Question 6.4: Compute the moment of inertia of the shape shown in Figure 6...
Compute the moment of inertia of the shape shown in Figure 6–11 with respect to its centroidal axi
Objective Compute the centroidal moment of inertia.
Given Shape shown in Figure 6–11
Analysis The centroid of the composite shape is at the intersection of the horizontal and vertical axes of symmetry. This coincides with the centroid of both the square and the circle. The composite shape can be considered to be the square with the circle removed. Therefore, we can compute the total value of I_{T} by computing the value of I_{1} for the square and subtracting I_{2} for the circle. That is,
I_{T} = I_{1} – I_{2}
Results
I_{1} = \frac{s^{4}}{12} = \frac{(50)^{4}}{12} = 520.8 \times 10^{3} mm^{4}
I_{2} = \frac{\pi D^{4}}{64} = \frac{ \pi (35)^{4}}{642} = 73.7 \times 10^{3} mm^{4}
For the composite section,
I_{T} = I_{1} – I_{2} = 447.1 \times 10^{3} mm^{4}