SECTIONAL PROPERTIES CALCULATOR  I BEAM
Beam is a structural element used in construction works to support loads and moments. Beams are generally manufactured from steel and aluminum.
Different shapes and dimensions are supplied by beam suppliers.
I beam is a type of beam
often used in trusses in buildings. I beam is generally manufactured from
structural steels with hot and cold rolling or welding processes. Top and bottom plates of a I beam are named as flanges and the vertical plate which connects the flanges is named as web. Different dimensions of I beam exist in the market and can be supplied by the beam suppliers. Due to its shape, I beam has high moment of inertia and stiffness which makes it resistant to bending moments. The web provides resistance against shear forces. These beams are not resistant to torsional loading (twisting) and they shall not used in the cases where torsion is dominant.
The following calculator has been developed to calculate the sectional properties of structural I beams.
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} 


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:
Second Moment of Area: The
capacity of a crosssection to resist bending.
Radius of Gyration (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.
List of Equations:
I SECTION (IBEAM) 

Step 
Parameter/Condition 
Symbol 
Equation 
1 
Cross section area 
A 
A = 2Bh + Hb 
2 
Area moment of inertia 
I_{xx} 
I_{xx} = H^{3}b/12 + 2[h^{3}B/12 + hB(H+h)^{2}/4] 
3 
Area moment of inertia 
I_{yy} 
I_{yy} = b^{3}H/12 + 2(B^{3}h/12) 
4 
Section modulus 
S_{xx} 
S_{xx} = 2I_{xx}/(H + 2h) 
5 
Section modulus 
S_{yy} 
S_{yy} = 2I_{yy}/B 
6 
Center of gravity 
x_{cog} 
x_{cog}=B/2 
7 
Center of gravity 
y_{cog} 
y_{cog}=H/2 + h 
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 
Eccentric Compression Load On IBeam

An example about the calculation of factor of safety of a compression member
which is loaded eccentrically. 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