Q3 A thick-walled steel (Young's modulus E = 210GPa) compound cylinder has the following dimensions: • Internal radius, r₁ = 0.15m • Interface radius, rm = 0.3m • Outer radius, r = 0.6m (a) Calculate the radial interference, 8, required to achieve a radial stress at the interface of σr = -100MPa. (b) Calculate the residual circumferential stresses due to the radial interference calculated in (a), at the interface radius for both the inner and outer cylinder. (c) Calculate the circumferential stress, at the inner radius, due to the interference fit, and hence determine the internal pressure required to return this stress to zero. (d) The internal pressure is gradually increased in a "burst test". Using the Tresca criterion, determine at what pressure yield can be expected at the interface radius. The yield stress of the material, σy = 400MPa.

Mechanics of Materials (MindTap Course List)
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ISBN:9781337093347
Author:Barry J. Goodno, James M. Gere
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Chapter2: Axially Loaded Members
Section: Chapter Questions
Problem 2.3.19P: Repeat Problem 2.3-18, but assume that the bar is made of copper alloy. Calculate the displacements...
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Q3
A thick-walled steel (Young's modulus E = 210GPa) compound cylinder has the following
dimensions:
• Internal radius, r₁ = 0.15m
• Interface radius, rm = 0.3m
• Outer radius, r = 0.6m
(a) Calculate the radial interference, 8, required to achieve a radial stress at the interface of σr =
-100MPa.
(b) Calculate the residual circumferential stresses due to the radial interference calculated in (a),
at the interface radius for both the inner and outer cylinder.
(c) Calculate the circumferential stress, at the inner radius, due to the interference fit, and hence
determine the internal pressure required to return this stress to zero.
(d) The internal pressure is gradually increased in a "burst test". Using the Tresca criterion,
determine at what pressure yield can be expected at the interface radius. The yield stress of
the material, σy = 400MPa.
Transcribed Image Text:Q3 A thick-walled steel (Young's modulus E = 210GPa) compound cylinder has the following dimensions: • Internal radius, r₁ = 0.15m • Interface radius, rm = 0.3m • Outer radius, r = 0.6m (a) Calculate the radial interference, 8, required to achieve a radial stress at the interface of σr = -100MPa. (b) Calculate the residual circumferential stresses due to the radial interference calculated in (a), at the interface radius for both the inner and outer cylinder. (c) Calculate the circumferential stress, at the inner radius, due to the interference fit, and hence determine the internal pressure required to return this stress to zero. (d) The internal pressure is gradually increased in a "burst test". Using the Tresca criterion, determine at what pressure yield can be expected at the interface radius. The yield stress of the material, σy = 400MPa.
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