Perfect Frames (Trusses)

Frames 

A plane truss is defined as a system of bars all lying in one plane and joined together at their ends in such a way as to form a rigid framework. the trusses are mostly used to railway bridges. the frames or trusses can be classified in two categories:

(i) Perfect Frame  (ii) Imperfect Frame

Rail Bridge : A good example of Truss

Perfect Frames 

A perfect frame is that. which is made up of members just sufficient to keep it in equilibrium, when loaded without any change in its shape. In other words, a perfect frame has zero degree of freedom. a perfect frame must satisfy the following relation

                  n= 2j-1

                  where  n = number of members

                               j =  number of joints

Imperfect frame 

An imperfect frame is that, which contains more or less number of members required to keep it in equilibrium, when loaded, without any change in shape. In other words, an imperfect frame has more or less number of members than given by the equation 2j-3.

Analysis of perfect frames 

The forces in the members of a frame can be found out either by analytical method or by graphical method

Analytical Method 

In analytical method, Forces in the members are found by considering the equilibrium of the forces. i.e.

Ʃ F_x = 0

Ʃ F_y = 0

Ʃ M = 0

There are two types of analytical methods.

1.                 Method of joints

2.                 Method of sections

Method of joints

In method of joints, equilibrium of joints is considered to find the forces acting in the members at that joint. In this method, we select those joints only on which not more than two unknown forces are acting.

Similarly, equilibrium of other joints can also be used to find the forces in other members.

This method is very lengthy and always preferred when forces in the members are to be found out. If it is required to find the force in a single member then the method of section is preferred.

Method of section

In method of section, we cut the frame or truss into two section by an imaginary plane passing through the member in which the force is being calculated. After cutting the truss, consider the equilibrium of any one section either LHS or RHS under the influence of external forces only.

Above Truss is cut through section o-o' 

Equilibrium of  LHS and RHS 

Now by considering the equilibrium of any section and taking the moments of external forces about any point, the required forces can be calculated.