02-05ChapGere.0009

02-05ChapGere.0009 - equal to U 1 1 U 2 5 2.22 in-lb 5...

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Problem 2.7-7 The truss ABC shown in the figure supports a horizontal load P 1 5 300 lb and a vertical load P 2 5 900 lb. Both bars have cross-sectional area A 5 2.4 in. 2 and are made of steel with E 5 30 3 10 6 psi. (a) Determine the strain energy U 1 of the truss when the load P 1 acts alone ( P 2 5 0). (b) Determine the strain energy U 2 when the load P 2 acts alone ( P 1 5 0). (c) Determine the strain energy U 3 when both loads act simultaneously. Solution 2.7-7 Truss with two loads 142 CHAPTER 2 Axially Loaded Members P 1 5 300 lb P 2 5 900 lb A 5 2.4 in. 2 E 5 30 3 10 6 psi L BC 5 60 in. b 5 30 8 sin b 5 sin 30 85 2 EA 5 2(30 3 10 6 psi)(2.4 in. 2 ) 5 144 3 10 6 lb F ORCES F AB AND F BC IN THE BARS From equilibrium of joint B : F AB 5 2 P 2 5 1800 lb F BC 5 P 1 2 P 2 Ï 3 5 300 lb 2 1558.8 lb L AB 5 L BC cos 30 8 5 120 Ï 3 in. 5 69.282 in. cos b 5 cos 30 85 Ï 3 2 1 2 (a) L OAD P 1 ACTS ALONE (b) L OAD P 2 ACTS ALONE (c) L OADS P 1 AND P 2 ACT SIMULTANEOUSLY N OTE : The strain energy U 3 is not
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Unformatted text preview: equal to U 1 1 U 2 . 5 2.22 in.-lb 5 319.548 3 10 6 lb 2-in. 144 3 10 6 lb 1 ( 2 1258.8 lb) 2 (60 in.) R 5 1 2 EA B (1800 lb) 2 (69.282 in.) U 3 5 1 2 EA B ( F AB ) 2 L AB 1 ( F BC ) 2 L BC R 5 370.265 3 10 6 lb 2-in. 144 3 10 6 lb 5 2.57 in.-lb 1 ( 2 1558.8 lb) 2 (60 in.) R 5 1 2 EA B (1800 lb) 2 (69.282 in.) U 2 5 1 2 EA B ( F AB ) 2 L AB 1 ( F BC ) 2 L BC R 5 0.0375 in.-lb U 1 5 ( F BC ) 2 L BC 2 EA 5 (300 lb) 2 (60 in.) 144 3 10 6 lb Force P 1 alone P 2 alone P 1 and P 2 F AB 1800 lb 1800 lb F BC 300 lb 2 1558.8 lb 2 1258.8 lb P 1 P 2 B C A L BC 30 ° L AB P 1 = 300 lb P 2 = 900 lb B C A 60 in. 30 ° A-PDF Split DEMO : Purchase from www.A-PDF.com to remove the watermark...
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