# MODULUS OF ELASTICITY OF CONCRETE

|Concrete is a composite mixture of materials (coarse, fine aggregates, cement with water). It has high compressive strength and low tensile strength. The modulus of elasticity of concrete is different for different mixes. The concrete fails under the tensile stresses. At the low stresses, the elasticity of concrete is constant and at high stresses, the cracking start to develop.

The concrete has a very low coefficient of thermal expansion. Under tension and shrinkage stresses, all concrete structures will crack to some extent. As we now concrete show different properties under different water-cement ratio and having a different concrete mix (**M15, M20 etc**).

#### Modulus of elasticity of concrete

It is defined as the ratio between the normal stress to normal strain below the proportional limit of a material called modulus of elasticity **Ec**.

Modulus of elasticity = unit stress/unit strain

With the compressive strength test on the concrete specimen (**cylinder of 15 cm diameter and 30 cm length having a volume 15 cm cube**), the modulus of elasticity of concrete is calculated with the help of stress and strain graph.

According to ACI codes, the modulus of elasticity of concrete can e measure with the formula,

And with normal density or weight of concrete, these two relationships can be simplified as,

#Where

**Ec** = Modulus of elasticity of concrete.

**f’c** = Compressive strength of concrete.

According to

- ACI 318–08, (Normal weight concrete) the modulus of elasticity of concrete is ,
**Ec =4700 √f’c****Mpa**and - IS:456 the modulus of elasticity of concrete is
**5000√f’c, MPa.**

The main factors which may affect the values determination of modulus of elasticity are,

- Strength of concrete
- State of Wetness of Concrete:

This table showed that we get different elasticity in different mixes,

#Where

**Gpa** = Gigapascal

**Mpa** = Megapascal

The value of modulus of elasticity of concrete may vary and depends on the followings factors,

- Mixture design.
- Coarse aggregate properties.
- Loading rate.
- Curing conditions.
- Mineral Admixtures.
- Chemical admixtures.

The density of the concrete is around **150 lb/cu ft** or (**2,400 kg per cubic meter**).

#### Elasticity

It is defined as the ability of the material to come back to its original position (size and shape) after releasing forces.

- The elasticity behaviour is different for different materials.
- By applying forces, the lattice of material changes its shape and size and goes back to its original positions after releasing force.
- It is divide into
**Linear or Finite**elasticity.

#### Units

Units of elastic modulus are followings:

- In SI unit MPa or N/mm
^{2}or KN/m^{2}. - In FPS unit psi or ksi or psf or ksf.

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nice information.