Second moment of area - I-Beam (W-section)


An I-beam, also known as H-beam, W-beam (for “wide flange”), Universal Beam (UB), Rolled Steel Joist (RSJ), or double-T (especially in Polish, Bulgarian, Spanish, Italian and German), is a beam with an I- or H-shaped cross-section. The horizontal elements of the “I” are known as flanges, while the vertical element is termed the “web”. I-beams are usually made of structural steel and are used in construction and civil engineering.

The web resists shear forces, while the flanges resist most of the bending moment experienced by the beam. Beam theory shows that the I-shaped section is a very efficient form for carrying both bending and shear loads in the plane of the web. On the other hand, the cross-section has a reduced capacity in the transverse direction, and is also inefficient in carrying torsion, for which hollow structural sections are often preferred.

The 2nd moment of area, also known as moment of inertia of plane area, area moment of inertia, or second area moment, is a geometrical property of an area which reflects how its points are distributed with regard to an arbitrary axis. The second moment of area is typically denoted with either an I for an axis that lies in the plane or with a J for an axis perpendicular to the plane. In both cases, it is calculated with a multiple integral over the object in question. Its dimension is L (length) to the fourth power. Its unit of dimension when working with the International System of Units is meters to the fourth power, m4, or inches to the fourth power, in4, when working in the Imperial System of Units.

The 2nd moment of area of a symmetric W-Section I-beam is shown here.

Related formulas


I2nd moment of area (mm4)
btotal width of the profile (mm)
htotal height of the profile (mm)
tweb thickness (mm)
hwweb height (mm)