# Analytical Methods for the Forces

## Analytical Methods:

There are mainly two analytical methods for finding out the forces, in the members of a perfect frame are important from the subject point of view:

## 1. Method of Joints:

In this method, each and every joint is treated as a free body in equilibrium. The unknown forces are then determined by equilibrium equation Σ V = 0 and Σ H = 0, Sum of all the vertical forces and horizontal forces is equated to zero.

Note:
1. The members of the frame may be named either by Bow’s methods or by the joints at their ends.

2. While selecting the joint, for calculation work, care should be taken that at any instant, the joint should not contain more than two members in which the forces are unknown.

## 2. Method of Sections:

This method is particularly convenient, when the forces in a few members of a frame are required to be found out. In this method, a section line is passed through the member or members in which the forces are required. A part of the structure, on any one side of the section line, is then treated as a free body in equilibrium under the action of external forces. The unknown forces are then found out by the application of equilibrium or the principles of statics,

Σ M = 0

Note:
1. To start with, we have shown section line 1-1 cutting the members AB and BC. Now in order to find out the forces in the member AC, section line 2-2 may be drawn.

2. While drawing a section line, care should always be taken not to cut more than three members in which the forces are unknown.