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

Tags: Equations for Plate Support