Structural dynamics

1.Analysis carried on static loads are called static analysis and on dynamic loads are called as dynamic analysis.Building's dead load,live load are static loads while earthquake ,wind loads are dynamic loads. Dynamic loads will vary with time and motion shall be taken into consideration in dynamic analysis. And two additional loads such as inertia forces and damping forces are also taken into consideration in dynamic analysis.

2.For a linear system the relationship between the lateral forces Fs and resulting deformation U.

fs = ku

where k is the lateral stiffness which is constant in case of linear and vary in case of Non linear displacement (U).

Force displacement relationship becomes Non-linear and in elastic at large deformations. Force Fs corresponding to deformation is not single valued and depends on history of deformation and whether deofrmations are increasing or decreasing.

fs = fs (u,v).

Linear displacement in small deflection while Non-linear displacement in case of large deflection.

3.Mass componeent : The roof mass without the stiffness or damping of the frame. The external force (fi) on the mass componenet is related to the acceleration by fi = mu..

mu+fd+fs = p(t)

Stiffnes componenet : The frame without damping or mass. The external force fs on the stiffness componenet is related to displacement u by fs = ku, if the system is linearly elastic.

Damping componenet :The frame with its damping property but no stiffness or mass. The external force fs on the damping componenet is related to velocity by fd = cv.

4. Natural period of vibration of the sysytem (Tn): The time required for the undamped system to complete one cycle of free vibration. (unit - sec).It is related to natural circular frequency of vibration wn (Unit - radians)

Tn = 2pi/wn or wn=2pi/Tn

Natural cyclic frequency of vibration of the system - the number of cycles (or one complete revolution)executed by system in 1 second (unit - hertz).

5.Response spectrum : A plot of peak value of a response quantity (u,v,a) as a function of natural vibration period Tn of the system is called response spectrum for that quantity.

Types are deformation response spectrun, relative velocity response spectrum and acceleration response spectrum.

Response spectrum method is used for dynamic analysis ,Response reduction factor is taken into consideration for designing the structure as per seismic zone. ie 3 to 5 as per IS code 1893 part I.