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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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…
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