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.

Herramienta de ingeniería gratuita

Calculadora de momento de inercia de la sección

Calcule las propiedades de la sección transversal: momento de inercia I, módulo de sección W, área A y radio de giro r, para formas comunes.

CírculoRectánguloViga I#165

Forma de la sección transversal

Diámetro d (mm)

Diámetro Exterior D (mm)

Diámetro Interior d (mm)

Ancho b (mm)

Altura h (mm)

Altura total H (mm)

Ancho del ala B (mm)

Espesor del alma tw (mm)

Espesor del ala tf (mm)

Altura total H (mm)

Ancho del ala B (mm)

Espesor del alma tw (mm)

Espesor del ala tf (mm)

Preajustes rápidos

Resultados

Momento de inercia I

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Módulo de sección W

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Área de la sección transversal A

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Radio de giro r

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Distancia a la fibra extrema c

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Círculo sólido

Círculo hueco (tubo)

Rectángulo

Viga I (simétrica)

Relaciones generales

ℹ️ El módulo de sección W = I/c relaciona el momento flector con la tensión: σ = M/W. El radio de giro r = √(I/A) se utiliza en el análisis de pandeo.