In solid mechanics and structural engineering, section modulus is a geometric property of a given cross-section used in the design of beams or flexural members.
Any relationship between these properties is highly dependent on the shape in question.
The section moduli for various profiles are often available as numerical values in tables that list the properties of standard structural shapes.
[2] Note: Both the elastic and plastic section moduli are different to the first moment of area.
Different codes use varying notations for the elastic and plastic section modulus, as illustrated in the table below.
The table below shows formulas for the elastic section modulus for various shapes.
It represents the section's capacity to resist bending once the material has yielded and entered the plastic range.
Engineers often compare the plastic moment strength against factored applied moments to ensure that the structure can safely endure the required loads without significant or unacceptable permanent deformation.
The PNA is defined as the axis that splits the cross section such that the compression force from the area in compression equals the tension force from the area in tension.
The plastic section modulus is calculated as the sum of the areas of the cross section on either side of the PNA, each multiplied by the distance from their respective local centroids to the PNA.
[1] The table below shows formulas for the plastic section modulus for various shapes.
[14] In structural engineering, the choice between utilizing the elastic or plastic (full moment) strength of a section is determined by the specific application.
Engineers follow relevant codes that dictate whether an elastic or plastic design approach is appropriate, which in turn informs the use of either the elastic or plastic section modulus.
While a detailed examination of all relevant codes is beyond the scope of this article, the following observations are noteworthy: