Triangle Moment of Inertia | Online Calculator

Cross Section Geometrical Properties Calculators

Second Moment of Area of a Triangle

The area moment of inertia of the section A about any axis is the sum of elementary areas dA, multiplied by the square of their distance to this axis.

Ix = ∫A y2dA

When performing calculations, it is often necessary to calculate the moments of inertia of complex sections about various axes. For standard cross-sections of bars, the moments of inertia are given in the tables ISO 657, DIN1025-5, ASTM A6, EN 10025 etc. In other cases, this Section may be used in order to calculate the moments of inertia of a circle, ring, triangle, rectangular contour, non-standard welded channel, L-beam, and I-beam.

In this calculation, a triangular cross-section of base width B and height H is considered. As a result of calculations, the area moment of inertia Ix0 about centroidal axis, moment of inertia Ix1 about base, moment of inertia Ix2 about vertex, and cross-sectional area A are determined.

Also, from the known bending moment M in the section, it is possible to calculate the maximum bending stress σ of the respective triangular beam.

Moment of inertia of triangle
Moment of inertia of a triangle

INITIAL DATA

H - Triangle height;

B - Base of triangle;

M - Bending moment in cross section.

RESULTS DATA

Ix0 - Area moment of inertia about centroidal axis;

Ix1 - Area moment of inertia about base;

Ix2 - Area moment of inertia about vertex;

A - Cross section area;

σ - Bending stress in cross section.

Height (H)

Base (B)

Moment of inertia (Ix0)

Moment of inertia (Ix1)

Moment of inertia (Ix2)

Section area (A)

Bending moment (M)

Bending stress (σ)

BASIC FORMULAS

Ix0 = B*H 3 / 36;

Ix1 = B*H 3 / 12;

Ix2 = B*H 3 / 4;

A = B*H / 2;

σ = M*y / Ix0;

y - distance from X0 axis to the vertex.

INITIAL DATA

H - Triangle height;

B - Base of triangle;

M - Bending moment in cross section.

RESULTS DATA

Ix0 - Area moment of inertia about centroidal axis;

Ix1 - Area moment of inertia about base;

Ix2 - Area moment of inertia about vertex;

A - Cross section area;

σ - Bending stress in cross section.

OTHER CALCULATORS

AREA MOMENTS OF INERTIA
BEAM CALCULATORS
TORSION OF BARS
CIRCULAR FLAT PLATES
BUCKLING
ELASTIC CONTACT
IMPACT LOADS
NATURAL FREQUENCIES
PRESSURED SHELLS
FLUID DYNAMIC
COMPOSITES
SPRINGS
THREAD CONNECTIONS
SHAFT CONNECTIONS
BEARINGS
DRIVES
FATIGUE
HEAT TRANSFER