A steel cable is used to support an elevator cage at the bottom of a 1700-ft-deep mineshaft. A uniform normal strain of 220 μin./in. isproduced in the cable by the weight of the cage. At each point, the weight of the cable produces an additional normal strain that isproportional to the length of the cable below the point. Assume D = 1700 ft and d= 700 ft. If the total normal strain in the cable at thecable drum (upper end of the cable) is 520 uin./in., determine(a) the strain in the cable at a depth of 700 ft.(b) the total elongation of the cable.DrumCableAnswers:(a)ε =(b) 8 =yiiElevator cageDXμin./in.in.

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Answered: (a) the strain in the cable at a depth…

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(a) the strain in the cable at a depth of 700 ft. (b) the total elongation of the cable.

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 7.7.4P: An element of material in plain strain is subjected to strains x = 0.0015, , y . = -0.0002, and xy =...

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Question

A steel cable is used to support an elevator cage at the bottom of a 1700-ft-deep mineshaft. A uniform normal strain of 220 μin./in. is
produced in the cable by the weight of the cage. At each point, the weight of the cable produces an additional normal strain that is
proportional to the length of the cable below the point. Assume D = 1700 ft and d= 700 ft. If the total normal strain in the cable at the
cable drum (upper end of the cable) is 520 uin./in., determine
(a) the strain in the cable at a depth of 700 ft.
(b) the total elongation of the cable.
Drum
Cable
Answers:
(a)
ε =
(b) 8 =
y
i
i
Elevator cage
D
X
μin./in.
in.

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