State and explain the analytical methods for finding out the forces in perfectframe?

Analytical methods for finding out the forces in a perfect frame include the method of joints and the method of sections.

1. Method of Joints: This method involves analyzing each joint (or node) in the frame separately. The sum of the forces in all directions should be equal to zero, as per Newton's second law. This is because a joint in a perfect frame is in equilibrium, meaning it's not moving. Therefore, the sum of the horizontal forces and the sum of the vertical forces should both be zero. By applying this principle to each joint, you can solve for the unknown forces.

2. Method of Sections: This method involves cutting the frame through the members where the forces need to be determined. This will separate the frame into two sections. Then, you can consider the equilibrium of each section separately. The sum of the moments about any point in each section should be zero, as per the principle of moments. By applying this principle, you can solve for the unknown forces.

Both methods require a good understanding of statics and the principles of equilibrium. They also require careful bookkeeping to keep track of all the forces and their directions.