Composite Laminas - Rectangle + Triangle

Basic Concepts

A composite lamina is made by combining two or more simple laminas.
When a rectangular lamina is combined with a triangular lamina, it forms a specific type of composite lamina.

The centre of mass of a composite lamina is the point where the entire mass of the lamina can be considered as concentrated.
The position of the centre of mass for a composite lamina is based on the individual centres of mass of each component lamina and their respective weights.
For a rectangle + triangle composite lamina, the centre of mass can be located by drawing diagonals for the rectangle and medians for the triangle, and then using the principles of moments.

The x-coordinate of the centre of mass (\( \bar{x} \)) of a composite lamina can be calculated using the formula: \( \bar{x} = \frac{ \sum (m_i x_i)} { \sum m_i} \) where \(m_i\) is the mass of each component i and \(x_i\) is the x-coordinate of the centre of mass of the component i.
The same formula applies for finding the y-coordinate of the centre of mass (\( \bar{y} \)).
The masses of the rectangle and triangle and the distances of their centres of mass from a chosen origin should be known in advance or given in the problem.

Understanding the concept of composite laminas is crucial in fields like engineering, construction, and physics, where laminas of complex shapes are often encountered.
Knowledge about the centre of mass of a composite lamina helps in balancing and stabilising structures and systems.
Being able to calculate the centre of mass of a composite lamina is a fundamental skill in structural engineering and design. It is also applicable in designing efficient load-bearing structures.