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

p5.46 At a temperature of 15°C, a gap of D = 5 mm exists between
the two polymer bars shown in the accompanying figure. Bar
(1) has a length L 1 = 700 mm, a cross-sectional area A 1 = 1,250 mm 2 ,
a coefficient of thermal expansion α 1 = 130 × 10 −6 /°C, and an elastic
modulus E 1 = 1,400 MPa. Bar (2) has a length L 2 = 500 mm, a
cross-sectional area A 2 = 3,750 mm 2 , a coefficient of thermal expansion
α 2 = 80 × 10 −6 /°C, and an elastic modulus E 2 = 3,700 MPa.
The supports at A and D are rigid. Determine
(a) the lowest temperature at which the gap is closed.
(b) the normal stress in the two bars at a temperature of 100°C.
(c) the longitudinal normal strain in the two bars at 100°C.
FIGURE p5.46
Δ
L 1 L 2
(1) (2)
A B C D
A
(1)
FIGURE p5.48
B
p5.49 Rigid bar ABC is supported by two identical solid bronze
[s Y = 331 MPa; E = 105 GPa; α = 22.0 × 10 −6 /°C] rods and a single
solid steel [s Y = 250 MPa; E = 200 GPa; α = 11.7 × 10 −6 /°C] rod,
as shown in Figure P5.49. Bronze rods (1) each have diameter d 1 =
25 mm and length L 1 = 3.0 m. Steel rod (2) has length L 2 = 4.0 m.
(a) Calculate the diameter d 2 required for steel rod (2) so that the
deflection of joint B is zero for any change in temperature.
(b) Using the value of d 2 determined in part (a), determine the
maximum temperature decrease that is allowable for this
assembly if a factor of safety of 2.0 is specified for the normal
stress in each rod.
d
(2)
L 1 L 2
C
p5.47 A bronze [E = 15,200 ksi; α = 12.2 × 10 –6 /°F] rod (2) is
placed within a steel [E = 30,000 ksi; α = 6.3 × 10 –6 /°F] tube (1).
The two components are connected at each end by 0.5 in. diameter
pins that pass through both the tube and the rod, as shown in Figure
P5.47. The outside diameter of tube (1) is 3.00 in. and its wall
thickness is 0.125 in. The diameter of rod (2) is 2.25 in. and the
distance between pins is L = 21 in. What is the average shear stress
in the pins if the temperature of the entire assembly is increased by
90°F?
(1)
(1)
a
a
A B C
(2)
L 2
L 1
Pin
Steel Tube (1)
Pin
FIGURE p5.49
L
Bronze
Rod (2)
p5.50 A polymer cylinder (2) is clamped between rigid heads
by two steel bolts (1), as shown in Figure P5.50. The steel [E =
29,000 ksi; α = 6.5 × 10 −6 /°F] bolts have a diameter of 0.50 in. The
FIGURE p5.47
(1)
p5.48 A titanium [E = 16,500 ksi; α = 5.3 × 10 –6 /°F] bar (1) and
a bronze [E = 15,200 ksi; α = 12.2 × 10 –6 /°F] bar (2), each restrained
at one end, are fastened at their free ends by a single-shear
pin of diameter d = 0.4375 in., as shown in Figure P5.48. The length
of bar (1) is L 1 = 19 in. and its cross-sectional area is A 1 = 0.50 in. 2 .
The length of bar (2) is L 2 = 27 in. and its cross-sectional area is
A 2 = 0.65 in. 2 . What is the average shear stress in the pin at B if the
temperature changes by 40°F?
a
b
FIGURE p5.50
(2)
(1)
c
c
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