COSMOS Chapter 6 Solution 37

COSMOS: Complete Online Solutions Manual Organization System Chapter 6, Solution 37. FBD Truss: ΣFz = 0: Bz + 987 N = 0 B z = − 987 N k ΣM x = 0: − ( 0.47 m ) C y − ( 0.16 m )( 987 N ) + ( 0.08 m )( 940 N ) = 0 C y = −176.0 N j Joint FBDs: Joint D: FAD = FAD FBD = FBD FCD = FCD ΣFy = 0: ΣFx = 0: ΣFz = 0: − 0.8 m i − 0.08 m k ( 0.8 m )2 + ( 0.08 m )2 FAD ( −10i − k ) 101 = − 0.8 m i − 0.16 m j − 0.2 m k ( 0.8 m ) 2 2 + ( 0.16 m ) + ( 0.2 m ) − 0.8 m i + 0.39 m k ( 0.8 m )2 + ( 0.39 m )2 = 2 = FCD ( − 80i + 39k ) 89 4 FBD − 940 N = 0, FBD = 4935 N, 21 10 80 20 − FAD − FCD − ( 4935 N ) = 0 89 21 101 1 39 5 − FAD + FCD − ( 4935 N ) + 987 N = 0 89 21 101 Solving: FBD ( − 20i + 4 j − 5k ) 21 FCD = − 534 N, FAD = − 422 101 N, FBD = 4.94 kN T ! FCD = 534 N C ! FAD = 4.24 kN C ! continued Vector Mechanics for Engineers: Statics and Dynamics, 8/e, Ferdinand P. Beer, E. Russell Johnston, Jr., Elliot R. Eisenberg, William E. Clausen, David Mazurek, Phillip J. Cornwell © 2007 The McGraw-Hill Companies. COSMOS: Complete Online Solutions Manual Organization System Joint C: FBC = FBC 0.16 m j − 0.59 m k ( 0.16 m ) 2 + ( 0.59 m ) 2 = FBC (16 j − 59k ) 3737 16 FBC − 176 N = 0, FBC = 11 3737 N 3737 ΣFy = 0: FBC = 672 N T ! ΣFz = 0: − FAC − ( ) 59 39 11 3737 N + ( 534 N ) = 0 89 3737 FAC = − 415 N, FAC = 415 N C ! Joint B: FAB = FAB ΣFy = 0: − 0.16 m j + 0.12 m k ( 0.16 m )2 + ( 0.12 m )2 − 4 FAB − 5 ( = FAB ( − 4 j + 3k ) 5 ) 16 4 11 3737 N − ( 4935 N ) = 0 21 3737 FAB = −1395 N, FAB = 1.395 kN C ! Vector Mechanics for Engineers: Statics and Dynamics, 8/e, Ferdinand P. Beer, E. Russell Johnston, Jr., Elliot R. Eisenberg, William E. Clausen, David Mazurek, Phillip J. Cornwell © 2007 The McGraw-Hill Companies.