Rectangular Plate Bending Alpha · 2026-09-02
Maximum stress, deflection and edge reaction of a uniform-thickness rectangular plate
Rectangular Plate Bending — Coefficient-Table Method
This calculator gives the maximum stress, deflection and edge reaction of a uniform-thickness rectangular plate carrying a transverse load, from the classical coefficient-table method (thin-plate, small-deflection theory). Unlike a circular plate, a rectangular plate has no simple closed-form solution: the response is read from coefficients tabulated against the side ratio a/b and then put into a short formula.
How a result is produced:
- The side ratio r = a/b is formed — this is the only table argument, and a enters the calculation in no other way.
- r is clamped to the range covered by the table for the selected case. Values are never extrapolated: the curves have already flattened out by a/b \approx 4, so extrapolating would overestimate.
- The coefficients \alpha, \beta (and \gamma where given) are interpolated linearly in a/b.
- They go into the formula for the selected case, for example \sigma_{max} = \beta q b^2 / t^2 and y_{max} = -\alpha q b^4 / (E t^3).
Two things worth knowing before you read the numbers:
- The short side b is the reference length. Every coefficient is defined against b, never against the long side or the area.
- The location of maximum stress depends on the support condition — it is not always at the centre. A free edge or a fixed edge moves the peak onto that edge, so the calculator reports the location next to the value.
Coefficients are tabulated for \nu = 0.3 and interpolated in a/b; several cases carry only 2-3 significant figures. Not valid beyond the small-deflection limit (|y| \lesssim t/2).
Engineering data
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