What is kinematic indeterminacy of a structure?

What is kinematic indeterminacy of a structure?

The degree of kinematic indeterminacy (DKI) is the minimum number of movements (degrees of freedom, DOF) with which the kinematic configuration of the overall structure can be defined, that is, the number of unknown independent movements of the structure.

What is static and kinematic indeterminacy of a structure?

If it cannot be analyzed by the equation of static equilibrium alone, then it is called a statically indeterminate structure. Eg: Fixed beam. A structural system is said to be kinematically indeterminate if the displacement components of its joints cannot be determined by the compatibility equation alone.

How do you find the indeterminacy of a structure?

Determinate Structure: if equilibrium equations are sufficient to analyse for unknown forces, Structure is said to be statically determinate. If the equilibrium equations are not sufficient to analyse the structure for the unknown forces, the structure is said to be statically indeterminate.

What are the different indeterminacy in the structure?

The indeterminacy in a structure may be external, internal or both. A structure is said to be externally indeterminate if the number of reactions exceeds the number of equilibrium equations. Beams shown in Fig. 1.8(a) and (b) have four reaction components, whereas we have only 3 equations of equilibrium.

What is kinematic indeterminacy and what is the method to determine it?

Degree of kinematic indeterminacy (Dk) refers to the total number of independent available degree of freedom of all joints. The degree of kinematic indeterminacy may be defined as the total number of unrestrained displacement component of all joints.

What is the kinematic indeterminacy of propped cantilever?

Consider a propped cantilever. It has a KI = 1 as we do not know the rotation at hinge support. We know from compatibility conditions that translations in x and y directions at hinge are zero, while rotation and translations in x and y directions are zero for fixed support.

What is the kinematic indeterminacy of a cantilever beam?

It has a KI = 1 as we do not know the rotation at hinge support. We know from compatibility conditions that translations in x and y directions at hinge are zero, while rotation and translations in x and y directions are zero for fixed support.

How do you find the kinematic indeterminacy of a frame?

Numericals to calculate degree of indeterminancy of structure

1. Q) Find the degree of Kinematic indeterminacy and Static indeterminacy of the structure as shown in the figure.
2. Ds = DSe + DSi [ Let equation——(1)]
3. DSe = (R-3) – (M’-1)
4. Degree of Kinematic indeterminacy(DK) = 4.
5. and Degree of Static indeterminacy(DS) = 1.

How do you find kinematic indeterminacy frames?

35. Kinematic Indeterminacy • Kinematic Indeterminacy = Degree of Freedom • If the displacement component of joint can’t be determined by Compatibility Equation , it is called Kinematic Indeterminant Structure.

What is the kinematic indeterminacy at the two supports of a fixed beam?

If we consider a fixed-fixed beam, its KI=0 as we know that all deflections on both the ends are zero and there is no unknown deflection in this case.

What is the kinematic indeterminacy of fixed beam?

What is kinematic indeterminacy for fixed beam?

What is kinematic indeterminacy?

What is kinematic indeterminacy? It is defined as the number of non-zero joints displacement of the structure. It is also called the Degree of freedom. For better understand, I have made a chart summary of important formulae. r=3 + (additional equation due to internal thing if any)

What is the dynamic and kinematic indeterminacy of hinged support?

In hinged support, dynamic indeterminacy will be one (1). In roller support, kinematic indeterminacy will be two (2) with axial deformation and one (1) if axial deformation is neglected. If there is an internal hinge with two members then dynamic indeterminacy will be two (2).

What are the types of the degree of indeterminacy?

Types of the degree of indeterminacy 1 The degree of static indeterminacy (Ds) 2 The degree of kinematic indeterminacy (Dk) More

What is kinematically determinate structure?

When a structure is loaded, it undergoes deflection at the joints i.e. translation and rotation. In slope deflection method of analysis, these deflections are treated as unknown quantities. If these unknown quantities can be found by applying compatibility conditions alone then the structure is Kinematically Determinate.