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Loading Uniformly decreasing from fixed edge to simply supported edge Stress and Deflection Equatio
Flat Rectangular Plate, Three Edges Fixed, One Edge (a) Simply Supported Loading Uniformly decreasing from fixed edge to simply supported edge Stress and Deflection 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 Load Uniformly Decreasing from Fixed Edge to Simply Supported Edge Plate
Rectangular plate;
Three Edges Fixed 
Load uniformly decreasing from fixed
edge to simply supported edge 
At x = 0, z = 0
Stress
Reaction Force
Stress at x = ±a/2, z = 0.4b
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}

0.018

0.064

0.120

0.192

0.303

0.356

0.382

β_{2}

0.019

0.068

0.124

0.161

0.181

0.168

0.132

γ_{1}

0.106

0.195

0.265

0.323

0.383

0.399

0.400

γ_{2}

0.075

0.152

0.212

0.245

0.262

0.258

0.250

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