## 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.