Determining the support reactions of a frame

[hobbyenthusia]

Here is a link to the problem:
http://img62.imageshack.us/img62/374/frameow.jpg"
I am trying to find the support reactions at A and B.
I separated the frame at the hinge(call it C) into two parts and took the moment equation about point A.
This gave me: $\Sigma$Ma = -60(25) - 62.5(12.5) + Cx(25) + Cy(25)
The forces in the y:$\Sigma$ Fy = -62.5 + Cy + Ay
The forces in the x: $\Sigma$ Fx =60 + Ax - Cx

From here I am unsure what to do as I have four unknowns and only three equations.

 

[PhanthomJay]

Hello hobbyenthusia(st), welcome to these forums!

Try looking at the other part of the frame that includes the support at B. That should give you a total of 6 equations with a total of 6 unknowns.

 

[hobbyenthusia]

I completely missed that. Thank you.
After taking the moments for each side is it as simple as solving Cx in terms of Cy or vice versa and finishing it up?

 

[PhanthomJay]

Yes, solve for Cx and Cy and the rest will follow. Please watch plus and minus signs! If Cx is assumed or found to act to the left on the left section, it must act to the right on the right section.

 

[DeeNos]

How can I determine the support reactions at A and B for this frame?

To determine the support reactions at A and B for this frame, you can use the equations of equilibrium. Since there are no external forces acting on the frame, the sum of all forces in the x and y directions must be equal to zero. This will give you two equations:

\Sigma Fx = 0
\Sigma Fy = 0

You can then use the moment equation about point A to get a third equation:

\Sigma Ma = 0

With these three equations, you can solve for the four unknowns (Ax, Ay, Cx, Cy). However, you will need to make some assumptions about the direction of the support reactions in order to solve the equations. For example, you can assume that the support reactions at A and B are vertical and that the reaction at C is horizontal. This will give you enough information to solve for all four unknowns.

Alternatively, you can also use a free body diagram approach to solve for the support reactions. Draw a separate free body diagram for each part of the frame (left and right of the hinge). Then, apply the equations of equilibrium to each diagram to get a total of four equations. Again, you will need to make some assumptions about the direction of the support reactions, but this approach may be easier to visualize and solve for the unknowns.

In summary, to determine the support reactions at A and B for this frame, you will need to use the equations of equilibrium and make some assumptions about the direction of the support reactions. This will allow you to solve for all four unknowns and determine the support reactions at A and B.