three distinct stages: an elastic, plastic and tensile membrane stage. The development of displacements, strain measurements as well as the horizontal forces within this investigation confirmed a load transfer process from an elastic bending mechanism, over a plastic stage towards a tensile membrane mechanism controlled by tension. As tensile membrane forces developed, the load bearing capacity was able to increase until approximately 3 times the service load for slab 1 and 2.6 times for slab 2 (despite the removal of the central support). For slab 3 the ultimate collapse load even amounted to about 3.6 times the service load. Hence, the importance of quantifying this additional bearing capacity became clear, especially in robustness analysis, as otherwise one disregards an inherently available and very large additional safety.The test results provide a unique set of detailed experimental data (crack widths, deformations, rotation angles, displacements, etc.) allowing for a detailed analysis and refined comparisons with respect to the structural response under tensile membrane action as well as regarding the failure criteria.Finite element modelling was used to simulate the structural behaviour of oneway slabs under large deformations and tensile membrane actions. On the basis of the experimental findings, the numerical model was validated with special attention to material models, mesh definition and boundary conditions accounting for highly non-linear material performances as well as geometrical non-linear behaviour. In summary, the load-displacement curves until the failure of the top reinforcement bars, displacements, rotation angles, the development of strains and tensile membrane forces were calculated within a reasonable tolerance and showed good agreement with the laboratory tests. As such, it is demonstrated that the developed finite element model is a suitable tool being capable to predict the structural response under tensile membrane forces. By means of this developed finite element model, a parametric study was conducted. In this study the influence of several geometries (various span lengths, thicknesses and reinforcement ratios), material assumptions (various steel qualities and ultimate reinforcement strains) and boundary conditions are investigated and discussed.A literature study with respect to analytical models for tensile membrane action was performed serving as a starting point for the analytical investigation. On the basis of the standard plastic theory an analytical model is proposed firstly considering perfectly restrained edges. The loading response, the formation of tensile membrane action and the failure load is accounted for. Further, the proposed method was applied and refined in order to simulate the structural behaviour of the conducted slab experiments by incorporating non-linear horizontal movements of the restraining system. The calculation results were compared with numerical and experimental findings and the analysis results show good agreement.In the presented PhD thesis it is demonstrated by means of experimental, numerical as well as analytical investigations that the development of tensile membrane behaviour as a result of horizontal edge restraint is capable of generating a considerable strength reserve significantly increasing the loading response of one-way reinforced concrete slabs when very large deformations occur. The insights gained from these investigations give strong evidence of the beneficial contribution of tensile membrane action to the loading capacity and robustness of concrete structures in accidental load situations. The developed numerical and analytical calculation techniques are shown to be feasible tools not only to quantify the loading response corresponding to the experimentally observed ultimate limit state behaviour but also to predict the structural response under tensile membrane action for other boundary conditions and material characteristics serving as a general calculation framework to include tensile membrane action in conventional design when robustness is considered.