Structural Concrete - Hassoun

22 Chapter 2 Properties of Reinforced Concrete
2.7 MODULUS OF ELASTICITY OF CONCRETE
One of the most important elastic properties of concrete is its modulus of elasticity, which can
be obtained from a compressive test on concrete cylinders. The modulus of elasticity, E c , can be
defined as the change of stress with respect to strain in the elastic range:
E c = unitstress
(2.4)
unitstrain
The modulus of elasticity is a measure of stiffness, or the resistance of the material to deformation.
In concrete, as in any elastoplastic material, the stress is not proportional to the strain,
and the stress–strain relationship is a curved line. The actual stress–strain curve of concrete can be
obtained by measuring the strains under increments of loading on a standard cylinder.
The initial tangent modulus (Fig. 2.4) is represented by the slope of the tangent to the curve
at the origin under elastic deformation. This modulus is of limited value and cannot be determined
with accuracy. Geometrically, the tangent modulus of elasticity of concrete, E c , is the slope of the
tangent to the stress–strain curve at a given stress. Under long-time action of load and due to the
development of plastic deformation, the stress-to-total-strain ratio becomes a variable nonlinear
quantity.
Figure 2.4 Stress–strain curve and modulus of elasticity of concrete. Lines a–d represent
(a) initial tangent modulus, (b) tangent modulus at a stress, f c
,(c) secant modulus
at a stress, f c
,and(d) secant modulus at a stress f
c ′ ∕2.