Structural dynamics

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

Ans: In Static Analysis,force applied on a particular structure vary very slowly w.r.t time and thus, is assumed to be constant with respect to time,while in Dynamic analysis,forces vary w.r.t time.If the forces vary quickly w.r.t time than the movement cannot be disregarded.Thus,two additional forces must be taken into account in Dynamic analysis i.e Inertia Forces and Damping Forces.Moreover,the need for DOF for defining the stiffness properties in Dynamic analysis is less than the DOF required for Static analysis.

2. Explain the following with relevant force-displacement graph.

a)Elastic behavior

b)Inelastic behavior

c)Plastic behavior

d)Non-linear Inelastic behavior

Ans:

Elastic behavior:- After the application of force in the structure, if the restoring force in a structure is directly proportional to its deformation then that behavior is known as elastic behavior of structures.This is not valid for larger displacements.

Inelastic behavior:- If a structure,after the removal of load does not come to its original shape than the behavior is known as Inelastic behavior.Here,restoring force is not directly proportional to the deformation.

Plastic behavior:- If a structure,after applying a small amount of load deforms significantly then the structure is said to show plastic behavior.

Non-linear Inelastic behavior:- If upon application of load,the deformation is not proportional to the force applied and after the removal of the load,the structure doesnt return into its original shape then it is known as Non-linear Inelastic behavior.

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

Ans: For SDOF, the applied external force is distributed among the three components i.e inertial force,stiffness force and dampening force.

inertial force=ma;stiffness force=Ku;dampening force=cv

where,a=acceleration,u=displacement and v=velocity.

ma+Ku+cv=p(t)........is the equation of motion.

After taking the movement of ground into consideration p(t)=ma`,where a`=acceleration of the ground movement.

Thus,the equation can be modified as;

ma+Ku+cv=ma`

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

Ans:

Natural period(Tn) is the type required for an undamped system to complete one cycle of free vibration.

Natural frequency(fn)is the number of revolutions/cycles completed in one second of free vibration.

Tn=2π/wn ; fn=1/Tn

5. Explain in detail about Response spectrum & its Graph.

Ans: It is a central concept in earthquake engineering.It is a practical means of characterizing ground motions and their effects on structures on the basis of different Tn.It helps us in summarizing the peak response of all linear SDOF to a particular component of the ground motion.It also helps us in providing practical approach for the application of knowledge of structural dynamics to the deisgn of structures and development of lateral force requirement in building codes.

A plot of the peak value of a response quantity as a function of natural vibration period Tn of the system is called the response spectrum for that quantity.The response spectrum can be of 3 types.