Concrete is not an elastic material i.e., it will not recover its original shape on unloading. In addition, it is non-linear and exhibits a non-linear stress-strain curve. Hence, the elastic constants such as modulus of elasticity and Poisson’s ratio are not strictly applicable. However, they are used in the analysis and design of concrete structures, assuming elastic behavior. The modulus of elasticity of concrete is a key factor for estimating the deformation of buildings and members.
The use of HSC will result in higher modulus of elasticity and in reduced deflections and increased tensile strengths. It is normally related to the compressive strength of concrete and may be determined by means of Extensometer attached to the compression test specimen.
The Young’s Modulus of Elasticity may be defined as the ratio of axial stress to axial strain within the elastic range. When the loading is of low intensity, the initial portion of the curve is linear. However, in sustained loading, inelastic creep occurs even at relatively low stresses. More over the effects of creep and shrinkage will make the behavior of concrete in a non-linear manner.
Various definitions of Modulus of Elasticity are available, Initial tangent modulus and Secant tangent modulus as shown in below figure. Among these the secant modulus is found to represent the modulus of Elasticity of Concrete under service load conditions. It is drawn by connecting the origin to the stress-strain curve corresponding to 40% failure stress.
Ec = 5000 * √fck (MPa)
Poisson’s Ratio – It is defined as the ratio of lateral strain to longitudinal strain, under uniform axial stress. Experimental values range from 0.15 to 0.25. For design purposes the value of 0.2 is used.