Exercise $3(30$ points$)$

We have a cantilever beam made of a composite of steel and copper with perfect adhesion

$($See the next figure$).$ The initial temperature is $20C$ and we know that there are no residual

stresses at this temperature. Questions:

a$)$ Which material will be under tension, and which one will be under compression if

you increase the temperature? Explain why and include a schematic draw. $(10$

points$)$

b$)$ Calculate the residual forces that appear when you reduce the temperature to $10C.$

Please, add a schematic drawing to show the direction of each force. $(10$ points$)$

c$)$ Calculate the final length of the beam at $10C$ if the initial length is $3$ m $.(10$ points$)$

The elastic modulus of copper is $110$ GPa

The yield stress of the copper is $140$ MPa

The coefficient of thermal expansion of the copper is $1710-6(\frac{1}{}C)$

The elastic modulus of steel is $205$ GPa

The yield stress of the steel is $280$ MPa

The coefficient of thermal expansion of the steel is $10x10-6(\frac{1}{}C)$

Note: you can assume the width of the composite is constant across the length and equal

in both copper and steel. Provide the final results as a function of this width.