Challenge

Structural dynamics

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

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STATIC ANALYSIS

Static analysis can only be performed if the system being simulated does not depend on time,and if the loads being applied are constant.
Static analysis don't consider inertia.
Static refers to the force that has constant size,position and direction on or within a structure
There is no necessity to count inertia and damping forces in case of static analysis,but the elastic force should be accounted

DYNAMIC ANALYSIS

In dynamic analysis ,the system itself,the load application or both might change with time
The inertial force developed by the system due to accelaration are taken into account
Dynamic refers to a force on a structure that changes size, position or direction
In dynamic , two additional forces must be accounted such as inertia and damping force in equilibrium equation it can be disregarded in static analysis

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2. Explain the following with relevant force-displacement graph

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1.Elastic behavior

Elasticity , ability of a deformed material body to return to its original shape and size when the forces causing the deformations are removed
A body with this ability is said to behave elastically
The theory of elasticity is used to design safe and stable man-made structures such as skyscrappers and overbridges to make life convenient
From graph it is clearly mensioned that upto certain point from 'O' the graph is linear and shows elastic properties

2.Inelastic behavior

Deformation material that does not disappear on the removal of force produced by it
Inelastic material will experience no elongation or deflection and up to its ultimate strength is reached will just rupture suddenly usually through shear break
Example: wood, fabricetc..
In graph inelastic behavior has been shown in the upper shape of the curve upto point "a"

3.Plastic behavior

For stresses beyond 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 wrap is an example of plasticity
In graph the plastic behavior occurs during unloading after point "a"

2.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"

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

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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 linearly elastic

Damping component

Mass component

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

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Natural Period Of Vibration (Tn)

It is the time required for the undamped system to complete one cycle of free vibration
Units in seconds
It is realated to the natural circular frequency of vibration wn , in units of radians per second

Natural Cyclic Frequency (fn)

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5. Explain in detail about Response spectrum & its Graph

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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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