Related Resources: calculators
Polygonal Plate All Edges Fixed Stress and Deflection Equation and Calculator
Regular polygonal plate; all edges fixed 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 at the center
Stress at center of straight edge
n

3

4

5

6

7

8

9

10

∞

β_{1}

0.589

0.550

0.530

0.518

0.511

0.506

0.503

0.500

0.4875

β_{2}

1.423

1.232

1.132

1.068

1.023

0.990

0.964

0.944

0.750

α

0.264

0.221

0.203

0.194

0.188

0.184

0.182

0.180

0.171

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
Reference:
Roarks Formulas for Stress and Strain, 7th Edition