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

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