Structural dynamics
1. Differentiate Static analysis and Dynamic analysis with proper representing pictures.
Answer:
The difference between Static analysis and Dynamic analysis are:
STATIC ANALYSIS:
i). Load is not variable with time and neglected due to slow applying of load.
ii). Motion of the structure can be disregarded.
iii). There is no necessity to count Inertia and damping forces in case of static analysis, but the elastic force should be accounted.
iv). There is no inertia effect on static analysis.
DYNAMIC ANALYSIS
i). Load is variable with time due to fast applying of load and vibration.
ii). Motion can't be disregarded (can't be considered as static).
iii). Inertia and damping forces should be accounted for the calculation of dynamic analysis.
iv). Inertia effect is considered dynamic analysis.
2. Explain the following with relevant force-displacement graph.
Elastic behavior
Inelastic behavior
Plastic behavior
Non-linear Inelastic behavior
Answer:
Elastic behavior:
Elasticity , ability of a deformed material body to return to its original shape and size when the forces causing the deformations are removed. A body with this ability is said to behave elastically. The theory of elasticity is used to design safe and stable man-made structures such as skyscrappers and overbridges to make life convenient. From graph it is clearly mensioned that upto certain point from 'O' the graph is linear and shows elastic properties.
Inelastic behavior
Deformation material that does not disappear on the removal of force produced by it. Inelastic material will experience no elongation or deflection and up to its ultimate strength is reached will just rupture suddenly usually through shear break.
Example: wood, fabricetc..
In graph inelastic behavior has been shown in the upper shape of the curve upto point "a".
Plastic behavior:
For stresses beyond the elastic limit,a material exhibits plastic behavior. This means the material deforms irreversibly and does not return to its original shape and size, even when the load is removed. When stress is gradually increased beyond the elastic limit, the material undergoes plastic deformation.
Plastic wrap is an example of plasticity.
In graph the plastic behavior occurs during unloading after point "a".
Non-linear Inelastic behavior:
Materials have elastic behvior usually only upto a certain point after that deformation are plastic and the relation in this is not linear, that is non linear elastic behavior. Non-linear elastic behavior occurs after the line from "o" tends to bend towards point"a"
3. Explain Mass, Stiffness & Damping components in the equation of motion.
Answer:
Stiffness component:
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 stiffness or damping of the frame. The external force fi on the mass component is related to the accelaration.
4. Provide relationship between Natural period (Tn) & Natural frequency (f) and provide their definitions.
Answer:
Natural Period of Vibration (Tn):
It is the time required for the undamped system to complete one cycle of free vibration.
Units in seconds.
It is realated to the natural circular frequency of vibration wn , in units of radians per second .
Natural Cyclic Frequency (fn):
The number of cycles (or one complete revolution) executed by system in 1 sec.
Units in hertz.
5. Explain in detail about Response spectrum & its Graph.
Answer:
RESPONSE SPECTRUM
It is a central concept in earthquake engineering, response spectrum is a practical means of characterizing ground motions and their effects on structures of different Tn
It provides a convenient means to summarize the peak response of all possible linear SDF systems to a particular component of ground motion
It also provides a particular approach to apply the knowledge of structural dynamics to the design structures and development of lateral force requirements in building codes
A plot of the peak value of a response quantity (u,v and a) as a function of the natural vibration period Tn of the system,is called the response spectrum for that quantity
Each such plot is for SDF systems having a fixed damping ratio ζ and several such plots for different values ζ are included to cover the range of damping values encountered in actual structures
The response spectrum can be of 3 types , the deformation response spectrum is a plot of peak u, against Tn for fixed ζ . A similar plot for peak ú, is the relative velocity response spectrum, and for peak üT ,is the accelaration response spectrum
