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Regular polygonal plate Stress and Deflection Equation and Calculator
Regular polygonal plate; all edges simply supported with uniform loading over entire plate Stress and Deflection Equation and Calculator.
Per. Roarks Formulas for Stress and Strain for flat plates with straight boundaries and constant thickness
Regular Polygonal Plate
Uniform Loading over entire plate 
Stress at center
Deflection
Maximum slope at center of straight edge
n

3

4

5

6

7

8

9

10

15

∞

β

1.302

1.152

1.086

1.056

1.044

1.038

1.038

1.044

1.074

1.236

α

0.910

0.710

0.635

0.599

0.581

0.573

0.572

0.572

0.586

0.695

ε

1.535

1.176

1.028

0.951

0.910

0.888

0.877

0.871

0.883

1.050

Where:
q = Applied load (force) (lbs/in^{2})
v = Poisson’s ratio (assumed to be 0.3)
E = Modulus of Elasticity (lb/in^{2})
a = Radius of tangent circle (in)
t = Plate thickness (in)
σ = stress, (lbs/in^{2})
n = number of sides
β = Constant from table
α = Constant from table
ε = Constant from table
Reference:
Roarks Formulas for Stress and Strain, 7th Edition