# Reactions at beam ends when varying load position - clearing doubts

1. Oct 16, 2013

### kirakun

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

Well actually we were doing a beam experiment in class. It consisted of varying the position of a load and measuring the reactions to eventually analyse the relationship between the distance of load from 1 support with the 2 reactions.

The reactions were provided by two spring balances acting as supports and the readings were noted (In the diagrams I put the spring balance reactions as VA and VB respectively)

My confusion:

As we moved the position of the load, the beam started to incline, we were told to make the beam horizontal before taking any readings. I did not understand why and I still don't. So i decided to make calculations to see if re-aligning was necessary.

Please take a look at the calculations

Eventually i end up with VA and VB being identical in magnitudes.
So i conclude that whether the beam is inclined or not, the readings should have been the same.

However the readings when the beam is inclined and when it is not were not the same.
My understanding is that the springs extended more during inclination and lead to change in readings.
However I think that if we had inclined all the beams by the same angle and varied the load positions, the trend compared with those when the beam was kept horizontal would have been the same.

I would be grateful if you guys could help me out.
Thank you for your time and patience.

#### Attached Files:

File size:
18 KB
Views:
111
• ###### Inclined beam.jpg
File size:
21.7 KB
Views:
237
Last edited: Oct 16, 2013
2. Oct 16, 2013

### haruspex

In the idealised diagrams you posted, you are correct that it should not make any difference. But I wonder whether in practice the attachment points and the centre of mass of the beam were not all in a straight line. Any vertical displacement will start to matter when inclined.

3. Oct 16, 2013

### kirakun

Could you elaborate some more please, I do not understand where u say "the attachment points and the centre of mass of the beam were not all in a straight line"

Even if the there were vertical displacements of the loads, wouldn't the lines of action of the loads still be the same?

4. Oct 16, 2013

### haruspex

Suppose the beam has vertical thickness 2h and a weight is suspended from the top edge of the beam at distance x to the right of the beam's COM. If the beam is now tilted at angle theta to the right, the horizontal distance from the beam's COM to the point of attachment of the weight is x cos(θ) + h sin(θ).

5. Oct 16, 2013

### kirakun

Ohh, now i see. Hmm yes indeed, i did not take the thickness into consideration.
:)