Problem $2.(4$P$)$

Determine the elongation of the square hollow bar $($outside dimension $50$ mm and internal dimension $40$ mm $)$ when it is subjected to the axial force $P1=200kN.$ If this force is increased to $P2=400kN$ and released, find the permanent elongation of the bar. The bar is made of a metal alloy having a stress$-$strain diagram which can be approximated as shown in the figure on the right.

Step $1.$ Summarize from the text of the problem and figure what is know in consistent units.

Step $2.$ Find cross section area of the section

Step $3.$ Find Young's modulus using elastic range of stress$-$strain graph and stress for P$1$ is in elastic or plastic range

Step $4.$ If P$1$ produced stress below $250$MPa find strain and axial deformation under P$1$

Step $5.$ Find stress and strain for P$2$ and if it is in plastic range find permanent plastic strain after unloading to zero load.

Step $6.$ Find plastic permanent elongation of the bar after unloading to zero load.

$19$