10.1 : Elasticity in Concrete

Upon subjecting concrete to moderate or high uniaxial compressive or tensile stresses, the strain response is non-linear relative to the stress applied. As the stress is removed, the resulting stress-strain curve deviates from the original path traced during loading, creating a hysteresis loop, indicative of the concrete's non-linear and non-elastic properties. Typically, a material's modulus of elasticity, which is a measure of the material's stiffness, is inferred from the linear portion of the stress-strain curve's slope. However, due to concrete's non-linear stress-strain characteristic, various methods must be employed to determine its modulus of elasticity.

The tangent modulus is calculated from the slope of a line drawn tangent to the stress-strain curve at any selected point. The secant modulus uses the slope of a line from the origin to a point on the curve, which represents 40 percent of the failure load. Conversely, the chord modulus is determined by the slope of a line connecting two points on the curve: one representing a strain of 50 microinches per inch and the other 40 percent of the ultimate load. This adjustment accounts for the initial concavity seen in the curve. The initial tangent modulus is typically derived from the slope of the tangent drawn at the curve's origin.