Structural dynamics

1) More DOFs are typically necessary to define the stiffness properties of a structure compared to the DOFs necessary for dynamic analysis.

2)A SDOF system subjected to externally applied static force with no dynamic excitation.

For a linear system the relationship between the lateral force Fs and resulting deformation u is linear, that is 

Fs=Ku

Where K is the lateral stiffness of the system, its units are force/length.

Compute lateral stiffness of the frame with an intermediate realistic stiffness of the beam.

Assume L=2h  and  EIb=EIc

Force displacement relationship becomes non-linear and inelastic at large deformation.

Force Fs corresponding to deformation is not single valued and depends on history of deformation and whether deformations is increasing or decreasing.Thus the resisting force can be expressed as 

Fs=Fs(u,v)

3) The differential equation governing the displacement u(t) of an idealized single story frame subjected to an externally applied force P(t) can be derived using newtons second law of motion.

P-Fs-Fd=Mü

Mü+Fd+Fs=P(t)

Mü+CÚ+KU=P(t)

4) Natural cyclic frequency of vibration of the system the number of cycles (or one complete revolution) executed by system in sec (unit is hertz)

Fn=1/Tn

5) Acentral concept in earthquake engineering response spectrum is a practical means of characterizing ground motions and their effects on structures of different Tn.

It provides a convenient means to summerize the peak response of all possible linear SDF systems to a particular component of ground motion.

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

Each such plot is for SDF systems having a fixed damping ratio ζ and several such plots for different values of ζ

are included to cover the range of damping values encountered in actual structures.