a) Explanation Given information: The initial temperature ( T 1 ) is 70 ° F . The yield stress ( σ Y ) is 58 ksi . The coefficient of expansion for aluminum ( α a ) is 12.8 × 10 − 6 / ° F . The coefficient of expansion for steel ( α s ) is 6.5 × 10 − 6 / ° F The young’s modulus E is 10.9 × 10 6 psi . Calculation: Determine the temperature change to cause yielding using the relation as follows: δ = P L E A + L α a ( Δ T ) Y = L α s ( Δ T ) Y P A = σ = − E ( α a − α s ) ( Δ T ) Y = − σ Y ( Δ T ) Y = σ Y E ( α a − α s ) (1) Substitute 58 ksi for σ Y , 10.9 × 10 6 psi for E , 12 (b) To determine Find the temperature T 2 that will produce residual stress in the aluminum when the stress is equal to 58 ksi .

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ISBN: 8220100257063

Author: BEER

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Chapter 2.13, Problem 121P

To determine

Find the highest temperature T2 which does not produce residual stress.

(b)

To determine

Find the temperature T2 that will produce residual stress in the aluminum when the stress is equal to 58 ksi.

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Chapter 2.13, Problem 120P

Chapter 2.13, Problem 122P

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Chapter 2 Solutions

EBK MECHANICS OF MATERIALS

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Find the highest temperature T 2 which does not produce residual stress.

Solution Summary: The author calculates the temperature change to cause yielding using the relation as follows: cdelta =PLEA+Lalpha