# Limits of Euler-Bernoulli Beam Theory for Wide Plate in Flexure?

I'm looking for established limits or rules of thumb for the validity/accuracy of Euler-Bernoulli beam equations for particularly wide "beams". For example, a simply supported rectangular plate where the breadth(b) is much larger than the height (h) [e.g. b=120 inches, h=1 inch].

Is there a point at which a simply supported beam where b >> h would deflect more like a plate in plate theory rather than a beam in beam theory? If you can, please provide references. Thank you!

• May find checking out Timoshenko beams useful. Aug 25 '20 at 16:24

For a rectangular simply supported plate with length $$a$$ and width $$b$$ (Roark's Formulas for stress and strain):
$$\sigma_{max} = \sigma_b= \frac{\beta qb^2} {t^2}$$
$$\beta$$ ranges from 0.287 for a=b to 0.75 for a very long and narrow beam. 0.75 would make it equal to a beam. At a=5b ,$$\beta$$ is 0.74.
Approximately at $$a> 5b$$ the plate behaves very similarly to a beam.