BIZOMAT MAKEOS · Materials
Equivalent Thickness for Equal Stiffness or Strength
How thick must a part in the new material be to match the stiffness and strength of the original?
Wall or plate thickness needed in a substitute material (for example plastic replacing metal) for the same bending stiffness and for the same bending strength as the original, the governing thickness, and the resulting mass ratio.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Original thickness | mm | Thickness of the existing part. |
| Original modulus | GPa | Elastic modulus of the existing material. |
| Original allowable stress | MPa | Allowable bending stress of the existing material. |
| Original density | kg/m³ | Density of the existing material. |
| New material modulus | GPa | Elastic modulus of the new material at service temperature (use a creep modulus for sustained loads on plastics). |
| New material allowable stress | MPa | Allowable bending stress of the new material for the service conditions. |
| New material density | kg/m³ | Density of the new material. |
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: Original thickness
- What it is
- The wall or plate thickness of the existing part in its original material.
- 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 2 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Both equivalent thicknesses scale in proportion.
What this means: Original modulus
- What it is
- The elastic (Young’s) modulus of the original material, used for the equal-stiffness thickness.
- Units and format
- Enter a number in GPa: gigapascals (1 GPa = 1000 MPa). The form accepts 0.000001 GPa to 2000 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.
What this means: Original allowable stress
- What it is
- The allowable bending stress of the original material in this application, used for the equal-strength thickness.
- Units and format
- Enter a number in MPa: megapascals (1 MPa = 1 N/mm²). The form accepts 0.000001 MPa to 10000 MPa. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 250 MPa as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
What this means: Original density
- What it is
- The density of the original material, used only for the mass ratio.
- Units and format
- Enter a number in kg/m³: kilograms per cubic metre. The form accepts 0.000001 kg/m³ to 25000 kg/m³. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 7850 kg/m³ as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
What this means: New material modulus
- What it is
- The elastic modulus of the substitute material at its service temperature.
- Units and format
- Enter a number in GPa: gigapascals (1 GPa = 1000 MPa). The form accepts 0.000001 GPa to 2000 GPa. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 3 GPa as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The equal-stiffness thickness grows with the cube root of E₁ ÷ E₂.
- Get it right
- For plastics under sustained load, use a creep (long-term) modulus from the supplier rather than the short-term value.
What this means: New material allowable stress
- What it is
- The allowable bending stress of the substitute material for the service temperature, environment and load duration.
- Units and format
- Enter a number in MPa: megapascals (1 MPa = 1 N/mm²). The form accepts 0.000001 MPa to 10000 MPa. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 60 MPa as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The equal-strength thickness grows with the square root of S₁ ÷ S₂.
What this means: New material density
- What it is
- The density of the substitute material, used to compare the mass of the new part with the original.
- Units and format
- Enter a number in kg/m³: kilograms per cubic metre. The form accepts 0.000001 kg/m³ to 25000 kg/m³. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1200 kg/m³ as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The mass ratio rises in proportion.
Method and formulas
- Plates and walls of the same width in bending: stiffness ∝ E t³, so t₂ = t₁ (E₁ ÷ E₂)^(1/3).
- Strength ∝ S t², so t₂ = t₁ √(S₁ ÷ S₂).
- Governing thickness is the larger; mass ratio = ρ₂ t₂ ÷ ρ₁ t₁.
- Example: 2 mm of the original needs 8.1096 mm of the new material for equal stiffness.
Limitations
- Same shape and width, bending only; ribs and section changes are usually a better route for plastics.
- Plastics creep: use the long-term modulus for sustained loads.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Replace a metal panel or housing with plastic or composite
- Compare aluminium and steel panel thicknesses
- Estimate weight saving from a material change
Who it is for
- Design engineers
- Product engineers
- Materials engineers
What you get
- Thickness for equal stiffness
- Thickness for equal strength
- Mass ratio at the governing thickness
Interpreting the result
- If the stiffness thickness is impractical, add ribs or place material away from the neutral axis instead.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 575–580. Topic reference; no source tables or recommended settings are reproduced.
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Open the Equivalent Thickness for Equal Stiffness or Strength calculator