WIDE FLANGE I BEAM SIZES
Wide Flange I Beam Sizes Calculator has been developed according to ASTM A 6/A 6M standard to give basic dimensions and section properties of wide flange I beam.
Section properties which are calculated by the calculator are second area moment of
inertia, section modulus, radius of gyration.
These sectional properties are calculation results and there may be some minor
differences with the values given by structural steel suppliers.
The wide flange I beam (W shape) is a structural steel shape with I (or H) form. Top and
bottom plates of a I beam are named as flanges and
the vertical plate which connects the flanges is named as web. In wide flange
I beams, flanges are nearly parallel to each other.
Wide flange I beams are most commonly used structural steel shape in construction works.
Materials of wide flange beams are generally structural steels such as A36, A572, A588 and A992.
The designation of the wide flange I beam gives information about the width and weight per unit length. For example W12 X 96 means 12 inches depth and
96 pounds per foot weight per unit length. Depth values are generally approximate. For W12 x 96, actual depth value is 12.71.
Therefore the actual depth value is a dimension that must be checked while designing a structural steel system.
The dimensions of the standard wide flange I beams are defined in the annex of ASTM
A 6/A 6M standard.
This calculator covers sizes of wide flange I beams which are frequently used in
steel structures. It shall be referred to products of steel suppliers if
desired wide flange I beam size doesn't exist in this calculator.
Calculator:

OUTPUT PARAMETERS 
Parameter 
Symbol 
Value 
Unit 
Designation 
 


 
Weight per unit length 
W 


lb/ft

Cross section area 
A 


in^2

Depth 
d 


in

Web thickness 
t_{w} 


Flange width 
b_{f} 


Flange thickness 
t_{f} 


Fillet radius * 
R 


Second moment of area 
I_{xx} 


in^4

Second moment of area 
I_{yy} 


Section modulus 
S_{xx} 


in^3

Section modulus 
S_{yy} 


Radius of gyration 
r_{x} 


in

Radius of gyration 
r_{y} 


Note: Use dot "." as decimal separator.
Note: * The fillet radius , which is used to calculate the sectional properties
(Ixx, Iyy, Sxx..) of the structural wide flange beam, is a calculated value to
have an area which equals to the area value that is given in the ASTM A6 / A6M.
Fillet radius may vary from structural steel fabricator to fabricator but the
effect of this change on sectional properties will be minor.
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:
WSHAPE I BEAM 

Step 
Parameter/Condition 
Symbol 
Equation 
1 
Flange inner distance 
H 
H=d2t_{f} 
2 
Cross section area 
A 
A = 2b_{f}t_{f} + Ht_{w} + A_{fillets} 
3 
Area moment of inertia 
I_{xx} 
I_{xx} = H^{3}t_{w}/12 + 2[t_{f}^{3}b_{f}/12 + t_{f}b_{f}(H+t_{f})^{2}/4]+ I_{xx_fillets} 
4 
Area moment of inertia 
I_{yy} 
I_{yy} = t_{w}^{3}H/12 + 2(b_{f}^{3}t_{f}/12) + + I_{yy_fillets} 
5 
Section modulus 
S_{xx} 
S_{xx} = 2I_{xx}/(d) 
6 
Section modulus 
S_{yy} 
S_{yy} = 2I_{yy}/bf 
7 
Radius of gyration 
r 
r = (I/A)^0.5 
Reference:

Oberg, E., Jones, F. D., Horton, H. L., & Ryffel, H. H. (2012) .
Machinery's Handbook
. 29th edition. Industrial Press Inc., pp 2594  2597
 A 6/A 6M  05a , Standard Speciﬁcation for General Requirements for Rolled Structural Steel Bars, Plates, Shapes, and Sheet Piling
 Beer.F.P. , Johnston.E.R. (1992).
Mechanics of Materials
, 2nd edition. McGrawHill