Problem #4 (35 points): The stepped bar shown is made from two cylindrical segments: AB (steel; Es = 30 × 10° psi; dAB = 1 in.) and BCD (aluminum; E₁ = 10 × 10° psi; dBc = dcd = 2 in.). The dimensions given are for the bar with no load applied. With the loads applied as shown, the magnitude of the change in the diameter of section CD is 1.6 × 10 in. Neglect the thickness of the collar and weight of the bar in this analysis. 15 kip A 4 kip 4 kip 2 ft (a) Determine the normal stress in sections AB, BC, and CD. (b) Determine the total change in length of the stepped bar ABCD. Does the length increase or decrease? (c) Determine Poisson's ratio for the aluminum used for section BCD. Reminder: Put units on all answers. 1.5 ft 8 kip 8 kip C D 1 ft

Mechanics of Materials (MindTap Course List)
9th Edition
ISBN:9781337093347
Author:Barry J. Goodno, James M. Gere
Publisher:Barry J. Goodno, James M. Gere
Chapter1: Tension, Compression, And Shear
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Problem 1.10.13P: A large precast concrete panel for a warehouse is raised using two sets of cables at two lift lines,...
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This is an old practice exam. The answers are OAB = 19.10 ksi OBC = 2.228 ksi OCD = −2.865 ksi v = 0.2792
delta Ltot = 0.01585 in (increase) but why

Problem #4 (35 points): The stepped bar shown is made from two cylindrical segments: AB
(steel; Es = 30 × 10° psi; dAB = 1 in.) and BCD (aluminum; E₁ = 10 × 10° psi; dBc = dcd = 2 in.).
The dimensions given are for the bar with no load applied. With the loads applied as shown, the
magnitude of the change in the diameter of section CD is 1.6 × 10 in. Neglect the thickness of
the collar and weight of the bar in this analysis.
15 kip
A
4 kip
4 kip
2 ft
(a) Determine the normal stress in sections AB, BC, and CD.
(b) Determine the total change in length of the stepped bar ABCD.
Does the length increase or decrease?
(c) Determine Poisson's ratio for the aluminum used for section
BCD.
Reminder: Put units on all answers.
1.5 ft
8 kip
8 kip
C
D
1 ft
Transcribed Image Text:Problem #4 (35 points): The stepped bar shown is made from two cylindrical segments: AB (steel; Es = 30 × 10° psi; dAB = 1 in.) and BCD (aluminum; E₁ = 10 × 10° psi; dBc = dcd = 2 in.). The dimensions given are for the bar with no load applied. With the loads applied as shown, the magnitude of the change in the diameter of section CD is 1.6 × 10 in. Neglect the thickness of the collar and weight of the bar in this analysis. 15 kip A 4 kip 4 kip 2 ft (a) Determine the normal stress in sections AB, BC, and CD. (b) Determine the total change in length of the stepped bar ABCD. Does the length increase or decrease? (c) Determine Poisson's ratio for the aluminum used for section BCD. Reminder: Put units on all answers. 1.5 ft 8 kip 8 kip C D 1 ft
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