Important Formulas used in Structural Analysis

                                                        Topic: Structural Analysis

•  Degree of kinematic indeterminacy(Degree of freedom)

                      Pin jointed plane frame

                      DOF = 2J-R

                      Pin jointed space frame

                      DOF = 3J-R

                      Plane frame rigid joint

                      DOF = 3J-R

                      Space frame rigid joint

                      DOF = 6J-R

Note: 1. Beam joint is considered as rigid joint
2. One internal hinge introduced 4 additional degree of freedom for plane frame and 9 for space frame
3. Hinge is not a joint

• Degree of Static indeterminacy ( Ds)

Hunderson Rule ( Tree like structure method)
For plane frame
Ds= 3C -R'
For Space frame
Ds= 6C-R'
Where C = No of cuts required to make the structure tree like
R' = Number of constraints required to make structure tree like
Note: 1. Ds = Dse + Dsi
Dse= Number of support reaction-3
.Truss
Degree of indeterminacy = m+R-2J
Where m is total number of members
R is the reaction
J is number of joint
Note: 1.If m+R >2J Stable
2. If m+ R<2J Unstable
3. If all the support reactions are parallel then structure is not stable
4. For stability of structure the reactive forces should be non concurrent.
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