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Lessons · Engineering · stress: force over area

Stress: the force, spread over the area that carries it

Stress is force divided by area, σ = F / A. In N/mm² it is megapascals, and that is the unit steel is rated in.

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 bar snapped on the test rig and the load looked fine. It was fine for the bar on the drawing; the bar that was made had a notch, half the area, twice the stress. Every strength question is a stress question.

How to think about it

Find the area the force passes through, at the thinnest place. Divide. Keep newtons with square millimetres, or newtons with square metres, and the answer is in MPa or Pa without any factor to remember.

Worked example

σ = F / A
Force over the area it acts through.
A rod 20 mm × 30 mm carries 36 kN: A = 600 mm²
The cross-section. 36 kN is 36,000 N.
σ = 36,000 N / 600 mm² = 60 N/mm² = 60 MPa
One newton per square millimetre is exactly one megapascal.
Mild steel yields near 250 MPa, so this bar is at about a quarter of yield
The number means nothing until it is set beside what the material can take.

Your turn

A 10 mm × 10 mm bar under 25 kN. Write the stress.

σ = 25,000 /  = 250 MPa

The trap

Mixing units: 36 kN over 600 mm² typed as 36 / 600 gives 0.06 of nothing. Newtons over square millimetres or newtons over square metres; never kilonewtons over anything without converting first.

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