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Consider the following statements concerning elasticity of concrete 1. Stress-strain behaviour of concrete is a straight line up to 10% of ultimate stress. 2. Strain determination is obtained from tangent modulus. 3. Modulus of elasticity, of concrete is also called as secant modulus. Which of the above statements are correct?

Consider the following statements concerning elasticity of concrete 1. Stress-strain behaviour of concrete is a straight line up to 10% of ultimate stress. 2. Strain determination is obtained from tangent modulus. 3. Modulus of elasticity, of concrete is also called as secant modulus. Which of the above statements are correct? Correct Answer 2 and 3 only

Concept:

Modulus of elasticity of concrete is defined as the ratio of the applied stress to the corresponding strain. It demonstrates the ability of concrete to withstand deformation due to applied stress and also its stiffness (the ability of concrete to deflect elastically).

Concrete is not a truly elastic material; at stress below 30% of ultimate strength, it is linear. We can have different modulus as shown in the figure below:

The slope of stress –strain curve at beginning of curve is called initial tangent modulus.

The slope of stress –strain curve at any point on curve is called tangent modulus. It represents the instantaneous rate of change of stress as a function of strain. Hence, strain determination is obtained from tangent modulus.

The slope of line joining the any point on stress – strain curve to origin is called secant modulus.   As per IS 456:2000 the modulus elasticity of concrete can be calculated using formula, E = 5000√fck, where fck  is the characteristic compressive strength. This equation is based on secant modulus; hence, Modulus of elasticity, of concrete is also called as secant modulus.

Important points about modulus of elasticity of concrete:

1. It is a function of the modulus of elasticity of the aggregates and the cement matrix and their relative proportions.

2. It is almost constant at low stress levels but starts decreasing at higher stress levels.  

3. The elastic modulus of the hardened paste is in the order of 10-30 GPa and aggregates is about 45 to 85 GPa. The elastic modulus of the concrete composite is then in the range of 30 to 50 GPa.

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