# Modulus of Elasticity of Concrete- Determination and Importance in Design

Modulus of elasticity of concrete(Ec) is defined as the ratio of the applied stress to the corresponding strain. Not only does it demonstrate the ability of concrete to withstand deformation due to applied stress but also its stiffness. In other words, it reflects the ability of concrete to deflect elastically. Modulus of elasticity of concrete is sensitive to aggregate and mixture proportions of concrete.

In the design of concrete structures, modulus of elasticity is considerably important that requires to be defined. The linear analysis of elements, which is based on elastic theory, is used in some cases to satisfy requirements of ultimate and serviceability limit state such as in the design of concrete structures.

Common applicable codes around the world such as ACI Code, European Code, British Standards, Canadian standard association, and Indian standard have provided a formula for the computation of elastic modulus of concrete.

## Calculation of Elastic Modulus of Concrete

The computation of modulus of elasticity of concrete using equations of various codes are presented below :

### 1. Modulus of Elasticity Based on ACI 318-14

According to ACI 318-14 section 19.2.2, the modulus of elasticity of concrete is evaluated as follows :

For concrete, the unit weight(wc) ranges from 1440 to 2560 Kg per cubic meters.

For normal weight concrete :

### 2. Modulus of Elasticity Based on CSA

Modulus of elasticity for normal weight concrete based on Canadian Standard Association (CSA A23.3):

For high strength concrete:

### 3. Modulus of Elasticity Based on EC

Modulus of elasticity of concrete based on Euro code can be evaluated using the following expression:

Where,

Ecm: mean modulus of elasticity

fcm: mean compressive strength of concrete at 28 days according to Table 3.1 BS EN 1992-1-1: 2004

### 4. Modulus of Elasticity Based on British Standard

The value of Elastic modulus at 28 days of concrete age is given in BS 8110: Part II 1985:

Where:

ko: is 20 KN per square millimeter for normal weight concrete

fcu,28: concrete compressive strength at 28 days.

### 5. Modulus of Elasticity Based on IS 456

Concrete modulus of elasticity based on Indian standard can be calculated using the following expression:

## Importance in Design of Concrete Structure

It is highly crucial to define modulus of elasticity of concrete in the design of concrete structure. Linear analysis of elements, which is based on the theory of elasticity, is used to satisfy requirements of both ultimate and serviceability limit state for instance in the case of pre-stressed concrete that demonstrate uncracked section up to the failure.

In addition to compute deflections which are required to be limited under the serviceability requirements in all structures. Finally, knowledge of the modulus of elasticity of high strength concrete is very important in avoiding excessive deformation providing satisfactory serviceability and avoiding the most cost-effective designs.