How Do You Solve a 2D Statics Frame Problem with Multiple Unknowns?

[mw29715]

Homework Statement

I will attach a scanned pic of the problem, but it seems to be a basic frames problem. However, everything seems to have to many unknowns on it to solve. I feel like I'm missing something simple, but I can't seem to make any more progress.

Homework Equations

ƩM=0
ƩFv=0
ƩFh=0

The Attempt at a Solution

My attempt at a solution began with resolving the uniformly distributed load into a single force, 1050 lb. acting 3.5 feet from either side. The next step was to solve for any pin reactions that I could on the structure as a whole, which is:
Reaction at A Horizontal= 918.75 lb to the left
Reaction at F Horizontal= 918.75 lb to the right
I got these numbers from doing ƩM=0 around point A and F. I saw no way to solve for the vertical reactions at A and F, since any moment equations would eliminate both as they are colinear, and a moment equation around any other point would leave two unknown vertical forces. So I tried to move on to calculating forces on the individual members of the frames, but every piece seems to have to many unknown forces to solve for anything. I feel like I'm missing something basic, but we didn't spend much time on frames in class and have already moved on. I haven't had any problems with other frames in this section, so I'm at a loss. Any help would be greatly appreciated!

 

[PhanthomJay]

Finding the horiz force resctions is a good way to start. You should then break apart the members as you suggested and Note the known and unknown forces (in free body diagrams,), in the x and y directions . Don't forget Newton 3. It is helpful to recognize that the vertical and diagonal members are 2-force members that take axial load only along the direction of the member. The axial loads can be broken into their components using basic trig for vectors, where necessary. The other members can support axial, shear, and bending stresses.
Hint: Is there any horiz force at C when you draw the FBD of CD? What about when you draw the FBD of ABC, what is the value of the horiz force acting at C?

 

[mw29715]

Sorry, I'm still confused. If I break member CD out, I don't know any forces on it, so I can't solve for anything. If I break member ABC out, I have unknown horizontal and vertical forces at B and C, and an unknown vertical at A. So I can't solve for any unknowns there, either, since I have so many and can't use moment equations to eliminate enough. There are also no known forces on BE and five unknowns on FED, which has the same problem as ABC.

 

[PhanthomJay]

Sorry, I'm still confused. If I break member CD out, I don't know any forces on it, so I can't solve for anything.

you have unknown vertical forces at each end, Cy and Dy, right? Are there any horizontal forces Cx and Dx at those ends of this 2-force member that takes axial forces only?

If I break member ABC out, I have unknown horizontal and vertical forces at B

yes, Bx and By, which are the components of the force B in the diagonal member, trig related

and C

yes , Cy only if you understood my hints

, and an unknown vertical at A.

yes, Ay

So I can't solve for any unknowns there, either, since I have so many and can't use moment equations to eliminate enough. There are also no known forces on BE and five unknowns on FED, which has the same problem as ABC.

look at ABC and sum forces in the horizonal direction to solve for Bx. Then you know By, and can solve for Ay, and Cy...continue..

 

[rezeew]

Dear student,

Thank you for sharing your attempts at solving this 2D statics problem involving frames. It is understandable that you may feel stuck with the number of unknown forces present in the problem. However, it is important to remember that solving statics problems requires a systematic approach and careful application of the relevant equations.

Firstly, it is commendable that you were able to resolve the uniformly distributed load into a single force. This is a crucial step in simplifying the problem and reducing the number of unknowns. Moving on to solving for the pin reactions, it is correct to use the moment equilibrium equation around points A and F. However, it seems that you may have overlooked the fact that there are also vertical forces acting at these points. In order to solve for the vertical reactions, you can use the force equilibrium equation in the vertical direction (ƩFv=0) and solve for the unknown forces.

Once you have determined the reactions at the supports, you can move on to analyzing the individual members of the frame. It is important to remember that each member of the frame is in equilibrium, which means that the sum of all forces and moments acting on each member must equal zero. This will allow you to set up equations for each member and solve for the unknown forces.

In conclusion, it seems that you were on the right track with your approach to solving this problem. However, it is important to carefully consider all forces and moments acting on the structure and apply the relevant equilibrium equations to solve for the unknowns. I would suggest going back to the problem and reviewing all the forces and moments present, and then systematically applying the equations to solve for the unknowns. I hope this helps and good luck with your studies.