## Factors Affecting Modulus of Elasticity of Concrete

Modulus of elasticity of concrete is the ratio of stress to strain of the concrete under the application of loads. Considering the stress-strain curve of the first cycle, the modulus could be defined as the initial tangent modulus, secant modulus, tangent modulus or chord modulus as shown in figure below.

**Figure: Stress-strain curve for concrete**

The above modulus of elasticity is sometimes termed as static (secant) modulus of elasticity in comparison with dynamic modulus of elasticity obtained by vibration test of concrete prisms or cylinders. The latter is approximately equal to the initial tangent modulus and hence greater than the static or secant modulus. Two types of shrinkage are recognised namely, plastic and drying shrinkage.

**Plastic Shrinkage of Concrete**

The hydration of cement causes a reduction in the volume of the system of cement plus water to an extent about 1 percent of the volume of dry cement. This contraction is plastic stain and is aggravated due to loss of water by evaporation from the surface of concrete, particularly under hot climates and high winds. This can result in surface cracking.

**Drying Shrinkage of Concrete**

The shrinkage that takes place after the concrete has set and hardened is called drying shrinkage and most of it takes place in the first few months (it also coincides with the period of active creep and thus two are inextricably related). Withdrawal of water from concrete stored in unsaturated air voids causes drying shrinkage. A part of this shrinkage is recovered on immersion of concrete in water. It is termed moisture movement.

In the absence of other reliable data, the shrinkage can be estimated from Schorer’s formula:

Where, is the shrinkage strain and h represents relative humidity expressed as a fraction.

In an environment of average humidity of 50%, h= 0.5, = 0.0005 and it may be noticed that in fully saturated condition, (h = 0), = – 0.000125 which indicates swelling.

**Figure: Variation of drying shrinkage and moisture movement with alternate drying and wetting.**

The rate of change of shrinkage decreases with time. The tests indicate that 14 to 34 % of 20 years shrinkage occurs in two weeks, 40 to 70 percent in 3 months and 66 to 80 percent in one year.