The maximum load that a structural member will be allowed to carry is smaller

than the ultimate load it can bear. This is smaller load is referred to as the

allowable load. The ratio of the ultimate load to the allowable load is used to

define the factor of safety.

Factor $of$ safety $=F.S.=\frac{\text{u}\text{l}\text{t}\text{i}\text{m}\text{a}\text{t}\text{e}\text{l}\text{o}\text{a}\text{d}}{\text{a}\text{l}\text{l}\text{o}\text{w}\text{a}\text{b}\text{l}\text{e}\text{l}\text{o}\text{a}\text{d}}$

An alternative definition of the factor of safety is based on the use of stresses.

Factor $of$ safety $=F.S.=\frac{\text{u}\text{l}\text{t}\text{i}\text{m}\text{a}\text{t}\text{e}\text{s}\text{t}\text{r}\text{e}\text{s}\text{s}}{\text{a}\text{l}\text{l}\text{o}\text{w}\text{a}\text{b}\text{l}\text{e}\text{s}\text{t}\text{r}\text{e}\text{s}\text{s}}$

Imagine that a long steel wire hangs vertically from a high$-$altitude balloon. What

is the greatest length $($feet$)$ it can have without yielding under its own weight if the

steel yields at $40$ ksi and a factor of safety of $3\mathrm{.}0$ is mandated? The density of

steel is $490l\frac{b}{f}{t}^3.$