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

Equation Form Comments Typical Problems
3. Axial members connected to a rotating rigid element.
Problems in this category feature
a rigid bar or a rigid plate to
which the axial members are
attached.
20 in.
(2)
80 in.
The rigid element is pinned
so that it rotates about a fixed
point. Since the axial members
are attached to the rotating
element, their deformations are
constrained by the position of
the deflected rigid bar. The
relationship between member
deformations can be found from
the principle of similar triangles.
(1)
12 in.
32 in.
B
A
15 in.
C
P
120 in.
80 in.
(2)
(1)
A B C D
δ
a
δ
a
δ
=
b
1 2
δ
=−
b
1 2
If both members elongate or both
members contract as the rigid bar
rotates, then the first equation
form is obtained.
If one member elongates while
the other member contracts as the
rigid bar rotates, then the
geometry-of-deformation
equation takes the second form.
425 mm
425 mm
1,500 mm
A
(1)
B
(2)
C
54 in. 54 in. 24 in.
P
D
1,000 mm
(2)
P
40 in.
δ1 + gap δ2
=
a b
If there is a gap or clearance in a
joint, then the geometry-ofdeformation
equation takes the
third form.
A B C
(1)
30 in.
D
P
36 in. 48 in. 14 in.
ExAmpLE 5.6
A
A steel pipe (1) is attached to an aluminum pipe (2) at flange B. The pipes are attached to
rigid supports at A and C, respectively.
Member (1) has a cross-sectional area
— P
2
(1) (2)
B
— P
2
1.8 m 1.4 m
C
A 1 = 3,600 mm 2 , an elastic modulus E 1 =
200 GPa, and an allowable normal stress of
160 MPa. Member (2) has a cross-sectional
area A 2 = 2,000 mm 2 , an elastic modulus
E 2 = 70 GPa, and an allowable normal
stress of 120 MPa. Determine the maximum
load P that can be applied to flange B
without exceeding either allowable stress.
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