# How accurate is axisymmetric beam theory for modeling plate bending?

I often have to do a quick estimate of circular plate deflection and max stress under simple loading scenarios – uniform distributed pressure, central point load, line load, distributed annular pressure – without access to finite element.

Roarke's book has a whole set of formulas for this, but most I feel are pretty complex and cumbersome, and overkill for my usual purposes.

For a circular plate of radius $$R$$, if I model it as an axisymmetric beam of length $$R$$ with cantilevered or guided center boundary, and fixed or simply supported edge boundary as the case may be, will this be a fairly accurate first order estimate of the plate behavior, or will it be way off?

I am most commonly looking for max deflection, max stress, and reaction forces and moments for basic design purposes (e.g. are the bolts strong enough, is the plate thick enough).

I realize I haven't defined "fairly accurate estimate." The rigorous way to do this is plot the plate equation results, the beam approximation results, and finite element and/or real test data, and see how close they are, and in what regimes they diverge. Can someone perhaps identify a study that has done such comparisons?

• I think beam would be way off. However, circular plate also has analytic solution and when you are just checking existing design, the problem leads to a system of linear equations. Apr 1 at 11:19