Hooke's Law and Elastic Modulus

E = σ / ε (elastic)

In the linear-elastic range, stress is proportional to strain. E is the slope of the σ–ε curve (Young's modulus). Steel E ≈ 29×10⁶ psi (200 GPa). Concrete E is much lower (ACI 57 000 √f'c psi). Do not use E past yield.

$E$ (psi or GPa): Modulus of elasticity
$σ$: Axial stress
$ε$: Axial strain

Step-by-step solved example

Steel rod: σ = 20 ksi, E = 29 000 ksi. Elastic strain?

E is the slope of the elastic σ–ε line (materials view).

1. Hooke
ε = σ/E = 20/29000 = 6.90×10⁻⁴.
$ε = 6.90 \times 1 0^{- 4}$

Answer: 6.90×10⁻⁴

10 practice questions

0/10 correct

1.E for structural steel is about

2.ε = 0.001, E = 200 GPa. σ =

3.A steeper σ–ε slope means

4.Hooke's law stops being valid at

5.Aluminum E is about

6.Units of E are the same as

7.Concrete E compared with steel is

8.If strain doubles in the elastic range, stress

9.Secant modulus is

10.Wood E is typically