Cross Section Geometrical Properties Calculators

Second Moment of Area of a Rectangle

In this calculation, a rectangular cross-section of height H, width B, with rectangular hole dimensions H₁ × B₁ is considered. As a result of calculations, the area moment of inertia I_x about centroidal axis X, moment of inertia I_y about centroidal axis Y, and cross-sectional area A are determined.

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

Moment of inertia of the rectangle

Calculation of the moment of inertia of a the rectangle

INITIAL DATA

H - Cross section height;

H₁ - Hole height;

B - Cross section width.

B₁ - Hole width;

M_x - Bending moment in cross section in the direction of X axis.

RESULTS DATA

I_x - Area moment of inertia of the rectangle about centroidal axis X;

I_y - Area moment of inertia of the rectangle about centroidal axis Y;

A - Cross section area;

σ - Bending stress in cross section (on side B).

Metric Imperial

Height (H)

Width (B)

Height (H₁)

Width (B₁)

Moment of inertia (Ix)

Moment of inertia (Iy)

Section area (A)

Bending moment (M_x)

Bending stress (σ)

BASIC FORMULAS

I_x = (B*H³ - B₁*H₁³) / 12;

I_y = (H*B³ - H₁*B₁³) / 12;

A = B*H - B₁*H₁;

σ = M_x*H / 2I_x.

INITIAL DATA

H - Cross section height;

H₁ - Hole height;

B - Cross section width.

B₁ - Hole width;

M_x - Bending moment in cross section in the direction of X axis.

RESULTS DATA

I_x - Area moment of inertia of the rectangle about centroidal Axis X;

I_y - Area moment of inertia of the rectangle about centroidal Axis Y;

A - cross section area;

σ - Bending stress in cross section (on side B).

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