Structural dynamics

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

ANS:

Static analysis:

•   Static analysis of structures considers static loads acting on the structure such as dead, live loads which does not vary with time and are considered to be sudden. in static analysis siffness matrix alone is considered and the inertial forces are not considered motion of the structure is not considered.

Dynamic analysis: 

• Dynamic analysis of structures consider dynamic loads acting on the structure such as wind, earthquake loads which varies with time, these loads are sudden and does not follow a constant pattern  and vary time in dynamic analysis along with stiffness matrix, mass matrix and damping matrix is also included . motion of the structure is considered.
• So  the basic difference between static analysis and dynamic analysis is that the loads considered in static analysis does not vary time where as the loads consisder in dynamic analysis vary with time.

2. Explain the following with relevant force-displacement graph (40 marks)

1. Elastic behavior
2. Inelastic behavior
3. Plastic behavior
4. Non-linear Inelastic behavior

1. Elastic behavior:

• Elasticity, ability of a deformed material body to return to its original shape and size when the force causing the deformation are removed.
• A body with this ability is said behave elastically
• Form graph it is cleary mensioned that upto certain point from O the graph is linear and shown elastic properties.

2. Inelastic behavior

• Defomation material that does not disappear on the removal of force produced by it 
• Inelastic material will experience on elongation or deflection and up to ultimate strength is reached will jsut suddenly uslally throung shear break
• in graph inelastic behavior has been shown in the upper shape of the curve upto point a

3. Plastic behavior:

• For stresses beyond the elasticlimit, a material exhibits plastic behavior
• This means the material deforms irreversilbly and does not return tom 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
• In graph the plastic behavior occurs during unloading after point a.

4. Non - Liner inelastic behavior:

• Material have elastic behavior usually only upon a certain point after that deformation are plastic and the relation in this not liner that elastic behavior
• Non - linerelastic behavior occurs after the line from o tender to bend toward point a.

The graph represent the behavourial of the above mentioned systems and the graph obtained is based on the cyclic loading and unloading.

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

ANS:

Stiffness componet:

•  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 it on the mass componentn is related to the accelaration

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

ANS:

Natural period of vibration (Tn)

• It is the time required for the undamped system to completed one cycle of free vibration 
• Units in second 
• It is related to the natural circular frequency of vibration wn, in units of radians per second 

Natural cyclic Frequency:

• The number of cycles (or one complete revolution) executed by system in 1sec
• Unites in hertz

5. Explain in detail about Response spectrum & its Graph

 RESPONSE SPECTRUM:

• It is a central concept in earthquake engineering response spectrum is a practical means of characterizing ground motions and thier effects on structure of different Tn
• It provided a conveninet means to summarize the peak response of all possible linear SDF system to a particular component of ground motion
• It also provided a particular approach to apply the knowledge of structural dynamics to the design strctyures and development of lateral force requirment in building codes
• A plot of the peak value of a response quantity (u,v and a) as a functionof the natural
• Each such plot for SDF systems haviong a fixed damping ration and serveral such plots for differenrt vaule are included to cover the range of damping values encountered in actual strcutures
• The response spectrum can be of 3 type deformation response specttrum is a plot of peak u, agaist Tn for fixed . A similer plot peak u, is the relative velcity response spectrum , and for peak u is the accelaration response spectrum