# Homework Help: Calculate The Moments about the Point A, [Guidance needed]

1. Nov 5, 2009

### Dellis

Hi, I need some guidance regarding this exercise,

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

Calculate The Moments about the Point A

I attached the visual representation of the exercise, it has common A(PIN)---------B(ROLLER) element, then two forces going down( 5 Kips & 2 kips ), then the distances about point A and B( 6 ft-8ft-10ft )

2. Relevant equations

M= F x D

3. The attempt at a solution

I need guidance, I tried to do it myself and got up to here, if is wrong please guide me to the right route.

$$\Sigma$$M= 5(6)-7(14) + 2( 24 )= 30-98-48= -20

#### Attached Files:

• ###### Calculate Moments.JPG
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Last edited: Nov 5, 2009
2. Nov 5, 2009

### ronaldlover

as far as i am concerned, you are off to the right start.
I, as well, only got up to this far.
Meassage me when you make a break through. i would love to hear about it.

3. Nov 5, 2009

### Dellis

Really?, then we need to see others input on the exercise, that would be a good thing.

I am here wondering what if that is the actual answer to the exercise?, it is asking for the Moment right?, and basically that's all I got up to.

Lets wait for somebody else to give their input, clarify the situation.

4. Nov 5, 2009

### rl.bhat

Reaction on A and B is, say, R1 and R2.
What is R1 + R2?
Reaction on B is not equal to (5 + 2).
Whether the rod is in equilibrium? Whether the roller is free to move?

5. Nov 6, 2009

### Redbelly98

Staff Emeritus
Since the question asks for the moments (note plural), it seems you are to calculate the individual moments for the loads of 5 kips, 2 kips, and the roller separately.

Is this supposed to be in equilibrium, as rl.bhat asked? What can you say about the sum of the moments in that case?

Also, the roller force is not necessarily 7 kips. There is another force at point A, that you seem to have ignored when balancing all the forces.

6. Nov 6, 2009

### Dellis

But you forget it says ABOUT POINT A, it says nothing about Point B?????

I don't think its supposed to be in equilibrium, it just want the moments about Point A

You think their is a force at point A?, how can that even be found?, 5 - 1?. I don't understand.

Last edited: Nov 6, 2009
7. Nov 6, 2009

### Dellis

But is asking for the moments ABOUT POINT A, why would point B come into the equation? but since you asked there then

Reaction on B would be 10' + 2 kips then?

Last edited: Nov 6, 2009
8. Nov 6, 2009

### rl.bhat

It the system is not in equilibrium, what is the role of roller?
Two forces are acting on the rod in the downward direction. There must be reaction for these forces. According to your calculations, it is acting on B only. What about A? Whether the rod is not attached to the pin at A? If the rod is not in equilibrium, in which direction it is moving? If you take the moments about B due to 5 kips and 2 kips, you can see the moment due to 5 kips is greater that due to 2 kips. Do you mean that the roller roles in either direction? How can you find the moment ignoring B?

Last edited: Nov 6, 2009
9. Nov 6, 2009

### Dellis

I think you're confused by the fact this exercise is not like other common ones where the roller would be all way at the very end?. I never ignored B but you said I ignored A?, how so if 5 kips is part of A?, I didn't ignore B either since 2 kips is part of Point B.

In all honesty I just need some guidance here, I know you're trying to do that and I appreciate it. I think I am on the right path but I only found a moment and as stated above it actually says MOMENTS ABOUT POINT A.

This type of problem is clearly a basic status one but we're thinking too much making it complex.

Last edited: Nov 6, 2009
10. Nov 6, 2009

### stewartcs

The rod is in equilibrium since no other forces are shown acting on it that would cause it to move.

Hence, the sum of the moments about A must equal zero. The sum of the moments about B must equal zero. The reactions at A (since it is pinned it has a horizontal and vertical reaction) and B (since it is a roller it only has a vertical reaction) will be found by summing the forces in the x and y direction. All of your unknowns can be found by doing this.

The problem appears to just want you to calculate each moment about the point A. So just pick a convention (+/-, CW/CCW or whatever you want) and do the math (FxD) noting that the sum of the moments about A is zero.

Also, note that the drawing you attached seems to show that point A is at 6-ft, point B is at 8-ft and the end of the rod is at 10-ft. Hence, the 5 kip load is applied at 7-ft relative to the 6-ft origin. Thus the moment about a resulting from the 5 kip load would be 5 kips times 1 foot = 5 kip-ft (in the direction you chose based on your selected sign convention).

Hope this helps.

CS

11. Nov 6, 2009

### Dellis

Thanks for the very in depth post, I went counter clock wise for the calculations I did.

