# Natural Frequency Analysis of Multistorey Frames Using Staad Pro

Vibration (or Oscillation) is a time-dependent, repeated motion which a body undergoes when it is excited in its natural state or by an external force. Frequency is the number of cycles of vibration the system undergoes in a unit of time which is expressed in Hertz (Hz) or (cycles per second). When a structural system is undergoing undamped vibration in its natural state (under self excitation), it is said to be undergoing free vibration. A structure has as many natural frequencies as its degree of freedom, but the frequency with the highest mass participation is often regarded as the natural frequency.

We have made a post in the past on how to calculate the natural frequency of multistorey frames using the method described by Zalka (2012). When we compared the result with finite element analysis result from Staad Pro, a good agreement was observed. Furthermore, we have also carried out free vibration analysis of trusses, free vibration analysis of tank stands when filled with water, and modal analysis of mutistorey rigid frames.

In the video shown above, a ten storey frame of total height of 30 m (each storey height = 3m) was analysed to determine the natural frequency under a floor load of 40 kN/m at each level. All the columns are 400 mm x 400 mm in dimension while the beams are 600 mm x 400 mm. The support conditions were treated as fixed. When analysed using the steps described in the video, the results below were obtained;

The horizontal natural frequency was observed to be 0.587 Hz, with a period of 1.705 seconds. The mass participation factor for this mode vibration was found to be 81.89%. The implication of this is that when carrying out the wind load analysis, the frequency of the wind action should not be close to 0.587 to avoid resonance.

The vertical frequency of the structure was observed to be 5.854 Hz with a period of 0.171 seconds, and mass participation factor of 70.981%. This can be important when evaluating human-structure interaction if the building will be subjected to crowd action.

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