### Modulus of Elasticity of Concrete

The elasticity can be defined as that strain appears and disappears immediately on application and removal of stress. The modulus of elasticity of concrete is determined by subjecting a cube or cylinder specimen to uniaxial compression and measuring the deformations by means of dial gauges. The dial gauges reading divided by gauge length will give the strain and load applied divided by the area of the cross section will give stress. A series of readings are taken and stress-strain relationship is established.

Fig.1. Elastic Modulus Types From Stress Strain Curve For Concrete Mix |

The modulus of elasticity can also be determined by subjecting a concrete beam to bending and then using the deflection formulae and substituting the other parameters. The modulus of elasticity so found out from actual loading is called static modulus of elasticity. Concrete does not behave as an elastic material even under a short term loading. Stress-strain graph of concrete is not very much curved up to about 10 to 15% of the ultimate strength of concrete and hence the results are very accurate. For higher stresses the stress-strain relation will be greatly curved and the results are inaccurate.

### Different Modulus of Elasticity

There are different types of modulus of elasticity to specify the elastic property of the concrete structure. They are explained below:

#### Initial Tangent Modulus

As shown in the figure-1, in concrete no part of the graph is straight. The modulus of elasticity is found with respect to the tangent that is drawn to the origin. The modulus of elasticity that is found from this tangent is referred as initial tangent modulus. For higher stress value it gives a misleading picture.

#### Tangent Modulus

The tangent can also be drawn at any other point on the stress-strain curve. The modulus of elasticity calculated with respect to the tangent is then called tangent modulus.

#### Secant Modulus

A line can be drawn connecting a specified point on the stress-strain to the origin of the curve. If the modulus of elasticity is calculated with respect to the slope of this line, the modulus of elasticity is referred as the secant modulus.

The secant modulus is the most commonly used elastic modulus. There is no standard method in order to determine the secant modulus. The value of the secant modulus decreases with the increase in stress.

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Chord Modulus

The modulus of elasticity is found out with respect to the chord drwan between two specified points on the stress -strain curve is called chord modulus.

### Relation between modulus of elasticity and strength

The stronger the concrete, higher is the elastic modulus. The modulus of elasticty of concrete increases approximately with the square root of the compressive strength, fck.

i.e.

Where Ec is the static modulus of elasticity , As per IS:456-2000