Solving a System of Equations for Internal Forces at E

[Vidatu]

Homework Statement

The question is asking for the internal forces at E, but I get stuck solving the external reactions. After that, I can do it, and have, using electronically generated results. I just get stuck solving the system of equations I get after doing the determinant equations.

We ignore the reactions at E. Those will be applied in the next step, where I find the internal forces there. I just drew them into help me remember where they are, and to visualize the problem.

The moment occurring between O and C has a magnitude of 300 kNm, and acts in the k direction.

Homework Equations

$$\Sigma M_x = A_z + 0.4B_z - 0.75C_y - 5 = 0$$
$$\Sigma M_y = A_z + 0.75C_x = 0$$
$$\Sigma M_z = -A_y - 0.4B_x - 10 = 0$$
$$\Sigma F_x = C_x + B_x + +7 = 0$$
$$\Sigma F_y = C_y + A_y - 12 = 0$$
$$\Sigma F_z = B_z + A_z - 5 = 0$$

The Attempt at a Solution

I tried it for two different unknowns, and both times it didn't work. Sorry for the poor images; I did the work in pencil, and it wouldn't scan very well.

Here are the real answers, and when I put my equations into a computer, it solves them and gets these. As such, I know my equations are correct. My problem just pops up when I try and solve for each unknown. If anyone could help me see where I went wrong, I'd be very grateful to them.

 

[Vidatu]

So no one's able to help with this? Its driving me crazy; I've done the work on this four or five times now, and have gotten everything else I need for the question done already.

Strongly tempted to just say that I used a computer to solve the system, as that isn't even the main point of the problem .

 

[Shooting Star]

Perhaps the reason that nobody has been able to help was that there were no question anywhere.

 

[Vidatu]

Um, I'd have thought I made it clear that I would like someone to check my work, to see if they could spot any errors. I wasn't just posting this for fun.

Some reading comprehension skills may benefit you.

 

[Shooting Star]

Thankfully, my comprehension skills do not extend to reading nonsense. But your manners could do with some improving. I was only trying to help. I'll ignore your tone this time.

Ask other people if they have had the patience to go through your messy diagram.

 

[Vidatu]

I don't want to get in a fight, so I apologize. However, I do feel that you were overly snippy earlier.

Also, my diagram. is fine. Neatness is not a requisite for proficiency, nor is the diagram important in this case. As I said, I'm sure the formulas are correct, and I wrote them in digitally.

In any case, this isn't helping anyone. If you can see my problem, please point it out. If not, have a good day and leave me and my drawings alone.

 

[Ronka]

No need to fight folks :) why don't we fight the problem :)

could you make a better draw vidatu? cause i as well have a lil problem reading your draw

 

[Vidatu]

Hm. I had the arrows going the wrong way when I first uploaded this. All better now.

 

[Shooting Star]

Hey Vidatu,

I can assure you that I had absolutely no intention of being snippy. If I made you feel bad, I’m sorry. Let’s forget all this.

And this diagram is fantastic.

 

[Vidatu]

No problem. I've had a long day of solving shear/moment diagrams, and should probably go to bed soon. I guess I'm not in the best of moods.

So, anyway, can anyone see where I messed up?

 

[D H]

Homework Equations

$$\Sigma M_x = A_z + 0.4B_z - 0.75C_y - 5 = 0$$
$$\Sigma M_y = A_z + 0.75C_x = 0$$
$$\Sigma M_z = -A_y - 0.4B_x - 10 = 0$$
$$\Sigma F_x = C_x + B_x + +7 = 0$$
$$\Sigma F_y = C_y - A_y - 12 = 0$$
$$\Sigma F_z = B_z - A_z - 5 = 0$$

The Attempt at a Solution

Here are the real answers, and when I put my equations into a computer, it solves them and gets these. As such, I know my equations are correct. My problem just pops up when I try and solve for each unknown. If anyone could help me see where I went wrong, I'd be very grateful to them.

$$\bmatrix A_y \\ A_z \\ B_x \\ B_z \\ C_x \\ C_y \endbmatrix = \bmatrix -53.60 \\ 87.00 \\ 109.00 \\ -82.00 \\ -116.00 \\ 65.60 \endbmatrix \;\text{kN}$$

Those solutions don't agree with the relevant equations. Look at the expressions for $\sum F_y$ and $\sum F_z$ with those numbers. Either these numbers or your equations are incorrect.

 

[Vidatu]

Um, yeah. That's because I messed up typing in the equations. I've fixed that now.