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# What is the 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 tensile stresses. At low stresses, the elasticity of concrete is constant and at high stresses, the cracking starts to develop.

Concrete has a very low coefficient of thermal expansion. Under tension and shrinkage stresses, all concrete structures will crack to some extent. As we know concrete shows different properties under different water-cement ratios and has a diverse 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 of 15 cm cube), the modulus of elasticity of concrete is calculated with the help of a stress and strain graph.

According to ACI codes, the modulus of elasticity of concrete can e measured with the formula,
And with normal density or weight of concrete, these two relationships can be simplified as follows,

#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 elasticities in different mixes,

#Where

Gpa = Gigapascal

Mpa = Megapascal

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

• Mixture design.
• Coarse aggregate properties.
• Curing conditions.

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 behavior is different for different materials.
• By applying forces, the material’s lattice changes its shape and size and returns to its original position after releasing force.
• It is divided into Linear or Finite elasticity.

### Units

Units of elastic modulus are the followings:

• In SI unit MPa or N/mm2 or KN/m2.
• In FPS unit psi or ksi or psf or ksf.

Related topic:

1. civil Engineering conversion units
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