Structural dynamics
Ans 1:- A) STATIC ANALYSIS:-
i) Static analysis does not depend on time.
ii) In Static Analysis Loads are constant.
iii) In Static Analysis Loads are constant with respect to time.
iv) For mathematical Calculations we only consider Stiffness matrix, in Static Analysis.
v) In Static Analysis forces and loads are easy to calculate.
B) DYNAMIC ANALYSIS:-
i) Dynamic Analysis are depend on time.
ii) In Dynamic Analysis load is not constant.
iii) In Dynamic analysis loads are changes with respect to time.
iv) For mathematical Calculations we consider Stiffness matrix, as well as Mass & Damping matrix also.
v) Dynamic Analysis is complex to calculate.
Ans:- 2.1 ELASTIC BEHAVIOUR
IT is the ability of a body to resist any permanent change to it when STRESS & LOAD are applied and regain to its original shape & size when STRESS and LOAD is removed from the body.
The elastic behaviour is varies form material to material.
E.X:- Steel, Tendons and etc.
2.2 INELASTIC BEHAVIOUR
When Body not regain to its original shape and size after removing of STREES & LOADS then the behaviour of the body is called as INELASTIC BEHAVIOUR.
E.X:- Glass, Concrete and etc.
2.3 PLASTIC BEHAVIOUR
When stress is gradually increased beyond the elastic limit, the material undergoes plastic deformation.
Stresses beyond the elastic limit, a material exhibits plastic behavior.
E.g:- Steel, Rubber & etc.
Ans 3:- STIFFNESS COMPONENT
The external forces (fs) on the stiffness component of the structure can be related to the resulting displacement.
For linear systems this relationship can be obtained by the method of superposition and the concept of stiffness influence coefficients.
DAMPING Components in the equation of motion
ITS impact is evident from the steady decline in amplitude of a vibrating body.
Damping in structures is represented in an idealized manner called Equivalent Viscous Damping.
Damping force (fD) is related to the velocity across the linear viscous damper by
fD = C*U
Where, C = Viscous damping coefficient
U = Velocity
Sources of damping in vibrating Structures is
- Friction at steel connection
- Opening & closing of Microcracks in concrete
- Friction between the structure & non-Structural elements such as partion walls.
Ans 4:- Natural Period(Tn), The time required for the undamped system to complete one cycle of free vibration is called Natural period.
The unit of natural period is in Seconds(sec).
Tn = 2π/Wn
The Stiffer of two SDF systems having the same mass will have the shorter natural period i.e, less time to complete one cycle and higher the
natural frequency.
Natural Frequency(f), The number of cycles or one complete revolution executed by a system in 1 second is called Natural Frequency.
The unit of natural frequency is in hertz.
or Natural frequency is the resiprocal of natural time period.
f = 1/Tn
Ans 5:- RESPONSE SPECTRUM is a method to estimate the structure response to short, nondeterministic, transient, dynamic events.
such as, Earthquake, Shocks and etc,
Since, the exact time history of loads is not known it is difficult to perform a time dependent analysis.
A response Spectrum is a function of fequency or period, showing the peak response of a simple harmonic oscillator that is subjected to a transient event.
The response spectrum is a function of the natural frequency of the oscillator and of its damping. Therefore, it is not a direct representation of the frequency content of the excitation, but rather of the effect that the signal has on a postulated system with a single degree of freedom (SDOF).