Kinematic determinacy is a term used in structural mechanics to describe a structure where material compatibility conditions alone can be used to calculate deflections. A kinematically determinate structure can be defined as a structure where, if it is possible to find nodal displacements compatible with member extensions, those nodal displacements are unique. The structure has no possible mechanisms, i. Mathematically, the mass matrix of the structure must have full rank.
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Conditions of equilibrium are sufficient to analyse the structure. Bending moment and shear force is independent of the cross-sectional area of the components and flexural rigidity of the members.
No stresses are caused due to temperature change. No stresses are caused due to lack of fit or differential settlement. Additional compatibility conditions are required. Bending moment and shear force depends upon the cross-sectional area and flexural rigidity of the members.
Stresses are caused due to temperature variation. Stresses are caused due to lack of fit or differential settlement. Typically if one talks about 'determinacy', it is an internal determinacy that is meant.
If a structure cannot be analyzed for external and internal reactions using static equilibrium conditions alone then such a structure is called indeterminate structure. It is related with the support system of the structure and it is equal to number of external reaction components in addition to number of static equilibrium equations. It refers to the geometric stability of the structure. For geometric stability sufficient number of members are required to preserve the shape of rigid body without excessive deformation.
For 3D. For 2D truss. For 3D truss. It the number of unknown displacement components are greater than the number of compatibility equations, for these structures additional equations based on equilibrium must be written in order to obtain sufficient number of equations for the determination of all the unknown displacement components.
The number of these additional equations necessary is known as degree of kinematic indeterminacy or degree of freedom of the structure. A fixed beam is kinematically determinate and a simply supported beam is kinematically indeterminate. Mixed up. Then is this structure statically determinate? No, because the reactions are concurrent through the pin on the right. Due to the design of the structure, the internal roller cannot be supported and the structure is classified as unstable.
We can safely say that this structure is unstable, both by the equations of determinacy and by understanding how the structure will bend under loading. However, if the right-hand pin were fixed-end support this case would be considered a stable, statically determinate structure.
Civil Engg. Determinacy and Indeterminacy Statically Determinate Structures Conditions of equilibrium are sufficient to analyse the structure. Stability may also be defined as "The power to recover equilibrium. A structure that is internally unstable may still be stable if it has sufficient external support reactions.
An example is shown below in Figure. For 2D Rigid frame when all members are axially extensible. For 2D Pin jointed truss. Determination of the Number of Members and Joints 2. Instability due to Parallel Reactions 3. Instability due to Concurrent Reactions 4. Instability due to an Internal Collapse Mechanism 5.
Then, is this structure statically determinate? No, it is unstable because if we take a free-body diagram of the left side of the beam, and take a sum of moments about the center hinge, the sum of moments will be non-zero due to the vertical reaction at the left pin but we know that it has to be zero due to the existence of the pin. No, it is unstable due to the same reason above. Since there are no sources of instability, this structure is externally statically determinate. This structure can be described as 2 degrees externally statically indeterminate.
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The degree of indeterminacy is an equation used by engineers to describe the stability of a structure. There are two types of indeterminacy: 1 static and 2 kinematic. While the degree of static indeterminacy is dependent on the number of unknown forces , kinematic indeterminacy is described by the number of unknown forces impacted by movements. Kinematic indeterminacy KI is also referred to as the degrees of freedom, which is the freedom to move in various directions. In order to calculate the kinematic indeterminacy, we must first know the dimensions of the structure and its type. Here is an example of a Become a Study.
Kinematic indeterminacy and folding behavior of a class of overconstrained frameworks with symmetry
How do you find the kinematic indeterminacy of a structure?
Determinacy and Indeterminacy Study Notes for Civil Engineering
We'd like to understand how you use our websites in order to improve them. Register your interest. Symmetric overconstrained frameworks are extensively used as deployable structures and reconfigurable mechanisms. Owing to geometric singularity and redundant kinematic constraints, these structures are likely to be kinematically indeterminate while they are statically indeterminate. Effective methods capable of identifying the internal mechanisms and mobility of an overconstrained structure are preferred.