Young's Modulus of Normal-Weight Concrete

Concrete has no true Young's modulus: its stress-strain curve bends from the first increment of load, so codes define a secant modulus to about 45 % of f'c and then estimate it from compressive strength. The AASHTO expression that FHWA's design manuals print, Ec = 33 000 K₁ w_c^1.5 √f'c in ksi, puts 4000 psi (28 MPa) normal-weight concrete at about 3640 ksi, roughly 25 GPa: about an eighth of steel. Note the square root: doubling the strength of the mix raises stiffness by only 40 %.

The scatter is large and honest. Measured moduli for a given strength routinely fall ±20 % around the formula because aggregate stiffness dominates and aggregate is a local material; limestone, granite and river gravel mixes at the same f'c differ markedly. Lightweight concrete is far softer still. Worse, this is only the short-term modulus: creep under sustained load can multiply long-term deflection by two or three, which is why deflection checks use a reduced effective modulus or an explicit creep coefficient, and why cracked-section properties, not gross Ig, govern serviceability.