# CIRCULAR HOLLOW SECTION PROPERTIES CALCULATOR

Circular hollow section properties calculator for weight, area, section modulus and polar moment of inertia, J, calculation of circular hollow sections. INPUT PARAMETERS Parameter Value Outer diameter (d) mm cm m inch ft Inner diameter (d1) Length (L) Density (p) g/cm^3 kg/m^3 lb/in^3

 RESULTS Parameter Value Cross section area [A] --- mm^2 cm^2 inch^2 ft^2 Mass [M] --- kg lb Second moment of area [Ixx] --- mm^4 cm^4 inch^4 ft^4 Second moment of area [Iyy] --- Polar second moment of area [J] --- Section modulus [Sxx] --- mm^3 cm^3 inch^3 ft^3 Section modulus [Syy] --- Radius of gyration [rx] --- mm cm m inch ft Radius of gyration [ry] --- Centroid distance in x direction [xc] --- mm cm m inch ft Centroid distance in y direction [yc] ---

Note: Use dot "." as decimal separator.

### Definitions:

Polar Moment of Inertia: A geometric property of the cross section. Measure of ability how a beam resists torsion.

Radius of Gyration (Area): The capacity of a cross-section to resist bending.

Second Moment of Area: The distance from an axis at which the area of a body may be assumed to be concentrated and the second moment area of this configuration equal to the second moment area of the actual body about the same axis.

Section Modulus: The moment of inertia of the area of the cross section of a structural member divided by the distance from the center of gravity to the farthest point of the section; a measure of the flexural strength of the beam.

### Circular Hollow Section Formulas:

 HOLLOW CIRCLE (HOLLOW SHAFT) Parameter Symbol Equation Cross section area A A = πd2/4 - πd12/4 Area moment of inertia Ixx Ixx = πd4/64 - πd14/64 Area moment of inertia Iyy Iyy = πd4/64 - πd14/64 Section modulus Sxx Sxx = 2Ixx/d Section modulus Syy Syy = 2Iyy/d Centroid xc xc=d/2 Centroid yc yc=d/2 Mass M M = ALρ Radius of gyration r r = (I/A)^0.5 Polar moment of inertia J J = Ixx + Iyy

### Reference:

• Oberg, E. , Jones ,F.D. , Horton H.L. , Ryffel H.H., (2016) . Machinery's Handbook . 30th edition.  Industrial Press Inc., pp 226-235 .
• Oberg, E. , Jones ,F.D. , Horton H.L. , Ryffel H.H., (2012) . Machinery's Handbook . 29th edition.  Industrial Press Inc., pp 234-256.