Consider the sleeve made from two copper tubes joined by tin-lead solder over distance s. The sleeve has brass caps at both ends, which are held in place by a steel bolt and washer with the nut turned just snug at the outset. Then, two "loadings" are applied: n = 1/2 turn applied to the nut; at the same time the internal temperature is raised by ΔT = 30°C.
(a) Find the forces in the sleeve and bolt, Ps and PB, due to both the prestress in the bolt and the temperature increase. For copper, use Ec = 120 GPa and αc = 17 × 106 / °C; for steel, use Es = 200 GPa and αs = 12 × 106 / °C. The pitch of the bolt threads is p = 1.0 mm. Assume s = 26 mm and bolt diameter db = 5 mm.
(b) Find the required length of the solder joint, s, if shear stress in the sweated joint cannot exceed the allowable shear stress Ï„aj = 18.5 MPa.
(c) What is the final elongation of the entire assemblage due to both temperature change ΔT and the initial prestress in the bolt?

8= np Brass AT AT per sleeve Steel bolt L= 40 mm, di =25 mm, I = 4 mm *uu os = 7 d2= 17 mm, 12 = 3 mm