# Beam vs string

1. Jul 16, 2010

### Excom

Hallo

I have been thinking about when beam starts to behave like string.

My questions are: How much tension do you need to put on a beam before it starts to behave like a string? And when does the behaviour become purely string like?

Thanks

2. Jul 16, 2010

### Studiot

A beam can never behave like a string.

A string can only support tension; it cannot support compression. This is fundamental.

It is also fundamental to beam action that there is both tension and compression.

So anything capable of acting as a beam can support compression and cannot be a string.

3. Jul 18, 2010

### Cleonis

The beam acts as a beam when the upper half is under compression, and the bottom half is under tension.

If you take a long enough section of beam, and you can apply enough tension, then there will be a tension level where no part of the beam is under compression any more.

My hunch is that you would need to compute the force difference between top and bottom. Given a particular length of the beam, a particular mass per length unit, and a particular height of the beam you can compute how much force difference there must be between top and bottom of the beam.
Then you have the amount of tension that must be applied at the ends so that there is no longer any compression in the beam.

4. Jul 19, 2010

### Studiot

Cleonis you are quite correct that you can eliminate the compressions by 'prestressing'

The beam loading then becomes one of combined axial tension plus bending moment.

For a simply supported beam, breadth b and depth d, loaded at the most stressful section (the middle) by a point load Q and under an axial tension P the stress at any point A in the beam is given by

$${S_A} = \frac{P}{{bd}} \pm \frac{{6M}}{{b{d^2}}} = \frac{1}{{bd}}\left\{ {\frac{P}{1} \pm \frac{{6Qx}}{{2d}}} \right\}$$

We can certainly calculate the point at which the prestress just eliminates the compression, but since the moment varies with distance, x along the beam, from zero at the support to a max at the load point, this can only occur at one section at a time.

Equally the equation is nothing like the simple tension in a string. So I will leave it up to otheres to decide if this is 'string action' or not.

5. Jul 22, 2010

### Excom

Thanks for the answers.

Do any of you know some literature about the subject?

6. Jul 22, 2010

### Studiot

Look up combined axial and bending stresses

Here for instance

http://shjwc.sau.edu.cn/jpk/cllx/50/4/Chapter%208-Combined%20Bending%20Stresses.doc [Broken]

Note download the target and rename to docx.