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A copper rod 6cm in diameter is placed within a steel tube 8cm external diameter and 6cm internal diameter, of exactly the same length.  The two pieces are rigidly fixed together by two transverse pins 20 mm in diameter, one at each end passing through both rod and the tube.  Calculate the stresses induced in the copper rod, steel rube and the pins if the temperature of the combination is raised by 50° C.  Take:

         Es= 210 GPa,$\alpha _{s}$ = 0.0000115/ 0C

         Ec = 105 GPa, $\alpha _{c}$ = 0.000017 / 0C        

                             

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