158_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

158_Mechanics - Sec_2.5.qxd 152 3:00 PM Page 152 CHAPTER 2 Axially Loaded Members Problem 2.5-3 A rigid bar of weight W 750 lb hangs from three

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Unformatted text preview: Sec_2.5.qxd 9/25/08 152 3:00 PM Page 152 CHAPTER 2 Axially Loaded Members Problem 2.5-3 A rigid bar of weight W 750 lb hangs from three equally spaced wires, two of steel and one of aluminum (see figure). The diameter of the wires is 1/8 in . Before they were loaded, all three wires had the same length. What temperature increase T in all three wires will result in the entire load being carried by the steel wires? (Assume Es 30 106 psi, s 6.5 10 6/°F, and a 12 10 6/°F.) Solution 2.5-3 Bar supported by three wires increase in length of a steel wire due to temperature increase T 1 s S A S ( T)L increase in length of a steel wire due to load W/2 2 WL 2EsAs W = 750 lb increase in length of aluminum wire due to temperature increase T 3 a( S steel W 1 in. 8 As pd2 4 aluminum 750 lb d A Es EsAs 30 For no load in the aluminum wire: 1 2 as( ¢ T)L + 0.012272 in.2 106 psi ¢T 3 WL 2EsAs aa( ¢ T)L or 368,155 lb 10 /°F a 12 6 L Initial length of wires 10 /°F W 2EsAs(aa as) ; Substitute numerical values: 6 6.5 s T)L ¢T 750 lb (2)(368,155 lb)(5.5 * 10 ; 185°F 6 /° F) NOTE: If the temperature increase is larger than T, the aluminum wire would be in compression, which is not possible. Therefore, the steel wires continue to carry all of the load. If the temperature increase is less than T, the aluminum wire will be in tension and carry part of the load. ...
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This note was uploaded on 12/22/2011 for the course MEEG 310 taught by Professor Staff during the Fall '11 term at University of Delaware.

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