Kostenloser Moment of Area Rechner
Berechnen Sie den second moment of area (Ixx und Iyy) for a rectangular cross-section. Geben Sie width und Größe für sofortige Ergebnisse.
Ixx (about horizontal axis)
66,666,667 mm^4
Ixx (about horizontal axis) vs Width (b)
Formel
## Second Moment of Area for a Rectangle The second moment of area (often called moment of inertia of the cross-section) governs how a beam resists bending. ### Formula **Ixx = b h^3 / 12** **Iyy = h b^3 / 12** where b is the width and h is the height of the rectangle. The axis with the larger I value provides greater bending resistance. That is why beams are oriented with the taller dimension vertical.
Lösungsbeispiel
A rectangular timber section 100 mm wide and 200 mm tall.
- 01Ixx = 100 x 200^3 / 12 = 100 x 8,000,000 / 12 = 66,666,667 mm^4
- 02Iyy = 200 x 100^3 / 12 = 200 x 1,000,000 / 12 = 16,666,667 mm^4
- 03Ixx in cm^4 = 66,666,667 / 10,000 = 6,666.67 cm^4
Häufig Gestellte Fragen
What is the difference between moment of inertia and second moment of area?
In structural engineering, second moment of area (units of length^4) describes cross-section geometry. Mass moment of inertia (units of mass x length^2) describes rotational resistance. They are different physical quantities that share a similar name.
How do I compute I for non-rectangular shapes?
For circles I = pi d^4 / 64. For composite sections, use the parallel axis theorem: I_total = sum(I_local + A d^2) for each sub-shape, where d is the distance from each centroid to the overall centroid.
Why is the height cubed in the formula?
Bending resistance depends on how far material is from the neutral axis. Material farther away contributes disproportionately more, leading to the cubic relationship with depth.
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