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Loading Uniformly decreasing fixed edge to zero Equation and Calculator
Flat Rectangular Plate, Three Edges Fixed, One Edge (a) Free Loading Uniformly decreasing from fixed edge to zero at 2/3b Equation and Calculator.
Per. Roarks Formulas for Stress and Strain for flat plates with straight boundaries and constant thickness
Flat Rectangular plate, Three Edges Fixed, One Edge Loading Uniformly decreasing from fixed edge to zero at at 2/3b.
Rectangular plate;
Three Edges Fixed One Edge Free 
Loading Uniformly
decreasing from fixed edge to zero at at 2/3b 
At x = 0, z = 0
Stress and Reaction Force
Reaction Force
Stress and Reaction Force at x = ± a/2, z = 0.4b if a ≥ b or z = 0.2 b if a < 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}

0.017

0.056

0.095

0.141

0.215

0.277

0.365

β_{2}

0.019

0.050

0.068

0.099

0.114

0.113

0.101

γ_{1}

0.102

0.177

0.227

0.263

0.301

0.320

0.336

γ_{2}

0.082

0.129

0.146

0.157

0.163

0.157

0.146

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