AI Search

BIZOMAT MAKEOS · Materials

Panel Material Substitution (Equal Stiffness and Strength Thickness, Mass, Cost)

If I change this plate or panel to another material, how thick must it be to keep the same stiffness and strength, and what happens to weight and cost?

Substitution of a bending plate, cover or panel with another material: the thickness for equal bending stiffness and for equal bending strength, the governing thickness (as the equivalent stiffness thickness tool), mass per square metre and cost of the original and the new panel, the panel mass and cost over its area, and checks against the thickest stock available and whether the change saves weight.

Open the calculatorRuns in your browser. No account needed.

How this tool works

Inputs, units and where to find them

InputUnitTypical source
Original thicknessmmThickness of the existing panel.
Original modulusGPaElastic modulus of the existing material.
Original allowable stressMPaAllowable stress of the existing material.
Original densitykg/m³Density of the existing material.
Original material price$/kgPrice of the existing material.
New material
New modulusGPaElastic modulus of the new material.
New allowable stressMPaAllowable stress of the new material.
New densitykg/m³Density of the new material.
New material price$/kgPrice of the new material.
Thickest stock availablemmThickest sheet or plate of the new material you can get.
Panel aream²Area of the panel.

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
Illustration: Original thicknessThe cross-section of a plate or wall with a dimension across its thickness, marking Original thickness.t₁section through the materialExample: 2 mmOriginal thickness
What it is
The thickness of the existing panel, cover or plate that is being replaced by another 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 thicknesses for the new material scale in direct proportion to the original thickness.
What this means: Original modulus
Illustration: Original modulusA stress against strain graph whose straight starting slope is the stiffness value Original modulus.stressstrainE₁Example: 200 GPaOriginal modulus
What it is
The elastic modulus of the existing panel material, from its data sheet; it sets the stiffness the new panel must match.
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.
Get it right
Enter both moduli in GPa; only their ratio is used.
What this means: Original allowable stress
Illustration: Original allowable stressA test bar pulled from both ends: stress Original allowable stress is the force carried by each square millimetre of its cross-section.S₁stress = force ÷ areaExample: 250 MPaOriginal allowable stress
What it is
The allowable bending stress of the existing material, from your design code or material data.
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
Illustration: Original densityA cube of material: density Original density is its mass divided by the volume it fills.massvolumeρ₁Example: 7850 kg/m³Original density
What it is
The density of the existing material, used to work out the original panel mass.
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: Original material price
Illustration: Original material priceA price tag on one unit of measure; Original material price is the cost for each unit (per hour, per kilogram and so on).$cost foreach unitExample: $2/kgOriginal material price
What it is
The purchase price of the existing material per kilogram, from current supplier quotes.
Units and format
Enter a number in $/kg: money per kilogram. The form accepts $0/kg to $10000/kg. Required: the tool does not calculate until every input is valid.
Example
The form opens with $2/kg as a worked example. It is an illustration, not a recommended value: replace it with your own figure.

New material

What this means: New modulus
Illustration: New modulusA stress against strain graph whose straight starting slope is the stiffness value New modulus.stressstrainE₂Example: 70 GPaNew modulus
What it is
The elastic modulus of the replacement material, from its data sheet; a lower modulus needs a thicker panel for the same stiffness.
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 70 GPa as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
Effect on the result
The thickness for equal stiffness varies with the cube root of the modulus ratio.
What this means: New allowable stress
Illustration: New allowable stressA test bar pulled from both ends: stress New allowable stress is the force carried by each square millimetre of its cross-section.S₂stress = force ÷ areaExample: 150 MPaNew allowable stress
What it is
The allowable bending stress of the replacement material, from your design code or material data.
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 150 MPa as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
Effect on the result
The thickness for equal strength varies with the square root of the stress ratio.
What this means: New density
Illustration: New densityA cube of material: density New density is its mass divided by the volume it fills.massvolumeρ₂Example: 2700 kg/m³New density
What it is
The density of the replacement material, used to work out the new panel mass and the weight saving.
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 2700 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 price
Illustration: New material priceA price tag on one unit of measure; New material price is the cost for each unit (per hour, per kilogram and so on).$cost foreach unitExample: $5/kgNew material price
What it is
The purchase price of the replacement material per kilogram, from current supplier quotes.
Units and format
Enter a number in $/kg: money per kilogram. The form accepts $0/kg to $10000/kg. Required: the tool does not calculate until every input is valid.
Example
The form opens with $5/kg as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
What this means: Thickest stock available
Illustration: Thickest stock availableThe cross-section of a plate or wall with a dimension across its thickness, marking Thickest stock available.tsection through the materialExample: 6 mmThickest stock available
What it is
The thickest sheet or plate of the new material that you can buy or have in stock.
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 6 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
What this means: Panel area
Illustration: Panel areaA shaded shape whose enclosed surface is the area Panel area.AenclosedsurfaceExample: 1.5 m²Panel area
What it is
The area of one face of the panel, used to turn mass and cost per square metre into totals for the panel.
Units and format
Enter a number in m²: square metres. The form accepts 0.000001 m² to 100000 m². Required: the tool does not calculate until every input is valid.
Example
The form opens with 1.5 m² as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
Get it right
Enter square metres: 1 m² = 1,000,000 mm².

Method and formulas

  1. Equal bending stiffness: t₂ = t₁ ∛(E₁ ÷ E₂); equal bending strength: t₂ = t₁ √(S₁ ÷ S₂); the larger governs (as the equivalent stiffness thickness tool).
  2. Mass per m² = density × thickness; cost = mass × price.
  3. Panel mass and cost = per m² × area.
  4. Example: the new panel must be 2.838 mm (stiffness 2.838, strength 2.582 mm); it weighs 48.806% of the original and costs 57.469 $ against 47.1 $.

Limitations

  • Bending of flat panels; in-plane loads and buckling scale differently.
  • Same shape and supports; ribbing or forming can save more than thickness.
  • Example values are illustrations. Replace them with values for your actual task.

Typical uses

  • Swap a steel cover for aluminium or plastic
  • Estimate weight saving from a material change
  • Check a plastic guard against the steel original

Who it is for

  • Design engineers
  • Product designers
  • Value engineers

What you get

  • Thickness for equal stiffness and for equal strength
  • Mass and cost per square metre, old and new
  • Panel mass and cost

Interpreting the result

  • Lower-modulus materials need disproportionately more thickness for stiffness, so weight savings are smaller than density alone suggests.

References

  • Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 575–580. Topic reference; no source tables or recommended settings are reproduced.

BIZOMAT tools are screening and decision-support utilities. Verify important financial, engineering, safety, legal or operational decisions using appropriate professional standards and your organisation’s approved data.

Open the Panel Material Substitution (Equal Stiffness and Strength Thickness, Mass, Cost) calculator

Materials

Linear Thermal Growth

How much does an unrestrained dimension change with temperature?

About this tool →Materials

Stock Volume and Mass

What is the theoretical mass of this stock geometry?

About this tool →Materials

Differential Thermal Fit

How does clearance change at different part temperatures?

About this tool →Materials

Differential Thermal Expansion

How does a fit clearance change when the bore and shaft materials expand differently?

About this tool →Materials

Brinell Hardness from Indentation

What Brinell hardness does this indentation give, and is the test valid?

About this tool →Materials

Heat Flow Through a Layered Wall

How much heat flows through this insulated wall, and what are the layer temperatures?

About this tool →