## Robot Structural Analysis

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# Negative critical coefficients in buckling analysis

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Question from the user:*What does it mean with a negative critical coefficient?*

**Pawel Pulak**

Solved! Go to Solution.

# Re: Negative critical coefficients in buckling analysis

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The basic results of buckling analysis are critical coefficients (eigenvalues) and buckling shapes (eigenvectors) corresponding to these critical coefficients.

Each critical coefficient is the factor by which the loads of appropriate load case should be multiplied to obtain appropriate loss of stability (buckling shape or mode).

**Negative critical coefficient for some buckling mode means that the loads of appropriate load case shoud have opposite direction to result in such buckling shape. Of course in practice buckling modes with negative critical coefficients should be neglected.**

In some situations (for instance optimized truss girders with slender tendons working in tension for standard load conditions) positive critical coefficient can be preceded by a lot of negative ones. It is so because by default analysis is searching for critical buckling coefficients starting from zero and considering absolute values of them (so both positive and negative ones). It may result in necessity to calculate a lot of critical coefficients before finding the first positive one. It can be avoided setting non-zero shift to start searching from some positive value - see the attached screen capture.

**Pawel Pulak**

# Re: Negative critical coefficients in buckling analysis

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An interesting thing: after selecting ‘Block subspace iteration’ and defining the positive value of the shift and then returning to the selection of ‘Subspace iteration’, the program still runs calculations as with the ‘Block subspace’ method, or possibly applies the initial shift to the ‘Subspace’ method?

# Re: Negative critical coefficients in buckling analysis

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Probably you have not noticed that "Block subspace iteration" method was also used on the very beginning - prior to switching from "Subspace iteration" to "Block subspace iteration".

By default automatic choice of solver is active (see the attached screen capture) and in case of bigger models it results in using Sparse solver for static analysis. When Sparse solver is used then buckling analysis is run using "Block subspace iteration" method ignoring settings from parameters of buckling analysis.

**Pawel Pulak**