# Plate Uniformly Distributed Load - Supported On All Edges

Written by Jerry Ratzlaff on . Posted in Structural

### Plate Uniformly Distributed Load - Supported On All Edges Formula

$$\large{ M_A = \alpha_a \; w\; a\; b }$$

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

$$\large{ \Delta_{max} }$$  (at center)  $$\large{ = \frac{ 0.142 \;w\;a^4 }{ \lambda\;t^3 \left( 2.21 \; \left( \frac{a}{b} \right)^2 \;+\;1 \right) } }$$

$$\large{ \sigma_{max} }$$  (at center)  $$\large{= \frac{ 0.75 \;w\;a^2 }{ t^2 \left( 1.61 \; \left( \frac{a}{b} \right)^3 \;+\;1 \right) } }$$

$$\large{ M_a^\mu = \frac{ \left(1\;-\;\mu\;\mu_r \right) \;M_a \;+\; \left(\mu\;-\;\mu_r \right) \;M_b}{ 1\;-\; \mu_r^2} }$$

$$\large{ M_b^\mu = \frac{ \left(1\;-\;\mu\;\mu_r \right) \;M_b \;+\; \left(\mu\;-\;\mu_r \right) \;M_a}{ 1\;-\; \mu_r^2} }$$

Where:

$$\large{ \Delta }$$ = deflection or deformation

$$\large{ \alpha_a, \alpha_b }$$  (Greek aymbol alpha) = length to width ratio coefficient

$$\large{ \omega }$$  (Greek symbol omega) = load per unit area

$$\large{ b }$$ = longest span length

$$\large{ M }$$ = maximum bending moment

$$\large{ \sigma }$$  (Greek symbol sigma) = maximum stress

$$\large{ \lambda }$$  (Greek symbol lambda) = modulus of elasticity

$$\large{ t }$$ = plate thickness

$$\large{ \mu }$$  (Greek symbol mu) = Poisson's ratio of plate material

$$\large{ a }$$ = shortest span length

$$\frac{b}{a}$$$$\alpha_a$$$$\alpha_b$$
1.0 0.0363 0.0365
1.1 0.0399 0.0330
1.2 0.0428 0.0298
1.3 0.0452 0.0268
1.4 0.0469 0.0240
1.5 0.0480 0.0214
1.6 0.0485 0.0189
1.7 0.0488 0.0169
1.8 0.0485 0.0148
1.9 0.0480 0.0133
2.0 0.0473 0.0118