Question

t-section about
Find the moment of interial of the
the controid xx-axis)​

Answer 1

Step 1: Segment the beam section into parts

When calculating the area moment of inertia, we must calculate the moment of inertia of smaller segments. Try to break them into simple rectangular sections. For instance, consider the I-beam section below, which was also featured in our Centroid Tutorial. We have chosen to split this section into 3 rectangular segments:

SkyCiv, I-Beam, Moment of Inertia, Tutorial

Step 2: Calculate the Neutral Axis (NA)

The Neutral Axis (NA) or the horizontal XX axis is located at the centroid or center of mass. In our Centroid Tutorial, the centroid of this section was previously found to be 216.29 mm from the bottom of the section.

Step 3: Calculate Moment of Inertia

To calculate the total moment of inertia of the section we need to use the “Parallel Axis Theorem”:

Calculating the Moment of Inertia of a Beam Section- 1

Since we have split it into three rectangular parts, we must calculate the moment of inertia of each of these sections. It is widely known that the moment of inertia equation of a rectangle about its centroid axis is simply:

Calculating the Moment of Inertia of a Beam Section- 2

The moment of inertia of other shapes are often stated in the front/back of textbooks or from this guide of moment of inertia shapes. However the rectangular shape is very common for beam sections, so it is probably worth memorizing.

Now we have all the information we need to use the “Parallel Axis Theorem” and find the total moment of inertia of the I-beam section. In our moment of inertia example:

Calculating the Moment of Inertia of a Beam Section- 3

So there you have our guide on calculating the area of moment for beam sections. This result is critical in structural engineering and is an important factor in the deflection of a beam. We hope you enjoyed the tutorial and look forward to any comments you have.