A generic unified reinforced concrete model

2015

Structural Concrete

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properties are varied over time. Being strain based and applied at a cross-section, the M/Θ approach cannot directly simulate slip between the reinforcement and the adjacent concrete. While this approach can provide reasonable results for steel-reinforced beams that lie within the experimental tests from which EI eff was calibrated, when extended beyond this range, a poor correlation between predicted and observed deflections often occurs. This poses a significant problem for beams reinforced with FRP where, due to the high strength of the tendons, reinforcement ratios are low, resulting in tension stiffening being commonly overestimated. Despite extensive research on the tension stiffening behaviour of FRP reinforced concrete [9,10,17], empirically derived equations are still only applicable and restricted to the bounds of the test data from which they are derived.To overcome this empiricism associated with the strain-based M/χ approach, a displacement-based segmental M/Θ approach has been developed. This displacementbased approach was first developed for beams reinforced with either steel or FRP [19][20][21][22][23][24][25] and then extended for both the short-term loading of PC beams [26] and the longterm loading of ungrouted PC beams [27]. The benefit of the M/Θ approach is that it can directly simulate the mechanisms associated with tension stiffening and also concrete softening [28][29][30][31], which is in contrast to the M/χ approach, which requires empiricisms to allow for these mechanisms. Furthermore, the purely mechanics-based M/Θ results can be easily converted to moment/equivalent curvatures and, consequently, equivalent flexural rigidities EI equ that can be used in standard strain-based design practices. This method thereofre obviates the need for empirically derived values for curvatures or flexural rigidities. The M/Θ approach is now further extended here to accommodate the time-dependent behaviour of preand post-tensioned PC beams with grouted FRP or steel tendons.This paper first shows how, through the analysis of a segment of the beam, the M/Θ approach can simulate the effects of pre-and post-tensioning as opposed to the current M/χ strain-based approach, which deals with a section of the member. This is then followed by the analysis of the member subjected to applied loads and prior to cracking. Up to this point the M/Θ approach gives exactly the same results as the M/χ approach. The only benefit of the M/Θ approach at this stage is that the behaviour of the

Section: M/θ Analysis Prior To Crackingmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Displacement‐based simulation of time‐dependent behaviour of RC beams with prestressed FRP or steel tendons

Knight

2015

Structural Concrete

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“…The localised nature of these deformations makes the behaviour of RC members extremely complex as it is these localised behaviours that control the global behaviour of RC members. Thus it is very important that these behaviours are simulated (Oehlers, 2010a;Oehlers et al, 2011aOehlers et al, , 2011bOehlers et al, , 2012 in order to accurately replicate the global behaviours.…”

Section: Introductionmentioning

confidence: 99%

Simulating reinforced concrete members. Part 1: partial interaction properties

Proceedings of the Institution of Civil Engineers - Structures

Chen

et al. 2014

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Reinforced concrete members are extremely complex under loading because of localised deformations in the concrete (cracks, sliding planes) and between the reinforcement and concrete (slip). An ideal model for simulating behaviour of reinforced concrete members should incorporate both global behaviour and the localised behaviours that are seen and measured in practice; these localised behaviours directly affect the global behaviour. Most commonly used models do not directly simulate these localised behaviours that can be seen or measured in real members; instead, they overcome these limitations by using empirically or semi-empirically derived strain-based pseudo properties such as the use of effective flexural rigidities for deflection; plastic hinge lengths for strength and ductility; and energybased approaches for both concrete softening in compression and concrete softening after tensile cracking to allow for tension stiffening. Most reinforced concrete member experimental testing is associated with deriving these pseudo properties for use in design and analysis, and this component of development is thus costly. The aim of the present research is to reduce this cost substantially. In this paper, localised material behaviours and the mechanisms they induce are described. Their incorporation into reinforced concrete member behaviour without the need for empirically derived pseudo properties is described in a companion paper.

“…The analysis could be repeated for increasing rotations to quantify the relationship between M and θ as in Figure 3(a) where O-A are the results prior to cracking and O-B are the results after cracking. The problem here is that there is no transition from O-A to O-B that is a strain based approach cannot quantify tension stiffening (Oehlers 2010;Oehlers et al 2011aOehlers et al , 2012a. It will be shown later that the incorporation of partial-interaction theory into the moment-rotation analysis will be used to find a mechanics solution and, furthermore, that this mechanics approach can be used to include residual strains.…”

mentioning

confidence: 99%

Incorporating Residual Strains in the Flexural Rigidity of RC Members with Varying Degrees of Prestress and Cracking

Knight

Advances in Structural Engineering

et al. 2013

The deformation of reinforced concrete columns and beams is controlled by the variation of the flexural rigidity (EI) both along the member and with applied loads and time. Currently, the moment-curvature (M/χ) approach is used to quantify EI. Prior to cracking, the M/χ approach provides a pure mechanics based solution for EI; that is, the only components of the model that have to be determined empirically are the material stress-strain relationships. However after cracking, the M/χ approach has to be semi-empirical, that is EI has to be determined empirically because the M/χ approach cannot simulate the mechanics of tension-stiffening. An alternative approach for quantifying EI using a moment-rotation (M/θ) approach is described in this paper. It is shown that the M/θ approach gives exactly the same results as the M/χ approach prior to cracking but after cracking has an advantage over the M/χ approach in that it can quantify the mechanics of tension-stiffening, that is allow for bond slip and its effect on crack spacing and crack widths. This paper deals with the mechanics of incorporating creep, shrinkage, prestress, relaxation and thermal gradients (broadly referred to as residual strains) on the flexural rigidity of RC beams and columns at all levels of loading prior to concrete softening.