Problem 8.7 - Area Moment of Inertia

Problem Statement

The cross-section shows a concrete beam with two hollow round holes. Determine the area moment of inertia about the beam’s centroid. Assume lengths a = 5 in., b = 2 in., c = 6 in., d = 4 in., d1 = 3 in., and d2 = 6 in.

Picture with a cross section with two holes drilled. The cross section has a height of d+c+b and a width of a+a. The bottom hole is centered at height d with a diameter of d2. The top hole is centered at height c+d with a diameter of d1.

Figure 1: A cross section has two round holes.

[Problem adapted from © Kurt Gramoll CC BY NC-SA 4.0]