Finding Equilibrium Forces in a Two-Member Frame

[rico22]

Homework Statement

The two-member frame (see picture attached) supports the 200-lb cylinder and 500
lb–ft couple moment. Determine the force of the roller at B on member
AC and the horizontal and vertical components of force which the pin at
C exerts on member CB and the pin at A exerts on member AC. The
roller C does not contact member CB.

Homework Equations

The Attempt at a Solution

I split the frame into members AC and CB. The I found the forces acting on D(pulley) which gave me Dx = 200 lb and Dy = 200 lb. I plugged this into member CB; giving me the next equations:
ƩFx = 0: Cx +Bx -200 = 0
∴ Cx + Bx = 200

ƩFy = 0: Cy - 200 = 0
∴ Cy = 200

ƩMc = 0: 200(4) - 4Bx = 0
∴ Bx = 200 which also give me Cx = 0 from the summation of Forces in the x direction.
Then I plug the relevant values of Cx, Cy and Bx into the AC member; this gives me the following equations:
ƩFx = 0: Ax - Bx + 200(from cable) = 0
∴ Ax = 0

ƩFy = 0: Ay - 200 = 0
∴ Ay = 200
The issue that I am having is that this last answer is wrong according to the book. Its supposed to be Ay = 175 lbs. I know I didn't use the couple moment at all so, maybe this is the reason? But I really don't see how it could be 175 lbs. Any help would be greatly appreciated.

 

[PhanthomJay]

Homework Statement

The two-member frame (see picture attached) supports the 200-lb cylinder and 500
lb–ft couple moment. Determine the force of the roller at B on member
AC and the horizontal and vertical components of force which the pin at
C exerts on member CB and the pin at A exerts on member AC. The
roller C does not contact member CB.

Homework Equations

The Attempt at a Solution

I split the frame into members AC and CB. The I found the forces acting on D(pulley) which gave me Dx = 200 lb and Dy = 200 lb.

this is ok

I plugged this into member CB; giving me the next equations:
ƩFx = 0: Cx +Bx -200 = 0
∴ Cx + Bx = 200

ƩFy = 0: Cy - 200 = 0
∴ Cy = 200

No you cannot just isolate CB without including the pulley forces and torque.

The issue that I am having is that this last answer is wrong according to the book. Its supposed to be Ay = 175 lbs. I know I didn't use the couple moment at all so, maybe this is the reason?

well it has to factor in somewhere, right?

But I really don't see how it could be 175 lbs.

It is.

Any help would be greatly appreciated.

Before pulling the frame apart, try summing external forces = 0 and summing moments of external forces about A = 0. Only the cylinder weight and couple and reactions at A and C are external to the system.

 

[rico22]

Thank you for the reply. So if I take the entire frame would C then become a roller and not a pin?

 

[rico22]

ok I got it now... I was supposed to plug in the roller support reaction into the FBD of AC on top of Cy and Cx...that was throwing the whole thing off... thanks again.

 

[Dennis]

You are missing the normal reaction because of the roller.
Link to the solution.
https://faculty.uca.edu/njaustin/ENGR2311/Quizzes/quiz07.pdf

Good job guyz. Enjoy.