A flat aluminum alloy bar is fixed at both ends. Segment AB has a slight taper. If the temperature of the bar is raised uniformly by an amount ΔT = 20°F, find reactions at A and C. What is the displacement at B? Assume that L = 3 ft, t = 1/4 in., b₁ = 2 in., b₂ = 2.5 in., E = 10,400 ksi, and the coefficient of thermal expansion a = 13 X 10^-6 /°F.

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b2 A X 1/2 bi B L/2 SB b₁ C