Plastic Modulus Calculator

Formula

The formula to calculate the plastic modulus of a cross-section is:

\[ Z = \frac{2B_fT_f(D - T_f) + T_w(D - 2T_f)^2}{4} \]

Where:

\(Z\) is the plastic modulus (mm³)
\(B_f\) is the flange width (mm)
\(T_f\) is the flange thickness (mm)
\(D\) is the overall depth of the section (mm)
\(T_w\) is the web thickness (mm)

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.

Example Calculation

Let's assume the following values:

Flange Width (Bf) = 200 mm
Flange Thickness (Tf) = 20 mm
Overall Depth (D) = 300 mm
Web Thickness (Tw) = 10 mm

Using the formula:

\[ Z = \frac{2 \times 200 \times 20 \times (300 - 20) + 10 \times (300 - 2 \times 20)^2}{4} = 729,000 \text{ mm}^3 \]

The Plastic Modulus (Z) is 729,000 mm³.