COSMOS Chapter 4 Solution 161

COSMOS: Complete Online Solutions Manual Organization System Chapter 4, Solution 161. Free-Body Diagram: λCD = First note = λCE = = − ( 23 in.) i + ( 22.5 in.) j − (15 in.) k 35.5 in. 1 ( −23i + 22.5j − 15k ) 35.5 ( 9 in.) i + ( 22.5 in.) j − (15 in.) k 28.5 in. 1 ( 9i + 22.5 j − 15k ) 28.5 W = − ( 285 lb ) j From free-body diagram of plate (a) ΣM x = 0:  22.5    22.5    T  (15 in.) −   T  (15 in.) = 0  35.5    28.5   ( 285 lb )( 7.5 in.) −  ∴ T = 100.121 lb or T = 100.1 lb
continued COSMOS: Complete Online Solutions Manual Organization System  23   9  ΣFx = 0: Ax − T   +T =0 35.5    28.5  (b)  23  (  9  Ax − (100.121 lb )   + 100.121 lb )  =0 35.5    28.5  ∴ Ax = 33.250 lb   22.5     22.5   ΣM B( z -axis ) = 0: − Ay ( 26 in.) + W (13 in.) − T    ( 6 in.) − T    ( 6 in.) = 0   35.5     28.5   or   22.5   − Ay ( 26 in.) + ( 285 lb )(13 in.) − (100.121 lb )    ( 6 in.)  35.5      22.5   − (100.121 lb )    ( 6 in.) = 0  28.5    ∴ Ay = 109.615 lb   15   ΣM B( y -axis ) = 0: Az ( 26 in.) − T    ( 6 in.) −   35.5     23     (15 in.) T    35.5     15     9  − T    ( 6 in.) + T    (15 in.) = 0   28.5     28.5   or 1  −1 Az ( 26 in.) +  ( 90 + 345) − ( 90 − 135) (100.121 lb ) = 0 28.5  35.5  ∴ Az = 41.106 lb or A = ( 33.3 lb ) i + (109.6 lb ) j + ( 41.1 lb ) k
 22.5   22.5  ΣFy = 0: By − W + T   +T  + Ay = 0  35.5   28.5   22.5 22.5  B y − 285 lb + (100.121 lb )  +  + 109.615 lb = 0  35.5 28.5  ∴ By = 32.885 lb  15   15  ΣFz = 0: Bz + Az − T   −T =0  35.5   28.5  15   15 Bz + 41.106 lb − (100.121 lb )  + =0 35.5 28.5   ∴ Bz = 53.894 lb or B = ( 32.9 lb ) j + ( 53.9 lb ) k