Structural dynamics

1.

STATIC ANALYSIS

• Static analysis can only be performed if the system being simulated does not depend on time,and if the loads being applied are constant.
• Static analysis don't consider inertia.
• Static refers to the force that has constant size,position and direction on or within a structure
• There is no necessity to count inertia and damping forces in case of static analysis,but the elastic force should be accounted

DYNAMIC ANALYSIS

• In dynamic analysis ,the system itself,the load application or both might change with time
• The inertial force developed by the system due to accelaration are taken into account
• Dynamic refers to a force on a structure that changes size, position or direction
• In dynamic , two additional forces must be accounted such as inertia and damping force in equilibrium equation it can be disregarded in static analysis

2.

1.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

2.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"

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 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"

4.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.
• 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.
• 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.

• 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