Moment of Inertia of a Rectangular Section compared to a Circular Section

The moment of inertia is a property of a shape that describes its resistance to bending. It is an important parameter in structural analysis and design. For a given area (A) and depth (h), the moment of inertia of a rectangular section is compared to that of a circular section as follows:


A rectangular section has a constant width (b) and a variable depth (h). The moment of inertia (I) of a rectangular section is given by the formula:

I = (1/12) * b * h^3

The moment of inertia increases with the cube of the depth (h). Therefore, increasing the depth of a rectangular section significantly increases its moment of inertia. This makes the rectangular section more resistant to bending.


A circular section has a constant radius (r). The moment of inertia (I) of a circular section is given by the formula:

I = (π/4) * r^4

The moment of inertia increases with the fourth power of the radius (r). Therefore, increasing the radius of a circular section has a significant impact on its moment of inertia. This makes the circular section more resistant to bending.


When comparing the moment of inertia of a rectangular section to that of a circular section for a given area (A) and depth (h), we need to consider the following:

- The rectangular section has a constant width (b), while the circular section has a constant radius (r).
- The rectangular section has a moment of inertia that increases with the cube of the depth (h), while the circular section has a moment of inertia that increases with the fourth power of the radius (r).

Conclusion:
In general, for a given area (A) and depth (h), the moment of inertia of a circular section is greater than that of a rectangular section. This means that a circular section is more resistant to bending compared to a rectangular section. However, it is important to note that the comparison depends on the specific dimensions of the rectangular and circular sections being considered.