Help with weight calculation on panel

Here's a thought in response. It is off the wall though maybe better than nothing.

A simply supported beam gets twice as stiff if twice as wide. This is a simpler case than a beam that's twice as thick, which is MUCH stiffer. A triangular beam acts like a narrow beam at one end, and a wide beam at the other - that's evident.

If we took a beam of constant width, I assert (with very little backup for the position) that we could map the deflections of a triangular beam to it. A point load would no longer be at the center, but at the position on a parallel beam where there is as much area to one side as the triangular beam has. So the equivalent beam is point loaded at one quarter of its length. Now the question of the equivalent beam's width.I make a simplifying, practical assumption. The support at the pointy end has finite width, let's call the width

There you are. Worth possibly as much as you paid for it....

Brian Whatcott Altus OK

Formulas for Stress and Strain, Roark, 4th ed., McGraw-Hill Page 233, Case 64: Edges supported, Distributed load of intensity, w, over the entire surface

Max y = (w * a^4 * (m^2 -1)) / (81 * E * t^3 * m^2) at the center of the triangle where w = unit applied load (lb per sq. in.) a = height of triangle (inches) m = reciprocal of Poisson's ratio E = modulus of elasticity t = thickness of plate (inches)

Jim Y

Thanks Jim, but this is the formula for the triangle being supported at the edges. My case calls for the triangle being supported at the end points only (i.e. the three corners). I still haven't been able to find the answer to this.

Thanks again tough. James

the entire surface

Triangle supported at corner, area at support = 0 stress = infinite strain = infinite

I think you need to re examine the problem.

-- Jonathan

Barnes's theorem; for every foolproof device there is a fool greater than the proof.

To reply remove AT

You won't get an analytical solution for this case because the loading conditions render the assumptions in classic beam or plate theory inappropriate.

Firstly, applying a point load to a plate is always problematic.

More importantly, supporting a plate at its corners only means that just close to the corners there has to be a shear and/or membrane reaction, whereas simple beam or plate theory ignores these contributions.

It is (obviously) possible to work out that total deflection, but only n a case by case basis, there is no one size fits all solution.

Normally we'd use FEA if the deflections are small, or nonlinear structural code if the deflections are large.

You will probably need to model, or think about, your supports - are they pin joints or encastre, fixed or sliders? Or as is most common, none of the above.

Cheers

Greg Locock