# How to Calculate the Modulus of elasticity of concrete?

We know the modulus of elasticity of steel is 2*105 Mega Pascale for all grades of steel. But how can we Calculate the Modulus of elasticity of concrete?

Let us discuss it. The concept behind the modulus of elasticity of steel and concrete is the same. They use Hooks law. But for concrete, it is somewhat difficult to calculate the exact value of the modulus of elasticity of concrete as compared to steel. Because concrete is a brittle material and steel is ductile in nature.

Let’s go step by step:-

I told you concrete is a brittle material. Let’s see in the diagram. Concrete is not only non-elastic but also nonlinear. So, after unloading it does not follow the same path as steel.

You can see here the gap after unloading. So, it is not possible to apply hooks law directly.

But take a look over here. Only the initial part is linear and here we can use hooks law. So, according to hooks law modulus of elasticity will be,

Now the problem in this case of concrete is there are two types of strain.

Short term elastic strain (Due to Instantaneous load)

Long term elastic strain (Due to effect of creep and shrinkage)

Due to this situation, Short term elasticity due to short-term elastic strain is called short-term modulus of elasticity. And long term elasticity due to long-term elastic strain is called effective modulus of elasticity.

Now, let us understand how to calculate their values.

There are three ways to calculate the short term modulus of elasticity.

1. Draw a tangent at the origin of this curve. This is called the initial tangent modulus. (ITM)

2) You can choose tangent at a specified stress level. This is called the tangent modulus. (TM)

3) Finally we can also connect the stess level to the origine. Like in the figure below. This is called Secant modulus. (SM)

This is somewhat look like complicated for us, right??

So, IS code has simplified for us. That is according to 456-2000 Empirical formula is given by,

Where, Fck is the grade of concrete. Hence, if you are using M30 grade of concrete then Modulus of elasticity will be calculated as,

Now let us move toward. How to calculate effective modulus of elasticity.

Its formula is,

Where Theta is creep coefficient taken according to table above. If we take for 28 days then the calculation will be.

Happy Learning – Civil Concept

Contributed by,

Civil Engineer – Ranjeet Sahani 