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Old Jun 5th 2015, 01:02 AM   #1
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Reaction Force help

Hi guys, I'm currently working on a homework question but I'm a little bit stuck although I do know what I'm meant to be doing. My question asks me to find the torque being caused by a beam pulling down on another. I'll explain a little more the context of it - there is one beam (beam 1) spanning across from point A to point B, and it is fastened on to these points at each end. Right beside that beam (beam 1) which spans across from point A to point B is another beam (beam 2). This beam however only spans half the way out and is attached at point A. Beam 2 is securely attached all the way along beam 1 and is therefore causing it to twist.

So far I know that I need to use the formula: Torque=Force x Radius x sinQ
I have worked out the radius like this: (looking at a cross section of the end of the beams - beam 2 on left and beam 1 on right) I have assumed the pivot is in the centre of beam 1 and the radius is from there to the furthest edge of beam 2. Is this correct or do I need to work it out using rotational equilibrium or something?
sinQ: Would be sin90
Force: I think that I would need to find the reaction force being applied at each end of beam 2 (secured side will be acting up and the side secured to the edge of beam 1 will be acting down). By finding the reaction force that the beam is creating on point A I can then find the reaction force at the other end of beam 2 (I'm not sure how to do that??? Or is it equal except negative?) This is what I'm not sure how to do though. I have the weight and length of all of the beams too.

Any help regarding finding the reaction forces and radius would be greatly appreciated.

Thanks, Alex

Last edited by Alex; Jun 5th 2015 at 01:05 AM.
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Old Jun 5th 2015, 01:14 AM   #2
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Please be more specific in you descriptions. I think I can picture what you are describing, but your statements about fixity at points A and B are not clear.

What do you mean by beam 1 is fastened to A and B at the ends?

The problem is statically indeterminate if the beam is truly fastened.
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Old Jun 5th 2015, 01:28 AM   #3
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Sorry, it's quite hard to describe it all. What I mean by that is one end of Beam 1 is fixed the top of point A and the the other end at the top of point B. The end of Beam 2 is attached at the top of point A and only spans halfway out. Beam 2 is also attached to the side of beam 1. Thanks for the quick reply. Let me know if I need to be more specific.

Alex

Last edited by Alex; Jun 5th 2015 at 01:33 AM.
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Old Jun 5th 2015, 01:40 AM   #4
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Yes you do.

What exactly do you mean by fixed?

This has a specific meaning in beam theory.
It is also known as the support conditions.

Do you understand this, you cannot begin without it.
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Old Jun 5th 2015, 01:43 AM   #5
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No I haven't heard anything about beam theory (although I know about double cantilevers). By fixed I just mean it is bolted. I haven't had to do any questions that involve this. I have only had to know whether they are double cantilevers or simply supported.

Thanks, Alex

Last edited by Alex; Jun 5th 2015 at 01:50 AM.
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Old Jun 5th 2015, 01:54 AM   #6
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Each support can provide three possible reactions in a plane (2D).

These are the vertical and horizontal components and a moment.

Do you understand what statically determinate and statically indeterminate means?
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Old Jun 5th 2015, 02:10 AM   #7
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Yes I understand all of that (very roughly though). I'm still not 100% sure how to find the reaction force out of that though. I just did a bit of research and would I need to use static equilibrium to find the reaction force?

Thanks,
Alex
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Old Jun 5th 2015, 02:22 AM   #8
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OK I see that this is posted in pre-university physics so lets come back to this as an added extra for understanding.

You would never ever bolt down both ends of a simply supported beam, because either the beam will buckle or the bolts will shear. One end has to be free to move.
I will elaborate further at the end.

Anyway, back to your problem.

Both moments and couples are twisting effects.
The difference between a moment and a couple is that the moment depends upon the distance from the point of application and therefore varies with position in its plane of application.
A couple is the same about every point in its plane of application.

The upshot of this is that it matters where you apply a moment, but doesn't matter where you apply a couple to a solid body.

A torque is a form of couple where the turning effect is transferred along some axis and, like the couple, it doesn't matter where you apply it along that axis.
Think of a screwdriver.
You can turn it anywhere along the shaft, not just by the handle.

In relation to your problem this means that the total torque applied by beam 1 on beam 2 can be obtained by considering the weight of beam 2 as acting at its C of G so the torque equals the Wd where d is the distance of the COG of beam 2 from the centre line of beam 1.

How are we doing?

Last edited by studiot; Jun 5th 2015 at 02:25 AM.
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Old Jun 5th 2015, 03:49 AM   #9
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Ahh, that makes a lot of sense in what you are saying. I now have a far better understanding of it all Im not quite sure what you mean by this though?
"total torque applied by beam 1 on beam 2 can be obtained by considering the weight of beam 2 as acting at its C of G so the torque equals the Wd where d is the distance of the COG of beam 2 from the centre line of beam 1."

I'm still not quite sure about the radius though. Is there any working involved in that or is it just a matter of using the distance from the pivot in the centre of beam 1 to the edge (or centre point?) of beam 2. Because if I picked the middle of beam 1 as my pivot I would get a different radius to if I picked the edge of beam 1?

Thanks!
Alex

Last edited by Alex; Jun 5th 2015 at 03:56 AM.
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Old Jun 5th 2015, 04:09 AM   #10
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Have you drawn a diagram yet?

Here is mine. Does it look anything like yours?
Attached Thumbnails
Reaction Force help-beamtorque1.jpg  
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