**Branch :**First Year-Engineering Syllabus

**Subject :**Elements of Mechanical Engineering

**Unit :**Beam and Trusses

## Method of joints

**Method of joints:**** **In method of joints, we look at the equilibrium of the pin at the joints. Since the forces are concurrent at the pin, there is no moment equation and only two equations for equilibrium viz. . Therefore we start our analysis at a point where one known load and at most two unknown forces are there. The weight of each member is divided into two halves and that is supported by each pin. To an extent, we have already alluded to this method while introducing trusses. Let us illustrate it by two examples.

**Example 1: **I take truss ABCDEF as shown in figure 1 and load it at point E by 5000N. The length of small members of the truss is 4m and that of the diagonal members is m. I will now find the forces in each member of this truss assuming them to be weightless.

fig..(1)

We take each point to be a pin joint and start balancing forces on each of the pins. Since pin E has an external load of 5000N one may want to start from there. However, E point has more than 2 unknown forces so we cannot start at E. We therefore first treat the truss as a whole and find reactions of ground at points A and D because then at points A and D their will remain only two unknown forces. The horizontal reaction *Nx * at point A is zero because there is no external horizontal force on the system. To find *N _{2} * I take moment about A to get

which through equation gives

In method of joints, let us now start at pin A and balance the various forces. We already anticipate the direction and show their approximately at A (figure 2). All the angles that the diagonals make are 45° .

fig...(2)

The only equations we now have worry about are the force balance equations.