Stress
Internal force per unit area in a material.
Formula
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Example
A 1000 N load on a 0.01 m² bar produces σ = 1000/0.01 = 100 kPa.
How it works
Stress tells you how concentrated a force is over an area. The same force can be harmless on a large surface but damaging on a small one, because a smaller area means each square metre must carry more load. That is why we divide force by cross-sectional area: it gives the force intensity acting inside the material.
When to use it
Use this formula when checking whether a beam, rod, wire, bolt, or any loaded component is likely to be overloaded. It is also useful in material testing and design whenever you need to compare how different shapes or sizes handle the same force.
Worked example, step by step
A steel cable carries a tension force of 2,400 N and has a cross-sectional area of 0.0008 m². σ = F / A σ = 2400 / 0.0008 σ = 3,000,000 Pa σ = 3.0 MPa
Common mistakes to avoid
- Using the wrong area, such as the surface area instead of the cross-sectional area
- Forgetting to convert units, especially mm² to m² or kN to N
- Confusing stress with force and writing the answer in newtons instead of pascals
Did You Know?
Engineers deliberately design bridges and buildings to keep stress far below the material's breaking point.
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