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For structural engineers, the deformation of the system or relative displacement with respect to the ground is of great interest.

**Importance of response
quantities **

For structural engineers, the
deformation of the system or relative displacement with respect to the ground
is of great interest. Internal forces, base shear and moments are usually
related to displacement. Knowing the total displacement of the mass *u _{t}*(

1 Response history

For a given earthquake ground motion *u***˙˙*** _{g}*
(

The damping factor is 2%. The
only difference among the three systems is the natural periods. It is also seen
that the time required for a SDOF systems to complete a cycle of vibration when
subjected to earthquake ground motion is also equal to the natural period of
displacement. Peak displacement is shown in each case

The longer the natural period, the greater the peak
deformation. Figure 17.9 shows the deformation response of three systems to the
same ground motion. Vibration period *T _{n}* is the same for all
but damping is different. From Fig. 17.9 we can observe that systems with more
damping respond less than lightly damped systems because the natural periods of
three systems are same. Once

*Fs*(*t*) =* V _{b}*

Equivalent *static force* is introduced which is a
central concept in earthquake response of the structure. At any instant of time
*t*, the force *Fs* is the static (slowly) applied force that will
produce deformation *U*(*t*)

Observe that the equivalent
static force is *m* times *A*(*t*), the pseudo-acceleration, not
*m* times total acceleration.

The pseudo-acceleration response can be calculated from the
deformation response for the three systems *T _{n}* = 0.5:

For *T _{n}* = 1 s

Thus a static analysis of structure would be required at each
time when the response is desired. The base shear and base moment are
calculated as

*V _{b}*(

*V _{b}*(

Tags : Civil - Structural dynamics of earthquake engineering

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