Finding maximum deflection on triangular table

Sep 03, 2003 2 Replies
J

I need to build a horizontal platform to be used as the stand for a life-size statue of a man for display in an art studio. The platform is in the shape of an equilateral triangle, about 36" on each edge, 1/2" thick, made of plywood (material can be different depending on weight requirements). It is virtually a table with three legs in the form of 6" diameter cylinders (18 inches high) centered about 6" from each corner of the triangle. Here's the top view:



. / \ / _ \ / |_| \ / \ / \ / \ / _ _ \ / |_| |_| \ /_________________\


The statue will be standing up, so it will be supported by its two feet/legs in the middle of the platform (I'm told that its feet would be about 12" apart from each other and 4" x 10" in dimension). Its weight is yet unknown since someone else is building it and it's still not complete.



I need to know how to find the maximum deflection of the platform to give me more flexibility deciding on dimensions (e.g. thickness), the material, and the weight before I build the thing.



Any idea how I should go about solving this?



Thanks, James


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J

Thanks for this Greg. So it all boils down to

deflection = (4/3)(WL^3)/(Ebt^3) where, W = weight of statue, L = distance from centre of triangle to center of one of the legs, E = Young's Modulus (1e6 for Plywood), t = platform thickness, b = breath of the cantilever

Do you think that performing two separate deflection calculations with two different b values, then averaging the results would necessarily yield a more accurate result?

Cheers, James

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G

OK, this is roughly analagous to three cantilevers, built into the centre, with a point load applied at the tip.

So, just working on one cantilever, the applied load is one third of the weight of the statue =W/3

The breadth of the cantilever, b, is contentious, but 6 inches seems about right.

The length L is the distance from the statue to the centre of the leg,

15 inches

The thickness t is the thickness of the plywood

E is the Young's modulus of the tabletop

I=(1/12)*b*(t^3)

deflection=W/3*(L^3)/(3*E*I)

This should be conservative. Incidentally I think Brian proposed a similar solution,

Cheers

Greg Locock

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