Rigid
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
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Question
Rigid bar ABCD is supported by a pin connection at A and by two axial bars (1) and (2). Bar (1) is a 34-in.-long bronze [E = 15000 ksi, α=α= 9.2 × 10−6/°F] bar with a cross-sectional area of 1.75 in.2. Bar (2) is a 42-in.-long aluminum alloy [E = 10300 ksi, α=α= 11.9 × 10−6/°F] bar with a cross-sectional area of 2.25 in.2. Both bars are unstressed before the load P is applied. Assume L1=34 in., L2=42 in., a=30 in., b=42 in., and c=16 in. If a concentrated load of P = 27 kips is applied to the rigid bar at D and the temperature is decreased by 120°F, determine:
(a) the normal stresses in bars (1) and (2).
(b) the normal strains in bars (1) and (2).
(c) the deflection of the rigid bar at point D.
![Part 1
Rigid bar ABCD is supported by a pin connection at A and by two axial bars (1) and (2). Bar (1) is a 34-in.-
long bronze [E = 15000 ksi, a = 9.2 x 10-6/°F] bar with a cross-sectional area of 1.75 in.². Bar (2) is a 42-
in.-long aluminum alloy [E = 10300 ksi, a = 11.9 × 10-6/°F] bar with a cross-sectional area of 2.25 in.².
Both bars are unstressed before the load P is applied. Assume L₁=34 in., L₂=42 in., a-30 in., b-42 in., and
c=16 in. If a concentrated load of P = 27 kips is applied to the rigid bar at D and the temperature is
decreased by 120°F, determine:
(a) the normal stresses in bars (1) and (2).
(b) the normal strains in bars (1) and (2).
(c) the deflection of the rigid
bar at point D.
A
(1)
Answer: (
BO
L₁
b
(2)
с
in.) (27 kips) = 0.
Using a FBD of the beam, assuming members in tension, relate the force in the members and the applied
force P by summing moments about the pin at A. Assume counterclockwise is positive in writing the
equation.
in.) F₁ + (
L2
D
in.) F₂ + (](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbbb16848-0151-4811-b617-402fad34b898%2F2862beca-af17-445c-8c4c-c092f0189a3c%2Fdb1ke8_processed.png&w=3840&q=75)
Transcribed Image Text:Part 1
Rigid bar ABCD is supported by a pin connection at A and by two axial bars (1) and (2). Bar (1) is a 34-in.-
long bronze [E = 15000 ksi, a = 9.2 x 10-6/°F] bar with a cross-sectional area of 1.75 in.². Bar (2) is a 42-
in.-long aluminum alloy [E = 10300 ksi, a = 11.9 × 10-6/°F] bar with a cross-sectional area of 2.25 in.².
Both bars are unstressed before the load P is applied. Assume L₁=34 in., L₂=42 in., a-30 in., b-42 in., and
c=16 in. If a concentrated load of P = 27 kips is applied to the rigid bar at D and the temperature is
decreased by 120°F, determine:
(a) the normal stresses in bars (1) and (2).
(b) the normal strains in bars (1) and (2).
(c) the deflection of the rigid
bar at point D.
A
(1)
Answer: (
BO
L₁
b
(2)
с
in.) (27 kips) = 0.
Using a FBD of the beam, assuming members in tension, relate the force in the members and the applied
force P by summing moments about the pin at A. Assume counterclockwise is positive in writing the
equation.
in.) F₁ + (
L2
D
in.) F₂ + (
Transcribed Image Text:Part 2
Assume the rigid bar ABCD rotates clockwise around point A. Using a deflection sketch, relate the
deflections of points B and C. Assume positive deflections are down.
Answer: VB =
Part 3
VC.
Relate the deformations of member (1) and member (2).
Answer: ₁ =
82.
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