A straight and piecewise uniform bar ABCD of total length L is in Case 1 fixed at A in case 1 and in Case 2 fixed at both ends A and D. AB = BC = CD = L/3. The cross section area of segment CD is half of the area of the segment ABC, i.e. AABC = 2ACB. A point load of P is applied at B. Assume that bar material is linear and elastic and the modulus of elasticity is E.

Mechanics of Materials (MindTap Course List)
9th Edition
ISBN:9781337093347
Author:Barry J. Goodno, James M. Gere
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Chapter1: Tension, Compression, And Shear
Section: Chapter Questions
Problem 1.8.20P: A single steel strut AB with a diameter (a) Find the strut force Fs and average normal stress ds= 8...
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A straight and piecewise uniform bar ABCD of total length L is in Case 1 fixed at A in case 1 and in Case 2 fixed at both ends A and D. AB = BC = CD = L/3. The cross section area of segment CD is half of the area of the segment ABC, i.e. AABC = 2ACB. A point load of P is applied at B. Assume that bar material is linear and elastic and the modulus of elasticity is E.

 

В
C
D
В
C
P
-L
L
-L
3
Figure 1: Case 1: bar is fixed at A
Figure 2: Case 2: bar is fixed at A and D
L = 90cm, E = 70GPA, AcD= 4 cm? , P = 10KN
For both Cases:
a) Find the average normal stress on a perpendicular cross-section along the bar in terms
of the plot:
Average normal stress
x Position of the
A
В
cross section
b) Find the new length of segment ABC after deformation
(Note: Case 2 is a statically indeterminate case)
1/3
Transcribed Image Text:В C D В C P -L L -L 3 Figure 1: Case 1: bar is fixed at A Figure 2: Case 2: bar is fixed at A and D L = 90cm, E = 70GPA, AcD= 4 cm? , P = 10KN For both Cases: a) Find the average normal stress on a perpendicular cross-section along the bar in terms of the plot: Average normal stress x Position of the A В cross section b) Find the new length of segment ABC after deformation (Note: Case 2 is a statically indeterminate case) 1/3
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