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 direction on or within a structure.
• There is no necessity to count inertia and dambing 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 acceleration 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 skyscappers and overbridges to make life convenient.
• From graph it is clearly mensioned that upto certain point from '0' the graph is linear and shows the 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 through shear break.
• Examble: wood, fabric etc...
• In graph inelastic behaviour 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 the stress is gradually increased beyond the elastic limit, the material undergo 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 behavior 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 "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 linearle 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 extrernal force fi on the mass component is related to the acceleration.

4.

Natural period of vibration (Tn)

• It is the time required for the undambed system to complete one cycle of free vibration.
• Units in seconds.
• It is related 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 the system in 1 sec
• units in hertz

5.

Responce spectrum

• It is a central concept iun earthquake engineering, response spectrum is a practical means of characterizing ground motion and their effects on structures of different Tn.
• It provides a convenient means to summarise the peak response of all possible linear SDF systems to particular component of ground emotion.
• It also provides a particular approach to apply the knowledgre of structural dynamics to the design structures and development of lateral force requirements in building codes.
• A plot of the peak value of a responce quantity (u,v and a) as a function of the natural vibration period Tn of the system, is callled the response spectrum for that quantity.
• Each such plot is for caoital SDF system 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 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 acceleration response spectrum.rcrc