Plate Uniformly Distributed Load - Supported on Three Edges, One Short Edge Fixed UDL

Written by Jerry Ratzlaff on . Posted in Structural

Plate Uniformly Distributed Load - Supported on Three edges, One Short Edge Fixed UDL Formula

\(\large{ M_A =  \alpha_a \; w\; a\; b   }\)

\(\large{ M_{B1} =  \beta_b \; w\; a\; b   }\)

\(\large{ M_{B2} =  \alpha_b \; w\; a\; b   }\)

\(\large{ M_a^\mu =  \frac{ \left(1\;-\;\mu\;\mu_r \right) \;M_a \;+\; \left(\mu\;-\;\mu_r \right) \;M_b}{ 1\;-\; \mu_r}   }\)

\(\large{ M_b^\mu =  \frac{ \left(1\;-\;\mu\;\mu_r \right) \;M_b \;+\; \left(\mu\;-\;\mu_r \right) \;M_a}{ 1\;-\; \mu_r}   }\)

Where:

\(\large{ \alpha_a, \alpha_b }\)  (Greek aymbol alpha) = length to width ratio coefficient

\(\large{ \beta_a }\)  (Greek aymbol beta) = length to width ratio coefficient

\(\large{ \omega }\)  (Greek symbol omega) = load per unit area

\(\large{ b }\) = longest span length

\(\large{ M }\) = maximum bending moment

\(\large{ \mu }\)  (Greek symbol mu) = Poisson's ratio of plate material

\(\large{ a }\) = shortest span length

\(\frac{b}{a}\)\(\alpha_a\)\(\alpha_b\)\(\beta_a\)
1.0 0.0273 0.0334 -0.0892
1.1 0.0313 0.0313 -0.0867
1.2 0.0348 0.0292 -0.0820
1.3 0.0378 0.0269 -0.0760
1.4 0.0401 0.0248 -0.0688
1.5 0.0420 0.0228 -0.0620
1.6 0.0433 0.0208 -0.0553
1.7 0.0441 0.0190 -0.0489
1.8 0.0444 0.0172 -0.0432
1.9 0.0445 0.0157 -0.0332
2.0 0.0443 0.0142 -0.0338

Tags: Equations for Plate Support