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Plate Loading Uniformly Decreasing from Fixed Edge to Zero at 2/3 b Stress and Deflection Equation and Calculator
Flat Rectangular Plate; one edge fixed, opposite edge free, remaining edges simply supported loading Uniformly decreasing from fixed edge to zero at 2/3 b Stress and Deflection Equation and Calculator.
Per. Roarks Formulas for Stress and Strain Formulas for flat plates with straight boundaries and constant thickness
Rectangular plate; one edge fixed, opposite edge free, remaining edges simply supported loading Uniformly decreasing from fixed edge to zero at 2/3 b.
Rectangular plate; one edge fixed,
opposite edge free, remaining edges simply supported. 
Uniformly decreasing
from fixed edge to zero at 2/3 b. 
Stress Maximum at center of fixed edge:
and  R = γqb 
Symbols used:
q = Applied Load or Force to Flat Area of Plate (N/m^{2}, lbs/^{2})
v = Poisson’s ratio (assumed to be 0.2)
t = plate thickness, (m, in)
a = plate length, (m, in)
b = plate width, (m, in)
σ = stress, (N/m^{2}, lbs/in^{2})
R = Reaction force per unit length (N/m, lbs/in) normal to the plate surface exerted by the boundary support on the edge of the plate.
β = Constant From Table A
γ = Constant From Table A
Table A
a/b

0.25

0.50

0.75

1.0

1.5

2.0

3.0

β

0.033

0.094

0.146

0.200

0.272

0.339

0.400

γ

0.148

0.233

0.277

0.304

0.330

0.339

0.340

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