# Section Property Calculations

Because of the flexibility of the manufacturing method and the variety of shapes that can be manufactured, properties of cold-formed sections often must be calculated for a particular configuration of interest rather than relying on tables of standard values. However, properties of representative or typical sections are listed in the Cold-Formed Steel Design Manual, American Iron and Steel Institute, 1996, Washington, DC (AISI Manual).
Because the cross section of a cold-formed section is generally of a single thickness of steel, computation of section properties may be simplified by using the linear method. With this method, the material is considered concentrated along the centerline of the steel sheet and area elements are replaced by straight or curved line elements. Section properties are calculated for the assembly of line elements and then multiplied by the thickness, t. Thus, the cross section area is given by A = L x t, where L is the total length of all line elements;
the moment of inertia of the section is given by I = I’ x  t, where I  is the moment of  inertia determined for the line elements; and the section modulus is calculated by dividing I by the distance from the neutral axis to the extreme fiber, not to the centerline of the extreme element. As subsequently discussed, it is sometimes necessary to use a reduced or effective width rather than the full width of an element.
Most sections can be divided into straight lines and circular arcs. The moments of inertia and centroid location of such elements are defined by equations from fundamental theory as presented in Table 10.2.