Three rods of different materials are connected and placed between rigid supports at A and D, as shown. Properties for each ofthe 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 Crelative to rigid support A.Aluminum (1)Cast Iron (2)Bronze (3)L1 = 470 mmL2 = 170 mmL3 = 270 mmA1 = 1300 mm2A2 = 2800 mm2Az = 700 mm2E, = 70 GPaE2 = 155 GPaE3 = 100 GPaa1 = 22.5 x 10-6/°C a2 = 13.5 x 106/°C | a3 = 17.0 x 10-6/°CCast IronAluminumBronze(2)(1)(3)BCL,L3 Substitute force-temperature-deformation relationships into the geometry-of-deformationequation 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, atension force is positive and a compression force is negative.Find o1, 02, and 03, the normal stresses in rods (1), (2), and (3), respectively. By convention, a tensionstress is positive, and a compression stress is negative.Determine the magnitudes of the reaction forces at supports A and B. Note that the reactionforces are equal in magnitude to the forces exerted on the rigid supports. Since the magnitudesare required, be sure to enter positive values here.Determine 8, and 82, the deformations of rods (1) and (2), respectively. By convention, adeformation is positive for a member that elongates, and it is negative for a member that isshortened.Determine the deflections of joints B and C relative to rigid support A. Report a positive value fora deflection to the right and a negative value for deflection to the left.

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 Crelative 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 a1 = 22.5 x 106/0C a2 = 13.5 x 106/°C | a3 = 17.0 x 106/°C Cast Iron Aluminum (2) Bronze (1) (3) В D.

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 Crelative 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 a1 = 22.5 x 106/0C a2 = 13.5 x 106/°C | a3 = 17.0 x 106/°C Cast Iron Aluminum (2) Bronze (1) (3) В D.

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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Concept explainers

Bars

In civil engineering, bars refer to steel reinforcement bars or rebars. These are structural members primarily used for reinforcement purposes in masonry works. A bar is characterized by its cross-sectional area, which is negligible compared to its length. Bars are usually manufactured by steel which is uniform throughout the length, or by meshing multiple steel wires. Other materials of the bar include carbon steel, glass fiber, carbon fiber, and basalt fiber. The reinforcing bars are coated with epoxy resins and other materials to enhance some of their properties including corrosion resistance.

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 Crelative 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
Az = 700 mm2
E, = 70 GPa
E2 = 155 GPa
E3 = 100 GPa
a1 = 22.5 x 10-6/°C a2 = 13.5 x 106/°C | a3 = 17.0 x 10-6/°C
Cast Iron
Aluminum
Bronze
(2)
(1)
(3)
B
C
L,
L3

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.
Find o1, 02, and 03, the normal stresses in rods (1), (2), and (3), respectively. By convention, a tension
stress is positive, and a compression stress is negative.
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.
Determine 8, and 82, 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.
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.

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