02-02ChapGere.0026

02-02ChapGere.0026 - of thermal expansion of aluminum and...

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Thermal Effects Problem 2.5-1 The rails of a railroad track are welded together at their ends (to form continuous rails and thus eliminate the clacking sound of the wheels) when the temperature is 60°F. What compressive stress s is produced in the rails when they are heated by the sun to 120°F if the coefficient of thermal expansion a 5 6.5 3 10 2 6 /°F and the modulus of elasticity E 5 30 3 10 6 psi? Solution 2.5-1 Expansion of railroad rails SECTION 2.5 Thermal Effects 105 The rails are prevented from expanding because of their great length and lack of expansion joints. Therefore, each rail is in the same condition as a bar with fixed ends (see Example 2-7). The compressive stress in the rails may be calculated from Eq. (2-18). s 5 11,700 psi 5 (30 3 10 6 psi)(6.5 3 10 2 6 / 8 F)(60 8 F) s 5 E a ( ¢ T ) ¢ T 5 120 8 F 2 60 8 F 5 60 8 F Problem 2.5-2 An aluminum pipe has a length of 60 m at a temperature of 10°C. An adjacent steel pipe at the same temperature is 5 mm longer than the aluminum pipe. At what temperature (degrees Celsius) will the aluminum pipe be 15 mm longer than the steel pipe? (Assume that the coefficients
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Unformatted text preview: of thermal expansion of aluminum and steel are a a 5 23 3 10 2 6 /°C and a s 5 12 3 10 2 6 /°C, respectively.) Solution 2.5-2 Aluminum and steel pipes I NITIAL CONDITIONS L a 5 60 m T 5 10 8 C L s 5 60.005 m T 5 10 8 C a a 5 23 3 10 2 6 / 8 C a s 5 12 3 10 2 6 / 8 C F INAL CONDITIONS Aluminum pipe is longer than the steel pipe by the amount D L 5 15 mm. D T 5 increase in temperature d a 5 a a ( D T ) L a d s 5 a s ( D T ) L s From the figure above: d a 1 L a 5 D L 1 d s 1 L s or, a a ( D T ) L a 1 L a 5 D L 1 a s ( D T ) L s 1 L s Solve for D T : Substitute numerical values: a a L a 2 a s L s 5 659.9 3 10 2 6 m/ 8 C 5 40.3 8 C T 5 T 1 ¢ T 5 10 8 C 1 30.31 8 C ¢ T 5 15 mm 1 5 mm 659.9 3 10 2 6 m / 8 C 5 30.31 8 C ¢ T 5 ¢ L 1 ( L s 2 L a ) a a L a 2 a s L s d a L a ± L d s L s Aluminum pipe Steel pipe A-PDF Split DEMO : Purchase from www.A-PDF.com to remove the watermark...
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This note was uploaded on 09/20/2009 for the course COE 3001 taught by Professor Armanios during the Spring '08 term at Georgia Tech.

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