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### Loading Uniformly decreasing to zero at 2/3b Stress and Deflection Equation and Calculator

Flat Rectangular Plate, Three Edges Fixed, One Edge (a) Simply Supported Loading Uniformly decreasing from fixed edge to zero at 2/3b 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 Loading Uniformly decreasing from fixed edge to zero at 2/3b

 Rectangular plate; Three Edges Fixed Loading Uniformly decreasing from fixed edge to zero 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 = 0.2b if a < b

Reaction Force

Where used:
E = Modulus of Elasticity (lbs/in2)
q = Total load or force to Plate (lbs/in2)
v = Poisson’s ratio (assumed to be 0.3)
t = plate thickness, (in)
a = plate length, (in)
b = plate width, (in)
σb = stress, (lbs/in2)
R = Reaction Force (lbs/in)
β1,2 = Constant From Table A
γ1,2 = Constant From Table A

Table A

 a/b 0.25 0.5 0.75 1 1.5 2 3 β1 0.017 0.056 0.095 0.14 0.201 0.228 0.241 β2 0.019 0.05 0.068 0.098 0.106 0.097 0.074 γ1 0.101 0.177 0.227 0.262 0.294 0.301 0.301 γ2 0.082 0.129 0.146 0.157 0.165 0.162 0.158

Reference:

Roarks Formulas for Stress and Strain, 7th Edition