Slabs are structural members that are primarily subjected to bending and torsion. The analysis of slabs is difficult to perform even if linear elastic behaviour can be assumed. The analysis of slabs arises the difficulty of solving complex governing differential equation. Often slabs can be partially cracked. Load, creep and shrinkage all contribute to deformation and cracking in slabs. The combined effects of these problems complicate the analysis of slabs. Meanwhile, different models in available guidance have been proposed to represent these problems in the analysis with different degree of simplifications. They have been derived originally for beams and one-way spanning slabs. These models in general approximate the deformation without providing an insight into the short-term and long-term behaviour of the members under bending, particularly in the case of slabs. The case is more problematic when openings exist, wherein the existence of such openings will complicate the already complex analysis of slabs. Their influence has not been addressed critically under sustained loading. Accordingly, a more sophisticated method of analysis, considering the effects of these problems, is required.
This thesis presents a new numerical analysis procedure for the nonlinear analysis of reinforced concrete slabs. The layered cross-sectional analysis approach, based on fundamentals of Kirchhoff thin plate theory, is used together with the finite difference method for modelling of slab behaviour. The layered approach permits to include the nonlinear variation of material properties through the depth of the slab, which particularly aims to explore the role of tensile creep. The effects of cracking, tension stiffening, creep and shrinkage of the concrete are considered. The uniaxial stress-strain relationships for concrete and steel are used to model the nonlinear material behaviour, whereas the cracked tensile concrete is modelled as a linear brittle material. A maximum stress criterion has been adopted to represent the onset of cracking. A fixed smeared crack concept is utilized to simulate the crack orientation and propagation. Perfect bond is assumed between concrete and reinforcement. The reinforcement is smeared into a layer between concrete layers. The creep and shrinkage effects have been modelled as additional strains acting gradually on a concrete cross-section, with considering the effect of internal restraint provided by reinforcements.
The accuracy and efficiency of the proposed procedure are then demonstrated by comparisons with the results obtained from experimental tests on full-scale slabs at the University of Leeds. The short-term behaviour of the slabs was monitored until failure, while the long-term behaviour was recorded for a period of 90 days. The proposed procedure showed a reasonable agreement in predicting the load-deflection behaviour of solid slab. On the other hand, for slab with opening, the numerical results were found to have good correlation with test results within the service load range. Based on long-term analysis findings, for slabs with the opening, the method exhibited good agreement with those obtained from the experimental time-deflection curves when the tensile creep is equal to the compressive creep. Conversely, and as unexpectedly, the method presented fit better results with the experimental time-deflection curves of solid slab when the creep coefficient in tension is equal to seven times the creep coefficient in compression.
The verified procedure is used to conduct a parametric study to investigate the effect of different opening sizes on the behaviour of partially cracked slabs under sustained loading. The results showed that when the opening size increases, the instantaneous and long-term deflections increase significantly. On the other hand, the models offered by the CEB-FIP 2010 and Eurocode 2 (BSI, 2004) were also analysed critically. Results revealed that the approaches can predict with reasonable accuracy the load-deflection response and the long-term deflection of the solid slab, but in general the approaches overestimated the theoretical short-term and long-term deflections of the slab with opening. Notwithstanding, the theoretical results based on these approaches showed satisfactory agreement with the measured load-deflection curves within service load range.
