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167_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

167_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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SECTION 2.5 Thermal Effects 161 Misfits and Prestrains Problem 2.5-12 A steel wire AB is stretched between rigid supports (see figure). The initial prestress in the wire is 42 MPa when the temperature is 20°C. (a) What is the stress in the wire when the temperature drops to 0°C? (b) At what temperature T will the stress in the wire become zero? (Assume 14 10 6 /°C and E 200 GPa.) Solution 2.5-12 Steel wire with initial prestress Initial prestress: 1 42 MPa Initial temperature: T 1 20°C E 200 GPa 14 10 6 /°C (a) S TRESS WHEN TEMPERATURE DROPS TO 0°C T 2 0°C T 20°C NOTE: Positive T means a decrease in temperature and an increase in the stress in the wire. Negative T means an increase in temperature and a decrease in the stress. Stress equals the initial stress 1 plus the additional stress 2 due to the temperature drop. From Eq. (2-18): 2 E ( T ) 1 2 1 E ( T ) 42 MPa (200 GPa)(14 10 6 /°C)(20°C)
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