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

t = 8 mm, and E = 72 GPa, determine the overall elongation of the
bar for an axial force of P = 18 kN.
p5.3 Compound axial member ABC shown in Figure P5.3 has a
uniform diameter d = 1.25 in. Segment (1) is an aluminum [E 1 =
10,000 ksi] alloy and segment (2) is a copper [E 2 = 17,000 ksi]
alloy. The lengths of segments (1) and (2) are L 1 = 84 in. and L 2 =
130 in., respectively. Determine the force P required to stretch
compound member ABC by a total of 0.25 in.
P
A
(1)
Aluminum
L 1
L 2
B
(2)
Copper
C
P
d
p5.6 A compound steel (E =
30,000 ksi) bar is subjected to the
loads shown in Figure P5.6. Bar
(1) has a cross-sectional area A 1 =
0.35 in. 2 and a length L 1 = 105 in.
Bar (2) has an area A 2 = 0.35 in. 2
and a length L 2 = 85 in. Bar (3) has
an area A 3 = 0.09 in. 2 and a length
L 3 = 40 in. The loads and angles
are P = 40 kips, α = 36°,
Q = 13 kips, β = 58°, and R =
9 kips. Determine the vertical
deflection of end A.
D
P
α
C
B
β
v
Q
A
R
FIGURE p5.6
(1)
P
α
(2)
β
(3)
Q
u
L 1
L 2
L 3
FIGURE p5.3
p5.4 Three solid cylindrical rods are welded together to form the
compound axial member shown in Figure P5.4. The member is attached
to a fixed support at A. Each rod has an elastic modulus E =
40 GPa. Use the following values for the rod lengths and areas:
L 1 = 1,440 mm, L 2 = 1,680 mm, L 3 = 1,200 mm, A 1 = 260 mm 2 ,
A 2 = 130 mm 2 , and A 3 = 65 mm 2 . What magnitude of external load
P is needed to displace end D a distance u D = 60 mm to the right?
L 1 L 2 L 3
p5.7 Rigid bar DB in Figure P5.7 is supported at pin B by axial
member ABC, which has a cross-sectional area A 1 = A 2 = 75 mm 2 ,
an elastic modulus E 1 = E 2 = 900 MPa, and lengths L 1 = 400 mm
and L 2 = 600 mm. A load Q = 500 N is applied at end C of member
(2), and a load P = 1,500 N is applied to the rigid bar at a distance
a = 80 mm from pin support D and b = 50 mm from pin B. Determine
the downward deflections of
(a) pin B.
(b) pin C.
A
FIGURE p5.4
(1) (2) (3)
B
C
D
P
D
Rigid bar
P
A
B
(1)
L 1
p5.5 The assembly shown in Figure P5.5 consists of a bronze
rod (1) and an aluminum rod (2), each having a cross-sectional area
of 0.15 in. 2 . The assembly is subjected to loads P = 1,900 lb and
Q = 3,200 lb, acting in the directions shown. Determine the horizontal
displacement u B of coupling B with respect to rigid support A. Use
L 1 = 160 in., L 2 = 40 in., E 1 = 16 × 10 6 psi, and E 2 = 10 × 10 6 psi.
a
b
C
(2)
Q
L 2
v
FIGURE p5.7
A B C
u
P
Q
(1) (2)
L 1 L 2
FIGURE p5.5
p5.8 A steel [E = 200 GPa] bar (1) supports beam AB, as shown
in Figure P5.8. The cross-sectional area of the bar is 600 mm 2 . If
the stress in the bar must not exceed 330 MPa and the maximum
deformation in the bar must not exceed 15 mm, determine the maximum
load P that may be supported by this structure. Use dimensions
a = 5.0 m, b = 3.0 m, and c = 6.5 m.
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