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If I have an acrylic (plexiglass) panel, how can I compute how thick it must be to resist bending.

So, for example, if I have a sheet that is 24" x 36" and supported by the edges only (such as in a large light fixture), how thick does the sheet have to be to be self-supporting so that it does not bend in the middle?

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    $\begingroup$ The answer depends how it is fixed at the edges. Also, any thickness of panel will "bend in the middle" - the question is how much bending is unacceptable for what you want to do. $\endgroup$
    – alephzero
    Jul 21, 2021 at 0:48

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you need to have your acrylic material properties data sheet, such as its modulus of elasticity, E and its max stress, $\sigma s$, and poisons ratio. Usually the acceptable deflection, y ranges between $y<L/180, \ or \ y<L/360$

Then you try different thicknesses, t, till you get the smallest t with acceptable deflection.

Referring to Roark’s Formulas for Stress and Strain, by WARREN C. YOUNG RICHARD G. BUDYNAS seventh edition table 11.4 pp 507 For a rectangular plate simply supported at the edges uniformly loaded with q:

$$y_{max}= \frac{-\alpha qb^4}{Et^3}$$

$$ \sigma max = \sigma b = \frac{\beta qb^2}{t^2}$$

The coefficients, $\alpha \ and \ \beta $ are shown in the following table.

table

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    $\begingroup$ Might need to add that the plate dimensions are $a \times b$ with $a$ the long dimension $\endgroup$
    – D Duck
    Jul 21, 2021 at 8:49

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