﻿ Circular Plates Bending Moment Calculator | Distributed load

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 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.  ### INITIAL DATA

D - Plate outer diameter;

d - Plate hole diameter;

t - Plate thickness;

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

Di - 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

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 (q)

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:

Yd = 0 - Deflection at the inner edge;

θd = 0 - Slope at the inner edge;

YD = 0 - Deflection at the outer edge;

MrD = 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);

Di - 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

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) -