11. A ring (side view shown in Figure Q11) has a circular solid cross-section of 5 mm diameter. The ring itself has a radius of R = 100 mm and a very narrow gap at point A, that allows the two free ends to be pulled apart by forces P, increasing the size of the gap. ○ P A Figure Q11 P a) Show that the total strain energy of the ring due to the applied forces is: U = 3πP²R³ 2EI [12 marks] b) Find the maximum bending stress produced if forces of P = 8 N are applied. [6 marks] c) What minimum force P would cause the material in the ring to yield and at which locations could this yielding begin to occur? Useful information E for the ring material = 75 GPa Oyield for the ring material = 190 MPa [7 marks]
11. A ring (side view shown in Figure Q11) has a circular solid cross-section of 5 mm diameter. The ring itself has a radius of R = 100 mm and a very narrow gap at point A, that allows the two free ends to be pulled apart by forces P, increasing the size of the gap. ○ P A Figure Q11 P a) Show that the total strain energy of the ring due to the applied forces is: U = 3πP²R³ 2EI [12 marks] b) Find the maximum bending stress produced if forces of P = 8 N are applied. [6 marks] c) What minimum force P would cause the material in the ring to yield and at which locations could this yielding begin to occur? Useful information E for the ring material = 75 GPa Oyield for the ring material = 190 MPa [7 marks]
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 7.6.13P: A solid spherical ball of magnesium alloy (E = 6.5 × l0-6 psi, v = 0.35) is lowered into the ocean...
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Question
![11.
A ring (side view shown in Figure Q11) has a circular solid cross-section of 5 mm
diameter. The ring itself has a radius of R = 100 mm and a very narrow gap at point
A, that allows the two free ends to be pulled apart by forces P, increasing the size of
the gap.
○
P
A
Figure Q11
P
a) Show that the total strain energy of the ring due to the applied forces is:
U =
3πP²R³
2EI
[12 marks]
b) Find the maximum bending stress produced if forces of P = 8 N are applied.
[6 marks]
c) What minimum force P would cause the material in the ring to yield and at
which locations could this yielding begin to occur?
Useful information
E for the ring material = 75 GPa
Oyield for the ring material = 190 MPa
[7 marks]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2bd51202-2136-4706-ad4a-44ee589e8ffa%2Fb1ec70c1-3b77-43e5-86eb-a6d70a2c2d5d%2Fy3437pg_processed.jpeg&w=3840&q=75)
Transcribed Image Text:11.
A ring (side view shown in Figure Q11) has a circular solid cross-section of 5 mm
diameter. The ring itself has a radius of R = 100 mm and a very narrow gap at point
A, that allows the two free ends to be pulled apart by forces P, increasing the size of
the gap.
○
P
A
Figure Q11
P
a) Show that the total strain energy of the ring due to the applied forces is:
U =
3πP²R³
2EI
[12 marks]
b) Find the maximum bending stress produced if forces of P = 8 N are applied.
[6 marks]
c) What minimum force P would cause the material in the ring to yield and at
which locations could this yielding begin to occur?
Useful information
E for the ring material = 75 GPa
Oyield for the ring material = 190 MPa
[7 marks]
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