1
© 2002-2003, L.D. Sturges
EM 324
Mechanics of Materials
Torsional Loading
Torsion
– the twisting of a
straight bar
when it is
loaded by moments
(torques)
that tend to
produce rotation about the
longitudinal axis
.
Synonyms
:
Torques, twisting moments.
© 2002-2003, L.D. Sturges
EM 324
Mechanics of Materials
Torsional Loading (cont)
Definition
:
Positive torque
– the
torque
vector points outward
from the “cut” surface.
According to the
right-hand-rule
, this is a
counter-clockwise torque
when viewed from
the “part discarded.”
© 2002-2003, L.D. Sturges
EM 324
Mechanics of Materials
Torsional Loading (cont)
Approximations/Assumptions
:
•
Circular shaft (solid or hollow).
•
Straight; constant diameter.
•
Shearing strains are small.
•
Plane section before twisting – remains
plane.
•
A diameter before twisting – remains
straight.

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2
© 2002-2003, L.D. Sturges
EM 324
Mechanics of Materials
Torsional Shearing Strain
Take a short
segment of a
shaft rotated by
a negative torque
T
(not shown).
The right end of the shaft will rotate through an
angle
θ
as shown.
© 2002-2003, L.D. Sturges
EM 324
Mechanics of Materials
Torsional Shearing Strain (cont)
Inscribe a line
AB
down
the side of the shaft.
The right end of the line
will rotate taking
B
to
B'
and making an angle
of
φ
between the lines
AB
and
AB'
.
© 2002-2003, L.D. Sturges
EM 324
Mechanics of Materials
Torsional Shearing Strain (cont)
The length of the line/arc
BB'
is
A square element of
material at
B
will
deform into a
parallelogram.
'
BB
L
c
φ
θ
=
=