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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
; 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
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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