Circular Plates under Concentrated Load Calculators

Circular Flat Plates Calculators







Circular Plate with Inner Edge Fixed

In this calculation, a circular plate with outer diameter D, inner diameter d, thickness t is considered. The inner edge of the plate is fixed. The plate is under load w distributed along the diameter d1.

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

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

Circle plate with inner edge fixed
calculation of Circle plate with inner edge fixed

INITIAL DATA

D - Plate outer diameter;


d - Plate hole diameter;


t - Plate thickness;


d1 - Diameter of applied load;


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


w - Load along the circumference d1;


ν - Poisson's ratio;


Е - Young's modulus.

RESULTS DATA

Мri - Bending moment in the radial direction at the calculated point (at any point of Di);


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


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


Yi - Total deflection at the calculated point;


σi - Equivalent stress at the calculated point.

Outer diameter (D)

Inner diameter (d)

Plate thickness (t)

Load (w)

Load diameter (d1)

Diameter for calculation (Di)

Poisson's ratio (ν)

Young's modulus (Е)

Radial moment (Мri)

Tangential moment (Мti)

Angle of slope (αi)

Deflection (Yi)

Equivalent stress (σi)

BASIC FORMULAS

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

Y1 = 0 - Deflection at the inner edge;

α1 = 0 - Slope at the inner edge;

R2 = 0 - Support reaction at the outer edge;

Мr2 = 0 - Radial moment at the outer edge.

INITIAL DATA

D - plate outer diameter;


d - Plate hole diameter;


t - Plate thickness;


d1 - Diameter of applied load;


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


w - Load along the circumference d1;


ν - Poisson's ratio;


Е - Young's modulus.

RESULTS DATA

Мri - Bending moment in the radial direction at the calculated point (at any point of Di);


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


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


Yi - Total deflection at the calculated point;


σi - 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)

-

OTHER CALCULATORS

AREA MOMENTS OF INERTIA
BEAM CALCULATORS
TORSION OF BARS
CIRCULAR FLAT PLATES
BUCKLING
ELASTIC CONTACT
IMPACT LOADS
NATURAL FREQUENCIES
PRESSURED SHELLS
FLUID DYNAMIC
COMPOSITES
SPRINGS
THREAD CONNECTIONS
SHAFT CONNECTIONS
BEARINGS
DRIVES
FATIGUE
HEAT TRANSFER