****An
earthquake produces seismic waves that cause the earth’s crust to vibrate. These
waves impart a momentary acceleration to the earth’s crust and it starts moving
in the direction in which the wave is travelling at that instant. The
characteristics of vibration, such as intensity, duration, etc at any location
depend upon a number of factors which includes as follows; * Magnitude f
earthquake

  • Depth of focus
  • Epi-central
    distance
  • The characteristics
    of the material through which the seismic waves travel.

Inertia force:

When the ground motion occurs, the foundation of the structure must also move
with it to avoid its rupture. When the foundation moves, the structure on it
tries to stay back due to inertia. Consequently, the structure is subjected to
inertia forces. In the earthquake-resistant design of structures, the inertia
forces due to earthquake are considered in addition to the normal loads and
forces.

When the horizontal shaking of ground is set up, the horizontal inertia forces
are generated at the level of the mass of the structure, which is generally
assumed to be concentrated at the floor levels. These inertia forces are then
transferred from the slab through the walls or columns to the foundation and
finally to the strata below the foundation. In earthquake resistant design it is
ensured that each of the structural components including floor slabs, walls,
columns, beams, and foundations can safely transfer the inertia forces through
them. Moreover, the connections between the various structural elements needs to
be properly design and constructed.

Response spectrum:
[http://4.bp.blogspot.com/-SUTzcp0CvMU/VRQfiMbNxbI/AAAAAAAABMQ/UE0Yp91seno/s1600/images7.jpg]

If the buildings were rigid, then every point on it would be moved by the same
amount as the ground and consequently the inertia force would be equal to the
mass multiplied by the ground acceleration. But the buildings are flexible and
different parts move back-and-forth by different amounts during ground shaking.

The natural period of vibration of a structure is the time period of its
un-damped, free vibrations. Te fundamental natural period of vibration is that
for the first (or fundamental) mode of vibration of that structure. Each
structure has a unique fundamental period of vibration at which it tends to
vibrate when it is allowed to vibrate freely without any external excitation.
The fundamental natural period depends upon the form and configuration of
structure, the stiffness (or flexibility) of the various structural members, the
type and material of construction, etc. For the determination of the fundamental
natural period of vibration a structure can be done using the structural code
which gives the empirical formulae to be utilized.

For the estimation for seismic forces in structures, the response spectra are
commonly used in practice. The response spectrum of a structure shows the
maximum response induced by the structure during the ground motion. It is
generally plotted in terms of maximum absolute acceleration against natural
period; sometimes the maximum relative velocity or the maximum relative
displacements may also be used. During plotting the response spectrum, it is
assumed that the structure has single degree of freedom and it may have
different dampening. In other words, the maximum response spectrum represents
the maximum acceleration of an idealized single degree freedom systems having a
certain natural period of vibration and dampening when it is subjected to
earthquake ground motion.

Use of response spectrum:

  1. The response of the system decreases as the damping of the system increases.
    In buildings usually 5 percent damping is allowed/assumed.
  2. As the natural period increases, the acceleration ratio first increases to a
    maximum value and then decreases. For the structural system shown, the
    greatest acceleration occurs when natural period is about 0.3 s.
  3. In the usual practice in the earthquake-resistant design to represent the
    structural response by the response factor or spectral coefficient in the
    normalized form as �Sa/g�.
  4. The response spectrum helps the earthquake engineer to predict how a
    particular structure with a certain natural period will respond to the
    earthquake.
  5. The response spectra are commonly used in the estimation of seismic forces.