Lessons · Engineering · Hooke's law and Young's modulus
Hooke's law: stress and strain are proportional, and E is the ratio
Below yield, σ = E × ε. E is Young's modulus, the stiffness of the material: about 200 GPa for steel, 70 GPa for aluminium.
Hone is a place to practise a career, one idea a day. This is one of its lessons, written out in full and free to read without an account.
What it is for
A client wants aluminium instead of steel to save weight, same shape. The load has not changed and neither has the stress, but the frame now deflects nearly three times as much, and the door no longer closes. E is the number that would have said so.
How to think about it
Keep stress and E in the same unit; 200 GPa is 200,000 MPa. Then strain is stress over E, or stress is E times strain. Stiffness is E; strength is yield. They are different numbers and different questions.
Worked example
σ = E × ε, up to the yield pointHooke's law. Beyond yield the material stops coming back.
Steel: E = 200 GPa = 200,000 MPaWritten in MPa so it matches the stress.
Stress 120 MPa → ε = 120 / 200,000 = 0.0006Six hundred microstrain.
Aluminium, E = 70 GPa, at the same stress: ε = 120 / 70,000 = 0.00171Nearly three times the stretch for the same load. Same strength question, different stiffness answer.
Your turn
Steel at 50 MPa, E = 200,000 MPa. Write the strain.
ε = 50 / 200,000 =
Solve one, graded on the server
The trap
Using E in GPa with stress in MPa. 120 / 200 = 0.6 is a strain of sixty percent, and steel does nothing of the kind. The units were a thousand apart.