### What is the Modulus of Elasticity?

**Modulus of elasticity** (also known as **elastic modulus**, the **coefficient of elasticity**) of a material is a number which is defined by the ratio of the applied stress to the corresponding strain within the elastic limit. Physically it indicates a material’s resistance to being deformed when a stress is applied to it. Modulus of elasticity also indicates the stiffness of a material. Value of elastic modulus is higher for the stiffer materials.

\[\text {Modulus of Elasticity,}\; E=\frac{f}{s} \]

Here, f= applied stress on a body

s= strain to correspond to the applied stress

#### Units of Elastic Modulus

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.

### Modulus of Elasticity of Concrete

Modulus of Elasticity of Concrete can be defined as the slope of the line drawn from stress of zero to a compressive stress of **0.45 f’_{c}**. As concrete is a heterogeneous material. The strength of concrete is dependent on the relative proportion and modulus of elasticity of the aggregate.

To know the accurate value of elastic modulus of a concrete batch, laboratory test can be done. Also, there are some empirical formulas provided by different code to obtain the elastic modulus of Concrete. These formulas are based on the relationship between modulus of elasticity and concrete compressive strength. One can easily obtain an approximate value of modulus of elasticity of concrete using 28 days concrete strength (*f’*_{c}) with these formulas.

#### Elastic Modulus of Concrete from ACI Code

Different codes have prescribed some empirical relations to determine the Modulus of Elasticity of Concrete. Few of them are given below.

According to ACI 318-08 section 8.5,

Modulus of elasticity for concrete,

\[E_{c}=w_c^{1.50}\times0.043\sqrt{f'_{c}} \quad MPa \]

This formula is valid for values of w_{c} between 1440 and 2560 kg/m^{3}.

For normal-weight concrete,

\[E_{c}=4700\sqrt{f'_{c}} \quad MPa\\

(in \quad FPS \quad unit \quad E_{c}=57000\sqrt{f'_{c}} \quad psi)

\]

#### Elastic Modulus of Concrete from BNBC

According to BNBC 2006 section 5.13.2.1,

For stone aggregate concrete,

\[E_{c}=44\ w_c^{1.50}\sqrt{f'_{c}} \quad N/mm^2

\]

When w_{c} between 15 and 25 kN/m^{3} and √*f’*_{c }in N/mm^{2}.

\[E_{c}=4700\sqrt{f'_{c}} \quad N/mm^2

\]

for normal density concrete

For brick aggregate concrete,

\[E_{c}=3750\sqrt{f'_{c}} \quad N/mm^2

\]

### Test to Determine Elastic Modulus of Concrete

The following video (source: youtube.com) will help you to get a good idea about the experimental procedure of determining modulus of elasticity of concrete. In this video, test procedure to determine elastic modulous of concrete is illustrated following the EN 12390-13 code.

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