تم الحل ✓
categoryهندسة ميكانيكية
schoolبكالوريوس
event_available2026-07-15
السؤال
Transcribed Image Text:
Part 1
At a temperature of 60°F, a 0.04-in. gap exists between the ends of the two bars shown. Bar (1) is an aluminum alloy [E = 10,000 ksi; v = 0.32; α=12.5 x 10-6/°F] bar
with a width of 3.0 in. and a thickness of 0.85 in. Bar (2) is a stainless steel [E 28,000 ksi; v = 0.12; α=9.6 x 10-6/°F] bar with a width of 1.5 in. and a thickness of 0.85
in. The supports at A and C are rigid. Assume h₁=3.0 in., h2=1.5 in., L₁=28 in., 42=50 in., and A =0.04 in. Determine
(a) the lowest temperature at which the two bars contact each other.
(b) the normal stress in the two bars at a temperature of 245°F.
(c) the normal strain in the two bars at 245°F.
(d) the change in width of the aluminum bar at a temperature of 245°F.
A
(1)
h₁
h₂
B
=
Li
L2
Determine the lowest temperature, T contact, at which the two bars contact each other.
Answer: contact =
°F
Find a geometry-of-deformation relationship for the case in which the gap is closed. Express this relationship by entering the sum б₁ + S2, where S₁ is the axial deflection
of Bar (1), and 2 is the axial deflection of Bar (2).
Answer: 81 +82 =
in.
Part 5
Find the force in the Bar (1), F1, and the force in Bar (2), F2, at a temperature of 245°F. By convention, a tension force is positive and a compression force is negative.
Answers:
F1
F2
=
=
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kips
kips
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Part 6
Find 1 and 2, the normal stresses in Bars (1) and (2), respectively. By convention, a tension stress is positive and a compression stress is negative.
Answers:
01
=
02=
ksi
ksi
Part 7
Determine 1 and 2, the deformations of Bars (1) and (2), respectively. By convention, a deformation is positive for a member that elongates, and it is negative for a
member that is shortened.
Answers:
δι =
in.
82 =
in.
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Part 8
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SUBMIT ANSWER
Determine &1 and 2, the normal strains in Bars (1) and (2), respectively. By convention, a normal strain is positive for a member that elongates, and it is negative for a
member that is shortened.
Answers:
με
82 =
με
Part 9
Determine €1,01
the component of the normal strain in Bar (1) due to the internal force F₁. This would be the normal strain in Bar 1 for an internal force F₁ with no effect of
the temperature increase included. Also, determine the accompanying lateral strain due to the Poisson effect & lat 1,0, where the lateral strain here is the strain in the
direction of the width of 3.0in.
Answers:
€1,σ =
Elat 1,0
με
=
με
ww
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Part 10
Determine lat 1,T
the component of the lateral strain caused by the temperature change.
Answer: Elat 1,T=
the tolerance is +/-2%
με
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Part 11
Determine the total lateral strain and the corresponding change in width of the aluminum bar at a temperature of 245°F.
Answers:
Elat 1 =
Swidth
με
in.
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