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L3 -Strain gage -L = 420 mm - PROBLEM 1.4-6

Mechanics of Materials (MindTap Course List)

9th Edition

ISBN:9781337093347

Author:Barry J. Goodno, James M. Gere

Publisher:Barry J. Goodno, James M. Gere

Chapter7: Analysis Of Stress And Strain

Section: Chapter Questions

Problem 7.7.31P: Solve Problem 7.7-13 by using Mohr’s circle for plane strain.

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Question

A circular aluminum tube with a length of L = 420 mm is loaded in compression by forces P (see figure). The hollow segment of length LB has outside and inside diameters of 60 mm and 35 mm, respectively. The solid segment of length 2L/3 has a diameter of 60 mm. A strain gauge is placed on the outside of the hollow segment of the bar to measure normal strains in the longitudinal direction.

a. If the measured strain in the hollow segment is 6jy = 470 x 10, what is the strain ε_s in the solid part? Hint: The strain in the solid segment is equal to that in the hollow segment multiplied by the ratio of the area of the hollow to that of the solid segment.

b. What is the overall shortening δ of the bar?

c. If the compressive stress in the bar cannot exceed 48 MPa, what is the maximum permissible value of load P?

L3
-Strain gage
-L = 420 mm -
PROBLEM 1.4-6

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