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Loading Uniformly Decreasing to 1/3b Stress and Deflection Equation and Calculator.
Flat Rectangular Plate, Three Edges Fixed, One Edge (a) Free Loading Uniformly decreasing from fixed edge to zero at 1/3 b Stress and Reaction Loading Equation and Calculator.
Per. Roarks Formulas for Stress and Strain for flat plates with straight boundaries and constant thickness
Rectangular plate;
Three Edges Fixed One Edge Free 
Loading Uniformly
decreasing from fixed edge to zero at 1/3 b 
At x = 0, z = 0
Stress and Reaction Force
Reaction Force
Stress and Reaction Force at x = 0, z = b
Reaction Force
Where used:
E = Modulus of Elasticity (lbs/in^{2})
q = Total load or force to Plate (lbs/in^{2})
v = Poisson’s ratio (assumed to be 0.3)
t = plate thickness, (in)
a = plate length, (in)
b = plate width, (in)
σ_{b} = stress, (lbs/in^{2})
R = Reaction Force (lbs/in)
β_{1,2} = Constant From Table A
γ_{1,2} = Constant From Table A
Table A
a/b

.25

0.50

0.75

1.0

1.5

2.0

3.0

β_{1}

0.014

0.035

0.047

0.061

0.075

0.080

0.082

β_{2}

0.010

0.024

0.031

0.030

0.025

0.020

0.013

γ_{1}

0.088

0.130

0.146

0.155

0.161

0.162

0.162

γ_{2}

0.046

0.069

0.079

0.077

0.074

0.074

0.082

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