'Simplified' Vibration Analysis for EC 5

Tips & Tricks

000694 28 February 2017

In RF‑/TIMBER Pro, you can now also perform the vibration analysis known from DIN 1052 for the design according to EN 1995‑1‑1. In this analysis, the deflection under permanent and quasi-permanent action at the ideal one‑span beam may not exceed a limit value (6 mm according to DIN 1052).

If the relationship shown in the graphic between natural frequency and deflection is considered for a hinged one‑span beam that is subjected to a constant uniform load, then the 6 mm result in a minimum natural frequency of about 7.2 Hz. If we take into account the fact that in most National Annexes of EC 5, a minimum natural frequency of 8.00 Hz is to be considered, then we obtain a maximum deflection of about 5 mm. If the structural system deviates from a hinged one‑span beam (for example a continuous beam, cantilevers, fixities), then the limit deflection is to be considered.

Example

If a hinged two‑span beam with the same span length and a maximum allowable deflection of 5 mm (6 mm in DIN 1052) is analyzed, then the natural frequency is not on the safe side. In this example, the deflection of the two‑span beam is 3 mm in both spans. If we now compare this to the limit deflection (5 mm in EC 5), then the check of the natural frequency (10.2 Hz) would be satisfied.

Because, however, the structural system deviates from that of a one‑span beam, a different maximum allowable deflection applies, which can be calculated from the graphic. In this case, the result is about 2 mm (corresponds to 8 Hz). The actual first natural frequency of the two‑span beam is thus:

f = 11.432 / root (3 mm) = 6.6 Hz,

which is below the minimum frequency of 8 Hz required by EN 1995‑1‑1.

Last but not least, the vibration analysis includes also analyses for residential floors (stiffness criterion, velocity of vibration, acceleration of vibration, etc.; see EN 1995‑1‑1 or Hamm/Richter 2010).