Kinematic Indeterminacy
Objective:
To determine the degree of kinematic indeterminacy of different type of structures such as beams, trusses, frames etc., having various conditions of construction.
SOME FACTS:
(1) Determination of DKI is the first step in structural analysis using displacement methods such as the slope deflection method, the moment distribution method and the matrix/direct stiffness method.
(2) Kinematic indeterminacy arises from unknown independent displacements (translations and rotations)
(3) The concept of kinematic indeterminacy is also important in other fields, such as robotics and biomechanics, where it is used to describe the motion of complex mechanisms and joints.
Structure - 1 Simply supported Beam Members are inextesible
2. No of Independent Rotations :
CONDITIONS:
Beam with 1 pinned and 2 roller supports
DKI =
2. No of Independent Rotations :
CONDITIONS:
Beam with 2 roller support at both the ends,
One pinned support and 2 internal hinges
DKI =
1. Enter Reactions (R) :
2. No of Joints (J) :
3. Inextensibility (Ci) :
CONDITIONS:
-Rigid Frame with fixed supports
-Having 3 In-extensibility conditions
DKI =
1. Enter Reactions (R) :
2. No of Joints (J) :
3. In-extensibility (Ci) :
3. No of Releases (f) :
CONDITIONS:
-Rigid Frame with hinge
-Having inextensibility conditions
-included Additional rotations(f) at hinges
DKI =
1. Enter Reactions (R) :
2. No of Joints (J) :
DKI =
CONDITIONS:
-Plane truss with one pinned support and
roller support
1. Enter Reactions (R) :
2. No of Joints (J) :
3. No of Members (M) :
CONDITIONS:
Plane Frame with one fixed support
one pinned and one roller support.
DKI =
