Materials

141/3335–8FE Reference Handbook 10.4 · Materials · Modulus of Elasticity of Concrete

Handbook formula

ACI Elastic Modulus of Concrete

E_{c} = 57, 000 f_{c}^{'} (psi, normalweight) E_{c} = 33 w_{c}^{1.5} f_{c}^{'} (psi)

ACI 318 / Handbook: the general expression is E_c = 33 w_c^{1.5} √f'c with w_c in pcf and f'c, E_c in psi. For normalweight concrete w_c ≈ 145 pcf this collapses to E_c = 57 000 √f'c. SI companion for normalweight is E_c ≈ 4700 √f'c (MPa). Use E_c for elastic deflections and stiffness, not for φMn strength design.

$E_{c}$ (psi): Modulus of elasticity of concrete
$f_{c}^{'}$ (psi): Specified compressive strength
$w_{c}$ (pcf): Unit weight of concrete

Step-by-step solved example

Normalweight concrete with f'c = 4000 psi. Compute E_c from 57 000 √f'c.

ACI normal-weight Ec = 57,000 √f'c (psi).

1. Square root
√4000 = 63.25.
$4000 = 63.25$
2. ACI normalweight
E_c = 57 000 × 63.25 = 3.60×10⁶ psi.
$E_{c} = 3.60 \times 1 0^{6} psi$

Answer: E_c ≈ 3.60×10⁶ psi

10 practice questions

0/10 correct

1.ACI normalweight E_c in psi is

2.For f'c = 4000 psi, 57 000 √f'c is nearest

3.The 57 000 constant assumes a unit weight near

4.The general ACI formula (any weight) is

5.f'c = 9000 psi. Normalweight E_c is nearest

6.SI normalweight companion is about

7.Doubling f'c multiplies E_c by

8.Lightweight structural concrete (w_c ≈ 110 pcf) should use

9.f'c = 2500 psi. 57 000 √f'c =

10.E_c from this formula is intended for