COSMOS Chapter 6 Solution 38

COSMOS: Complete Online Solutions Manual Organization System Chapter 6, Solution 38. FBD Truss: ΣM BD = 0: ΣM x = 0: ΣFz = 0: ( 4 ft )( 50 lb ) + ( 4 ft )( Ez ) = 0 E z = − ( 50 lb ) k ( 4 ft )( 300 lb ) + ( 4 ft )( − 50 lb ) + ( 4 ft )( Dz ) = 0 D z = − ( 250 lb ) k Bz − 50 lb − 250 lb = 0 B z = ( 300 lb ) k ΣM Bz = 0: ( 2 ft )( 300 lb ) − ( 4 ft ) ( C y ) = 0 C y = (150 lb ) j AB = AC = 20 ft AD = AE = 6 ft CD = 4 2 ft ΣFx = 0: ΣFy = 0: B x = − ( 50 lb ) i Bx + 50 lb = 0 By + 150 lb − 300 lb = 0 B y = (150 lb ) j FAE = FAE = 2 ft i − 4 ft j + 4 ft k ( 2 ft )2 + ( 4 ft )2 + ( 4 ft )2 FAE ( 2i − 4 j + 4k ) 3 Joint FBDs: Joint E: ΣFz = 0: ΣFx = 0: 2 FAE − 50 lb = 0, 3 1 FDE + ( 75 lb ) = 0, 3 FAE = 75.0 lb T ! FDE = − 25 lb FDE = 25.0 lb C ! ΣFy = 0: − FCE − 2 ( 75 lb ) = 0, 3 FCE = − 50 lb FCE = 50.0 lb 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 − 2 ft i − 4 ft j + 4 ft k FAD = FAD ( 2 ft ) Joint D: ΣFx = 0: 2 + ( 4 ft ) + ( 4 ft ) − 4 ft i − 4 ft j FCD = FCD ΣFz = 0: 2 ( 4 ft ) 2 + ( 4 ft ) 2 = 2 ft i + 4 ft k FAC = FAC ( 2 ft ) ) Joint B: FAB = FAB 2 + ( 4 ft ) 2 = FAC = 0 ! FBC − 100 lb = 0, − 2 ft i + 4 ft k ( 2 ft ) 2 ΣFz = 0: + ( 4 ft ) 2 = FBD = 150.0 lb C ! FAC ( i + 2k ) 5 2 FAC = 0, 5 ΣFz = 0: ΣFx = 0: FAD ( − i − 2 j + 2k ) 3 2 FAD − 250 lb = 0, FAD = 375 lb, FAD = 375 lb T ! 3 1 1 FCD − ( 375 lb ) = 0, FCD = −100 2 lb 25 lb − 3 2 FCD = 141.4 lb C ! 1 2 − FBD − −100 2 lb − ( 375 lb ) = 0 3 2 FBD = − 150 lb Joint C: = FCD ( − i − j) 2 ( ΣFy = 0: 2 FBC = 100.0 lb T ! FAB ( − i + 2k ) 5 2 FAB + 300 lb = 0 5 FAB = −150 5 lb, 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. FAB = 335 lb C !