Metal Foams: A Design Guide

Torsion of shafts
T T,q
T T,q
Yield: sy
T
2
T
Fracture: sf T T
F
F,u
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F
R
d
do
di
Figure 6.5 Torsion of shafts
d
Design formulae for simple structures 73
Elastic deflection
Failure
Tf =
do Ksy θ =
T = Torque (Nm)
q = Angle of twist
g = Shear modulus (N/m 2 )
= Length (m)
d = Diameter (m)
K = See Figure 6.1 (m 4 )
s y = Yield strength (N/m 2 )
s f = Modulus of rupture (N/m 2)
Spring deflection and failure
F = Force (N)
u = Deflection (m)
R = Coil radius (m)
n = Number of turns
T
KG
(Onset of yield)
Tf = (Brittle fracture)
do 2Ksf u =
G d
Ff =
4
d3 64 FR
s
3n π
32 R
points on the surface closest to the centroid of the section (the mid-points of
the longer sides). It can be estimated approximately by inscribing the largest
circle which can be contained within the section and calculating the surface
stress for a circular bar of that diameter. More complex section-shapes require
special consideration, and, if thin, may additionally fail by buckling. Helical
springs are a special case of torsional deformation. The extension of a helical
spring of n turns of radius R, under a force F, and the failure force Fcrit, is
given in Figure 6.5.