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

p5.24 A composite bar is fabricated by brazing aluminum alloy
[E = 10,000 ksi] bars (1) to a center brass [E = 17,000 ksi] bar (2)
as shown in Figure P5.24. Assume that d = 0.75 in., a = 0.1875 in.,
and L = 20 in. If the total axial force carried by the two aluminum
bars must equal the axial force carried by the brass bar, calculate
the thickness b required for brass bar (2).
P
d
L
Aluminum (1)
(1)
P
Brass (2)
A 2 = 2,800 mm 2 and a length L 2 = 550 mm. After two loads of P =
4 kN are applied to flange B, determine
(a) the forces in bars (1) and (2).
(b) the deflection of flange B.
p5.27 In Figure P5.27, the two vertical steel [E = 200 GPa] rods
that support rigid bar ABCD are initially free of stress. Rod (1) has
an area A 1 = 450 mm 2 and a length L 1 = 2.2 m. Rod (2) has an area
A 2 = 325 mm 2 and a length L 2 = 1.6 m. Assume dimensions of a =
3.0 m, b = 1.0 m, and c = 1.25 m. After a load P = 80 kN is applied
to the rigid bar at D, determine
(a) the normal stresses in rods (1) and (2).
(b) the deflection of the rigid bar at D.
a
b
a
FIGURE p5.24
a
y,v
(2)
L 2
p5.25 An aluminum alloy [E = 10,000 ksi; s Y = 40 ksi] pipe (1)
is connected to a bronze [E = 16,000 ksi; s Y = 45 ksi] pipe at flange
B, as shown in Figure P5.25. The pipes are attached to rigid supports
at A and C, respectively. Pipe (1) has an outside diameter of
2.375 in., a wall thickness of 0.203 in., and a length L 1 = 6 ft. Pipe
(2) has an outside diameter of 4.50 in., a wall thickness of 0.226 in.,
and a length L 2 = 10 ft. If a minimum factor of safety of 1.67 is required
for each pipe, determine
(a) the maximum load P that may be applied at flange B.
(b) the deflection of flange B at the load determined in part (a).
A
(1)
P
FIGURE p5.25
(2)
B
L 1 L 2
C
L 1
A B C D
x,u
(1)
FIGURE p5.27
Rigid bar
p5.28 The pin-connected structure shown in Figure P5.28 consists
of a rigid bar ABCD and two bronze alloy [E = 100 GPa] bars, each
with a cross-sectional area of 340 mm 2 . Bar (1) has a length L 1 =
810 mm and bar (2) has a length L 2 = 1,080 mm. Assume dimensions
of a = 480 mm, b = 380 mm, and c = 600 mm. If the allowable normal
stress in bars (1) and (2) must be limited to 165 MPa each, determine
(a) the maximum load P that may be applied at D to the rigid bar.
(b) the deflection at D for the load determined in part (a).
b
c
P
p5.26 A rectangular polypropylene [E = 6,200 MPa] bar (1) is
connected to a rectangular nylon [E = 1,400 MPa] bar (2) at flange B.
The assembly (shown in Figure P5.26) is connected to rigid supports
at A and C. Bar (1) has a cross-sectional area A 1 = 1,100 mm 2
and a length L 1 = 1,450 mm. Bar (2) has a cross-sectional area
a
A
(1)
L 1
L 2
L 1
L 2
P
A
(1) P B (2)
FIGURE p5.26
C
B
(2)
y,v
b
C
D
c
P
FIGURE p5.28
x,u
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