157_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

157_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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Unformatted text preview: Sec_2.5.qxd 9/25/08 3:00 PM Page 151 SECTION 2.5 Thermal Effects 151 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 is produced in the rails when they are heated by the sun to 120°F if the coefficient of thermal 6.5 10 6/°F and the modulus of elasticity E 30 106 psi? expansion Solution 2.5-1 Expansion of railroad rails The rails are prevented from expanding because of their great length and lack of expansion joints. T 120°F 60°F 60°F E ( T) Therefore, each rail is in the same condition as a bar with fixed ends (see Example 2-7). (30 106 psi)(6.5 11,700 psi ; The compressive stress in the rails may be calculated from Eq. (2-18). 10 6/°F)(60°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 of thermal expansion of aluminum and steel are a 23 10 6/°C and s 12 10 6/°C, respectively.) Solution 2.5-2 Aluminum and steel pipes INITIAL CONDITIONS or, La 60 m T0 10°C Ls 60.005 m T0 10°C a 23 10 6/°C s 12 10 6/°C ¢T T )La s s( aLa sLs From the figure above: La L s( T)Ls ; s Ls 659.9 10 6 m/°C 15 mm + 5 mm 659.9 * 10 T )Ls T 6 T0 + ¢ T 10°C + 30.31°C 40.3°C a L La) ¢ L + (Ls aaLa asLs ¢T increase in temperature a( La Substitute numerical values: Aluminum pipe is longer than the steel pipe by the amount L 15 mm. a T )La Solve for T: FINAL CONDITIONS T a( ; m/° C 30.31° C Ls ...
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