Sectional Properties Calculator for Composite Shapes

Calculate Sectional Properties for Your Design

Rectangle 1 Properties
Rectangle 2 Properties
Rectangle 3 Properties (Optional, leave blank to omit)

Results:

Total Area (A): mm2

Centroid X (&Xmacr;): mm

Centroid Y (&Ymacr;): mm

Moment of Inertia (Ixx): mm4

Moment of Inertia (Iyy): mm4

Unlock accurate structural analysis with our Sectional Properties Calculator. Easily determine the area, centroid (X̄, ȳ), and moment of inertia (Ixx, Iyy) for composite sections. Essential for engineers designing beams, columns, and other structural elements. Get precise results quickly for your projects.

Formula:

The Sectional Properties Calculator determines the fundamental geometric characteristics of a cross-section, crucial for structural analysis. It uses the following principles for a composite section made of multiple elements:

  • Area (A): The sum of the areas of individual components. A = Σ Ai
  • Centroid (X̄, ȳ): The geometric center of the composite section, calculated as: X̄ = (Σ Ai * xci) / A
    ȳ = (Σ Ai * yci) / A
    Where Ai is the area of an individual component and (xci, yci) is its centroid relative to a global origin.
  • Moment of Inertia (Ixx, Iyy): A measure of a section's resistance to bending. For the composite section about its own centroidal axes, using the Parallel Axis Theorem:Ixx = Σ (Ixxi + Ai * (ȳ - yci)2)
    Iyy = Σ (Iyyi + Ai * (X̄ - xci)2)
    Where Ixxi and Iyyi are the moments of inertia of individual components about their own centroidal axes. For a rectangle with width w and height h, Ixx_rect = (w * h3) / 12 and Iyy_rect = (h * w3) / 12.

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