Examples based on Centroid of Composite Linear Elements is solved with following timestamps:

0:00 – Mechanics of Solid Lecture series
0:18 – Examples based on Centroid of Composite Linear Elements
5:28 – Practice Question

Following points are covered in this video:
1. Examples based on Centroid of Composite Linear Elements
2. Examples based on Composite Area
3. Practice Example on CG for composite Area
4. Centre of Gravity
5. Centre of Gravity for Area
6. Centroid of Area

Engineering Funda channel is all about Engineering and Technology. Here this video is a part of Mechanics of Solids or Engineering Mechanics.

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Details of Centroid of Composite Sections:

The centroid and center of gravity of a composite shape can be found using the principles of calculus and integration. The composite shape is divided into small areas, and the centroid and center of gravity of each area are calculated. These values are then combined using integration to find the centroid and center of gravity of the entire shape.

To find the centroid of a composite shape, the shape is divided into small areas, and the x and y coordinates of the centroid of each area are calculated. The x and y coordinates are then multiplied by the area of each small area, and the products are summed up. The sum is divided by the total area of the composite shape to get the x and y coordinates of the centroid of the entire shape.

The formula for the x coordinate of the centroid of a composite shape is:

x̄ = ( Σ(A * x) ) / A

where x̄ is the x coordinate of the centroid, A is the total area of the composite shape, A is the area of each small area, and x is the x coordinate of the centroid of each small area.

Similarly, the formula for the y coordinate of the centroid of a composite shape is:

ȳ = ( Σ(A * y) ) / A

where ȳ is the y coordinate of the centroid, A is the total area of the composite shape, A is the area of each small area, and y is the y coordinate of the centroid of each small area.

To find the center of gravity of a composite shape, the shape is divided into small volumes, and the x, y, and z coordinates of the center of gravity of each volume are calculated. The x, y, and z coordinates are then multiplied by the mass of each small volume, and the products are summed up. The sum is divided by the total mass of the composite shape to get the x, y, and z coordinates of the center of gravity of the entire shape.

The formulas for the x, y, and z coordinates of the center of gravity of a composite shape are similar to those for the centroid, but with mass replacing area and z added for three-dimensional shapes:

x̄ = ( Σ(m * x) ) / m

ȳ = ( Σ(m * y) ) / m

z̄ = ( Σ(m * z) ) / m

where x̄, ȳ, and z̄ are the x, y, and z coordinates of the center of gravity, m is the total mass of the composite shape, m is the mass of each small volume, and x, y, and z are the x, y, and z coordinates of the center of gravity of each small volume.

By using these formulas, the centroid and center of gravity of any composite shape can be found, allowing for accurate predictions of its behavior and stability.