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162_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

162_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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156 CHAPTER 2 Axially Loaded Members Solution 2.5-7 Steel rod with bronze sleeve L 1 36 in. L 2 12 in. E LONGATION OF THE TWO OUTER PARTS OF THE BAR 1 s ( T )( L 1 L 2 ) (6.5 10 6 /°F)(500°F)(36 in. 12 in.) 0.07800 in. E LONGATION OF THE MIDDLE PART OF THE BAR The steel rod and bronze sleeve lengthen the same amount, so they are in the same condition as the bolt and sleeve of Example 2-8. Thus, we can calculate the elongation from Eq. (2-21): d 2 ( a s E s A s + a b E b A b )( ¢ T ) L 2 E s A s + E b A b S UBSTITUTE NUMERICAL VALUES : s 6.5 10 6 /°F b 11 10 6 /°F E s 30 10 6 psi E b 15 10 6 psi d 1 1.0 in. d 2 1.25 in. T 500°F L 2 12.0 in. 2 0.04493 in. T OTAL ELONGATION 1 2 0.123 in. ; A b p 4 ( d 2 2 d 1 2 ) 0.44179 in. 2 A s p 4 d 1 2 0.78540 in. 2 Problem 2.5-8 A brass sleeve S is fitted over a steel bolt B (see figure), and the nut is tightened until it is just snug. The bolt has a diameter d B 25 mm, and the sleeve has inside and outside diameters d 1 26 mm and d 2 36 mm, respectively. Calculate the temperature rise
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