Question

In the frame shown, members ACE and BCD are connected by a pin at C, and by the link DE. Determine reaction force at A, the force in link DE for the loading shown, and components of force exerted at C on member BCD.

(FDE = 561 N, Cy = 216 N; Cx = 795 N; Ay = 480 N; Ax = 300 N).

Answer 1

Members ACE and BCD are connected by a pin at C and by the link DE. For the loading shown, determine the force in link DE and the components of the force exerted at Con member BCD 480 3 SOLUTION Reaction Forces. Consider the entire frame as a free body to determine the unknown reactions exerted from the pin at A and the roller at . The pin at A exerts two unknown forces. ty The wheel at B exerts one unknown forces perpendicular to the rolling surface. Equilibriumequations M,-0: -. (480 N)(0.11n) + RB(0.16m):0 450 N RB 300N RAr-300N RAy 480 N

Force at C and in DE. To determine these forces, 480 N we consider BCD as a free body, removing the 300 N member ACE and DE to expose the joint forces. The reaction at C has an unknown magnitude and direction, and therefore represented by two 80 N unknown forces 300 N The direction of the force exerted at D from DE Sm is known, since DE is a two-force member, WE estimate that the force is acting towards the joint i.e, DE is in compression. DE 170 mm Σ.MC:0:-(300 N)(0.06 m)-. (480 N)(0.1 m) +FDE (8/17)0.25 m)0 FDE 561 N Ro 795 N R216 N Fx #0: 300 N-RCr + FDE(1 5 / 17):0

10 1 1-20 480 N 60 mn 100m CRo 795 N 300 N FE 561 N 130 Free Body Diagrams of ACE and DE. The firee body diagrams are as shown. 220 mm We can check the equbm of ACE - FDE (15/170.3) FDE(8/10) Ror(0.22) 15 (56) (15/17)00.3)-(561) 8/17)(0.1)+(79500.22) Σ =-300 N + 795 N-(561 N)(1 5 / 17) =0 (V) EF, -480 N-216 N-(561N8/17)-0 o

Answer 2

In the frame shown, members ACE and BCD are connected by a pin at C and by the link DE. For the loading shown, determine the force in link DE and the components of the force exerted at C on member BCD. 160 mm 480 N 60 mm 80 mm 60 mm 100 mm 150 mm

Define the state of the problem Assuming that Frame can be treated as a rigid body. The external reactions involve only three unknowns, compute the reactions by considering the free-body diagram of the entire frame. 160 mm 480 N 80 mm 60 mm 100 mm 150 mm

Construct physical model (FBD) B C 480 N 80 150 α-28.070 160 mm 60 mm 480 N 60 60 mm 100 mm 150 m 80 mm 60 mm 100 mm 150 mm 220 mm B 80 mm α 28.070 100 mm 29

Construct mathematical model and solve equations 480 N 300 N 80 150 160 mm 160 mm 480 N 480 N 300 N B 80 mm 80 mm 60 mm 100 mm 150 mm 60 mm 100 mm 150 mm .J ΣΜ4-0:-480( 100) + B( 160-0 B-300 N-+ A 300N A,- 300 N

300 NB C 480 N 300 N B 216 N 480 N α 28.070 α 28.070 60 mm 60 mm 795 N DE 60 mm 100 mm 150 mm 60 mm 100 mm 150 mn Foe sin 28.07 (250)-480(100) 300(60) 0 FDE 561 N (C) 61 N C, 795 N C-795 N 561 N -216 N

Member BCD 300 N T 480 N 220mB 300 N B 216 N 480 N o 28.07 60 mm 795 N 561 N C 795 N 80 mm 561 N α 28.070 60 mm 100 mm 150 mm 100 mm 216(100)-795(80) +300(300)-480(100)-0 OK.

480 N 300 N Conclusion 160 mm 480 N 300 N B 216 N 480 N o 28.07 60 mm 795 N 561 N 80 mm 60 mm 100 mm 150 m 60 mm 100 mm 150 mm 300 N 480 N 561 N 220 mm B 795N 216 N 561 N 561 N α 28.070 80 mm 100 mm