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Flat Rectangular Loaded Plate Stress and Strain Formula and Calculator
Flat Rectangular Plate; one edge fixed, opposite edge free, remaining edges simply supported Uniform loading over entire plate 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 Uniform loading over entire plate
Rectangular plate; one edge fixed,
opposite edge free, remaining edges simply supported 
Uniform loading
over entire plate 
Stress Maximum at center of fixed edge:
and  R = γ_{1}qb 
Stress Maximum at center of free edge:
and  R = γ_{2}qb 
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 _{max} = maximum 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_{1} = From Table A
β_{2} = From Table A
γ_{1} From Table A
γ_{2} From Table A
Table A
a/b

0.25

0.50

0.75

1.0

1.5

2.0

3.0

β_{1}

0.044

0.176

0.380

0.665

1.282

1.804

2.450

β_{2}

0.048

0.190

0.386

0.565

0.730

0.688

0.434

γ_{1}

0.183

0.368

0.541

0.701

0.919

1.018

1.055

γ_{2}

0.131

0.295

0.526

0.832

1.491

1.979

2.401

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