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Stress-Strain Behaviour of Concrete

A typical relationship between stress and strain for normal strength concrete is presented in Figure 1. After an initial linear portion lasting up to about 30 – 40% of the ultimate load, the curve becomes non-linear, with large strains being registered for small increments of stress. The non-linearity is primarily a function of the coalescence of microcracks at the paste-aggregate interface. The ultimate stress is reached when a large crack network is formed within the concrete, consisting of the coalesced microcracks and the cracks in the cement paste matrix. The strain corresponding to ultimate stress is usually around 0.003 for normal strength concrete. The stress-strain behaviour in tension is similar to that in compression.

The descending portion of the stress-strain curve, or in other words, the post-peak response of the concrete, can be obtained by a displacement or a strain controlled testing machine. In typical load controlled machines, a constant rate of load is applied to the specimen. Thus any extra load beyond the ultimate capacity leads to a catastrophic failure of the specimen. In a displacement controlled machine, small increments of displacement are given to the specimen. Thus, the decreasing load beyond the peak load can also be registered. The strain at failure is typically around 0.005 for normal strength concrete, as shown in Figure 2. The post peak behaviour is actually a function of the stiffness of the testing machine in relation to the stiffness of the test specimen, and the rate of strain. With increasing strength of concrete, its brittleness also increases, and this is shown by a reduction in the strain at failure.

Figure 1. Stress-strain relationship for ordinary concrete

Figure 2. Complete stress-strain curve including post-peak response

It is interesting to note that although cement paste and aggregates individually have linear stress-strain relationships, the behaviour for concrete is non-linear. This is due to the mismatch and microcracking created at the interfacial transition zone.

Understanding the post peak response of concrete

Concrete belongs to a class of materials that can be called ‘Strain – softening’, indicating a reduction in stress beyond the peak value with an increase in the deformation (as against the strain hardening behaviour commonly exhibited by metals like steel). Figure 3 shows different types of material behaviour.

Figure 3. Different types of material behaviour (post peak response)

Although the ductility of concrete is several orders of magnitude lower than steel, it still exhibits considerable deformation before failure. In conventional testing machines, where the test is performed under control of loading rate, a sudden failure of the specimen occurs as soon as the maximum load level is reached – the machine gives small increments of load to the specimen and the resultant deformation is measured, as a result, when the incremental load goes over the maximum level, the specimen fractures suddenly. This is depicted in Figure 4. In order to obtain the entire stress-strain graph, inclusive of the post peak region, deformation or strain controlled test must be performed.

Figure 4. Modes of testing – Green indicates load control, red indicates displacement control

A displacement controlled test is possible using a machine with a servo valve, in a closed loop. As shown in the schematic diagram in Figure 5, the machine compresses the concrete specimen at a constant displacement rate of the specimen – the LVDT on the specimen provides feedback to the controller, which then indicates to the servo valve the degree of piston movement to be provided (to keep the specimen displacement constant). In this way, the load response of the specimen is continuously studied as it undergoes incremental displacements. Failure occurs when the cracks in the specimen grow to an ‘unstable’ size.

Figure 5. Closed loop servo controlled test system

Acknowledgements

Prof. Jason Weiss, School of Civil Engineering, Purdue University.

Stress-Strain Behaviour of Concrete A typical relationship between stress and strain for normal strength concrete is presented in Figure 1. After an initial linear portion lasting up to about 30

Stress-Strain Curve for Concrete

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Stress strain curve of concrete is a graphical representation of concrete behavior under load. It is produced by plotting concrete compress strain at various interval of concrete compressive loading (stress). Concrete is mostly used in compression that is why its compressive stress strain curve is of major interest.

The stress and strain of concrete is obtained by testing concrete cylinder specimen at age of 28days, using compressive test machine. The stress strain curve of concrete allows designers and engineers to anticipate the behavior of concrete used in building constructions.

Finally, the performance of concrete structure is controlled by the stress strain curve relationship and the type of stress to which the concrete is subjected in the structure.

Stress-strain Curve for Concrete

Fig. 1 and Fig. 2 shows strain stress curve for normal weigh and lightweight concrete, respectively. There is a set of curves on each figure which represents the strength of the concrete. So, higher curves show higher concrete strength. Fig. 3 shows how the shape of concrete stress strain curve changes based on the speed of loading.

Despite the fact that, speed of testing and concrete density influences the shape of the stress-strain curve, but it can be noticed that, all curves show nearly the same character. i.e. they undergo the same stages under loading. Various portions of concrete stress stain curve are discussed below:

Fig. 1: Set of Stress Strain Curve for Normal Density Concrete

Fig. 2: Stress Strain Curve for Lightweight Concrete

Fig. 3: Stress Strain Curve of Concrete Varies Based on Speed of Testing

1. Straight or Elastic Portion

Initially, all stress strain curves (Fig.1 and Fig. 2) are fairly straight; stress and strain are proportional. With this stage, the material should be able to retain its original shape if the load is removed. The elastic range of concrete stress strain curve continues up to 0.45fc’ (maximum concrete compressive strength).

The slope of elastic part of stress strain curve is concrete modulus of elasticity. The modulus of elasticity of concrete increases as its strength is increased. ACI Code provides equations for computing concrete modulus of elasticity.

2. Peak Point or Maximum Compress Stress Point

The elastic range is exceeded and concrete begin to show plastic behavior (Nonlinear), when a load is further increased. After elastic range, the curve starts to horizontal; reaching maximum compress stress (maximum compressive strength).

For normal weight concrete, the maximum stress is realized at compressive strain ranges from 0.002 to 0.003. however, for lightweight concrete, the maximum stress reached at strain ranges from 0.003 to 0. 0035.The higher results of strain in both curves represent larger strength.

For normal weight concrete, the ACI Code specified that, a strain of 0.003 is maximum strain that concrete can reach and this value used for design of concrete structural element. However, the European Code assumes concrete can reach a strain of 0.0035, and hence this value is used for the design of concrete structural element.

3. Descending Portion

After reaching maximum stress, all the curves show descending trend. The characteristics of the stress strain curve in descending part is based on the method of testing.

Long stable descending part is achieved if special testing procedure is employed to guarantee a constant strain rate while cylinder resistance is decreasing. However, if special testing procedure is not followed, then unloading after peak point would be quick and the descending portion of the curve would not be the same.

Stress strain curve of concrete is a graphical representation of concrete behavior under load. It is produced by plotting concrete compress strain at various interval of concrete compressive loading (stress). Concrete is mostly used in compression that is why its …