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Structure I

Consider structural elements $(1)$ and $(2)$:

having lengths of $5$a and $4a,$ respectively,

having the same cross$-$sectional areas of $A,$ and

having yield strengths of ${}_{Y1}$ and ${}_{Y2},$ respectively, for both tension and compression, where

${}_{Y1}=2{}_{Y2}.$

Structure I is a truss made up of elements $(1)$ and $(2),$ whereas Structure II is a rod also made up

of elements $(1)$ and $(2),$ both as shown above. The loading $P$ acts on Structures I and II$.$ Let $F{S}_{\text{I}}$

and $F{S}_{II}$ represent the factors of safety against yielding for Structures I and II$,$ respectively.

Consider the weight of the structural elements to be small.

Choose the correct response below regarding the factors of safety for the two structures:

i$)F{S}_{\text{I}}>F{S}_{II}$

ii$)F{S}_{\text{I}}=F{S}_{II}$

iii$)F{S}_{\text{I}}$

$iv$