BIZOMAT 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. |
What each input means
Open an input to see what it is, its units, the worked example and the common mistakes, with a small diagram.
What this means: Pressure
- What it is
- The uniform pressure acting over the flat cover, the design or test pressure the cover must hold.
- Units and format
- Enter a number in MPa: megapascals (1 MPa = 1 N/mm²). The form accepts 0.000001 MPa to 500 MPa. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1 MPa as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Thickness for stress rises with the square root of pressure.
- Get it right
- Use the pressure difference across the cover (gauge pressure when the outside is atmospheric); MPa, and 1 bar = 0.1 MPa.
What this means: Unsupported radius
- What it is
- The radius of the part of the cover that spans freely: to the bolt circle or gasket for a simply supported cover, to the weld for a clamped one.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 5000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 100 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Thickness for stress rises in proportion to the radius.
- Get it right
- Radius, not diameter.
What this means: Edge support
- What it is
- How the edge of the cover is held: clamped (welded or heavily bolted, no rotation) or simply supported (gasketed and free to rotate).
- Units and format
- Choose one of 2 options from the list: Clamped (welded or heavily bolted); Simply supported (gasketed, free to rotate).
- Example
- The form opens with “Clamped (welded or heavily bolted)” selected as a worked example. Choose the option that matches your case.
- Effect on the result
- A simply supported edge gives higher stress and deflection, so a thicker cover.
What this means: Elastic modulus
- What it is
- The stiffness of the plate material (Young’s modulus), from the material data sheet. It governs the deflection only.
- Units and format
- Enter a number in GPa: gigapascals (1 GPa = 1000 MPa). The form accepts 0.000001 GPa to 500 GPa. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 200 GPa as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Enter it in GPa, not MPa: 1 GPa = 1000 MPa, so divide a data-sheet value given in MPa by 1000.
What this means: Poisson’s ratio
- What it is
- The ratio of sideways contraction to lengthwise stretch for the plate material, from the material data sheet. It enters the plate stiffness and the simply supported formulas.
- Units and format
- Enter a plain number with no unit. The form accepts 0.1 to 0.5. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0.3 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
What this means: Allowable bending stress
- What it is
- The bending stress you allow in the cover, from your design code or material data with your margin included.
- Units and format
- Enter a number in MPa: megapascals (1 MPa = 1 N/mm²). The form accepts 0.000001 MPa to 2000 MPa. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 160 MPa as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Thickness for stress falls with the square root of the allowable.
- Get it right
- Pressure vessel covers must use the stress and formula of the applicable code.
What this means: Allowable centre deflection
- What it is
- The largest deflection at the centre of the cover you accept, set by sealing, fit or what sits against the cover.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 100 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0.1 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Thickness for deflection falls with the cube root of the allowed deflection.
What this means: Thickness chosen
- What it is
- The new (nominal) thickness of the cover you intend to use. The tool subtracts the corrosion allowance before checking stress and deflection.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 1000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 12 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- It must be larger than the corrosion allowance, or the tool stops.
What this means: Corrosion allowance
- What it is
- Extra thickness allowed for metal lost to corrosion or erosion over the cover’s life, added to the thickness needed and taken off the thickness chosen.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0 mm to 20 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
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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Open the Circular Cover Plate Design (Thickness for Stress and Deflection) calculator