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

Written by Jerry Ratzlaff on . Posted in Structural

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

$$\large{ M_{A1} = \beta_a \; w\; a\; b }$$

$$\large{ M_{A2} = \alpha_a \; w\; a\; b }$$

$$\large{ M_B = \alpha_b \; w\; a\; b }$$

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

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

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 0.0334 0.0273 -0.0892
1.1 0.0349 0.0231 -0.0892
1.2 0.0357 0.0196 -0.0872
1.3 0.0359 0.0165 -0.0843
1.4 0.0357 0.0140 -0.0808
1.5 0.0350 0.0119 -0.0772
1.6 0.0341 0.0101 -0.0735
1.7 0.0333 0.0086 -0.0701
1.8 0.0326 0.0075 -0.0668
1.9 0.3316 0.0064 -0.0638
2.0 0.0303 0.0056 -0.0610