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

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