The bar ABCDE having three different cross$-$sectional areas is firmly attached to support $A,$ as

shown below. Four axial loads are applied to the bar, $P_1=160kN$ acts at point $B,P_2=130kN$

acts at point $C,P_3=120kN$ acts at point $D,$ and $P_4=40kN$ acts at point $E.$ The modulus of

elasticity of the bar is $E=200$GPa. The coefficient of thermal expansion is $=12{10}^{-6}C.$

a$)$ Calculate the reaction at the support A and draw the Axial Force Diagram $($AFD$)$ of the

entire bar. Clearly indicate tension or compression.

b$)$ Determine the axial stress in MPa of the four sections of the bar ${}_{AB},{}_{BC},{}_{CD}$ and ${}_{DE}.$

Clearly indicate tension or compression.

c$)$ Calculate the displacements in $mm$ at four points B$,$ C$,$ D$,$ and E$.$ Clearly indicate

elongation or contraction.

d$)$ Draw displacement diagram of the entire bar.

e$)$ In addition to the four axial loads shown in the figure, if the entire bar is also subject to

an increase of temperature by $T=60C,$ calculate the displacement in $mm$ at point $D.$

Clearly indicate elongation or contraction.

Section DE

$d=30mm$

$d_i=25mm$

$d_o=35mm$

$d=35mm$