Problem_11_30

# Problem_11_30 - Problem 11.30 Given: Let the steel in...

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Problem 11.30 Given: Let the steel in cylinder in Problem 11.29 have a yield stress of Y = 500 MPa. Determine the magnitude of T 0 necessary to initiate yielding in the cylinder based on the: a) maximum shear-stress criterion of failure and b) octahedral shear-stress criterion of failure. Solution: From Problem 11.29 a 100 mm := b 250 mm := α 0.0000117 1 Δ °C := E 200 GPa := ν 0.29 := Y 500 MPa := To allow numerical solutions, let: T 0 1 Δ °C := Using Eq. 11.39 and 11.40 at: ra := σ rr 0 := σ θθ α E T 0 21 ν () ln b a 1l n b a a 2 b 2 r 2 + r 2 b 2 a 2 ln b a 2.125 MPa = := or: σ θθ 2.125 MPa Δ °C T 0 = From Eq. 11.41: σ zz σ rr σ θθ + = σ zz 2.125 MPa Δ °C T 0 = a) Using maximum shear-stress criterion (note the 3-D Mohr's Circle below):

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## This note was uploaded on 01/11/2011 for the course MAE 3040 taught by Professor Mechanicsofsolids during the Spring '10 term at Utah State University.

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Problem_11_30 - Problem 11.30 Given: Let the steel in...

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