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 .

 

-

 

 

2

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 .

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

   

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

2