Consider two bars, same cross$-$section area $A=48m{m}^2$ but different

length: $I_1=192mm,$ and $I_2=67mm$

The two bars are in series and subjected to a force $F$ in tension.

For each of the following cases, determine the displacement as a

function of the force $F,$ and if some plasticity occurs, the $F_{\text{c}\text{r}\text{i}\text{t}\text{i}\text{c}\text{a}\text{l}}$

force the plasticity activates.

both material are perfectly elastic and their properties are

$E1=105$GPa, and $E2=63$GPa

both are perfectly plastic and their properties are such that

$E_1=105$GPa,$E2=63$GPa, and $Y_{s1}=Y_{s2}=181$MPa

both are elasto$-$plastic and their properties are such that $E_1=105$

GPa,$E2=63$GPa,$K_1=39$GPa,$K_2=24$GPa, and $Y_{s1}=Y_{s2}=181$MPa