# Statics: Two-member Frame

1. Jul 12, 2013

### rico22

1. The problem statement, all variables and given/known data

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.

2. Relevant equations

3. 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 im 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.

#### Attached Files:

• ###### two member frame.PNG
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2. Jul 12, 2013

### PhanthomJay

this is ok
No you cannot just isolate CB without including the pulley forces and torque.
well it has to factor in somewhere, right?
It is.
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.

3. Jul 13, 2013

### rico22

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

4. Jul 13, 2013

### 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.

5. Jul 11, 2017