02-06ChapGere.0005

02-06ChapGere.0005 - work done by the load P is equal to...

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148 CHAPTER 2 Axially Loaded Members S OLUTION OF EQUATIONS Combine Eqs. (6) and (3): or (7) This equation can be solved for x . S UBSTITUTE NUMERICAL VALUES INTO E Q . (7): 3 (8) (9) Units: x is in millimeters Solve for x program): x 5 497.88mm (a) S TRAIN ENERGY U OF THE BUNGEE CORD U 5 k d 2 2 Ê k 5 140 N / m Ê P 5 80 N 760 5 ¢ 1 2 142.857 x Ï 144,400 1 4 x 2 Ê (9) Ï (380 mm) 2 1 4 x 2 760 mm 5 B 1 2 (80 N)(1000 mm / m) 4(140 N / m) x R L 0 5 ¢ 1 2 P 4 kx Ï b 2 1 4 x 2 L 1 5 L 0 1 P 4 kx Ï b 2 1 4 x 2 5 Ï b 2 1 4 x 2 L 1 5 L 0 1 P 2 k B 1 1 b 2 4 x 2 5 Ï b 2 1 4 x 2 From Eq. (5): (b) D ISPLACEMENT d C OF POINT C (c) C OMPARISON OF STRAIN ENERGY U WITH THE QUANTITY P d C /2 U 5 6.55J The two quantities are not the same. The work done by the load P is not equal to P d C /2 because the load- displacement relation (see below) is non-linear when the displacements are large. (The
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Unformatted text preview: work done by the load P is equal to the strain energy because the bungee cord behaves elastically and there are no energy losses.) U 5 area OAB under the curve OA . of triangle OAB , which is greater than U . P d C 2 5 area P d C 2 5 1 2 (80 N)(168.8 mm) 5 6.75 J 5 168.8 mm d C 5 x 2 d 5 497.88 mm 2 329.09 mm U 5 6.55 J U 5 1 2 (140 N / m)(305.81 mm) 2 5 6.55 N ? m d 5 P 2 k B 1 1 b 2 4 x 2 5 305.81 mm Load P 80 N A B d C Large displacements Small displacements Displacement A-PDF Split DEMO : Purchase from www.A-PDF.com to remove the watermark...
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