HW10-Solution

HW10-Solution - HW10 - Solution Terry Cooke: Cal Poly San...

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Unformatted text preview: HW10 - Solution Terry Cooke: Cal Poly San Luis Obispo Chapter 4, Solution 95 Dimensions in mm We have six unknowns and six Eqs. of equilibrium–OK MC 0: ( 120k ) ( Dx i Dy j) (120 j 160k ) Ti (80k 200i) ( 720 j) 0 120 Dx j 120 Dy i 120Tk 160Tj 57.6 103 i 144 103 k 0 Equating to zero the coefficients of the unit vectors: k: i: j: Fx 0: 120T 144 103 0 (a) T Dy Dx Cx 1200 N 120 Dy 57.6 103 0 0 0 480 N 1600 N 1600 1200 400 N 120 Dx 160(1200 N) Cx Dx T Fy Fz 0: 0: Cy Dy 720 0 Cz 0 Cy 480 720 1200 N (b) C (400 N)i (1200 N) j D (1600 N)i (480 N) j Chapter 4, Solution 106 Free-Body Diagram: Five Unknowns and six Eqs. of equilibrium. Equilibrium is maintained ( MAC rB rA 1.2k 2.4k 0). AD AE TAD TAE MC 0.8i 0.6 j 2.4k 0.8i 1.2 j 2.4k AD AE 2.6 m 2.8 m AD AD AE AE TAD ( 0.8i 0.6 j 2.4k ) 2.6 TAE (0.8i 1.2 j 2.4k ) 2.8 rA TAE rB ( 3 kN) j 0 0 : rA TAD i j 0 0 0.8 0.6 k T 2.4 AD 2.6 2.4 i j 0 0 0.8 1.2 k T 2.4 AE 2.8 2.4 1.2k ( 3.6 kN) j 0 Equate coefficients of unit vectors to zero. i: j: 0.55385 TAD 1.02857 TAE 0.73846 TAD 0.68671 TAE TAD 4.32 0 0.92857 TAE 4.32 0 0 (1) (2) Eq. (1): 0.55385(0.92857) TAE 1.02857 TAE 1.54286 TAE TAE 4.32 2.800 kN TAE TAD 2.80 kN 2.60 kN Eq. (2): TAD 0.92857(2.80) 2.600 kN Fx Fy Fz 0: C x 0: C y 0: C z 0.8 (2.6 kN) 2.6 0.6 (2.6 kN) 2.6 2.4 (2.6 kN) 2.6 0.8 (2.8 kN) 0 2.8 1.2 (2.8 kN) (3.6 kN) 2.8 2.4 (2.8 kN) 0 2.8 Cx 0 Cy Cz 0 1.800 kN 4.80 kN C (1.800 kN) j (4.80 kN)k Chapter 4, Solution 114 Free-Body Diagram: Dimensions in mm ABH is equilateral rH/C rD/C rF/C MC 50i 250 j 300i 350i 250k T (0.5 j 0.866k ) ( 400 j) 0 T T (sin 30 ) j T (cos 30 )k 0: rH/C T rD D rF/C i j 50 250 0 0.5 k 0T 0.866 i j 300 0 0 Dy 0 k 0 Dz i 350 0 j k 0 250 400 0 0 Coefficient i: 216.5T 100 103 T 461.9 N 0 0 Dz 66.67 N T 462 N Coefficient of j: 43.3T 300 Dz 43.3(461.9) 300 Dz Coefficient of k: 25T 300 Dy 140 103 0 0 Dy 505.1 N D (505 N) j (66.7 N)k 25(461.9) 300 Dy 140 103 F 0 : C D T 400 j 0 0 Cx 0 Coefficient i: Coefficient j: Coefficient k: Cx Cy Cz (461.9)0.5 505.1 400 0 C y (461.9)0.866 66.67 0 Cz 336 N 467 N C (336 N) j (467 N)k ...
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This note was uploaded on 11/07/2010 for the course ME 211 taught by Professor Staff during the Fall '05 term at Cal Poly.

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