An earthquake produces seismic waves that cause the earths crust to vibrate. These waves impart a momentary acceleration to the earths 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.
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.
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:
- The response of the system decreases as the damping of the system increases. In buildings usually 5 percent damping is allowed/assumed.
- 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.
- 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.
- The response spectrum helps the earthquake engineer to predict how a particular structure with a certain natural period will respond to the earthquake.
- The response spectra are commonly used in the estimation of seismic forces.