# 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