Timothy A. Philpot - Mechanics of materials _ an integrated learning system-John Wiley (2017)

Successful application of the five-step solution method depends on the ability to
understand how twisting deformations are related in a system. The table that follows presents
considerations for two common categories of statically indeterminate torsion systems.
For each general category, possible geometry-of-deformation equations are discussed.
171
STATICALLy INdETERMINATE
TORSION MEMbERS
Geometry of Deformations for Typical Statically Indeterminate Torsion Systems
Equation Form Comments Typical Problems
φ1 = φ2 Problems in this category include a
tube surrounding an inner shaft. The
angles of twist for both torsional
members must be identical for this
type of system.
1. Coaxial torsion members.
T
A
(1)
360 mm
T
A
(1)
T
(2)
B
(2)
T
B
400 lb.ft
(1)
A
B
12 in.
(4)
(2)
20 in.
450 mm
(3)
C
12 in.
400 lb.ft
D
2. Torsion members connected end to end in series.
φ
φ
+ φ = 0
1 2
+ φ = constant
1 2
Problems in this category include
two or more members connected
end to end.
If there are no gaps or clearances in
the configuration, the member angles
of twist must sum to zero.
If there is a misfit between two
members or if the supports move as
the torque or torques are applied,
then the sum of the angles of twist of
the members equals the specified
angular rotation.
z
z
A
y
30 in.
z
y
A
325 mm
(1)
B
22 in.
A
y
(1)
T B
B
T B
400 mm
(2)
6 in. 8 in.
(1)
C
18 in.
(2)
B
C
(3)
T B
T C
325 mm
D
(3)
(2)
x
D
x
C
x