Nominal Stress, True Stress and Factor of Safety

Direct stress is the value obtained by dividing the load by original cross-sectional area. That is the reason why the value of stress started dropping after neck is formed in mild steel (or any ductile material). But actually as material is stressed its cross-sectional area changes. We should divide load by the actual cross-sectional area to get true stress in the material. To distinguish between the two values, the terms nominal stress and true stress is introduced.

Because we consider nominal stress, after neck formation started (after ultimate stress), stress-strain curve started sloping down and the breaking took place at lower stress (nominal). If we consider true stress, it is increasing continuously as strain increases as shown in Fig. 1.

Fig. 1 Nominal Stress - Strain Curve and True Stress - Strain Curve for Mild Steel

Factor of Safety

In practice, it is not possible to design a mechanical component or structural component permitting stressing up to ultimate stress for the following reasons.

1. Reliability of material may not be 100 per cent. There may be small spots of flaws.
2. The resulting deformation may obstruct the functional performance of the component.
3. The loads taken by designer are only estimated loads. Occasionally there can be overloading. Unexpected impact and temperature loadings may act in the lifetime of the member.
4. There are certain ideal conditions assumed in the analysis (like boundary conditions).

Actually ideal conditions will not be available and, therefore, the calculated stresses will not be 100 per cent real stresses. Hence, the maximum stress to which any member is designed is much less than the ultimate stress and this stress is called Working Stress. The ratio of ultimate stress to working stress is called factor of safety. Thus

In case of elastic materials, since excessive deformation create problems in the performance of the member, working stress is taken as a factor of yield stress or that of a 0.2 proof stress (if yield point does not exist). Factor of safety for various materials depends up on their reliability. The following values are commonly taken in practice.

1. For steel – 1.85
2. For concrete – 3
3. For timber – 4 to 6