Question

For a statically indeterminate pin jointed plane frame, the relation between number of ‘m’ and number of joints ’j’ is expressed as
1. m = 3j - 6
2. m > 2j - 3
3. m = 2j - 3
4. m > 3j - 6

Answer 1

Correct Answer - Option 2 : m > 2j - 3

Concepts:

A truss which has sufficient number of members to maintain its stability and satisfies equilibrium conditions is called a statically determinate and stable truss, otherwise it is statically indeterminate.

Let m = total no of members, r = no of reactions, J = no of joints

If m + r < 2j then truss is unstable.

If m+ r = 2j then truss is statically determinate and stability is checked by visual inspection.

If m + r > 2j then truss is statically indeterminate and stability is checked by visual inspection.

It is given in question that truss is pin jointed plane frame i.e. it lies in 2D, so generally, no of reactions involved are 3 ( two at pin support and 1 at roller support). Therefore, m > 2j-3 implies that truss is statically indeterminate.

Important point:

Degree of Static Indeterminacy (D_s) for 2 D truss is given as:

D_s = m + r – 2j

Where, m is the total members;  j is total joints, r is support reactions