216_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

# 216_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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Unformatted text preview: Sec_2.7.qxd 9/25/08 210 11:42 AM Page 210 CHAPTER 2 Axially Loaded Members A2 From triangle ACD: or 2b2 + 4x2 2 b a b + x2 L1 2 L1 (2) (3) SUBSTITUTE NUMERICAL VALUES INTO EQ. (7): tensile force in bungee cord * 1(380 mm)2 + 4x2 a1 760 L1/2 F x P L1 1 a ba ba b 2 2 x P b2 1+a b 2A 2x d x (4) P b2 1+ 2 2k A 4x L1 L0 + d P b2 L0 + 1+ 2 2k A 4x SOLUTION OF EQUATIONS P b 1+ 2 2k A 4x Combine Eqs. (6) and (3): 2 L1 L0 + (a) STRAIN ENERGY U OF THE BUNGEE CORD kd2 2 From Eq. (5): (5) Final length of bungee cord 497.88 mm U elongation of the entire bungee cord F k 142.857 1 b 144,400 + 4x2 x d original length 1b2 + 4x2 (8) (9) Units: x is in millimeters Solve for x (Use trial & error or a computer program): ELONGATION OF BUNGEE CORD Let (80 N)(1000 mm/m) d 4(140 N/m)x c1 760 mm F P/2 (7) This equation can be solved for x. EQUILIBRIUM AT POINT C Let F a1 L0 1b2 + 4x2 P12 b + 4x2 4kx P 12 b b + 4x2 4kx L0 + L1 k b2 P 1+ 2 2k A 4x 140 N/m P 305.81 mm U 1 (140 N/m)(305.81 mm)2 2 U 6.55 J (6) x 6.55 N.m ; (b) DISPLACEMENT C 80 N d C OF POINT 497.88 mm 168.8 mm ; C 329.09 mm ...
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