QUESTION $4($AXIAL LOADING$)[13$ POINTS$]$

In a Mechanics of Materials teaching laboratory, there is a bimetallic clamp that consists of

one $40$ mm diameter cylinder fabricated using Metal Q and two bolts fabricated using Metal s

with each having a diameter of $12$ mm $($FIG$.$ Q$4).$ The

To complete the assembly of the clamp, two plates were put in place and, then, the top plate

was subjected to an axial force such that the cylinder was loaded in compression and a response

tension force acted on each bolt. This ensured the bolts held the cylinder snug.

The assembly was carried out when the temperature in the laboratory was $22C.$

In a test using the clamp, its temperature was raised to $190C.$ Under these conditions,

a design requirement was that the axial stress in the cylinder, due to the mechanical loading,

must not exceed $12$ MPa $.$

For Metal Q$,$ modulus of elasticity$=69$ GPa and coefficient of thermal expansion $=24{10}^{-6}{C}^{-1}.$

For Metal S$,$ modulus of elasticity $=120$ GPa.

Calculate the coefficient of thermal expansion of Material S$.$