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Simply Supported Uniform Loading over 2/3 of plate from fixed edge Stress and Deflection Equation and C
Flat Rectangular Plate, Three Edges Fixed, One Edge (a) Simply Supported Uniform Loading over 2/3 of plate from fixed 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 Uniform Loading over 2/3 of Plate
Rectangular plate;
Three Edges Fixed 
Uniform Loading over 2/3
of plate from fixed edge 
At x = 0, z = 0
Stress
Reaction Force
Stress at x = 0, z = 0.6b
and 
At x = 0, z = b
Reaction Force
At x = ± a/2, z = 0.4b
Stress
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_{1,2,3,4} = Constant From Table A
γ_{1,2,3} = Constant From Table A
Table A
a/b

.25

0.50

0.75

1.0

1.5

2.0

3.0

β_{1}

0.020

0.080

0.164

0.274

0.445

0.525

0.566

β_{2}

0.003

0.016

0.044

0.093

0.193

0.252

0.286

β_{3}

0.012

0.043

0.081

0.108

0.112

0.091

0.066

β_{4}

0.031

0.111

0.197

0.255

0.284

0.263

0.204

γ_{1}

0.115

0.230

0.334

0.423

0.517

0.542

0.543

γ_{2}

0.002

0.015

0.048

0.088

0.132

0.139

0.131

γ_{3}

0.125

0.250

0.345

0.396

0.422

0.417

0.405

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