2nd order buckling - Plane frame

Tekla Structural Designer
Tekla Structural Designer

2nd order buckling - Plane frame

Problem definition

Calculate the buckling factor of the moment frame shown below.


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


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 %


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


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

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