Ground Motion

Generally ground motion is found from the seismograph and ground acceleration is found from the accelerograph.

see below
This is the accelerograph reading of an earthquake. We can find the peak ground acceleration (PGA) from this graph.

From this PGA spectral acceleration at short period and spectral acceleration at long period need to be calculated to develop the response spectrum or demand spectrum curve.

Figure of typical response spectra


So what is this Sa at T=0.3 sec and Sa at T = 1.0s and Why we need to calculate that ?

PGA is a ground acceleration (peak) due to ground motion. When ground starts shaking , all other elements above the ground also start shaking. But the shaking frequency of the different elements are different depending on the mass and stiffness (depends on height if all other element is constant) of the elements.

                                                             frequency and time period

                                                           Period mass spring


From the image shortest column has the highest frequency (faster to and fro motion) as the stiffness (how strongly it can stand on ground without buckle or bent or any disturbance)  is the highest for the shortest column.  More example can be found on this website.

So we can tell that acceleration of the ground due to ground motion will be different than the induced acceleration of the different buildings. (different buildings will vibrate differently-as the frequency is different- and induced acceleration will also be different) .

In a word acceleration in ground and therefore created acceleration in buildings will not be the same. That is why we need to calculate Sa at short period and Sa at long period of buildings due to ground motions.

From the above discussion Sa at short period controls the low rise buildings and Sa at long period controls the high rise buildings. Basically Sa is the acceleration of buildings due to ground motions.For the definition see here .

Following image can best illustrate the response spectrum ( pga and response of different height buildings )



Actually PGA tells the acceleration of the ground or a small particle situated on the ground..

SA tells the acceleration of the building due to striking that PGA.