Design strength and design load in LSM

Design strength

Design strength of a material is its characteristic strength divided by the partial safety factor for the material:

$$f_d=\frac{f_k}{\gamma_m}$$

For concrete $\gamma_m=1.5$ (so $f_{cd}=f_{ck}/1.5$, and in the stress block $0.446f_{ck}$), and for steel $\gamma_m=1.15$ (so $f_{yd}=f_y/1.15=0.87f_y$). The factor allows for variation in material strength, workmanship and member behaviour.

Design load

Design load is the characteristic load multiplied by the partial safety factor for load:

$$F_d=\gamma_f\,F_k$$

IS 456:2000, Table 18, gives $\gamma_f$: 1.5 for DL+LL, 1.2 for DL+LL+WL/EL, 1.5 for DL±WL/EL, and 0.9 for DL when it is favourable (0.9DL+1.5WL). The factor covers possible overloading and inaccuracies in analysis.

The member is safe when the design resistance (from design strengths) is at least the effect of the design loads: $R_d\ge S_d$.