KEVOS® MAKEOS · Strength
Circular Flat Plate under Pressure
What stress and deflection does uniform pressure cause in this round plate?
Maximum bending stress and centre deflection of a uniformly loaded circular flat plate with clamped or simply supported edges (small-deflection theory).
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Edge support | choice | Clamped for a plate welded or bolted rigidly all round; simply supported for a plate resting on a gasket or ledge. |
| Radius to the edge support | mm | Radius at which the plate is supported (gasket or bolt-circle radius as appropriate). |
| Plate thickness | mm | Minimum plate thickness. |
| Uniform pressure | MPa | Pressure difference across the plate (1 MPa = 10 bar). |
| Elastic modulus | GPa | Elastic modulus from the material data sheet or an approved materials database (steel is typically about 200 GPa). |
| Poisson’s ratio | Poisson’s ratio of the material (about 0.3 for steel). | |
| Allowable bending stress | MPa | Allowable bending stress from your design code. |
Method and formulas
- Plate rigidity D = E t³ ÷ 12(1 − ν²).
- Clamped: σmax = 3pa² ÷ 4t² at the edge; δ = pa⁴ ÷ 64D.
- Simply supported: σmax = 3(3 + ν)pa² ÷ 8t² at the centre; δ = (5 + ν)pa⁴ ÷ 64(1 + ν)D.
- Example: a 12 mm clamped plate of 100 mm radius at 1 MPa has σmax = 52.083 MPa and δ = 0.049371 mm.
Limitations
- Small deflections only (δ less than about half the thickness); larger deflections need membrane theory.
- Real edges lie between clamped and simply supported; bolted flanges and pressure vessel heads must follow their codes.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Check blind flanges, cylinder end caps and covers
- Size a window or inspection cover
- Compare clamped and simply supported edges
Who it is for
- Design engineers
- Structural and mechanical engineers
- Engineering students
What you get
- Maximum bending stress and location
- Centre deflection
- Deflection-to-thickness ratio
Interpreting the result
- If unsure of the edge condition, check both cases and use the worse result.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 288–290. Topic reference; no source tables or recommended settings are reproduced.
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