Challenge

Structural dynamics

BBusaramanu Mahesh1 Mar 2023

Question 1:

ANS: Differentiate Static analysis and Dynamic analysis.

Force displacement system

damping force

equation of motion -an external force

equation of motion -earthquake excitation

undamped free vibration systems,

viscously Damped free damping

Dynamic analysis:

response spectrum concept,

deformation,pseudo-velocity, and pseudo-acceleration response spectra

peak structural response from the response spectrum.

Quetion:2

ANS: Explain the following with the relevant force-displacement graph

Elastic behavior

A force-displacement graph will have force in N on the vertical axis and displacement in m on the horizontal axis. the area of the graph is =f.s. this quantity also represents the work done by the object.

2.InElastic behavior

used to define the material response in relation to the stress-strain diagram that in non-linear and that retains a permanent strain or returns to an unstrained state on complete unloading.

3. Plastic behavior

For stresses beyond the elastic limit,a material exhibits plastic behavior. this means the material deforms irreversibly and does not return to original position and shape and size. even the load is removed. when the stress is gradually increased beyond the elastic limit, the material undergoes plastic deformation.

4. Non-linear Inelastic behavior

Materials have elastic behavior usually only up to a certain load, which is called the yield point, after that the deformations are plastic. rubber, for instance, has an elastic stress-strain curve, but the relation is not linear -in such cases, nonlinear elastic models are required.

Quetion:3.

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

ANS:

Stiffness, damping, and mass components
.The SDOF system can be viewed as a combination of three pure, independent systems:
-the stiffness component: the frame without damage or mass. The external force Fs on the stiffness component is related to velocity by fd = cv
-the mass component of 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
Damping force Fo is related to the velocity across the linear viscous by FD = Cu.

Quetion:4

ANS:

Time period (T) is the amount of time an oscillating body takes to repeat itself, and Frequency (f or ν) is the number of times it repeats in one second or unit of time.
If you measure time in s (seconds) then the frequency is measured in Hz (cycles or periods per second).

Frequency is inversely proportional to the time period. f=1T.
Natural frequency, also known as eigenfrequency, is the frequency at which a system tends to oscillate in the absence of any driving force.

Quetion:5

ANS:

Response spectrum
1. 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.
2. Each such plot is for an SDF system having a fixed damping ratio and several such plots for different values of z are included to cover the range of damping values encountered in actual structures.
3. the response spectrum can be of 3 types. the deformation response spectrum is a plot of peak u. against Tn for fixed z. similar plot peak u is the relative velocity response spectrum, and peak u, is the acceleration response spectrum.

PSEUDO - ACCELERATION RESPONSE SPECTRUM
1. pseudo acceleration for an sdf system with natural frequency Wn is related to its peak deformation D=Uo due to earthquake ground motion.
A= W2D=((2X PIE)/Tn)^2 D
2. The quantity A has units of acceleration and is related to the peak value of base shear Vbo(Just another name for the peak value of the equivalent static force fso)
Vbo=Fso = mA.

Structural dynamics

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Ship work like this
in your own course.