Hooke’s Law (Uniaxial)

σ = E ε

In the linear-elastic range, uniaxial stress is proportional to axial strain. E is the slope of the stress–strain diagram. The relation does not apply after yielding or for large plastic strain.

$σ$ (Pa): Axial stress
$E$ (Pa): Modulus of elasticity
$ε$ (—): Axial strain

Step-by-step solved example

Steel with E = 200 GPa and ε = 0.0010. Find σ.

Linear σ = Eε up to yield. Slope is E.

1. Hooke
σ = Eε = (200×10⁹)(0.0010) = 200×10⁶ Pa.
$σ = 200 MPa$
2. Check range
200 MPa is below typical steel yield (~250–350 MPa), so the elastic assumption is reasonable.

Answer: 200 MPa

10 practice questions

0/10 correct

1.E = 200 GPa, ε = 5.0×10⁻⁴. σ =

2.σ = 150 MPa, E = 200 GPa. ε =

3.Hooke’s law holds

4.E of ordinary concrete is typically about

5.Strain ε is

6.E is the slope of

7.Aluminum E is about

8.σ = Eε assumes

9.ε = 0.0020, E = 70 GPa. σ =

10.Beyond yield, uniaxial Hooke’s law