SECTIONAL PROPERTIES CALCULATOR  ROUND HOLLOW STRUCTURAL TUBES AND SECTIONS
Round hollow structural sections are metal profiles with circular tube section.
They are also known as round steel tubes. ASTM A500 is the most common steel
specification for hollow structural section in North America. This specification
is for cold formed welded and seamless carbon steel tubing in round, square and
rectangular shapes. ASTM A501 is another standard for hot formed steel tubing.
Hollow round sections are used in structural applications.
The following calculator has been developed to calculate the sectional
properties of structural hollow round sections (tubes).
Calculator:
OUTPUT PARAMETERS 
Parameter 
Symbol 
Value 
Unit 
Cross section area 
A 



Mass 
M 



Second moment of area 
I_{xx} 



Second moment of area 
I_{yy} 


Polar second moment of area 
J 


Section modulus 
S_{xx} 



Section modulus 
S_{yy} 


Radius of gyration 
r_{x} 



Radius of gyration 
r_{y} 


CoG distance in x direction 
x_{cog} 



CoG distance in y direction 
y_{cog} 


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 crosssection 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.
Supplements:
List of Equations:
HOLLOW CIRCLE (HOLLOW SHAFT) 

Step 
Parameter/Condition 
Symbol 
Equation 
1 
Cross section area 
A 
A = πd^{2}/4  πd_{1}^{2}/4 
2 
Area moment of inertia 
I_{xx} 
I_{xx} = πd^{4}/64  πd_{1}^{4}/64 
3 
Area moment of inertia 
I_{yy} 
I_{yy} = πd^{4}/64  πd_{1}^{4}/64 
4 
Section modulus 
S_{xx} 
S_{xx} = 2I_{xx}/d 
5 
Section modulus 
S_{yy} 
S_{yy} = 2I_{yy}/d 
6 
Center of gravity 
x_{cog} 
x_{cog}=d/2 
7 
Center of gravity 
y_{cog} 
y_{cog}=d/2 
8 
Mass 
M 
M = ALρ 
9 
Radius of gyration 
r 
r = (I/A)^0.5 
10 
Polar moment of inertia 
J 
J = I_{xx} + I_{yy} 
Reference:

Oberg, E., Jones, F. D., Horton, H. L., & Ryffel, H. H. (2012) .
Machinery's Handbook
. 29th edition. Industrial Press Inc., pp 234  256