Shearing (torsion?) forces in a square tube 4

[drodrig]

Hi there,

The other day we were in a meeting and this question came up. We had dividing and non clear opinion.

We have some carbon fiber reinforced expoy square tubes. A square of 50 mm side, 0.2 mm thick and 300 mm long. Have a look to the attached picture

http://files.engineering.com/getfile.aspx?folder=4d09cc75-ca31-482b-8132-0149c270173e&file=box.png

Let's say the box is glued to a table (lower face fixed) and we make a force on the upper face.

The first question is if this is just shearing or could be named as torsion.

Then we were discussing why it is so stiff, does it depend on the inertia of the walls? the corners? elastic modulus?

One can have very thick walls, high elastic modulus but paper corners and it would bend...

What do you think??

 

[rb1957]

i'd describe this as shear, 'cause i see a continuous distributed reaction and i don't see the tube displacing as if loaded by torque.

i think the stiffness of this tube is determined by the moment ability of the lower corners; part of this will be dependent on the load transfer out of the tube into the supporting plate. once you lose this i think the tube can continue to react the load, reacting the off-set shear with a couple.

of course, the sides have to react transverse shear (as well).

Quando Omni Flunkus Moritati

 

[trainguy]

Agree with rb, but I'd consider that the upper corners help as well. If it's fully glued to the table, and you push to failure, you'll get 4 plastic hinges, not 2. The top will remain horizontal.

tg

 

[rb1957]

agree with tg !

Quando Omni Flunkus Moritati

 

[GregLocock]

Given that it is CF I bet you find it is very hard to estimate the stiffness or deflection in that scenario. It will depend almost entirely on the details of the fibre orientation and exact geometry of the corners.

Cheers

Greg Locock


New here? Try reading these, they might help FAQ731-376

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[hokie66]

Not torsion, and shear is unlikely to control. It is just a rigid frame in bending. Agree with Greg that the fibre orientation will control the stiffness and the strength.

 

[drodrig]

Hi there,

Thank you for the answers,

But I'm a bit confused;

On one hand we have shearing but everything depending on the corners (so, according to this, the wall thickness-inertia- and elastic modulus don't matter?)

On the other hand bending; I don't see the bending; it's not the typical beam.

The fibers are placed at +/-45º; but this doesn't matter; the question is more general. What is making the square stronger

Thanks to all!

 

[dhengr]

drodrig:
I can’t see your sketch in that png format, but looking at an end view of your tube section; the walls are .2mm thick, the four sides are 50mm in width or height and 300mm long, with a radius at the corners, and the bottom side glued to the table. If you applied a lateral load in the plane of the top side, and parallel to the 300mm length, that would induce a shearing force (reaction force/stress) in the two vert. sides. When you apply a lateral load in the plane of the top side perpendicular to the 300mm length, this causes the tube to parallelogram in shape, the two vert. sides leaning over by theta degrees. This lateral force is resisted by bending moments at the four corners of the tube; and the only shear stress involved is that which is related to this bending, and this was Hokie’s ref. to (portal) rigid frame bending. While your load is sort of a shearing load the way it is applied, it is reacted as a function of the way the shape sees it in each orientation, thus our resistance to calling it ‘shearing.’

The thickness moment of inertia and modulus of elasticity do make a difference, they are what contribute to resisting these moments, rotations and deflections. If these moments where the only thing to worry about wrapping 90̊ to the 300mm length would be the best fiber orientation, and laying the fibers parallel to the 300mm length would be the worst, and each orientation has some different material properties. The +/- 45̊ wrap is a good compromise. The wall thickness (increased), and lengths of the sides (decrease) influence the results greatly, and would reduce stresses and deflections. Maybe three layers would be better with the two outer layers wrapped 90̊ to the 300mm length and a middle layer wrapped at +/- 45̊. More generous corner radii will be an improvement too.