Circular Flat Plates Calculators

Circular Plate with Outer Edge Simply Supported and Inner Edge Fixed Under Distributed Load

In this calculation, a circular plate with outer diameter D, inner diameter d, thickness t is considered. The outer edge of the plate is simply supported and the inner edge is fixed. The plate is under linearly varying load taking a value q at the outer edge and distributed up to diameter d₁, at which q = 0.

As a result of calculations, the bending moments M in the radial and tangential directions, angle of plate inclination α_i, deflection Y_i and equivalent stresses σ_i at the calculated point, lying on a circle with diameter D_i are determined.

For the calculation, the elastic modulus E and Poisson's ratio ν of the plate should be specified.

Circle plate with outer edge simply supported and inner edge fixed under distributed load

calculation of Circle plate with outer edge simply supported and inner edge fixed under distributed load

INITIAL DATA

D - Plate outer diameter;

d - Plate hole diameter;

t - Plate thickness;

d₁ - Load limiting diameter (load applied from diameter D to d₁);

D_i - Diameter at which the bending moment, slope, stress and deflection are calculated;

q - Value of distributed load at diameter D;

ν - Poisson's ratio;

Е - Young's modulus.

RESULTS DATA

М_ri - Bending moment in the radial direction at the calculated point (at any point of D_i);

М_ti - Bending moment in the tangential direction at the calculated point;

α_i - Slope angle of the plate at the calculated point;

Y_i - Total deflection at the calculated point;

σ_i - Equivalent stress at the calculated point.

Metric Imperial

Outer diameter (D)

Inner diameter (d)

Plate thickness (t)

Load (q)

Load diameter (d₁)

Diameter for calculation (D_i)

Poisson's ratio (ν)

Young's modulus (Е)

Radial moment (М_ri)

Tangential moment (М_ti)

Angle of slope (α_i)

Deflection (Y_i)

Equivalent stress (σ_i)

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BASIC FORMULAS

Bending moments, slope, deflection and stress are determined by parametric equations depending on boundary conditions:

Y_d = 0 - Deflection at the inner edge;

θ_d = 0 - Slope at the inner edge;

Y_D = 0 - Deflection at the outer edge;

M_rD = 0 - Radial moment at the outer edge.

INITIAL DATA

D - Plate outer diameter;

d - Plate hole diameter;

t - Plate thickness;

d₁ - Load limiting diameter (load applied from diameter D to d₁);

D_i - Diameter at which the bending moment, slope, stress and deflection are calculated;

q - Value of distributed load at diameter D;

ν - Poisson's ratio;

Е - Young's modulus.

RESULTS DATA

М_ri - Bending moment in the radial direction at the calculated point (at any point of D_i);

М_ti - Bending moment in the tangential direction at the calculated point;

α_i - Slope angle of the plate at the calculated point;

Y_i - Total deflection at the calculated point;

σ_i - Equivalent stress at the calculated point.

MATERIALS PROPERTIES

Material	Young’s modulus Pa (psi)	Poisson’s ratio
Steel	1.86÷2.1×10¹¹ (2.7÷3.05×10⁷)	0.25÷0.33
Cast iron	0.78÷1.47×10¹¹ (1.1÷2.1×10⁷)	0.23÷0.27
Copper	1.0÷1.3×10¹¹ (1.45÷1.9×10⁷)	0.34
Tin bronze	0.74÷1.22×10¹¹ (1.1÷1.8×10⁷)	0.32÷0.35
Brass	0.98÷1.08×10¹¹ (1.4÷1.6×10⁷)	0.32÷0.34
Aluminum alloy	0.7×10¹¹ (1.0×10⁷)	0.33
Magnesium alloy	0.4÷0.44×10¹¹ (5.8÷6.4×10⁶)	0.34
Nickel	2.5×10¹¹ (3.6×10⁷)	0.33
Titanium	1.16×10¹¹ (1.7×10⁷)	0.32
Lead	0.15÷0.2×10¹¹ (2.2÷2.9×10⁶)	0.42
Zinc	0.78×10¹¹ (1.1×10⁷)	0.27
Glass	4.9÷5.9×10¹⁰ (7.1÷8.5×10⁶)	0.24÷0.27
Concrete	1.48÷2.25×10¹⁰ (2.1÷3.3×10⁶)	0.16÷0.18
Wood (along the grain)	8.8÷15.7×10¹⁰ (12.8÷22.8×10⁶)	-
Wood (across the grain)	3.9÷9.8×10¹⁰ (5.7÷14.2×10⁶)	-
Nylon	1.03×10¹⁰ (1.5×10⁶)	-

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