displacement, velocity and acceleration domains

[GraemeL]

I would appreciate if someone would provide definitions for the displacement, velocity and acceleration domains wrt a response spectrum.

I understand that the period is increasing as one shifts from the displacement to the velocity to the acceleration domain in a response spectrum, but I have not been able to find a definition of where these transition points are.

 

[Qshake]

If you view the response spectrum in it's entirety, you will see that it resembles a crude bell shape or perhaps a crude trapezoidal shape without a bottom. Thus for the trapezoid, the vertical legs are actually inclined and not true verticals.

With periods measured from the left to the right (small to large) please note the following.

The first leg of the crude trapezoid is the acceleration sensitive region. For most code based response spectrum, this part is actually cut off in favor of a maximum value that is usually something like 2.5A where A is the horizontal acceleration. This is also a region of extremely low period or very stiff structures. Most buildings and bridges will have periods greater than about 0.8s. So that you can see how the use of a maximum here works to the conservative side.

the upper part of the crude trapezoidal shape or horizontal region is the velocity sensitive region.

The seond or last inclined leg of our makeshift trapezoid is the displacement sensitive region. This will make sense as you look at the periods for this range. The higher the period the less stiff the structure and therefore the more displacement you will see.

You should check out texts such as Geotechnical Earthquake Engineering by Kraemer and Seismic Design Handbook by Farzad Naiem for more information.





Regards,
Qshake

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[GraemeL]

Thanks for that, after reading your reply I also found a description of this in Chopra's "Dynamics of Structures" p222ff that I borrrowed off a colleague.