The bar AB$,$ fixed at both ends, has a cross$-$sectional area of $\backslash (1200\backslash$mathrm$\{$~mm$\}^\{2\}\backslash )$ and is made of a steel which is assumed to be elastic, perfectly plastic with Young's modulus E $=200$ GPa and yield strength $\backslash (\backslash$mathrm$\{$Sy$\}=250\backslash$mathrm$\{$MPa$\}\backslash ).$

If a force F of $520$ kN is applied and then removed, determine the residual stress in the bar and the permanent displacement of Point C $.$

a$)$ Determine the residual stress in each segment.

b$)$ Find the permanent deformation at point $\backslash ($ C $\backslash ).$

c$)$ Determine the smallest load P needed to cause segment CB to yield.

$153$ MPa

$57\mathrm{.}46$ MPa

$172$ MPa $191$ MPa

$65\mathrm{.}15$ MPa $0\mathrm{.}246278$ mm

$0\mathrm{.}741248$ mm

$0\mathrm{.}229366$ mm