SECTIONAL PROPERTIES CALCULATOR  SOLID ROUND BAR
Round bars are solid bars with round or circular cross section. They are
generally produced from stainless steel , carbon steel, alloy and case hardening
steel and aluminum. Manufacturing method for round bars are cold/hot rolling and
drawing. Round bars are offered by manufacturers in variety of sizes. Steel
round bars are covered by ASTM A108 “Standard Specification for Steel Bar,
Carbon and Alloy, ColdFinished”, A36/A36m “Standard Specification for Carbon
Structural Steel” and ASTM A276 “Standard Specification for Stainless Steel Bars
and Shapes“ standards. Round bars are generally needed for the production of
axles, pins, shafts, etc.
The following calculator has been developed to calculate the sectional
properties of round bar.
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
distance from an axis at which the area of a body may be assumed to be
concentrated and at which the second moment area will be equal to the second
moment area of the actual body about the same axis. Radius of gyration is equal
to the square root of the quotient of the second moment area and the area.
Second Moment of Area: The
capacity of a crosssection to resist bending.
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.
List of Equations:
SOLID CIRCLE (SOLID SHAFT) 

Step 
Parameter/Condition 
Symbol 
Equation 
1 
Cross section area 
A 
A = πd^{2}/4 
2 
Area moment of inertia 
I_{xx} 
I_{xx} = πd^{4}/64 
3 
Area moment of inertia 
I_{yy} 
I_{yy} = πd^{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} 
Examples:
Link 
Usage 
Compression of Round Column

An example about the calculation of allowable load on a compression member.
Sectional properties of the member are also calculated. 
Reference:

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