Plate Deflection Calculator v1

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Plate deflection calculator


A loaded circular plate will deflect and a hole in its centre will cause it to deflect still further.

Whilst its predictability is not straightforward, this deflection and the consequent stresses can be determined within acceptable levels of accuracy if the maximum deflection is no more than 10% of its outside diameter and the material continues to obey Hooke's law.

This calculation procedure is not only useful for circular plates but it may also be applied to circular regions within plates that do not have a circular perimeter.


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Plates provides deflections and stresses in loaded circular disks and rings with; six edge support options and four possible loading conditions offering a total of 44 different combinations.

The plate deflection calculator is applicable to any circular ring or disk of constant cross section whose material obeys Hooke's law and deflects less than 10% of its major diameter. It identifies radial, tangential and shear stresses that can be combined using CalQlata’s Combined Stress calculator.

Irrespective of where you apply your load, Plates will calculate the reactions at its inside and outside edges and also at your designated radius between the two.

You can select the material for your disc (or ring) from CalQlata's Metals and Copper Alloys databases or from our SAE carbon steel properties page.

For help using this calculator see Technical Help

Plate Deflection Calculator - Options

The calculation options in Plates are for various combinations of edge support associated with a particular loading condition. See Plate Supports and Plate Loading Conditions below for a description of each. All calculation options require the same input data (except Disks which needs no inside diameter) and provides the same output data as follows:

You enter: and the plate deflection calculator will provide:
  • Plate thickness
  • Load per unit length
  • Outside diameter
  • Inside diameter (rings only)
  • Load diameter
  • Radius of calculated results
  • Young's modulus
  • Poisson's ratio
  • Tangential stress @ OD
  • Radial stress @ OD
  • Circumferential stress @ OD
  • Tangential bending moment @ OD
  • Radial bending moment @ OD
  • Shear force @ OD
  • Deflection @ OD
  • Slope @ OD (θₒ)
  • Tangential stress @ r
  • Radial stress @ r
  • Circumferential stress @ r
  • Tangential bending moment @ r
  • Radial bending moment @ r
  • Shear force @ r
  • Deflection @ r
  • Slope @ r
  • Tangential stress @ r
  • Radial stress @ r
  • Circumferential stress @ ID
  • Tangential bending moment @ ID
  • Radial bending moment @ ID
  • Shear force @ ID
  • Deflection @ ID
  • Slope @ ID

Plate Supports:

Edge supports are expressed as ‘outside edge’-‘inside edge’ for each ‘Ring’ calculation option and ‘outside edge’ for each ‘Disk’ calculation option. For example, a calculation option that states ‘Fixed-Free’ means that the outside edge of the Ring is ‘fixed’ in space (all movement is prevented) and the inside edge is unsupported (free to move in any direction). Support combination options available are listed below. Refer to our ‘Definitions’ page on this website for a definition of each support type.

Simple-Free, Simple-Guided, Simple-Simple, Simple-Fixed

Fixed-Free, Fixed-Guided, Fixed-Simple, Fixed-Fixed

Guided-Simple, Guided-Fixed

Free-Simple, Free-Fixed

Plate Loading Conditions:

The following loading conditions can be applied to your Disk or Ring:


A circular linear force per unit length applied at your defined radius.

Pressure (uniform)

A circular annulus of uniform pressure applied between the outside edge of your Disk or Ring and your defined radius.

Pressure (linearly variable)

A circular annulus of pressure varying linearly from a maximum value at the outside edge of your Disk or Ring to zero at your defined radius.

Point Load (centre of disk only)

A force applied uniformly over a small diameter to the centre of your Disk.

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