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.