The given system shown below consists of $3$ different segments which are made of $3$ different materials, steel, aluminium and copper. The temperature of the system is increased from $20C$ to $60C.$ Find the total deformation $($elongation or contraction$)$ between points A and $D.$

$E_{ST}=200$Gpa,$E_{AL}=70$GPa,$E_{Cu}=120$GPa

${}_{\text{S}\text{t}\text{e}\text{e}\text{l}}=\frac{{1210}^{-6}}{{?}^{o}C},{}_{\text{A}\text{l}\text{u}\text{m}}=\frac{{2410}^{-6}}{{?}^{o}C},{}_{Cu}=\frac{{1810}^{-6}}{{?}^{o}C}$

Modulus of Elasticity Values

$E_{\text{S}\text{t}\text{e}\text{e}\text{l}}=200$GPa,${}_{\text{A}\text{l}\text{u}\text{m}}=80$GPa,${}_{Cu}=120$GPa

$q,$

use these caws

${}_{\text{l}\text{o}\text{n}}=\frac{L}{L_0},{}_{\text{l}\text{a}\text{t}}=\frac{r}{r_0}$

A: Cross$-$sectional area

E: Modulus of Elasticity $L_0$ : Initial Length

$v=-\frac{{}_{\text{l}\text{a}\text{t}}}{{}_{\text{l}\text{o}\text{n}}},G=\frac{E}{2(1+v)}$

$$ L: Change in Length

$N$ : Internal Axial Force

$$: Axial Stress

$$ : Axial Strain

G: Shear Modulus

$v$: Poisson's Ratio

${}_{\text{l}\text{a}\text{t}}$: Lateralstrain

${}_{\text{l}\text{o}\text{n}}$: Longitudinal strain

${}_{\text{a}\text{v}\text{e}}=\frac{P}{A}$

$P$ :The normal force acting on the centroid of the area A: Cross section area

Deformation of an Axially Loaded Member

${}_P=\frac{NL}{AE}$

Thermal Expansion

$L=L_{o}t$

$t$ : Change in temperature

$$: Thermal expansion coefficient