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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.

Preview: Flat Rectangular Plate all edges fixed. uniform loading over small concentric circle of radius r_o calculator

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/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)
r_o - concentric circle radius (in)
σ_b = stress, (lbs/in²)
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	∞
β1	-0.238 7	-0.078	0.011	0.053	0.068	0.067	0.06
β2	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