SECTIONAL PROPERTIES CALCULATOR  SOLID RECTANGULAR BAR
Rectangular bars (including square bar) are solid bars (or flats) with rectangle
cross section. They are generally produced from stainless steel, carbon steel,
alloy steel and aluminum. Manufacturing method for rectangular bars are cold/hot
rolling and drawing. Rectangular bars are offered by manufacturers in variety of
sizes. Steel rectangular 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.
The following calculator has been developed to calculate the sectional
properties of rectangular solid 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} 


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.
Supplements:
Link 
Usage 
Simply Supported Beam Deflection Calculation Example

An example on calculation of max. deflection, max. shear force, max. bending moment and midspan slope/deflection of a simply supported beam
under multiple point loads and a distributed load. 
Rectangular Beam Design for Strength

This calculator has been developed to calculate normal stress, shear stress and Von Mises stress on a given cross section of a rectangular solid beam. 
List of Equations:
SOLID RECTANGLE 

Step 
Parameter/Condition 
Symbol 
Equation 
1 
Cross section area 
A 
A = BH 
2 
Area moment of inertia 
I_{xx} 
I_{xx} = BH^{3}/12 
3 
Area moment of inertia 
I_{yy} 
I_{yy} = HB^{3}/12 
4 
Section modulus 
S_{xx} 
S_{xx} = I_{xx}/y_{cog} 
5 
Section modulus 
S_{yy} 
S_{yy} = I_{yy}/x_{cog} 
6 
Center of gravity 
x_{cog} 
x_{cog}=B/2 
7 
Center of gravity 
y_{cog} 
y_{cog}=H/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