Statics Rigid Body Equilibrium Problem

[raniero]

Homework Statement

The given force F is equal to 5000N,γ=〖30〗^o and α=〖15〗^o.
The moment on member 4 is to be found.

The geometry of the structure was worked out separately.

Homework Equations

To solve the problem I tried to use the Equilibrium equations which state that forces in all directions should equal to zero and also that all moments should equal to zero.

The Attempt at a Solution

I tried to solve it by using equilibrium equations but force the three forces (which are equal), A, Fb and F32 resulted to zero.

I solved the problem graphically and these forces did not result to be equal to zero.

I solved the simultaneous equations using matrices with excel and the answers obtained are equal so I ruled out the possibility of a mathematical mistake.

What am I doing wrong here?

Any help would be greatly appreciated.

The equations of equivalence shown below and also the working of these equations are attached.

 

[afreiden]

I see you posted this question twice now and still have no responses.
Here's why your posts are so confusing:

The first thing I do is look just at your picture, without reading anything you wrote, and it looks like a bunch of cables connected together, but there are some parts of the picture that I find confusing, so I read on.

I then skim over your post as well as your .doc.

I find out that all of those "members" drawn as lines, that I assumed were cables, are in fact beams. According to your .doc, member FCD, for example, I am surprised to learn is a beam member with some sort of collar at C.

Now that I feel I understand what the picture is showing, and can perhaps solve the problem on my own, I decide to carefully read what you wrote and try my best to find your error.

Unfortunately, if any of your readers have gotten this far, they will now be met with free-body-diagrams and force labeling notations that are near impossible to interpret.

However, I mostly figured out what you did, so here are some thoughts and questions I have, addressing a few of your free-body-diagrams in your word .doc file:

Let's see if I understand... You drew two forces on the collar, "member 5." One of these forces physically represents the force that is felt by the collar from the beam, "member 6." You could've called it F65 to be consistent in notation, but Fc is ok too. The other force that you drew represents the force on the collar, "member 5," felt from the beam, "member 4." You chose to label it F45, and have drawn it so that the collar, "member 5," is in equilibrium. I guess my only question for this particular free-body-diagram is if you are sure about that 6.8 degrees?

Next, look at your free-body-diagram of the bar, "member 2." Why is there an applied moment, "M2?" Also, I believe your F32 vector is drawn wrong. That angle should be 75 not 15, and, accordingly, at joint A.

On the beam, "member 4," why is there an applied moment M4?

Hope that helps.

I didn't read your equations that carefully when I saw that you are using distances, for example, length "HG," which is nowhere to be found in yours pictures...

In general, when you seek help from random people on the internet, you need to be much more clear about what your particular problem is asking. It was a minor miracle that I was able to figure out that your problem contains beams, smooth collars, a mass-less block when you call everything "member" and draw beams as lines with no thickness...

 

[raniero]

Well, first of all thanks for the interest and response. This was my first assignment in which I had to work out mathematics and mechanics. I understand your argument and will try to follow your advice and try to be a little more informative about my diagrams, working, geometry and force labelling from now on both on this forum and also when writing an assignment.

Secondly, the wrong angle which you spotted which should have been 75 was the culprit which finally gave me a wrong answer (I knew it was wrong because I worked out the question graphically). Pity I have already handed in my assignment.

About the 6.8 degrees, I was given the diagram exactly as is, I created the 6.8 degrees since I was instructed to create geometrical measurements if they were missing.

I created a moment ‘M2’ on member 2 since it is a two force member and its forces are not on the same line of action. Moment M4 was required to be found.

Thanks again for the interest and the feedback.