Structural dynamics

1. Differentiate Static analysis and Dynamic analysis

with proper representing pictures (30 marks)

ANSWER -

STATIC ANALYSIS -

-Static refers to force that has

constant Size , position and direction

on or with in a structure .

-There is no necessary to count

inertia and damping forces in case

of static analysis , but elastic force

should be accounted

-in static analysis not consider Inertia .

-static analysis can only performed if

system will be Simulated ,

does not depends on time .

-Take Load will be applied constant .

DYNAMIC ANALYSIS -

In dynamic refers to force on a structures

that changes size , position ,and direction .

-in dynamic two additional forces may be

accounted such as inertia and damping

force .in equillibrium equation it can

be disrearded in static analysis .

-in dynamic analysis load application

or both might change with time .

-

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2. Explain the following with relevant

force-displacement graph (40 marks)

1. Elastic behavior
2. Inelastic behavior
3. Plastic behavior
4. Non-linear Inelastic behavior

1. ELASTIC BEHAVIOR -

-Elasticity , ability of deformed material body

to return its original shape and size when

force causing the deformation removed .

-the theory of elastcity is used to

design safe and stable man made structures

such as Skyscrappers and over bridge

to make life convinent .

2 . INELASTIC BEHAVIOUR -

THE behaviour of material in here

material not comes in original

shape after a certain ultimate limit .

and shown rupture suddenly

shown brittle material type qualities .

-because of material have no elongation

up to its ultimate strength .

ex.

WOOD , FABRICATES ETC.

3. PLASTIC BEHAVIOUR -

When stress is grudually increased

beyond elastic limit , material undergoes

platic behaviour .

-stress beyond the elastic limit

a material a material exhibits plastic behaviours .

-in plastic behaviour of material ,materials

shown continued deformation and not comes

its original shape after deformation will be start .

ex - plastic wrap

2 . NON LINEAR INELATIC BEHAVIOR -

-Material shows elastic behaviours

at certain limit after that deformation

will start and shows diffrent properties

of strenth of material as like 1st convert

to plastic behaviours and than next further

continue to start elongation and

than shown its non linear behaviour

its non linear behaviors of material .

3. Explain Mass, Stiffness & Damping components

in the equation of motion (30 marks)

STIFFNESS COMPONENTS -

-FRame without damping and mass .

-external force Fs = ku

k stiffness component related to U

deformation .

- if system is linearly elastic .

2 DAMPING COMPONENTS -

frame having damping property

without stiffness and mass .

-EXTERNAL FORCE of

damping components Fd = cv

is related to velocity .

-3MASS COMPONENT -

Roff mass without stiffness or

damping of frame .

-external force Fi =mu `[2 pi ] / [Wn]`

mass components related to

accelaration .

4. Provide relationship between Natural period (Tn)

& Natural frequency (f) and provide their definitions

answer -

NATURAL PERIO OF VIBRATION Tn

-it is time required for

undamped system to

complete one

cycle of free vibration .

-Units = seconds

Tn = `[ 2 pi ] / [W n ]`= 2π /Wn

it is related

natural circular frequency of vibration Wn

unit = radian / seconds

2. NATURAL CYCLIC FREQUENCY - F n

no. of cycles [or one complete revoluation ]

executed by system in 1 sec.

unit = hertz

Fn =1 / Tn

5. Explain in detail about Response spectrum & its Graph (25 marks)

Response spectrum means

of characterized ground

motion and there effect on

structure .

-it summarize peak response of all

possible linear SDF systems

- it also provided a particular

approch to apply knowledge of

structural dynamicks to design structures .

-and also helpful for find out devloped

lateral force requirement in building codes .

-plot of peak values of response quantity

[ U ,V AND a ] as a function of natural

vibration period = Tn

is called response Spectrum of that

Quaintity .

-each such plot for SDF system

having a fixed damping ration .

-response spectrum can be 3 types

Deformation response spectrum is

a plot of peak U ,

aginist Tn have fixed damping ration

-a similar plot U , is relative velocity

response spectrum .

and for peak is U^t is accelaration

response spectrum .

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