Enter the section depth, flange width, flange thickness, and web thickness into the calculator to determine the plastic modulus of a cross-section. The plastic modulus is a property that represents the distribution of material in the cross-section and is used in structural engineering to predict the plastic bending capacity of beams.

Plastic Modulus Formula

The following formula is used to calculate the plastic modulus of a cross-section. 

Z = frac{2BfTf(D - Tf) + Tw(D - 2Tf)^2}{4}

Variables:

  • Z is the plastic modulus (mm³)
  • Bf is the flange width (mm)
  • Tf is the flange thickness (mm)
  • D is the overall depth of the section (mm)
  • Tw is the web thickness (mm)

To calculate the plastic modulus, use the formula above where the section depth (D), flange width (Bf), flange thickness (Tf), and web thickness (Tw) are known. The plastic modulus is a measure of the cross-section’s ability to undergo plastic deformation under bending.

What is a Plastic Modulus?

The plastic modulus is a geometric property of a cross-section that is used in structural engineering to determine the moment capacity of a beam in the plastic range of deformation. It is a measure of the distribution of material away from the neutral axis of the section and is used in the design of steel structures, where plastic behavior is considered.

How to Calculate Plastic Modulus?

The following steps outline how to calculate the Plastic Modulus.

  1. First, determine the overall depth of the section (D) in millimeters.
  2. Next, determine the flange width (Bf) in millimeters.
  3. Next, determine the flange thickness (Tf) in millimeters.
  4. Next, determine the web thickness (Tw) in millimeters.
  5. Next, gather the formula from above = Z = (2BfTf(D – Tf) + Tw(D – 2Tf)²) / 4.
  6. Finally, calculate the Plastic Modulus (Z) in cubic millimeters.
  7. After inserting the variables and calculating the result, check your answer with the calculator above.

Example Problem : 

Use the following variables as an example problem to test your knowledge.

overall depth of the section (D) = 300 mm

flange width (Bf) = 150 mm

flange thickness (Tf) = 20 mm

web thickness (Tw) = 10 mm