Page 18 - Mechanical Engineer's Data Handbook

STRENGTHS OF MATERIALS 7
Strain energy in torsion

Strain energy U =+TO
2
for solid circular shaft u=L
4G

for hollow circular shaft u =
Thin tubular section
~ D ~ L
solid
where U=u - shaft
Z, = T/2tA; €'= TpL/4A2tG 4
n(D2 -d2)L
where =U hollow shaft
t = thickness 4
A = area enclosed by mean perimeter
p = mean perimeter
Torsion of hollow shaft
For a hollow shaft to have the same strength as an
equivalent solid shaft:
1 1-k2
W,
W,/
DJD, = f--- = vm
1 -k4'
ode, = gcF)
k = BJD,
where:
D,, Do, Di=solid, outer and inner diameters
W,, W, = weights of hollow and solid shafts
Oh, 6, =angles of twist of hollow and solid shafts
Thin rectangular bar and thin open section

Z, = 3 T/dt2; 0 = 3 TL/Gdt3 (rectangle)
z,=3T/Zdr2; e=3TL/GZdt3 (general case)
Edt2=(d,t:+d2t:+. . . Zdt3=(dlt:+dzt:+. . .)

k 0.5 0.6 0.7 0.8 0.9

DJD, 1.02 1.047 1.095 1.192 1.427
W,JW, 0.783 0.702 0.613 0.516 0.387
eje, 0.979 0.955 0.913 0.839 0.701