COSMOS Chapter 6 Solution 41

COSMOS: Complete Online Solutions Manual Organization System Chapter 6, Solution 41. (a) (b) To check for simple truss, start with ABDE and add three members at a time which meet at a single new joint, successively adding joints G, F, H and C. ∴ This is a simple truss ! There are six reaction force components, Ax, Ay, Az, By, Bz, and Gy, no two of which are colinear, so all can be determined with the six equilibrium equations. Motion is prevented by the constraints. ∴ Truss is completely constrained, and statically determinate. ! FBD Truss: ΣM AB = 0: ( 9.60 ft ) G y + (10.08 ft )( 240 lb ) = 0 G y = − 252 lb, ΣM z = 0: G y = − 252 lb j (11.00 ft ) ( By − 252 lb ) − (10.08 ft )( 275 lb ) = 0 B y = 504 lb j ΣFx = 0: ΣM y = 0: − Ax + 275 lb = 0, Ax = − 275 lb i − ( 9.6 ft )( 275 lb ) − (11.0 ft )( Bz ) = 0 Bz = − 240 lb, B z = − 240 lb k ΣFy = 0: − Ay + 504 lb − 252 lb = 0, A y = − 252 lb j ΣFz = 0: Az − 240 lb + 240 lb = 0 Az = 0 Determine zero force members: By inspection of joint C : FBC = FCD = FGC = 0 By inspection of joint F : FBF = FEF = FFG = 0 By inspection of joint A: with Az = 0, By inspection of joint H : FDH = 0 FAD = 0 And finally, considering joint D knowing that FAD = FCD = FDH = 0, and recognizing that the three remaining members are not co-planar, they must also carry zero load, FBD = FDE = FGH = 0. The only load bearing members are thus AB, AE, BE, BG, EG, EH, GH. 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 Now, by inspection of joint H, FGH = 275 lb C ! FCG = 0 ! from above, FDG = 0 ! FFG = 0 ! FBD Joint G: FBG = FBG −10.08j + 9.6k 13.92 FEG = FEG −11i + 9.6k 14.6 ΣFx = 0: ΣFy = 0: 275 lb − − 11 FEG = 0, 14.6 10.08 FBG − 252 lb = 0, 13.92 FEG = 365 lb T ! FBG = − 348 lb FBG = 348 lb 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.