COSMOS Chapter 4 Solution 62

COSMOS: Complete Online Solutions Manual Organization System Chapter 4, Solution 62. Free-Body Diagram: 1. Three non-concurrent, non-parallel reactions Completely constrained
(a) (b) Determinate
(c) Equilibrium
From free-body diagram of plate ΣM A = 0: C ( 30 in.) − 50 lb (15 in.) = 0 C = 25.0 lb
ΣFx = 0: Ax = 0 ΣFy = 0: Ay − 50 lb + 25 lb = 0 Ay = 25 lb A = 25.0 lb
2. Three non-current, non-parallel reactions Completely constrained
(a) (b) Determinate
(c) Equilibrium
From free-body diagram of plate B = 0
ΣFx = 0: ΣM B = 0: ( 50 lb )(15 in.) − D ( 30 in.) = 0 D = 25.0 lb
ΣFy = 0: 25.0 lb − 50 lb + C = 0 C = 25.0 lb
continued COSMOS: Complete Online Solutions Manual Organization System 3. Four non-concurrent, non-parallel reactions Completely constrained
(a) (b) Indeterminate
(c) Equilibrium
From free-body diagram of plate ΣM D = 0: Ax ( 20 in.) − ( 50 lb )(15 in.) ∴ A x = 37.5 lb
∴ D x = 37.5 lb
ΣFx = 0: Dx + 37.5 lb = 0 4. Three concurrent reactions Improperly constrained
(a) (b) Indeterminate
(c) No equilibrium
5. Two parallel reactions (a) Partial constraint
(b) Determinate
(c) Equilibrium
From free-body diagram of plate ΣM D = 0: C ( 30 in.) − ( 50 lb )(15 in.) = 0 C = 25.0 lb
ΣFy = 0: D − 50 lb + 25 lb = 0 D = 25.0 lb
6. Three non-concurrent, non-parallel reactions (a) Completely constrained
(b) Determinate
(c) Equilibrium
From free-body diagram of plate ΣM D = 0: B ( 20 in.) − ( 50 lb )(15 in.) = 0 B = 37.5 lb ΣFx = 0: Dx + 37.5 lb = 0 ΣFy = 0: Dy − 50 lb = 0
D x = 37.5 lb D y = 50.0 lb or D = 62.5 lb 53.1°
continued COSMOS: Complete Online Solutions Manual Organization System 7. Two parallel reactions (a) Improperly constrained
(b) Reactions determined by dynamics
No equilibrium
(c) 8. Four non-concurrent, non-parallel reactions Completely constrained
(a) (b) Indeterminate
(c) Equilibrium
From free-body diagram of plate ΣM D = 0: B ( 30 in.) − ( 50 lb )(15 in.) = 0 B = 25.0 lb
ΣFy = 0: Dy − 50 lb + 25.0 lb = 0 D y = 25.0 lb
ΣFx = 0: Dx + C = 0