Structural dynamics
1. ANS: DIFFERENTIATE BETWEEEN STATIC ANALYSIS AND DYNAMIC ANALYSIS WITH PROPER ANALYSIS:
AIM :
The main aim of this challenge is to gain the knowledge about the concept of structural dynamics which helps to understand the behaviour of the structure when it is subjected to the seismic force. The various that are related to the dynamic analysis are also leant.
PROCEDURE:
1. Differentiate static analysis and dynamic analysis with proper representing pictures.
1.A: Static analysis:
1. A static analysis can only be performed if the system being simulated does not depend on time, and if the loads being applied are constant.
2. Static analysis don't consider inertia.
3. In a static analysis, only the stiffness matrix of the FEA model is solved.
4. Static analysis require less computational time.
B. Dynamic analysis:
1. In a dynamic analysis,the system itself, if the load application, or both might change with time.
2. In a dynamic analysis, the inertial loads developed by the system due to acceleration are taken into account.
3. In a dynamic analysis, in addition to the stiffeness matrix the mass matrix ( and damping matrix, if not zero) is solved well.
4. Dynamic analyses require more computational time.
2. ANS : EXPLAIN ABOUT THE RELEVANT FORCE-DISPLACEMENT GRAPH:
1. ELASTIC BEHAVIOUR:
It is ability of the body to resist a distorting influence and to return to its original size and shape when that influence or force is removed. Solid objects will deform when adequate loads are applied to them if the material is elastic, the object will return to its intial shape and size after removal.
2. INELASTIC BEHAVIOUR:
The term "inelastic" is used to define the material response in relation to the stress - strain diagram that is non-linear and that retains a permenent strain or retains to an unstrained state on complete unloading.
3. PLASTIC BEHAVIOUR:
It is the ability of a solid material to undergo permenent deformation, a non reversible change of shape in response to applied forces.
4. NON-LINEAR INELASTIC BEHAVIOUR:
Materials have elastic behaviour usually only upto a certain point after that deformation are plastic and relation in this is not linear i.e., non linear elastic behaviour.
3. ANS: EXPLAIN ABOUT THE MASS, STIFFNESS & DAMPING COMPONENTS IN THE EQUATION OF MOTION.:
STIFNESS COMPONENTS :
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:
The frame with its damping property with no stiffness or mass. The external force on the damping component is related to velocity by fd=cv.
MASS COMPONENT:
The roof mass without the stiffness or damping of the frame. The external force fi on the mass component is related to the acceleration by fi = mu.
mu + fD + fs = p(t) ---> mu + cv+ ku = p(t).
4. ANS:
THE RELATIONSHIP BETWEEN NATURAL PERIOD Tn & NATURAL FREQUENCY f AND PROVIDE THEIR DEFINITIONS:
NATURAL PERIOD:
Natural period Tn of a building is the time taken by it to undergo one complete cycle of oscillation. It is an inherent property of a building controlled by its mass M and stiffness k. these three quantities are related by its units are seconds(s).
Tn = 2 X 3.14 (m/k )
NATURAL FREQUENCY:
The reciprocal (1/Tn ) of natural period of a building is called the natural frequency fn ; is unit is hertz(Hz).
5. ANS:
EXPLANATION ABOUT THE RESPONSE SPECTRUM CURVE:
1. Response spectrum is a practical means of characterizing ground motions and their effects on structures for different time period Tn.
2.It provide a convienent means to summarize the peak response of all possible linear SDF systems to a particular component of ground motion.
3. It also provides a particular approach to apply the knowledge of structural dynamics to the design of structures and development of lateral force requirements in building codes.
4. A plot of the peak value of a response quantity ( u,v, a )as a function of the natural vibration period Tn of the systemis called the response spectrum for that quantity.
5. Each plot is for SDF systems having a fixed damping ratio and several such plots for different values of are included values to cover the rangeof damping values encountered in actual strutures.
6. The response spectrum can be of 3 types the deformation response spectrum is a plot of peak u, against Tn for fixed a similar plot for peak v, is the relative velocity response spectrum and for peak uT, is the accelaration response spectrum.
CONCLUSION:
From the challenge carried out it can concluded that the concept of behaviour of a structure when subjected to the seismic force is learnt. The concept of analysing a structure by converting the dynamic force to the seismic force is also learnt.