Degree of Indeterminacy of Structures Problems (Beams)

Problem set (Beams):
    Find out all degree of indeterminacy of for following cases of beams.

Beam Problems

Solutions:

Problem Number	1	2	3	4	5	6	7	8
Degrees Of Freedom (f)	3	3	3	3	3	3	3	3
Number Of Joints or Nodes (j)	2	2	2	6	2	7	3	6
Number Of Loops (l)	0	0	0	1	0	2	0	0
Number Of Parts Involved (n)	1	1	1	1	1	1	2	5
Number Of Reactions (r)	0	2	3	3	3	3	7	14
External Static Degree Of Indeterminacy (Dse= r–f*n)	-3 (Unstable Structure)	-1 (Unstable Structure)	0	0	0	0	1	-1 (Unstable Structure)
Internal  Static Degree Of Indeterminacy (Dsi= f*l)	0	0	0	3	0	6	0	0
Static Degree Of Indeterminacy (Ds=Dse+Dsi)	-3	-1	0 (Statically Determinate Structure)	3	0 (Statically Determinate Structure)	6 (Statically Indeterminate Structure)	1 (Statically Indeterminate Structure)	-1
Kinematic Degree Of Indeterminacy (Dk= f*j-r)	6	4	3	15	3	18	2	4