Factor of safety: WSM and LSM

In WSM, safety is given by one factor of safety applied to the material strength to get a permissible stress. In LSM, safety is split into partial safety factors, one for material strength ($\gamma_m$) and one for loads ($\gamma_f$).

Working stress method

• Concrete: $\sigma_{cbc} = \dfrac{f_{ck}}{\text{F.O.S.}}$. For M20, $\sigma_{cbc} = 7$ N/mm$^2$, so the factor of safety is about $20/7 \approx 2.86$ (nearly 3 on cube strength).
• Steel: $\sigma_{st} = \dfrac{f_y}{\text{F.O.S.}}$. For Fe415, $\sigma_{st} = 230$ N/mm$^2$, giving $415/230 \approx 1.8$; for mild steel, $\sigma_{st} = 140$ N/mm$^2$, so $250/140 \approx 1.8$.
• Loads are taken at their working values with no factor.

Limit state method (IS 456:2000, cl. 36.4)

Design strengths: concrete $0.67f_{ck}/1.5 = 0.446f_{ck}$ in the stress block; steel $0.87f_y$ (i.e. $f_y/1.15$).

Comparison

A lower material factor is acceptable in LSM because the uncertainty in loads is accounted for separately by $\gamma_f$.