What is the moment of inertia of a cross-section?

The moment of inertia (second moment of area) I measures how the cross-section's area is distributed about the neutral axis. A larger I means more resistance to bending. Units are mm⁴ or cm⁴.

What is section modulus?

Section modulus W (or S) equals I/c, where c is the distance from the neutral axis to the extreme fiber. It directly relates bending moment to stress: σ = M/W. A larger W means lower bending stress.

What is the radius of gyration?

The radius of gyration r = √(I/A) is a measure of how far the area is distributed from the neutral axis. It is used in column buckling calculations to determine the slenderness ratio λ = L/r.

How do I calculate I for an I-beam?

For a symmetric I-beam: I = [B×H³ − (B−tw)×(H−2tf)³] / 12, where B is flange width, H is total height, tw is web thickness, and tf is flange thickness. This subtracts the hollow portions from the bounding rectangle.

What is the difference between Ix and Iy?

Ix is the moment of inertia about the horizontal (x) axis, and Iy is about the vertical (y) axis. For bending in the vertical plane (most common), Ix is used. For lateral bending, Iy applies. This calculator computes the primary axis I.

免費工程工具

截面慣性矩計算器

計算常見形狀的截面積特性 — 慣性矩 I、截面係數 W、面積 A 及迴轉半徑 r。

圓形矩形工字梁#165

截面形狀

直徑 d (mm)

外徑 D (mm)

內徑 d (mm)

寬度 b (mm)

高度 h (mm)

總高度 H (mm)

翼緣寬度 B (mm)

腹板厚度 tw (mm)

翼緣厚度 tf (mm)

總高度 H (mm)

翼緣寬度 B (mm)

腹板厚度 tw (mm)

翼緣厚度 tf (mm)

快速預設

結果

慣性矩 I

—

截面係數 W

—

截面積 A

—

迴轉半徑 r

—

至最外層纖維距離 c

—

實心圓

空心圓（管材）

矩形

工字梁（對稱）

一般關係式

ℹ️ 截面係數 W = I/c 將彎矩與應力相關聯：σ = M/W。迴轉半徑 r = √(I/A) 用於挫曲分析。

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