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2021-03-29

# Simplified Vibration Design for EC 5

With the RF-/TIMBER Pro add-on module, you can perform the vibration design known from DIN 1052 for the design according to EN 1995-1-1. In this design, the deflection under permanent and quasi-permanent action at the ideal one‑span beam may not exceed the limit value (6 mm according to DIN 1052). If you consider the relation between the natural frequency and the deflection for a hinged single-span beam subjected to a constant distributed load, the 6 mm limit value results in a minimum natural frequency of about 7.2 Hz.

If both equations are equated, the natural frequency of 7.2 Hz results in a deformation of 6 mm.

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, we obtain a maximum deflection of about 5 mm.

If the structural system deviates from a hinged single-span beam (for example, continuous beams, cantilevers, restraints), this must be taken into account accordingly in the deflection limitation.

## Example:

We analyze a three‑span beam in a dwelling house. To avoid discomfort caused by persons, the system shall have a minimum fundamental frequency of 8 Hz. In order to consider this in RF‑/TIMBER Pro, you can use the formula for three-span beams (see the PDF document below) to determine the maximum allowed deflection of the central span.

In this case, the middle span may deform by -1 mm to comply with the frequency criterion. The actual deflection under permanent load (2.1 kN/m) is obtained as -0.683 mm. Thus, the design of the natural frequency is complied with, and the natural frequency of the beam is greater than 8 Hz. A check calculation results in a natural frequency of 9.76 Hz.

A more precise calculation with the RF‑/DYNAM Pro — Natural Vibrations add-on module results in a natural frequency of 9.86 Hz. The video shows the procedure.

Furthermore, it should be noted that further designs (stiffness criterion, vibration velocity, vibration acceleration) must be performed for the vibration design of apartment ceilings. Notes can be found in [1] or [2], for example.

Author

Mr. Rehm is responsible for developing products for timber structures, and he provides technical support for customers.