Section Modulus Calculator Formula

Understand the math behind the section modulus calculator. Each variable explained with a worked example.

Use the Section Modulus Calculator

Formulas Used

Elastic Section Modulus Sxx

sxx = width_b * pow(height_h, 2) / 6

Plastic Section Modulus Zxx

zxx = width_b * pow(height_h, 2) / 4

Shape Factor (Z/S)

shape_factor = 1.5

Variables

VariableDescriptionDefault
width_bWidth (b)(mm)100
height_hHeight (h)(mm)200

How It Works

Section Modulus of a Rectangle

Section modulus links bending moment to bending stress directly.

Elastic Section Modulus

S = b h^2 / 6

Derived from S = I / c where I = b h^3 / 12 and c = h / 2.

Plastic Section Modulus

Z = b h^2 / 4

Z represents the full plastic capacity when the entire cross-section has yielded. The ratio Z/S is called the shape factor; for a rectangle it is always 1.5.

Worked Example

A 100 mm x 200 mm rectangular section.

width_b = 100height_h = 200
  1. 01Sxx = 100 x 200^2 / 6 = 100 x 40000 / 6 = 666,667 mm^3
  2. 02Zxx = 100 x 200^2 / 4 = 100 x 40000 / 4 = 1,000,000 mm^3
  3. 03Shape factor = 1,000,000 / 666,667 = 1.5

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