Seismic Force Calculation

[rajbeer]

As per the Indian Code the seismic force is

a)Directly proportional to the Weight of the building
b)Design Horizontal Acceleration Spectrum Value.

QUESTION 1)Why is the seismic force directly proportional to the weight of the building?

The Design Horizontal Acceleration spectrum as per the is equal to:

((Z*I) / (2*R)) *(S/g)

where,
Z is the zone factor which is a function of the seismology of the zone which is more for zones which are seismologiclly more active and less for zones which are seismologically less active.Fine.

S/g is the spectral acceleration coefficient which is a function of soil type and natural period of vibration.

Now, "R" is the response reduction factor which is 1.5 for brittle buildings and 5 for a ductile moment resisting frame .This means that a brittle building is designed for about three times more seismic design force than a ductile building.Right?

QUESTION 2 : But, can I say that in case of a brittle building the seismic design force and actual earthquake force will be very close and for a ductile building the seismic design force will be much less than the actual earthquake force?

QUESTION 3: Why is the spectral acceleration coefficient more for buildings with less values of natural period of vibration and less for buildings with large values of natural period of vibration?

[Sukhoi]

Hi rajbeer

QUESTION 1: The seismic codes allow the used of a simplified seismic analysis that asume that the seismic force applied to the structure is proportional to the building weight. Using the seismic static coefficient (C), the total shear applied on the base of the structure is calculated using the following formulae (it may vary depending on the seismic code that you are using but i guess it may be very similar)

Q = C x I x P (Chilean seismic code)

Where ´P´ is the total weigth of the structure and ´I´ correspond to is importance level. From now the equivalent static forces applied on the differents storys of the structure are calculated based on Q, and the height of current story

This simplified method of analysis is allowed for buildings of low importance or buildings of no more than 5 storyes. (Chilean seismic code)

QUESTION 2:The reason for that is that the forces that we calculated by modal analysis or static equivalent forces are based upon the linear behaviour hypothesis. If the building is very brittle that mean that the structure can´t go much farther from his yielding point, and if it does, will colapse. That mean that we must calculate this kind of structures using the elastic force provided by the spectrum without reduction R=1 or close.
On the other case, if the structure is very ductile, means that it won´t collapse even if reach his yielding point. This structures can be deformated beyond his yielding point and don´t collapse (the structe can disspate part of the energy that came from the earthquake). In that cases we can reduce the elastic forces obtained by the spectrum on the structure. The way we do that is dividing the elastic force by ´R´ that reflects the capacity of the structure of dissipate energy.
We must recongnize however that this is a "tricky" way of introduce the non linear beahaviour on the analysis
There is an excellent explanation of this on the book of Anil Chopra: ´Dynamic of Structures´ (and with better english of course )

QUESTION 3: This is true in most cases. The stiff structures have natural oscillating periods that are very similar to the predominat period of the earthquake, wich means that this structures may resonate under the earthquake. On the other hand, the flexible structures have long natural oscillating periods and their don´t ´tuned´with the earthquake so the forces applied on them are lower.
In Mexico city the earthquakes have long predominant periods so the flexible structures (tall buldings) suffer more (in this case the spectrum have a peack near of long periods)

Well I hope help to clarify your doubts. (it´s a hard matter anyway)