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Load Uniformly Decreasing from z = 0 to z = (1/3) b Flat Rectangular Plate Equation and Calculator
Flat Rectangular Plate, Two Edges Fixed, Two Edges Free Load Uniformly Decreasing from z = 0 to z = (1/3) b Equation and Calculator.
Per. Roarks Formulas for Stress and Strain for flat plates with straight boundaries and constant thickness
Flat Rectangular plate, Two Edges Fixed, Two Edges Free Load Uniformly Decreasing from z = 0 to z = (1/3) b.
Rectangular plate;
Two Edges Fixed Two Edges Free 
Load Uniformly
Decreasing from z = 0 to z = (1/3) b 
At x = 0, z = 0
Stress and Reaction Force
Reaction Force
Stress and Reaction Force at x = 0, z = 0.2b
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

.125

0.25

0.375

0.5

0.75

1.0

β_{1}

0.025

0.052

0.071

0.084

0.100

0.109

β_{2}

0.014

0.028

0.031

0.029

0.025

0.020

γ_{1}

0.193

0.217

0.170

0.171

0.171

0.171

γ_{2}

0.048

0.072

0.076

0.075

0.072

0.072

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