Three rods of different materials are connected and placed between rigid supports at A and D, as shown. Properties for each of the three rods are given in the accompanying table. The bars are initially unstressed when the structure is assembled at 20°C. After the temperature has been increased to 120°C, determine(a) the normal stresses in the three rods.(b) the force exerted on the rigid supports.(c) the deflections of joints B and C relative to rigid support A.Aluminum (1)Cast Iron (2)Bronze (3)L1 = 470 mmL2 = 170 mmL3 = 270 mmA1 = 1300 mm2A2 = 2800 mm2A3 = 700 mm2E1 = 70 GPaE2 = 155 GPaE3 = 100 GPaα1 = 22.5 x 10-6/°Cα2 = 13.5 x 10-6/°Cα3 = 17.0 x 10-6/°CSubstitute force-temperature-deformation relationships into the geometry-of-deformation equation to derive the compatibility equation. Then, find the force in rod (1), F1, the force in rod (2), F2, and the force in rod (3), F3. Be sure to use the correct sign for each force. By convention, a tension force is positive and a compression force is negative.Answer:F1 = kNF2 = kNF3 = kNFind σ1, σ2, and σ3, the normal stresses in rods (1), (2), and (3), respectively. By convention, a tension stress is positive, and a compression stress is negative.Answers:σ1 = MPaσ2 = MPaσ3 = MPaDetermine the magnitudes of the reaction forces at supports A and B. Note that the reaction forces are equal in magnitude to the forces exerted on the rigid supports. Since the magnitudes are required, be sure to enter positive values here.Answers:|RA| = kN|RB| = kNDetermine δ1 and δ2, the deformations of rods (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:δ1 = mmδ2 = mmDetermine the deflections of joints B and C relative to rigid support A. Report a positive value for a deflection to the right and a negative value for deflection to the left.Answers:uB = mmuC = mm Cast IronAluminum(2)Bronze(1)(3)|ABCDL,L2L3

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Answered: Three rods of different materials are…

Structural Analysis

6th Edition

ISBN:9781337630931

Author:KASSIMALI, Aslam.

Publisher:KASSIMALI, Aslam.

Chapter2: Loads On Structures

Section: Chapter Questions

Problem 1P

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Question

Three rods of different materials are connected and placed between rigid supports at A and D, as shown. Properties for each of the three rods are given in the accompanying table. The bars are initially unstressed when the structure is assembled at 20°C. After the temperature has been increased to 120°C, determine

(a) the normal stresses in the three rods.
(b) the force exerted on the rigid supports.
(c) the deflections of joints B and C relative to rigid support A.

Aluminum (1)	Cast Iron (2)	Bronze (3)
L₁ = 470 mm	L₂ = 170 mm	L₃ = 270 mm
A₁ = 1300 mm²	A₂ = 2800 mm²	A₃ = 700 mm²
E₁ = 70 GPa	E₂ = 155 GPa	E₃ = 100 GPa
α₁ = 22.5 x 10^-6/°C	α₂ = 13.5 x 10^-6/°C	α₃ = 17.0 x 10^-6/°C

Substitute force-temperature-deformation relationships into the geometry-of-deformation equation to derive the compatibility equation. Then, find the force in rod (1), F₁, the force in rod (2), F₂, and the force in rod (3), F₃. Be sure to use the correct sign for each force. By convention, a tension force is positive and a compression force is negative.

Answer:

F₁ =	kN
F₂ =	kN
F₃ =	kN

Find σ₁, σ₂, and σ₃,the normal stresses in rods (1), (2), and (3), respectively. By convention, a tension stress is positive, and a compression stress is negative.

Answers:

σ₁ =	MPa
σ₂ =	MPa
σ₃ =	MPa

Determine the magnitudes of the reaction forces at supports A and B. Note that the reaction forces are equal in magnitude to the forces exerted on the rigid supports. Since the magnitudes are required, be sure to enter positive values here.

Answers:

\|R_A\| =	kN
\|R_B\| =	kN

Determine δ₁ and δ₂, the deformations of rods (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:

δ₁ =	mm
δ₂ =	mm

Determine the deflections of joints B and C relative to rigid support A. Report a positive value for a deflection to the right and a negative value for deflection to the left.

Answers:

u_B = mm

u_C = mm

Cast Iron
Aluminum
(2)
Bronze
(1)
(3)
|A
B
C
D
L,
L2
L3

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u_B =	mm
u_C =	mm