Explanation The pate is made of steel and for steel, E = 200 G P a ν = 0.30 Now, according to the Von-Mises criterion for biaxial stress conditions, ( σ 1 − σ 2 ) 2 + ( σ 2 − σ 3 ) 2 + ( σ 3 − σ 1 ) 2 = 2 Y 2 When σ 3 is zero under biaxial stress conditions ( σ 1 − σ 2 ) 2 + ( σ 2 − 0 ) 2 + ( 0 − σ 1 ) 2 = 2 Y 2 N o w , σ 1 = σ 2 This gives, σ 1 = Y So, the change in the volume is given by Δ = 1 − 2 ν E ( σ 1 + σ 2 + σ 3 ) Δ = 1 − 2 × 0.3 200 ( 350 + 350 + 0 ) Δ = 0

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Chapter 2, Problem 2.86P

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The change in volume of using the von-Mises criterion and when the material changes to copper .

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