FORMULAS Emax = V₁E+ (1-V₁) Em Ogel 1 [r+rs(f-2)]¹/2/nQ5 The fuel rods of a nuclear reactor consist of solid uranium cylinders of diameter 70 mm. During operation, a typical rod experiences

a temperature distribution approximated by the equation T(r) = 600 -0.1² °C, where r is the radius in mm. The properties of uranium are E = 172 GPa, v = 0.28, and a = 11 x 10-6 per °C. (a) Find the maximum tensile, compressive and shear stresses in the fuel rod if the outer surface is traction-free and plane strain conditions can be assumed. (14 marks) (b) If the fuel rod is now permitted to expand axially, determine the maximum tensile, com- pressive and shear stresses. (6 marks) [You may assume that the radial and hoop stresses in an axi-symmetric disk in a state of plane strain are Orr 000 = (3-2v)p²r² 8(1-v) (1+2v)p²,² 8(1-v) with the corresponding radial displacement + Ea (1-0)² /rTdr +/ Ea (1-v)r² afr rTdr _ ( 1-20)/(1+1) ²²³³ + 0(1+1) [T rTdr + 8E(1-v) (1-v)r where the symbols have their usual meanings] A+ EaT (1-v) B + A A(12v)(1+ v)r E B (1 + v) B Er