Structural dynamics

1. Differentiate Static analysis and Dynamic analysis with proper representing pictures

Ans :

Static analysis	Dynamic analysis
static analysis doesnot consider inertia force along with static force	dynamic analysis consider inertia force along with dynamic force
The displacement obtained by static analysis are more	The displacement obtained by dynamic analysis are less
There is no necessity to count inertia and damping forces in case of static analysis , but the elastic force should be accounted	two additional forces must be accounted such as inertia and damping force in equilibrium equation it can be disregarded in static analysis

2. Explain the following with relevant force-displacement graph (40 marks)

1)Elastic behavior :

Elasticity, ability of a deformed material body to return to its original shape and size when the forces causing the deformation are removed. A body with this ability is said to behave (or respond) elastically To a greater or lesser extent, most soild materials exhibit elastic behaviour, but there is a limit to the magnitude of the force and the accompanying deformation within which elastic recovery is possible for any given material. This limit, called the elastic is the maximum stress or force per unit area within a solid material that can arise before the onset of permanent deformation.From graph it is clearly mensioned that upto certain point from O the graph is linear and shows elastic properties

2) Inelastic behavior :

Inelastic behavior of material only lasts up to a certain strength ,material that cannot from it original shap and size after the deformation are called inelastic . Inelastic material will experience no elongation or deflection and up to its ultimate strength is reached will just rupture suddenly usually through shear break. inelastic behavior has been shown in the upper shape of the curve upto point a

3)Plastic behavior :

The elastic limit, a material exhibits plastic behavior. This means the material deforms irreversibly and does not return to its original shape and size, even when the load is removed. When stress is gradually increased beyond the elastic limit, the material undergoes plastic deformation .plastic behavior occurs during unloading after point a

4)Non-linear Inelastic behavior :

Materials have elastic behvior usually only upto a certain point after that deformation are plastic and the relation in this is not linear, that is non linear elastic behavior .Non-linear elastic behavior occurs after the line from o tends to bend towards point a

3. Explain Mass, Stiffness & Damping components in the equation of motion

Ans :

stiffness component :

The frame without damping or mass .The external force fs on the stiffness component is related to displacement u by fs= ku ,If the system is linear elastic

Damping component :

The frame with its damping property with no stiffness or mass . The external force on the damping component is related to velocity by fd =cv

Mass component :

The roof mass without stiffness or damping of the frame . The external force fi on the mass component is related to the accelartion

4. Provide relationship between Natural period (Tn) & Natural frequency (f) and provide their definitions

Ans :

Natural Period of vibration ( Tn )

It is the time required for the undamped system to complete on cycle of free vibration (unit in second ) , It is realated to the natural circular frequency of vibration wn, in units of radians per second

Natural cyclic Frequency ( fn ) :

The number of cycles (or one complete revolution ) executed by system in 1 sec , units in hertz

5. Explain in detail about Response spectrum & its Graph

Ans :

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