Structural dynamics

1.Difference between Static analysis and Dynamic analysis

DYNAMIC ANALYSIS	STATIC ANALYSIS
1.Load is variable with time due to fast applying oF load and vibration.	1.Load is not variable with time and neglected due to slow applying of load.
2. Inertia effect is considered in dynamic analysis.	2.There is no inertia effect on static analysis
3.Motion of the structure can be disregarded.	3.Motion can not be disregarded
4.In dynamic , two additional forces must be accounted such as inertia and damping force in equilibrium equation it can be disregarded in static analysis	4.There is no necessity to count inertia and damping forces in case of static analysis,but the elastic force should be accounted

2)

1. Elastic Behavior:-

Elastic behavior is the property of the material to which the material can retain it's shape. From the mentioned graph it is clearly mentioned that upto a certain point from "O" the graph is linear and shown its elastic properties.

2. Inelastic Behavior:-

Inelastic behavior is the property of the material when the material can't retain it's previous shape after a certain deformation. In the aforementioned graph inelastic behavior has been shown in the upper shape of the curve upto point "a".

3. Plastic Behavior:-

Plastic behavior occurs when the material completely lost it's ductility. In the mentioned graph plastic behavior occurs during unloading after point "a".

4. Non-linear Inelastic Behavior:-

Non-linear inelastic behavior occurs after the line from "O" tends to bend towards point"a".

3)

The Stiffness Component:- The frame is without damping or mass. The external force fs on the stiffness component is related to displacement u by fs= Ku, if the system is linearly elastic.

The Damping Component:- The frame with its damping properties but no stiffness or mass. The external force on the damping component is related to velocity by fd=CV.

The Mass Component:- The roof mass without the stiffness or damping of the frame. The external force fi on the mass component is related to the acceleration by fi=m(Ü)

4)

Natural Period of vibration (Tn):- The time required for the undamped system to complete one cycle of free vibration (unit is seconds)

• It is related to the natural circular frequency of vibration, Wn, in units of radians per second.

Tn= (2π/Wn)

Natural cyclic frequency (f):- The number of cycles (or one complete revolution) executed by system in one second (unit is hertz)

fn =(1/Tn)

• Therefore, the relation between natural period of vibration of the system(Tn) and natural frequency(fn)

fn=(1/Tn)

5)RESPONSE SPECTRUM:-

• It is a central 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 summarize the peak response of all possible linear SDF systems to a particular component of ground motion
• It also provides a particular approach to apply the knowledge of structural dynamics to the design structures and development of lateral force requirements in building codes
• 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 the 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 ζ are included to cover the range of damping values encountered in actual structures
• The response spectrum can be of 3 types , the deformation response spectrum is a plot of peak u, against Tn for fixed ζ . A similar plot for peak ú, is the relative velocity response spectrum, and for peak ü^T ,is the accelaration response spectrum
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