Bending a Beam to Produce Uniform Tension

[mrh5529]

Hello.

I am attempting to build a fixture which will place uniform tension onto one surface of a rectangular beam. I know that I must force the beam to deflect along a set path, but I am having trouble determining what the equation for this path needs to be. Any guidance on this would be very helpful. Thanks!

Mike

 

[Studiot]

Hello mike, welcome to Physics Forums.

You need to explain you intentions in more detail.

What do you mean by "on one surface"?
What surface? A longitudinal tension along an outer face is called shear!

Tension is normal to some surface. Which would that be in your case?

From what I think you mean, a constant longitudinal tension can be developed by

1) An axial traction load

2) An applied couple

 

[S_Happens]

I wrote a reply, but didn't save it and lost internet connection.

Basically I think it's much more simple than Stuidot alludes to, and also specific to bending.

Putting one face under uniform tension should be as easy as orienting that face away from the center of curvature, then bending with constant curvature.

How you do this depends on what you have available and/or what you want to accomplish. An easy way might be to bend around something that already has constant curvature. If materials and shape might be changing, or if you need specific tension then you'll have to give more details on what you're doing.

 

[Studiot]

An easy way might be to bend around something that already has constant curvature.

The OP asked about a beam, not something bent around a former.

 

[S_Happens]

I didn't think about it in detail, just that it occurred to me as a way to achieve constant curvature in a beam. I imagined pinned ends and pressing the object into the beam. Would this provide difficulty beyond simply applying a load or moment?

Edit- A pin and a roller really so that it's not indeterminate.

 

[Studiot]

I think we need to hear from the mike exactly what he means,

I agree that a constant tension implies a constant curvature.
Since the tension is one half of the bending moment couple it implies a constant moment since $\frac{1}{\rho } = \frac{M}{{EI}}$ as we are told the beam has a constant? rectangular cross section.

A constant moment can only be achieved by applying a couple, not a force which subjects the beam to a variable moment depending upon the distance from the force.
This was my method (2) in post #2.

It has occurred to me that by " constant across a section" mike may mean uniform across an exploratory free body section, similar to the stress block we assume for compression in the concrete that we assume in some theories of reincforced concrete.

Alternatively for an isotropic beam that has developed a full plastic moment both the compression and tension stress blocks will be rectangular at the exploratory section.