Moment of Inertia of a Three-rods Beam | Online Calculator

Cross Section Geometrical Properties Calculators

Second Moment of Area of a Three-rods Beam

In some cases, when calculating the multi-rod beam, it is necessary to calculate the area moment of inertia of the double or triple cross section.

In this calculation, a triple cross-section of arbitrary geometries, with sectional areas A1, A2, A3, moments of inertia about centroidal axes Ix1, Ix2, Ix3, located at distance Y from each other is considered. As a result of calculations, the total moment of inertia Ix about centroidal axis X is determined.

Moment of inertia of triple cross section
Calculatiom of moment of inertia of triple cross section

INITIAL DATA

Ix1 - Area moment of inertia of the section 1 about centroidal axis X1;

Ix2 - Area moment of inertia of the section 2 about centroidal axis X2;

Ix3 - Area moment of inertia of the section 3 about centroid axis X3;

A1 - Area of the cross-section 1;

A2 - Area of the cross-section 2;

A3 - Area of the cross-section 3;

Y - Distance between centroidal axes of cross-sections.

RESULTS DATA

Ix - Area moment of inertia of the triple cross-section.

Moment of inertia (Ix1)

Moment of inertia (Ix2)

Moment of inertia (Ix3)

Section area (A1)

Section area (A2)

Section area (A3)

Distance (Y)

Moment of inertia (Ix)

BASIC FORMULAS

Ix = Ix1 + Ix2 + Ix3 + A1*[Y - A1*Y / (A1 + A2)]2 + [A2 + A3]*[A1*Y / (A1 + A2)]2

INITIAL DATA

Ix1 - Area moment of inertia of the section 1 about centroidal axis X1;

Ix2 - Area moment of inertia of the section 2 about centroidal axis X2;

Ix3 - Area moment of inertia of the section 3 about centroidal axis X3;

A1 - Area of the cross-section 1;

A2 - Area of the cross-section 2;

A3 - Area of the cross-section 3;

Y - Distance between centroidal axes of cross-sections.

RESULTS DATA

Ix - Area moment of inertia of the triple cross-section.

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