Modulus of Elasticity of Concrete | Stress Strain Curve of Concrete | Static Modulus of Elasticity

Lecture-28 Modulus of Elasticity of Concrete | Stress – Strain Curve of Concrete | Static Modulus of Elasticity and Dynamic Modulus of Elasticity |
Relation between Modulus of Elasticity and Compressive Strength by Dr K Mohan

Modulus of elasticity of concrete also known as elastic modulus of concrete is the ratio of the applied stress to the corresponding strain of the concrete under the application of loads.

Modulus of elasticity is the measure of stiffness of a material. The stiffness of a component means how much it deflects under a given load.
• The modulus of elasticity of hardened cement paste is around 10 to 30 GPa and that of aggregate is between 45 to 85 GPa. Concrete generally has an modulus of elasticity varying between 30 to 50 GPa.

Stress – Strain Curve of Concrete:
• The stress – strain curve for hardened cement paste is almost linear. The aggregate is more rigid than the cement paste and will deform less i.e., have a lower strain, under the same applied stress. The stress – strain curve of concrete lies between those of the aggregate and the cement paste.
• A typical stress – strain curve of concrete (in compression) is shown in Figure. The relationship is fairly linear in the initial stages but subsequently becomes non – linear reaching a maximum and then a descending portion is obtained before concrete finally fails.

• 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 “Initial tangent modulus” is given by the slope of a line drawn tangent to the stress – strain curve at the origin.
• The “Tangent modulus” is given by the slope of a line drawn tangent to the stress – strain curve at any point on the curve.
• The “Secant modulus” is given by the slope of a line drawn from the origin to a specified point on the curve (corresponding to a 40 % stress of the failure stress.
• The “Chord modulus” is given by the slope of a line drawn between two specified points on the stress – strain curve.

Static Modulus of Elasticity and Dynamic Modulus of Elasticity:

• Modulus of Elasticity for concrete determined from an experimental stress – strain curve is generally termed as static modulus of elasticity (Ec).
• Whereas the modulus of elasticity determined through longitudinal vibration test (by velocity of sound or frequency of sound) is termed as dynamic modulus of elasticity (Ed).

Relation between Modulus of Elasticity and Compressive Strength:
• Modulus of elasticity of concrete increases approximately with the square root of the strength.
• The IS: 456 – 2000 gives modulus of elasticity as:
• Ec = 5000 √fck, where Ec = Modulus of elasticity and fck = Characteristic compressive strength of concrete

Relation between Static and Dynamic Modulus of Elasticity:

• Dynamic modulus of elasticity of concrete is approximately taken as equal to the initial tangent modulus of elasticity of concrete.
• Dynamic modulus of elasticity is generally 20, 30 and 40 % higher than the static modulus of elasticity for high, medium and low strength concrete respectively.
• Approx. relationship between the two moduli expressed as GN /m2 is given by:
Ec = 1.25 Ed – 19
• This relationship is valid for normal weight concrete. This relationship does not apply to light weight concrete or for very rich concrete with cement content 500 kg / m3.
• For light weight concrete the relationship can be
Ec = 1.04 Ed – 4.1
Factors Affecting Modulus of Elasticity:

1. Strength of Concrete:
• It is one of the most important factors which affect the modulus of elasticity.
• Higher strengths give higher value of modulus of elasticity.

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