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

pRoBLEmS
p5.39 A circular aluminum alloy [E = 70 GPa; α = 22.5 × 10 –6 /°C;
v = 0.33] pipe has an outside diameter of 220 mm, a wall thickness
of 8 mm, and a length of 5 m. The pipe supports a compressive
load of 650 kN. After the temperature of the pipe drops by 45°C,
determine
(a) the axial deformation of the pipe.
(b) the change in diameter of the pipe.
p5.40 A solid 0.125 in. diameter steel [E = 30,000 ksi; α =
6.5 × 10 –6 /°F] wire is stretched between fixed supports so that it is
under an initial tensile force of 40 lb. If the temperature of the wire
drops by 75°F, what is the tensile stress in the wire?
p5.41 An American Iron and Steel Institute (AISI) 1040 hotrolled
steel [E = 207 GPa; α = 11.3 × 10 –6 /°C] bar is held between
two rigid supports. The bar is stress free at a temperature of 25°C.
The bar is then heated uniformly. If the yield strength of the steel is
414 MPa, determine the temperature at which yield first occurs.
p5.42 A high-density polyethylene [E = 128 ksi; α = 88 ×
10 −6 /°F; v = 0.4] bar is positioned between two rigid supports, as
shown in Figure P5.42. The bar is square with cross-sectional dimensions
of 2.50 in. by 2.50 in. and length L = 48 in. At room
temperature, a gap of D = 0.25 in. exists between the block and the
rigid support at B. After a temperature increase of 120°F, determine
(a) the normal stress in the bar.
(b) the longitudinal strain in the bar.
(c) the transverse (i.e., lateral) strain in the bar.
(1)
L (2)
1
a
b
L 2
A
FIGURE p5.43
p5.44 Two ductile cast iron [E = 24,400 ksi; α = 6.0 × 10 –6 /°F]
bars are connected with a pin at B, as shown in Figure P5.44. Each
bar has a cross-sectional area of 1.50 in. 2 . If the temperature of the
bars is decreased by 75°F from their initial temperature, what force
P would need to be applied at B so that the total displacement
(caused both by the temperature change and by the applied load) of
joint B is zero? Use a = 10 ft and β = 55°.
A
β
L 3
B
(3)
D
P
Rigid bar
β
C
C
L
Δ
a
B
A
FIGURE p5.42
B
FIGURE p5.44
P
p5.43 Rigid bar ABC is supported by bronze rod (1) and
stainless steel rod (2) as shown in Figure P5.43. A concentrated
load P = 24 kips is applied to the free end of bronze rod (3).
Determine the deflection of rod end D after the temperature of
all rods has increased by 130°F. Use the following dimensions
and properties:
a = 3.5 ft, b = 6.5 ft.
Rod (1): d 1 = 1.00 in., L 1 = 12 ft, E 1 = 15,200 ksi,
α 1 = 12.20 × 10 –6 /°F.
Rod (2): d 2 = 0.75 in., L 2 = 9 ft, E 2 = 28,000 ksi,
α 2 = 9.60 × 10 –6 /°F.
Rod (3): d 3 = 1.25 in., L 3 = 6 ft, E 3 = 15,200 ksi,
α 3 = 12.20 × 10 –6 /°F.
p5.45 A solid aluminum alloy [E = 69 GPa; α = 23.6 × 10 –6 /°C]
rod (1) is attached rigidly to a solid brass [E = 115 GPa; α = 18.7 ×
10 –6 /°C] rod (2), as shown in Figure P5.45. The compound rod is
subjected to a tensile load P = 6 kN. The diameter of each rod is
10 mm. The rods lengths are L 1 = 525 mm and L 2 = 675 mm. Compute
the change in temperature required to produce zero horizontal deflection
at end C of the compound rod.
A
L 1
(1)
B
FIGURE p5.45
L 2
(2)
C
P
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