What is the correct method to determine the moment of inertia of a symmetrical Tsection about its centroidal axis?

Explanation:

The parallel axis theorem is used to calculate the moment of inertia of a composite shape like a T-section.

Process: The moment of inertia of the T-section is determined by summing the moments of inertia of its individual components (flange and web), with adjustments for their distances from the centroidal axis of the entire section.

Steps:

1. Calculate the moment of inertia of the flange about its own centroid.

2. Calculate the moment of inertia of the web about its own centroid.

3. Apply the parallel axis theorem to shift these moments to the centroidal axis of the entire T-section.

 Additional InformationParallel Axis Theorem

• Definition: The parallel axis theorem is used to calculate the moment of inertia of a body about any axis, given its moment of inertia about a parallel axis through the centroid.

• Use: This theorem is useful when you want to shift the moment of inertia from the centroid of a shape to another axis (e.g., calculating the moment of inertia of a composite shape like a T-section, where individual parts are displaced from the centroid).

Perpendicular Axis Theorem

• Definition: The perpendicular axis theorem applies to planar objects (objects lying in a single plane). It relates the moments of inertia about two axes that are perpendicular to each other in the plane to the moment of inertia about an axis perpendicular to the plane.

• Use: This theorem is typically used for flat shapes (e.g., thin plates) when you need the moment of inertia about an axis that is perpendicular to the plane of the object. It is not applicable for calculating the moment of inertia of 3D shapes or composite shapes like a T-section.

Key Differences:

• Parallel axis theorem is used when shifting the axis of rotation for a shape (e.g., when calculating moments of inertia of components in a composite shape).

• Perpendicular axis theorem is used for planar shapes to relate moments of inertia about perpendicular axes within the same plane to the moment of inertia about an axis perpendicular to the plane.