Fundamental Frequency of a Structure

[EIT2]

RE: ASCE 7-98-6.2 In determining whether a building or structure is flexible or rigid, how is the fundamental frequency or fundamental natural frequency determined?
Is there a difference between "fundamental" and "fundamental natural" frequency?

 

[Drej]

The fundamental/natural frequency is the frequency at which resonance is said to occur in a system or body - remember the Tacoma Narrows bridge, where the torsional vibration mode of 0.2 Hz induced by initial 35mph winds (then a cable support snapped and winds changed to 42mph - disaster!)started an eventual catastrophic collapse? This frequency (and other fundamental frequencies/mode shapes) can be ascertained by either finite element models or by forced vibration tests.

Hope this helps
-- drej --

 

[dooron]

My simplified observations, Natural frequencies, there are 1st,2nd,etc. modes. The 1st being the fundumental-slowest and most likely to occur in nature due to wind, or earthquake or movement of traffic, etc rail wheels.
The frequency is found by many calculations methods (see any frequency analysis book for formulaes), all of which are approximations, because the damping characterisitics can never be exactly modelled and these have a big affect on behaviour. For chimneys we have eddy shedding , struhl no. and wind speed to give us the fist mode frequency. For steel frames we apply a unit load, deflect the frame sideways with this load, release the load suddenly, and watch the frame oscillate.

 

[ARIFSIDDIQUI]

every structures is having it's own natural freauency depending on its structural configurations like plan and in particular the height of the building the calculations for the natural frequency for rough idea is very simple but for actula analysis you need to have a proper modelling and structure must be designed such that natural frequence of structure and the natural frequency of earthquake should not be same if it is unavided the proper resonance considerations should be given to the structural design.

fundamental natural frequency can be relkated to the fndamental mode shapes of the building under the dyanmic situations in general the funamental mode shape of the structure is when it oscillates free standinglike cantilever and it is many times is critical for the design because the mass participation is many times maximum in this mode shaoe only no. of mode shaoes will depend on thie face that atleast 90% mass participation must be ensured for any structural dynamic s analysis.

hope this may help you

ARIF ALI SIDDIQUI
STRUCTURAL DESIGN ENGINEER
IMCC 8 JANTAR MANTAR MARG
NEW DELHI INDIA

 

[kvram]

Dear EIT2,
Mr. ARIF ALI SIDDIQUI has attemted to answer in a right way. I will add few more sentences.
1) Fundamental frequency is the lowest frequency for the various modes of vibrationof a structure. Both natural and fundamental frequecies are refering the same
2) Any structure will have as many mode shapes of vibrations as degree of freedom. Every mode of vibrationhas a uniform mode shape
3) The structure resosnates if the oparating frequency of machine which suuports matches with natural frequency of the structure.
4) Normally we designed the structure such that it does not fall with in 10% closer between natural & operating frequencies. If it is happened to be , then either change the mass or stiffness of the structure to make it safe.

For further details , refer text book on Dynamics by Mario paz.

KVRam.