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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 r_{o} (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. Uniform loading over small concentric circle of radius r_{o}.
Rectangular plate;
all Edges Fixed 
Stress at center of long edge:
Stress at center:
if r_{o} < 0.5t
if r_{o} ≥ 0.5t then r'_{o} = r_{o}
Deflection at center:
Symbols used:
E = Modulus of Elasticity (lbs/in^{2})
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)
r_{o}  concentric circle radius (in)
σ_{b} = stress, (lbs/in^{2})
γ_{max} = Deflection (in)
β_{1,2} = Constant From Table A
α = Constant From Table A
Table A
a/b

1.0

1.2

1.4

1.6

1.8

2.0

∞

β_{1}

0.238 7

0.078

0.011

0.053

0.068

0.067

0.06

β_{2}

0.7542

0.8940

0.9624

0.9906

1.0000

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