Concrete is a construction material composed of a variety of different materials (cement, water, fine and coarse aggregates). Compressive strength of concrete is high, while tensile strength is poor. The modulus of elasticity of concrete varies depending on the mixture design. Tensile stresses cause the concrete to break. Concrete’s elasticity remains stable at low stresses, but begins to crack at high stresses.

The coefficient of thermal expansion of concrete is extremely low. C concrete structures can break to some degree when subjected to strain and shrinkage stresses. Concrete exhibits a range of properties when the water-cement ratio is varied and the concrete mix is varied (M15, M20, etc).

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## Elasticity

It is described as the material’s ability to revert to its original position (size and shape) following the application of forces.

- Different materials exhibit varying degrees of elasticity.
- By applying forces, the material’s lattice changes shape and size and then returns to its original positions when the force is released.
- It is classified as either linear or finite elasticity.

## What is the Modulus of Elasticity of Concrete?

The modulus of elasticity (Ec) of concrete is defined as the ratio of applied stress to strain. It demonstrates not only the concrete’s ability to resist deformation due to applied stress, but also its stiffness. In other words, it represents the concrete’s elastic deflection ability. The modulus of elasticity of concrete is highly dependent on the aggregate and mixture proportions.

The modulus of elasticity of normal-density concrete ranges from 14,000 to 41,000 MPa.

Modulus of elasticity plays a significant role in the design of concrete structures and must be described. In certain cases, such as when designing pre-stressed concrete structures, the linear analysis of components, which is based on elastic theory, is used to satisfy criteria for ultimate and serviceability limit states.

The ACI Code, the European Code, the British Standards, the Canadian standard association, and the Indian standard have all given a method for calculating the elastic modulus of concrete.

## Calculating the Modulus of Elasticity of Concrete

The modulus of elasticity of concrete is computed using equations from different codes:

### 1. Modulus of Elasticity according to ACI 318

ACI 318 (2014) defines the modulus of elasticity of concrete as follows for normal weight concrete:

### 2. E according to Canadian Standard Association (CSA)

Elastic modulus of normal weight concrete in accordance with CSA:

## Importance of E in Structural Design

When designing concrete structures, it is important to define the modulus of elasticity of the concrete. Linear analysis of elements, which is founded on elasticity theory, is used to satisfy specifications for both ultimate and serviceability limit states, as is the case with pre-stressed concrete that exhibits an uncracked segment up to the point of failure.

Additionally, compute deflections that must be limited in accordance with serviceability criteria for all structures. Finally, understanding the elasticity modulus of high strength concrete is critical for preventing unnecessary deformation, ensuring adequate serviceability, and avoiding the most cost-effective designs.

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