So you're saying keep on that same route but add the multiplication of 5 x 1 to the

calculation?, I figured when the others said I was ignoring Point A's force that they wanted

me to find it by doing 5 x 1 but didn't tell me, I threw a guess and said 5 + 1 clearly not the

right way.

12. Nov 6, 2009

### stewartcs

I'm saying that you need to find each moment separately and that their sum should be zero.

The 5 kip-ft I gave you was the first moment due to the 5 kip load applied 1 foot from point A (presuming I've interpreted the distances on your drawing correctly). You need to do the same for the reaction at B and the 2 kip load at the end of the beam. Their sum should be zero since the beam is in static equilibrium.

So, there are three moments about point A. The first one was just given to you. Now use the same approach and find the other two.

Hint: Find the reaction at point B (vertical direction) first.

CS

13. Nov 6, 2009

### ronaldlover

I see.
well i agree since it is asking ony for a moment not moments. so therefore there are 3 moments in point A and one was given to you.

CS is on the correct track as far as i can see.

14. Nov 6, 2009

### Dellis

Oh alright, thanks for clearing that up

Last edited: Nov 6, 2009
15. Nov 6, 2009

### Redbelly98

Staff Emeritus
Thanks for chiming in and helping!

Are you sure about this interpretation of the distances given in the figure? To me, it seemed pretty clear that the values were distances in between the different load points. I'm uncomfortable with just assuming the 5 kips point is halfway between points A and B.

16. Nov 9, 2009

### stewartcs

Hi Red,

No I'm not sure at all that's why I said "seems to show". Nevertheless, the OP should be able to tell from the book drawing (which hopefully is more clear and standardized). I can certainly see your point though. Thanks for clarifying.

CS

17. Nov 9, 2009

### Dellis

Ok I tried doing the exercise, but I need somebody to check it for me. please! this is due tomorrow morning, check it for me, I think its correct.

$$\Sigma$$F=

Reaction A - 5 k + 5.57 k - 2 k = 0

Reaction A = 1.43 k

$$\Sigma$$M= 5k x 6ft- Reaction B x 14ft + 2k x 24ft= 0

Reaction B = [30 k ft + 48 k ft]/14 ft

Reaction B = 5.57 k

18. Nov 9, 2009

### stewartcs

Yes, the vertical reactions are equal to 1.43 kips at A and 5.57 kips at B (presuming the distances given are those between the points and not at the points).

CS

19. Nov 9, 2009

### Dellis

Well yea but I figured maybe doing this part would open up the process of finding the moments, in a easier manner?

So if the reaction is 1.43kips at POINT A, then if it is asking for the moments at POINT A

that means I need to do what I learned while doing that other exercise, going from left to

right looking at the distances ABOUT POINT A?, then calculate.

Last edited: Nov 9, 2009
20. Nov 9, 2009

### stewartcs

How did you find the reaction at B? It would have required you to sum the moments about A in order to find the reaction at B. So you probably have already done the work!

Look back a few posts where we talked about starting at point A and calculating each individual moment using FxD.

CS

21. Nov 9, 2009

### Dellis

I thought it was 7?, I guess not then but let me look back at page 1

even though you just told me how to do it there, perhaps I already did do the work here.

22. Nov 9, 2009

### Dellis

Damn I don't get it, when I looked at this problem again today it reminded me of the
other one I just did, so I attacked it again with the mindset of knowing how to approach it but clearly I a running into issues understanding the distances and all that again.

23. Nov 9, 2009

### stewartcs

OK, here is a summary of what you should have done:

$$\Sigma{F_y} = R_{Ay} -5 + R_{By} -2 = 0$$

which reduces to:

$$R_{Ay} + R_{By} = 7$$ kips

Now, since there are two unknowns, we need another equation in order to solve them simultaneously right?...So summing the moments about A we have:

$$\Sigma{M_A} = 5(6) - R_{By}(14) + 2(24) = 0$$

Solving for the reaction at B we get:

$$14R_{By} = 78$$

$$R_{By} = 5.57$$ kips

Now plug that into the first equation and you get your 1.43 kips for the vertical reaction at A.

So, to find the moments about point A (now that you know the missing reaction at B)...just use FxD....you'll end up with three moments that will sum to zero...

Note that we have found the moments already in the process of finding the reactions, so just pick them out from the calculations above.

Does this help?

CS

24. Nov 9, 2009

### Dellis

Yeah you broke it down in a more calculated manner, where I can see what is going on, I will be here trying to figure things out and post my solution.

25. Nov 9, 2009

### stewartcs

Always try to approach these problems systematically like this...it will greatly simplify them for you.

CS