Concrete stress-strain behaviour

In an earlier state of the art report (1) various properties of sulphur concretes were outlined. In the last few years, researchers have concentrated on the topics of durability (moist environment, biological and chemical attack, cycles of freezing and thawing), stress-strain behaviour and mix proportioning. 

Sulphur concrete (without additives) will typically have a near-linear stress-strain curve up to failure, which occurs explosively at a strain usually between 0.0005 and 0.002. The peak stress varies from 20 to 70 MPa depending on the mix design. Sulphur concrete is thus a strong but brittle concrete material the brittleness need not necessarily be a grave disadvantage cast iron was used for a long period of time as a construction material. Any modification to the stress-strain behaviour should be evaluated carefully to see whether the modification is potentially useful. Two different approaches have been used to modify stress-strain behaviour. The modifications are (a) polymerization of the binder 04, j>, 17) and (b) use of the thermodynamically stable orthorhombic sulphur as the binder with alteration of the bond behaviour (3, 18). The matrices of both types of concrete are thus "modified" sulphur. 

Sulphur concretes appear well suited for use in environments corrosive to Portland cement concretes. The extensive work by the U.S. Bureau of Mines shows their material performs admirably in such environments. When used as a lining, the initial stress-strain behaviour will allow the material to adapt to the main structural element and relieve internal stresses without cracking. Corrosion resistance will be maintained by the material thereafter, even though the stress strain behaviour alters. On its own, the material retains sufficient strength to withstand typical loads involved in this type of application (eg. liquid container). Sudicrete has not been tested much in this area, although laboratory tests show similar promise. 

Sulphur concretes have undergone substantial development in the last six years. Recent effort has been directed towards improved durability and less brittle stress-strain behaviour has been achieved. A technology has been developed to produce a material (Sudicrete) with the same stress strain behaviour after three years as that observed soon after casting. Other materials show a consistent reversion to brittle behaviour with time. Nevertheless, there is considerable room for improvement in mix design. 

C.Vipulanandan, N.Dharmarajan, and E.Ching (1987). Stress-Strain Behaviour of Polymer Concrete Systems. Proceedings of the Fifth International Congress on Polymers in Concrete, Brighton, England, pp. 165-170. 

On the basis of other references, Mander et al. (1988) presented a calculation of the stress-strain behaviour of concrete. The ultimate compression strain of confined concrete can be calculated as ... 

Many researchers have studied the stress-strain behaviour of concrete confined with FRP composites. Enhancement in the compressive strength of concrete as a result of external wrapping of FRP was first demonstrated by Fardis and Khalili [62,63]. Although the mechanical aspects of FRP confinement of concrete leading to an improvement in its behaviour is very similar to that of steel, there are some major differences between the two One of the problems with FRP confinement of concrete is that the strength of FRP jacket cannot be fully utilised until the lateral strain in the confined concrete is very high. In some cases, the concrete will crush before the potential strength of FRP jacket is fully mobilised [65-67]. 

The concrete section in the present beams is also rectangular, and can therefore be considered as partially confined. Most importantly, the concrete in the beam crushed before FRP rupture, which is consistent with insufficient confinement as reported by Xiao and Wu (2003) and Aire et al. (2001). It follows therefore that, in the present case, it can be reasonably assumed that the stress-strain curve shown in Fig. 8.12(d) would be the most suitable one for this analysis. Unfortunately, there are no available models that could predict the stress-strain behaviour of this type of partially confined rectangular concrete section. Therefore a partially confined concrete material model is developed to produce the necessary curve. 

Binici, B. (2005), An analytical model for stress-strain behaviour of confined concrete . Engineering Structures, Vol. 27, Issue 7, pp. 1040-1051. 

Oakley, D. R., Proctor, B. A. (1985) Tensile stress-strain behaviour of glass fibre reinforced cement composites , in Froc. of RILEM Symp. on Fibre Reinforced Cement and Concrete, A. M. Neville ed.. Construction Press, pp. 347—59. 

Tanigawa, Y., Hatanaka, S., Mori, H. (1980) Stress-strain behaviour of steel fiber reinforced concrete under compression, Trans, of the Japan Conor. Inst., 2 187-94. 

Figure 7.19 Effect of volume fraction of steel fibres on the stress-strain behaviour of concrete [44].

J.B. Mander, M.J.N. Priestley and R. Park, Observed stress-strain behaviour of confined concrete , ASCE Journal of Structurai Engineering. 114,1988,1827 1849. 

R.V. Velasco, R.D. Toledo Filho, E.M.R. Fairbairn, P.R.L. Lima and R. Neumann, Spalling and stress-strain behaviour of polypropylene fibre reinforced HPC after exposure to high temperatures , in M. di Prisco, R. Felicetti and G.A. Plizzari (eds) Fibre-Reinforced Concretes BEFiB 2004, Proc. RILEM PRO 39, RiLEM Pubiications, Bagneux, 2004, Vol. 1, pp. 699-708. 

G. Campione, S. Mindess and G. Zingone, Compressive stress-strain behaviour of normal and high-strength carbon-fiber concrete reinforced with steel spirals . Ad Mate/ T. 96,1999, 27-34. 

Thanks to the full transmission of stress between the mortar and aggregate grains, their contribution to composite strength of high performance concrete is increased and that effect may be observed on stress-strain curves. The different behaviour of specimens made of ordinary concrete and of high... 

Concrete has a viscous behaviour when it is loaded with a constant stress it shows a strain that increases with time. Conventionally an elastic deformation is considered when it occurs during application of the load, while subsequent deformation is attributed to creep. It is possible to define a modulus of elasticity for concrete that can be evaluated with short-term tests [9]. Similarly as for the tensile strength, empirical formulae are available that give an approximate correlation of the modulus of elasticity with the compressive strength [1,9]. A dynamic modulus can also be estimated with non-destructive tests that measure the rate of propagation of ultrasonic vibrations through concrete [1],... 

The practical calculations of deformations and displacements of specimens and elements made of concrete-like composites are based on simple assumptions of Young s modulus and Poisson ratio, corrected by experimental observations. In such an approach, the strain-stress behaviour of concretelike composites, as determined after the testing of specimens and elements, is generally considered as non-linear and non-elastic, as shown in Figure 8.3 for a case of bending or axial compression. Therefore, several different values of Young s modulus are distinguished, namely ... 

Both coefficients E and v are approximations for much more complicated material behaviour. The relation between stress and strain varies with the load, as shown in Figure 8.3. Poisson ratio depends upon the quality of the material, but it also varies with position and direction in a considered element and with the level of loading. This more complex image of the strain fields has been examined by many authors and has been demonstrated by precise measurements executed inside concrete elements. A special measuring device with 9-gauges was used for this purpose (Figure 8.4), which measured all six strain components, and the possibility of evaluation of the scatter was ensured, thanks to the three additional gauges. Interested readers are referred to papers by Brandt (1971, 1973) and Babut and Brandt (1977). 

A model of the post-peak cyclic behaviour of the concretes investigated for the tensile-tensile and the tensile-compressive loading is proposed. The average stress-total deformation curves are split into two parts the ascending parts in which a tmique relation exists between the stress and the strain that consists of an elastic ccanponent and an iirreversible one ... 

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