Of the many multiple safety factor formats in vogue, perhaps the simplest to understand is the Load and Resistance Factor Design (LRFD) format, which is adopted by the ACI Code [Ref. 3.5, 3.8, 3.9]. Applying the LRFD concept to the classical reliability model, adequate safety requires the following condition to be satisfied :

where Rn and Sn denote the nominal or characteristic values of resistance R and load effect S respectively; and denote the resistance factor and load factor respectively. The resistance factor accounts for â€˜under-strengthâ€™, i.e., possible shortfall in the computed â€˜nominalâ€™ resistance, owing to uncertainties related to material strengths, dimensions, theoretical assumptions, etc., and accordingly, it is less than unity. On the contrary, the load factor , which accounts for â€˜overloadingâ€™ and the uncertainties associated with Sn, is generally greater than unity.

Eq. 1 may be rearranged as which is representative of the safety concept underlying WSM,Â here denoting the â€˜factor of safetyâ€™ applied to the material strength, in order to arrive at the permissible stress for design. Alternatively, Eq. 1 may be rearranged as

which is representative of the safety concept underlying ULM, here denoting the so-called â€˜load factorâ€™ (ULM terminology) applied to the load in order to arrive at the ultimate load for design.