The modulus of elasticity is the material characteristic value for the elastic deformation(strain) behavior of a material subjected to pressure, force, or tension expressed in kN/mm² or N/mm². The modulus of elasticity indicates the ratio of stress to the associated elastic deformation.

Modulus of Elasticity (E) = Stress/Strain

It is therefore defined by the relationship between the applied stress and the resulting change in length (elongation) within a load range in which stress and deformation are still proportional to one another. The greater the modulus of elasticity, the more resistance the material offers to deformation (i.e. the stiffer the material).

The modulus of elasticity of concrete has to be taken into account in the verifications for restrained deformation (constrained stresses) and for verifications of deformation where the deflection has a significant influence.

## Importance in Design

In the event of an emergency braking of a train on a railway bridge, large horizontal forces act that has to be transmitted to the ground. To ensure that the overall deformations of the construction remain as small as possible, the structural engineer will specify the highest possible rigidity of the concrete. The executing contractor must then ensure that the concrete that he installs has the appropriate modulus of elasticity.

Also Read: Experimental Modulus of Elasticity of Concrete

A high modulus of elasticity is usually advantageous for deformation verifications. When analyzing restraint stresses, on the other hand, a lower value is more advantageous, since lower restraint stresses occur in an elastic material when deformation is restricted.

## Effects of the modulus of elasticity on structures

Physically, the elastic behavior of homogeneous material is determined by the binding force between the atoms and the distance between the atoms. The stronger this binding force, the steeper the stress-strain curve in the zero-crossing area and the higher the modulus of elasticity of the material.

However, concrete is not a homogeneous building material, it is usually regarded as a two-material system (cement binder and aggregate) with respect to the modulus of elasticity. The modulus of elasticity of concrete depends on the moduli of elasticity of these two materials (cement and aggregates.

The modulus of elasticity is approximately understood as the secant modulus of the stress-strain curve in the elastic range (where Hooke’s law is valid). The secant modulus indicates the gradient of the stress-strain curve between the origin in σc = 0 up to 40% of the mean value of the concrete compressive strength fcm. The secant modulus corresponds approximately to the modulus of elasticity determined in the building material test. The secant modulus is used for deformation calculations.

## Elastic modulus of concrete value

The modulus of elasticity of normal concrete is between 27 kN/mm² for concrete C12/15 and 44 kN/mm² for concrete C90/105 aged 28 days (table values from DIN EN 1992-1-1 for concrete with aggregates containing quartzite). Modulus of elasticity of the cement aggregate mix ranges from 5 kN/mm² to 20 kN/mm² and the modulus of elasticity of concrete having quartzite or greywacke is approximately equal to 60 kN/mm².

## How to calculate modulus of elasticity of concrete

### Concrete containing quartzite:

Overall, there is a close relationship between concrete compressive strength and modulus of elasticity, which is therefore usually derived for static calculations from the compressive strength of the concrete. DIN EN 1992-1-1 establishes the following analytical relationship for concrete with aggregates containing quartzite:

Modulus of elasticity of concrete (Ec) =22(fcm10)0.3

with Ecm = mean modulus of elasticity as secant

and fcm = mean cylinder compressive strength of the concrete

Table 3.1 in DIN EN 1992-1-1 assigns corresponding values for the modulus of elasticity to the individual compressive strength classes C12/15 to C90/105. However, the use of these values can lead to an overestimation or underestimation of this design value. Watch this video for more information.

### Experimental determination:

More precise values are provided by the experimental determination of the modulus of elasticity using an almost non-destructive, uniaxial pressure test. The test specimen is loaded up to a third of the concrete compressive strength, which must have been previously determined on other test specimens. When the load increases, the respective load, and the corresponding deformation are recorded.

Worth reading: Modulus of Elasticity of Steel

In order to keep the influence of the viscous and delayed elastic deformation to a minimum, the test specimen is loaded cyclically. The static modulus of elasticity is then determined from the resulting stress-strain curve.

According to DIN EN 12390-13, two test methods (methods A and B) are possible, whereby method B enables determination in analogy to the previous test standard DIN 1048-5. The dynamic modulus of elasticity is determined e.g. B. via resonance frequency measurements with an ultrasonic measuring device. The ratio of dynamic to the static modulus of elasticity is not constant but depends on the pore space of the cement stone.

### Modulus of elasticity formula

#### For concrete Using ACI 318-14 code:

Ec = 57000*fc

Where fc = compressive strength of the concrete in psi

#### Canadian standard code:

Ec = 4500*fc

Where fc = compressive strength of the concrete in Mpa

#### Euro code:

Ec =22(fcm10)0.3

fcm = mean cylinder compressive strength of the concrete

Ec = Ko + 0.2fc

Where:

Ko = 20 KN/mm2for normal weight concrete

Fc = compressive strength of concrete at 28 days

##### Modulus of elasticity of normal concrete according to DIN EN 1992-1-1/DIN EN 1992-1-1/NA

compressive strength class | fck,cyl | fck,cube | Ecm |

N/mm² | |||

C12/15 | 12 | 15 | 27000 |

C16/20 | 16 | 20 | 29000 |

C20/25 | 20 | 25 | 30000 |

C25/30 | 25 | 30 | 31000 |

C30/37 | 30 | 37 | 33000 |

C35/45 | 35 | 45 | 34000 |

C40/50 | 40 | 50 | 35000 |

C45/55 | 45 | 55 | 36000 |

C50/60 | 50 | 60 | 37000 |

C55/67 | 55 | 67 | 38000 |

C60/75 | 60 | 75 | 39000 |

C70/85 | 70 | 85 | 41000 |

C80/95 | 80 | 95 | 42000 |

C90/105 | 90 | 105 | 44000 |

C100/115 | 100 | 115 | 45000 |

Where fck,cyl – characteristic compressive strength of concrete, tested on cylinder after 28 days

fck, cube – characteristic compressive strength of concrete, tested on cube after 28 days

Ecm – mean modulus of elasticity of normal concrete (secant value between σc = 0 and 0.4 fcm) with fcm = fck,cyl + 8

## Conclusion:

The modulus of elasticity for the heterogeneous material concrete is discussed in detail. Various techniques for the calculation of the elastic modulus of concrete have been summarized above. For more information related to the experimental determination of modulus of elasticity please visit https://coolcivilengineering.com/experimental-modulus-of-elasticity-of-concrete/ and subscribe to our channel.