1st order modal - Simply supported beam

Tekla Structural Designer
2020
Tekla Structural Designer

1st order modal - Simply supported beam

Problem definition

Determine the fundamental frequency of a 10 long simply supported beam with uniform EI and mass per unit length equal to 1.0.

Assumptions

Shear deformations are excluded. The number of internal nodes varies from 0-5. Consistent mass is assumed.

Key results

The theoretical value for the fundamental frequency is calculated as:

Where m is the total mass of the beam.

No. internal nodes Solver value % error
0 1.0955 10.995 %
1 0.9909 0.395 %
2 0.9878 0.081 %
3 0.9872 0.026 %
4 0.9871 0.011 %
5 0.9870 0.005 %

Conclusion

As the element is subdivided the result converges to the correct theoretical value.

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