How Do You Design a Structure With an Appropriate Safety Factor?

A structure is designed with an appropriate safety factor by comparing its expected maximum working load or stress with the load or stress that would cause failure. The factor must provide sufficient reliability without creating unnecessary mass, cost or material use.

The factor of safety is:

$$\text{Factor of safety} = \frac{\text{failure load}}{\text{safe working load}}$$

Equivalently, designers can calculate allowable stress:

$$\text{Allowable stress} = \frac{\text{limiting material strength}}{\text{factor of safety}}$$

First, identify all expected loads, including static, dynamic, impact and cyclic loads. Then determine the load paths, supports and resulting internal stresses, such as tension, compression, shear, bending and torsion.

Next, identify the most likely failure mode. The relevant limiting value might be yield strength, ultimate tensile strength, fatigue strength or the load causing buckling. Designers then select a safety factor by considering uncertainty and the consequences of failure.

For example, a member has a yield strength of $240\,\text{MPa}$ and a selected safety factor of $3$. Its allowable stress is:

$$\frac{240}{3} = 80\,\text{MPa}$$

For an axial load of $40{,}000\,\text{N}$, the minimum cross-sectional area is:

$$A = \frac{F}{\sigma} = \frac{40{,}000}{80} = 500\,\text{mm}^2$$

The design should then be tested or modelled and refined if necessary. A common misconception is that the highest possible safety factor is always best. Excessive safety factors can make products unnecessarily heavy, expensive and environmentally damaging.

In an IB Design Technology HL response on B3.2 structural systems application and selection, define the factor of safety, show a calculation, identify the critical failure mode and justify why the chosen value is appropriate for the loading, material, manufacture and consequences of failure.