# Help with a beam experiment

1. May 31, 2014

### Primoz

Hello!
I have a problem/question and would appreciate your thoughts and experience.

So I have a »tip loaded cantilevered beam« as shown in the picture. On it's end there are a force and a torque acting in an unknown direction in the 2D plane.

I have to experimentally determine the force and the torque. Could you help me figure out how could this be done since I don't have any expirience with lab equipment.

I thought about strain gauges, but is it even possible to determine both the force and torque with cleverly arranged strain gauges in this case? And since I don't have much expirience with strain gauges I am concerned about how accurate they are... It's a very indirect method that requires a calculation with a lot of unsure variables such as E-Module, beam cross section etc.

Do you know any simple alternatives how this could be done? It doesn't need to be super accurate, but enough to pull some conclusions from the experiment. (I need to measure the force and torque to compare them to values I calculated with my theoretical model)

BTW: I am most interested in the horizontal component of the force F.

How about if both force and torque would be acting in an unknown direction in 3D space?

Thanks!

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2. May 31, 2014

### Simon Bridge

You can't - there is not enough information to do that.

The best you will be able to manage is to determine the net force or torque on the beam.
If you knew more, like that the force was in the y-x plane and the torque was in the z-x pane then that would be easier.

If you start out with a beam under stress, then a strain guage will not help you - the beam has to start relaxed.
But if you know the material properties of the beam you can figure out the net force on it by it's deformation.

3. May 31, 2014

### Primoz

Yes, the beam will be relaxed at first and then the load will be brought upon it.

So the stress in the beam should be as follows: Coordinate system: x right; z down

Fx -> normal force in x -> normal stress σ in x
Fz -> shear force in z & bending moment around y -> tensile stress τ in z & normal stress σ in x
Tx -> torsion torque -> tensile stress τ
Tz -> bending moment around z -> normal stress σ in x

So when all of this is superpositioned the stress situation is quite complex...
It would be ok if I could determine only the force, but the torque also affects the stress and therefore deformations that we need to measure to determine the force. So I am not quite sure where to position the strain gauge to get useful numbers.

4. May 31, 2014

### Simon Bridge

You realize that torque is force x distance? In other words, it is another force.
This force gets added to the linear force and the total is what you end up measuring.

Where you position the strain gauge will depend on the design of the gauge (consult the manual), how accurate you need to be, and what you know about the beam already.

5. May 31, 2014

### Primoz

Yes, yes - that's exactly what I was trying to say, but apparently I wasn't clear enough... =) - When I measure the strain I cannot determine how much of it was caused by the force F and how much by the torque T (in the picture), right? - So too many unknowns...

I asked if this can even be done, because I had similar concerns and your answer that it cannot be done is still useful! Thanks! =)

6. Jun 2, 2014

### nvn

Primoz: Yes, this perhaps can be done, for the given 2-D plane. Are you using one rectangular rosette strain gauge on each side of your cantilever beam, near the fixed support? Each leg of each strain gauge needs to be labeled, so we can write equations using your strain gauge legs. What is the cross-sectional shape of your beam?

Last edited: Jun 2, 2014
7. Jun 10, 2014

### koolraj09

Without getting into the details, for a 2D case, here's what I thought....we would need two strain gauges that measure strain in x and y directions respectively. That will give the force in horizontal and vertical direction. A "less" stiffer torsional spring can be used to measure the torque applied..though it would not be that accurate. The spring can be connected to an extended portion on the beam, the deflection of spring will indirectly provide the torque.