Another way to prove this relation is as follows. In 2-dimensional space, the equilibrium of each joint is specified by three scalar force equations. There are in total 2j such equations for a plane truss with j joints. For the entire truss composed of m members, there are m unknowns (tensile or compressive forces in the member) plus 3 unknown support reactions in the general case of satically determinate plane truss. Thus, for any plane truss, the equation m+3=2j will be satisfied, if the truss is statically determinate internally.
An important point to be noted: A member of the truss is a two force member. Hence, the forces are collinear. A member of the truss is either in tension or compression.
Trusses |