Stability and Determinacy of Structures

The stability of a structure can be divided into: external stability (ii) internal stability

The reactive forces should be non parallel and non concurrent. External Stability If the supports can provide the required number of independent reaction components for static equilibrium of the structure it called externally stable. The reactive forces should be non parallel and non concurrent.

Stable support system

Unstable support systems Parallel reaction (unstable) Concurrent reaction (unstable) P

Internal Stability If it can maintain its geometry under the action of all kinds of forces tending to deform it. (geometry of unstable, known as mechanisms).

Unstable structures (mechanisms)

Stability and Determinacy in Beams If r = number of reactions c = number of internal hinges Then ;- If r < 3+c -----> the system is unstable If r = 3+c -----> the system is stable and determinacy If r > 3+c -----> the system is stable and indeterminacy

Examples

Stability And Determinacy In Trusses If m=number of bars(members) r = number of reactions j = number of joints Then: m+r < 2j ----> unstable m+r =2j -----> stable and determinate m+r > 2j ------> stable and indeterminate

Examples

Examples

Examples

Stability and Determinacy of Rigid Frames If m=total number of members r=number of reactions j=number of joints c=number of internal hinges then: - if 3m+r < 3j+c ------> the frame is unstable if 3m+r = 3j+c ------> the frame is statically determined provide it is also stable if 3m+r > 3j+c ------> the frame is statically indeterminate

Examples

Examples

H.W.

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