Bonus Homework Assignment – Computation of the Moment of Inertia of an I-beam – Fusion of Engineering, Control, Coding, Machine Learning, and Science

By completing the following homework assignment (successfully and completely), you will obtain 10 extra points on the midterm exam.

Consider the cross-section of the I-beam shown in the figure below.

Assuming that the dimensions $a$ , $b$ , and $h$ , are given, perform the following steps:

1.) Compute the moment of inertia by solving the integral

(1) $\begin{align*}I=\iint_{A} y^{2} dA\end{align*}$

Solve this integral step-by-step and write down all the steps necessary to solve this double integral.

2.) Verify the results in step 1. by using the formulas available in tables given online (search for these formulas).

3.) Explain what is a Huygens-Steiners theorem (Parallel Axis Theorem) and use this theorem to solve the problem in step 1.

Complete points will be given only if all the 3. points are accurately and successfully solved!