
Fig : A hinged arch
The simple plane truss is built up from an elementary triangle by adding two new members for each new pin. For simple plane truss, the following relation exists:
m=2j-3
where m is the number of member and j is the number of pin joints. This can be proven as follows:
It is seen that to increase one joint in a rigid truss, two more members are required. The following table gives number of members m versus number of joints j.

| Trusses |
Two members connected at a joint form a hinged arch , as shown below. A hinged arch may be added to any stable truss to form another stable truss, as long as the angle of the arch is other than 180º. A truss which can be assembled in this manner is called a simple truss . |