Normal and shear stress, strain

Stress: force spread over an area

A force tells you how hard something is pushed or pulled; it does not tell you whether the material will survive. A 10 kN load that is fine for a thick steel bar can snap a thin wire. What matters is how concentrated the force is, which is stress:

with $P$ the internal axial force and $A$ the cross-sectional area. The SI unit is the pascal (Pa); in practice engineers use megapascals, and $1 \text{ MPa} = 1 \text{ N/mm}^2$, which makes calculations in newtons and millimetres convenient.

Normal stress acts perpendicular to the area (tension is positive, compression negative). Shear stress acts along the area, as in a bolt or a rivet being sliced across:

Strain: how much it stretches

Strain is the change in length per unit of original length. It has no units.

For most metals the strain at working loads is tiny (a few hundred micro-strain), so it is often quoted in $\mu\varepsilon$ ($10^{-6}$).

Hooke's law

Within the elastic range, stress and strain are proportional:

The constant $E$ is the elastic modulus (Young's modulus). For steel it is about 200 GPa, for aluminium about 70 GPa and for timber roughly 10 GPa along the grain.

Factor of safety

Real loads are uncertain and real materials vary, so members are designed to be stronger than strictly needed. The factor of safety compares the failure stress to the actual stress:

A FoS of 1 means the member is just yielding. Typical design values range from about 1.5 to 4 depending on the consequences of failure.