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