# 2nd order buckling - Plane frame

## Problem definition

Calculate the buckling factor of the moment frame shown below.

## Assumptions

All elements are constant and equal
*EI*. Axial deformations are ignored; to achieve this the cross section
area is set to 1000. The number of elements per member is varied between 0 and 5.

## Key results

The theoretical buckling load is calculated by

where

Which can be solved using Newtons method and five iterations

No. internal nodes/members | Solver value | % error |
---|---|---|

0 | 6.243 | 0.17 % |

1 | 6.243 | 0.01 % |

2 | 6.242 | 0.00 % |

3 | 6.242 | 0.00 % |

4 | 6.242 | 0.00 % |

5 | 6.242 | 0.00 % |

## Conclusion

A good match is shown between the solver and theory. The discrepancy decreases as the level of discretization is increased.

## References

Timoshenko, S. and J. M. Gere. 1961. *Theory of Elastic Stability*. 2nd Edition.
McGraw-Hill Book Company.