KEVOS® MAKEOS · Strength
Circular Cover Plate Design (Thickness for Stress and Deflection)
How thick must this flat circular cover be to carry the pressure within the allowable stress and deflection, and what end force does it put on the bolts?
Design of a flat circular plate or end cover under uniform pressure, with the edge clamped or simply supported: the thickness needed for the allowable bending stress and the thickness needed for the allowable centre deflection, the governing thickness, the stress and deflection at the thickness chosen (as the circular plate tool), and the total pressure force the cover passes to its bolts.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Pressure | MPa | Uniform pressure on the cover (design or test pressure). |
| Unsupported radius | mm | Radius of the unsupported area (to the bolt circle or gasket for a simply supported cover, to the weld for a clamped one). |
| Edge support | choice | How the edge is held. |
| Elastic modulus | GPa | Elastic modulus of the plate. |
| Poisson’s ratio | Poisson’s ratio of the plate. | |
| Allowable bending stress | MPa | Allowable bending stress (your design value). |
| Allowable centre deflection | mm | Largest deflection at the centre you accept (for sealing or fit). |
| Thickness chosen | mm | Thickness you intend to use, before corrosion allowance. |
| Corrosion allowance | mm | Corrosion allowance added to the thickness needed. |
Method and formulas
- Stress: clamped σ = 3 p a² ÷ (4t²) at the edge; simply supported σ = 3(3 + ν) p a² ÷ (8t²) at the centre; so t = a √(k p ÷ σ_a).
- Deflection: clamped w = p a⁴ ÷ (64 D); simply supported w = (5 + ν) p a⁴ ÷ [64(1 + ν) D], with D = E t³ ÷ [12(1 − ν²)]; solve for t.
- Thickness needed = the larger of the two plus corrosion allowance; end force = p π a².
- Example: 1 MPa on a 100 mm radius needs 9.4843 mm (stress 6.8465 mm, deflection 9.4843 mm).
Limitations
- Thin-plate theory: deflection should stay below about half the thickness.
- Pressure vessel covers must follow the applicable code formula.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Size a flat end cover for a tank, cylinder or housing
- Check a blanking plate for a test pressure
- Compare clamped and simply supported edges
Who it is for
- Design engineers
- Mechanical engineers
- Fabrication supervisors
What you get
- Thickness for stress and for deflection
- Stress and deflection at the thickness chosen
- Pressure force on the bolts
Interpreting the result
- A simply supported cover is much more stressed than a clamped one: clamping the edge is worth up to 1.6× in stress.
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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