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### Uniform Loading on Small Concentric Circle on Flat Plate Stress and Deflection Equation and Calculator

Flat Rectangular Plate; all edges fixed. Uniform loading over small concentric circle of radius ro (note definition of r'o) Stress and Deflection Equation and Calculator.

Per. Roarks Formulas for Stress and Strain for flat plates with straight boundaries and constant thickness

 Rectangular plate; all Edges Fixed

Stress at center of long edge:

Stress at center:

if ro < 0.5t

if ro ≥ 0.5t then r'o = ro

Deflection at center:

Symbols used:
E = Modulus of Elasticity (lbs/in2)
W = Total applied load or force to Plate (lbs)
v = Poisson’s ratio (assumed to be 0.3)
t = plate thickness, (in)
a = plate length, (in)
b = plate width, (in)
ro - concentric circle radius (in)
σb = stress, (lbs/in2)
γmax = Deflection (in)
β1,2 = Constant From Table A
α = Constant From Table A

Table A

 a/b 1.0 1.2 1.4 1.6 1.8 2 ∞ β1 -0.238 7 -0.078 0.011 0.053 0.068 0.067 0.06 β2 0.7542 0.894 0.9624 0.9906 1 1.004 1.008 α 0.0611 0.0706 0.0754 0.0777 0.0786 0.0788 0.0791

Reference:

Roarks Formulas for Stress and Strain, 7th Edition

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