Page 204 - Standard Handbook Of Petroleum & Natural Gas Engineering

Strength of Materials 189

Figure 2-28. Torsional loading of a right circular cylinder.

The strain due to the torque T is given by

2(1+V) Tr
y& =-- (2-86)
E J
and the total angular deflection between any two surfaces perpendicular to the
z axis is

TL
0 = 2(1+v)- (2-87)
EJ
where L is the distance between the two surfaces.
Example 2-19
A uniform steel bar 3 ft long and 2.5 in. in diameter is subjected to a torque of
800 ft-lb. What will be the maximum torsional stress and the angular deflection
between the two ends?
Assume E = 30 x lo6 psi and v = 0.3.
Then
n
J = -(1.254 - 04) = 3.83 in.4
2

800 ft-lbll2 in.ll.25 in.1
T& = = 3133 psi
I ft I 13.83 in.4

800 ft-lb) 12 in1 3 ftll2 in.[ in.' I
e = 2(1+ 0.3)
lftl I ft 130 x lo6 1b13.83 in.*
= 7.8xlO-'rad- 360" = 0.45"
2 x: rad