About

In structural engineering and physics, the geometric properties of a beam's cross-section determine its ability to resist bending and deflection. The Moment of Inertia (I) quantifies the distribution of area around a neutral axis and is the key parameter in the Euler-Bernoulli beam equation.

This tool allows engineers and students to calculate critical properties—including Area (A), Moment of Inertia (I_x, I_y), and Elastic Section Modulus (S_x, S_y)—for common structural shapes like I-beams, Hollow Rectangular Sections (Tube), and C-Channels.

Formulas

For an I-beam (Doubly Symmetric), calculating I_x involves subtracting the void areas from the bounding box:

I_x = BH³ − bh³12

Where:

B = Total Width, H = Total Height
b = Web width (subtracted portion: B - t_w)
h = Inner height (subtracted portion: H - 2t_f)

Reference Data

Property	Symbol	Formula (Rectangle)	Physical Meaning
Area	A	b × h	Resistance to axial load (tension/compression).
Moment of Inertia (X)	I_x	bh³12	Resistance to bending about the X-axis.
Section Modulus	S	Ic	Used to calculate max bending stress (σ = M/S).

Frequently Asked Questions

Moment of Inertia (I) represents stiffness and is used to calculate deflection (how much it bends). Section Modulus (S) represents strength and is used to calculate stress (when it will break or yield).

I-beams are designed to be loaded vertically. Most of the material (flanges) is placed far away from the X-axis (neutral axis), maximizing Ix. This makes them efficient for resisting gravity loads.