Structural dynamics

Answers-

1]

Static Analysis              

-It is in  linear state and does not vary with time

-It does not depend on time 

-Static force does not change in sixe, position or direction

-In this inertia forces are produced due to their masses

-Example: Hydraulic lifting cranes, stone on ground, etc.

  Dynamic Analysis

-It is acts as a non linear and does vary with time

-It is depenf on time

-Dynamic forces chnage in either size, postitin or direction

-In this inertia forces are considerd in the analysis

-Example:Earthquake, moving car, hammering a metal, etc.

2]

a.Elastic Behaviour-Ability of deformed matrrial body to return to its original shape and size when force causing the deformation are removed

Example:Rubber band. spring. etc.

b.Inelastic Behaviour-Deformatoion material that does not disappear on removal  of force that produced it

Example:wood, fabric, etc.

c.Plastic Behaviour-The material deforms irreversibly and does not return to its original shape and size even whe load is removed.

d.Non-linear elastic behaviour-Materials have elastic behaviour usually only upto a certain point after that deformation are plastic and relation in this is not linaer i.e. non linear elsatic behaviour.

3]Equation of motion 

P-fs-fD=m*u(acceleration)

m*u+fD+fs=P(t)

m*u+c*u(velocity)+k*u=P(t)

where,

m-Mass

k-Stiffness

fD-Damping force

   -Damping force is related to velocity across linear viscous damper by

  fD=c*u      c-viscous damping coeff       u-velocity

Equation of motion:Earthquake excitation

m*u(acceleration)+c*u(velocity)+k*u=-m*ug(t)

4]

Natural Period(Tn):-Time required for undamped system to complete one cycle of free vibration.

                            -Unit is Seconds

                        Tn=2π/Wn      

Natural Frequency(f):-Number of cycle (or one complete revolution) executed by system in one second 

                               -Unit is hertz  

                             f=1/Tn

Natural vibration properties Wn, Tn and f are depend only on mass and stiffness of structure.

5]

Response Spectrum-

-A plot of peak value of response quantity (u, v and a) as a function of natural vibration perod(Tn) of system is called Response Spectrum for that quantity.

-Pseudo acceleration for an SDF system with natural frequency is related to its peak deformation, D=uo

due to earthquake ground motion 

A=(Wn)□">□□*D

  =(2π/Tn)□">□□*D

-Steps involve in construction of Response Spectrum

Step1-Numerically define ground acceleration 

Step2-Select natural vibration period and damping ratio at SDF system

Step3-Compute deformation rsponse of this SDF system due to ground motion

Step4-Determine uo, peak value u(t)

Step5-Spectral ordinates are D=uo, V=(2π/Tn)*D and A=(2π/Tn)□">□□*D