Library / Mechanical / MEC-32
Mechanical
Direct stress
Force per unit area.
- Ref
- MEC-32
- Rev
- v1
- Field
- Mechanical
- Result
- σ [MPa]
F is the axial force, entered in newtons, and A the cross-sectional area in mm². Because 1 N/mm² equals 1 MPa, the answer comes straight out in megapascals. Tension and compression use the same formula; only the sign differs.
Force per unit area. It is the quantity compared with a material’s strength.
Calculator
- Diameter of the equivalent round section22.57 mm
- Stress if the area is halved250 MPa
What drives the result
Each variable is moved across its typical range while the others stay at the values above. The longest bar is the key driver.
- A 50 kN load on a 400 mm² section (about 23 mm diameter) gives 125 MPa, about half the yield strength of mild steel.
- Stress is what the material feels; two bars of different size carrying the same load are not equally loaded.
Chart data as tables
Ranked variables
| Variable | Typical range | Lowest result | Highest result | Swing (MPa) | Local step | Change in result |
|---|---|---|---|---|---|---|
| A Cross-sectional area | 1 to 100,000 mm² | 0.5 | 50,000 | 50,000 | +10% | −9.09 % |
| F Axial force | 1 to 1e7 N | 0.0025 | 25,000 | 25,000 | +10% | +10 % |
Sweep of Cross-sectional area
| Cross-sectional area (mm²) | Stress (MPa) |
|---|---|
| 1 | 50,000 |
| 4.217 | 11,860 |
| 17.78 | 2,812 |
| 74.99 | 666.8 |
| 316.2 | 158.1 |
| 1,334 | 37.49 |
| 5,623 | 8.891 |
| 23,710 | 2.108 |
| 100,000 | 0.5 |
Sweep one variable
Variables and how each one contributes
Stress
What the equation gives you. Everything else feeds it.
Axial force
The load along the axis of the member, in N. Directly proportional: twice the load doubles the stress.
Cross-sectional area
The area of the cross-section that carries the load, in mm². Inverse: a larger area gives a proportionally lower stress. A 10 % rise in A lowers σ by about 9 %.
Worked example with the values above
- Write the load and the area: F = 50,000 N, A = 400 mm².
- Divide: 50,000 / 400.
- σ = 125 MPa (N/mm²).
Assumptions and limits
- The load acts through the centroid, so the stress is uniform across the section.
- The section is away from holes, notches and the points where the load is applied, where stress is higher.
Common mistakes
- Using the gross area where a bolt hole removes some of the section. Use the net area.
- Entering the area in m² with the force in N, which gives pascals, not megapascals.
Statistics and uncertainty
σ = F/A, so errors in load and area both pass straight through. Because A depends on the diameter squared, a 2 % tolerance on a diameter gives about 4 % on the area and on the stress. Loads on structures are usually the more uncertain input, which is why a factor of safety is applied.
Where it is used
- Checking a tie rod, bolt or strut against its yield strength.
- Comparing a working stress with an allowable one.
Maths you need
- Area of a circle: πd²/4
- Units: 1 N/mm² = 1 MPa