• Second moment of area moment of inertiaSecond area moment calculation and radius of gyration of common shapes about weak and strong axes
  • Cubic orientation of primary and shear stresses and principal stress cosine rotationCombine primary and shear stresses into equivalent and principal stresses & their cosines
  • Nucleus and electron shells of atomic elementFind, sort and reorganise the properties of nature's atomic elements with active periodic table
  • Formulas included in Engineering PrinciplesCalculate unknowns in principle engineering formulas: stress, moments, power, energy, capstans, fluids, etc.
  • Properties of a triangle with inscribed and circumscribed circlesCalculate the properties of triangles and triangular configurations including inscribed and circumscribed circles
Area Moment calculation1 Combined Stress calculation2 Elements database3 Engineering Principles calculation4 Trigonometry calculation5
access to the technical calculator
Technical Help 2ᴺᴰ Moment of Area 2ᴺᴰ Moment of Area+ Added Mass & Drag Areas & Volumes Balancing (rotary) Beam Strength Beam Strength+ Bearings (low friction) Bearings (plain) Bending Moments BiMetallic Strip Buoyancy Carbon Steel Catenary Catenary+ Cathodic Protection Centrifugal Force Colebrook & Fanning Column Buckling Combined Stress Co-ordinates Copper Alloys Electrical Current Elliptical Curves Engineering Basics Explosions Fans Fatigue Flange Gaskets Flanges Floors Fluid Forces Fluid Numbers Friction Galvanic Corrosion Gears Hardness Conversion HPHT Flexible Pipe Lift Rigging Logs & Trig Machining Tolerances Metal Properties Mode Shapes Ocean Waves Optical Lenses Padeyes Partial Pressures Piling Pipe Flow Pipe Flow+ Pipe Strength Plastic Stress in Beams Plate Deflection Pressure Vessels Reel Capacity Resolution of Forces Screw Thread Machining Screw Threads Shafts Shock Loads Spring Strength Spring Coefficients Steel Beam Sizes Stress Concentration Table of the Elements Thermal Conductivity Trigonometry UniQon Upheaval Buckling Velocity & Acceleration Vessel Motions Vessel RAOs Vibration Damping Vortex Shedding Walls, Barriers & Tanks Weight Lifting Welding Wire Rope

Circular Plate Deflection Calculator

A plate is generally regarded as a metal block with similar face dimensions (length, breadth, circular, etc.) the shortest dimension of which is at least ten times its thickness. That said, Plates is equally applicable to those of greater thickness as deflection due to shear is included in the calculations.

The calculations included in Plates are primarily intended for the evaluation of diaphragms, membranes, caps and venturi plates associated with pipes, tubes and structures but can be equally applied to 'burst-disks' and in fact any uniformly loaded plate with annulus supports.

Whilst CalQlata's 'Sheets' calculator addresses non-circular plates and sheets, it is possible to use 'Plates' to obtain approximate results local to the loading condition for non-circular plates. However, the loaded area must be sufficiently distant from the edges of the plate to avoid edge effects. The further the loading from the edges, the closer the approximation.

Strength and Rigidity

As with CalQlata's Beams calculator, the strength of a plate is dependent upon the yield stress of the material from which it is manufactured, thereby defining the maximum load that may be applied before it will permanently deform (or break if brittle), and....

its rigidity is dependent upon its thickness along with the Young's modulus of its material, thereby defining the expected deflection in the plate for any given load

Both the above characteristics will define the behaviour of a plate under load. Refer to Applicability below

Supports

Circular plate deflection calculation edge support options

Fig 1. Various Support Options

Fig 1 shows principal support types. Refer to our Definitions page on this website for a description of each.

Design

When designing a plate for a particular application, you need to define your limiting criteria, e.g.:
1) strength or maximum allowable stress
or
2) rigidity or maximum permissible deflection

You simply alter the material and/or the thickness of your plate and recalculate until you have achieved your strength and rigidity limits, not forgetting of course to add your corrosion allowance (where necessary) to your final plate thickness.

Plate Deflection Calculator - Technical Help

Units

As with all CalQlata's programs, unless otherwise stated, you get out what you put in.
For example:
If you enter a force (F) in lbs and the radii and diameters (r and Ø) in inches, you should enter the Young's modulus (E) in the same units (lbf/in²) and all your output data will be in the same units.

Combined Stress

Plates provides you with two tensile stress results (tangential and radial) and a circumferential shear at three locations: outside edge, inside edge and your designated radius.

These stresses can be combined using CalQlata's Combined Stress calculator.

Multiple / Simultaneous Loading Conditions

Should you have a plate with more than one applied load you simply add the results together at your specified location as described in the example below:

Circular plate deflection calculation muliple loading conditions

Fig 2. Multiple Loading Conditions

Plate Deflection Calculation Example:

Apply the following loading conditions:
1) circular line load (w) of 10/unit length @ Ø: 200
2) annular pressure (p) of 0.23 @ Ø: 200
... to a flat round steel ring, simply supported at its outside diameter and unsupported at its inside diameter, with the following dimensional and material properties:
  Outside diameter (Øₒ): 1000
  Inside diameter (Øᵢ): 100
  Thickness (t): 15
  Young's modulus for the material (E): 207000
  Poisson's ratio for the material (ν): 0.3

Step 1:
Enter input data for Loading Condition 1 (Simple-Free Line-Load Ring) as shown in Fig 2 and copy and paste all data into your spreadsheet

Step 2:
Enter input data for Loading Condition 2 (Simple-Free Uniform Pressure Ring) as shown in Fig 2 and copy and paste all data into your spreadsheet

Step 3:
Add results from both calculations in your spreadsheet

Applicability

As with CalQlata's Beams calculator, Plates only applies to homogeneous materials that obey Hooke's law and plates of constant thickness that retain their principal dimensions during and after deformation.

Therefore, the results obtained where stresses exceed yield for the material and/or deflections are greater than about 10% of the outside diameter will be approximate, and the greater the excess, the greater the approximation.

Further Reading

You will find further reading on this subject in reference publications(4 & 20)

      Go to the calculator
CalQlata™ Copyright ©2011-2017 CalQlata info@calqlata.com Site Map Terms of website use Our Store