Consider a thick-walled cylinder with inner radius a and outer radius b under internal pressure Po. The material is elastic-perfectly-plastic, with yield stress yo. Assume the Tresca yield criterion holds. (a) What is the stress distribution in the initial elastic state and in the subsequent elastic- plastic state as the pressure is gradually raised? (b) What is the radius of the plastic zone as a function of the internal pressure? (c) What is the limiting pressure at which the entire cylinder is plastically deforming? (d) Simplify your result for a thin-walled tube.
Consider a thick-walled cylinder with inner radius a and outer radius b under internal pressure Po. The material is elastic-perfectly-plastic, with yield stress yo. Assume the Tresca yield criterion holds. (a) What is the stress distribution in the initial elastic state and in the subsequent elastic- plastic state as the pressure is gradually raised? (b) What is the radius of the plastic zone as a function of the internal pressure? (c) What is the limiting pressure at which the entire cylinder is plastically deforming? (d) Simplify your result for a thin-walled tube.
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
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![Consider a thick-walled cylinder with inner radius a and outer radius b under internal pressure
Po. The material is elastic-perfectly-plastic, with yield stress yo. Assume the Tresca yield
criterion holds.
(a) What is the stress distribution in the initial elastic state and in the subsequent elastic-
plastic state as the pressure is gradually raised?
(b) What is the radius of the plastic zone as a function of the internal pressure?
(c) What is the limiting pressure at which the entire cylinder is plastically deforming?
(d) Simplify your result for a thin-walled tube.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff0e69105-edad-4e40-a986-7d2af8f1b9bd%2Fa4571ebd-9be9-4489-9b32-e06fa2564474%2Ff5nuo9a_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Consider a thick-walled cylinder with inner radius a and outer radius b under internal pressure
Po. The material is elastic-perfectly-plastic, with yield stress yo. Assume the Tresca yield
criterion holds.
(a) What is the stress distribution in the initial elastic state and in the subsequent elastic-
plastic state as the pressure is gradually raised?
(b) What is the radius of the plastic zone as a function of the internal pressure?
(c) What is the limiting pressure at which the entire cylinder is plastically deforming?
(d) Simplify your result for a thin-walled tube.
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