Q1 A thick-walled steel, compound cylinder has the following dimensions: Internal radius, r₁ = 0.1m Interface radius, rint = 0.2m Outer radius, ro = 0.35m Young's Modulus, Esteel = 210GPa (a) Calculate the interference, 8, required to achieve a radial interface stress of -100 MPa. (b) Calculate the residual circumferential stresses, due to the interference fit at the interface radius, rint, for the inner and outer cylinders. (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) Plot the radial stresses, as a consequence of superposition of the interference fit and internal pressure determined in (c), at the inner, interface and outer radii. Interpolate an approximate radial stress distribution through these points. Answers a) 0.346 mm (b) σ0,inner-166.7 MPa, σ0,outer = 197.0 MPa (c) σ0=-266.7 MPa, pi = 226.4 MPa

Mechanics of Materials (MindTap Course List)
9th Edition
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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Q1
A thick-walled steel, compound cylinder has the following dimensions:
Internal radius, r₁ = 0.1m
Interface radius, rint = 0.2m
Outer radius, ro
= 0.35m
Young's Modulus, Esteel = 210GPa
(a) Calculate the interference, 8, required to achieve a radial interface stress of -100 MPa.
(b) Calculate the residual circumferential stresses, due to the interference fit at the interface
radius, rint, for the inner and outer cylinders.
(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) Plot the radial stresses, as a consequence of superposition of the interference fit and internal
pressure determined in (c), at the inner, interface and outer radii. Interpolate an approximate
radial stress distribution through these points.
Answers
a) 0.346 mm
(b) σ0,inner-166.7 MPa, σ0,outer = 197.0 MPa
(c) σ0=-266.7 MPa, pi = 226.4 MPa
Transcribed Image Text:Q1 A thick-walled steel, compound cylinder has the following dimensions: Internal radius, r₁ = 0.1m Interface radius, rint = 0.2m Outer radius, ro = 0.35m Young's Modulus, Esteel = 210GPa (a) Calculate the interference, 8, required to achieve a radial interface stress of -100 MPa. (b) Calculate the residual circumferential stresses, due to the interference fit at the interface radius, rint, for the inner and outer cylinders. (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) Plot the radial stresses, as a consequence of superposition of the interference fit and internal pressure determined in (c), at the inner, interface and outer radii. Interpolate an approximate radial stress distribution through these points. Answers a) 0.346 mm (b) σ0,inner-166.7 MPa, σ0,outer = 197.0 MPa (c) σ0=-266.7 MPa, pi = 226.4 MPa
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