# SECTIONAL PROPERTIES CALCULATOR - C CHANNELS (C BEAMS)

Structural C channels, also known as C beams are structural beams with C shaped cross section. Top and bottom plates of a C channel are named as flanges and the vertical plate which connects the flanges is named as web. The materials of C channels are generally steel, aluminum and stainless steel. Manufacturing methods of C channels are hot rolling and extrusion.

The following calculator has been developed to calculate the sectional properties of structural C channels (beams) with straight leg (untapered leg).

##### Calculator:

 INPUT PARAMETERS Parameter Symbol Value Unit Flange-flange inner face height H mm cm m inch ft Width B Flange thickness h Web thickness b Length L Density p g/cm^3 kg/m^3 lb/in^3

 OUTPUT PARAMETERS Parameter Symbol Value Unit Cross section area A --- mm^2 cm^2 inch^2 ft^2 Mass M --- kg lb Second moment of area Ixx --- mm^4 cm^4 inch^4 ft^4 Second moment of area Iyy --- Section modulus Sxx --- mm^3 cm^3 inch^3 ft^3 Minimum section modulus Syy --- Radius of gyration rx --- mm cm m inch ft Radius of gyration ry --- CoG distance in x direction xcog --- mm cm m inch ft CoG distance in y direction ycog ---

##### Definitions

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.

Second Moment of Area: The capacity of a cross-section 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:

 C SECTION (C-BEAM) Step Parameter/Condition Symbol Equation 1 Cross section area A A = 2Bh + Hb 2 Area moment of inertia Ixx Ixx = H3b/12 + 2[h3B/12 + hB(h+H)2/4] 3 Area moment of inertia Iyy Iyy = b3H/12 + bH(xcog-b/2)2+ 2B3h/12+ 2Bh(xcog - B/2)2 4 Section modulus Sxx Sxx = Ixx/ycog 5 Minimum section modulus Syy Syy = Iyy/(B-xcog) 6 Center of gravity xcog xcog = (2hB2/2 + b2H/2)/A 7 Center of gravity ycog ycog= 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 = Ixx + Iyy

##### Supplements:

 Link Usage Aluminum Channel Sizes Online tool to show basic dimensions and sectional properties of standard aluminum C channels. Steel Channel Sizes Online tool to show basic dimensions and sectional properties of standard steel C channels.

##### Reference:

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