# I-Beam Calculator

## Moments and Bending Moments of Inertia, Area, Mass

I-beams, also called "wide flange" or W-beams, are preferred in construction because their I-shape allows them to withstand strong shearing and bending forces. See also Hollow Rectangular Beams. To calculate loads and forces on an I-beam, you need to know the cross-sectional area, the moments of inertia in the x- and y-directions, as well as the bending moments of inertia (aka area moments of inertia) in the x- and y-directions.

Using the image above as a guide, enter the dimensions of the I-beam into the calculator. D is the width of the flange, d is the width of the web (center support column), H is the height of the web, and h is thickness of the flange. In the calculator, L is the total length of the beam and δ is the density of the material.

For the calculator, enter distances in centimeters and the density in kg/cm^{3}. Remember 100 cm = 1 meter and 1000 grams = 1 kg. Use the Had2Know conversion calculator if needed.

### Area, Volume, Mass Equations

The area of an I-beam's cross-section is calculated by adding the areas of the three rectangles that make up the I-shape. The volume is simply area times length. And finally the mass is equal to the density times the volume. The formulas areArea = Hd + 2hD

Volume = (Hd + 2hD)L

Mass = (Hd + 2hD)Lδ

### Moments of Inertia

Not to be confused with the*bending*or

*area moment of inertia*below, the moment of inertia quantifies an object's resistance to being spun around an axis. When the axis passes through the centroid in the x-direction or y-direction, the respective equations are

I

_{X}= (δ⋅HdL)(H

^{2}+ L

^{2})/12 + 2[ (δ⋅hDL)(h

^{2}+ L

^{2})/12 + (δ⋅hDL)(H+h)

^{2}/4 ]

I

_{Y}= (δ⋅HdL)(d

^{2}+ L

^{2})/12 + 2(δ⋅hDL)(D

^{2}+ L

^{2})/12

To calculate the moment of inertia about an axis that is parallel to one of the centroidal axes, use the

*Parallel Axis Theorem*:

I

_{N}= I

_{C}+ mr

^{2}

where I

_{N}is the new moment of inertia about the line N, I

_{C}is a centroidal moment of inertia, m is the mass, and r is the distance between axes.

### Area Moments of Inertia

The area moment of inertia is also known as the bending moment or second moment of inertia. Its units are cm^{4}and should not be confused with the "regular" moment of inertia above, whose units are kg⋅cm

^{2}. Among beams with the same cross-sectional area but different shapes, I-beams have high bending moments in the x-direction, which means they are good at resisting shearing and bending when force is applied to the flanges. The bending moments in the x- and y-directions passing though the center of the I are

I

_{X-area}= H

^{3}d/12 + 2[ h

^{3}D/12 + hD(H+h)

^{2}/4 ]

I

_{Y-area}= d

^{3}H/12 + 2[ D

^{3}h/12 ]

To find the area moment of inertia with respect to an axis that is parallel to a centroidal axis, there is another version of the

*Parallel Axis Theorem*:

I

_{N-area}= I

_{C-area}+ Ar

^{2}

where A is the area of the cross-section.

© *Had2Know 2010
*