Structural dynamics

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

DYNAMIC ANALYSIS:

• In a dynamic analysis, the system itself, the load application, or both might change with time.
• In a dynamic analysis, the inertial loads developed by the system due to acceleration are taken into account.
• In a dynamic analysis, in addition to the stiffness matrix, the mass matrix (and damping matrix, if not zero) is solved as well.
• Dynamic analyses require more computational time.

STATIC ANALYSIS:

• A 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 analyses don’t consider inertia.
• In a static analysis, only the stiffness matrix of the FEA model is solved.
• Static analyses require less computational time.

2.Explain the following with relevant force-displacement graph

Elastic behavior

Inelastic behavior

Plastic behavior

Non-linear Inelastic behavior

Elastic behaviour:

• It is the ability of a body to resist a distorting influence and to return to its original size and shape when that influence or force is removed. Solid objects will deform when adequate loads are applied to them; if the material is elastic, the object will return to its initial shape and size after removal.

Inelastic behaviour

• The term, “inelastic” is used to define the material response in relation to the stress-strain diagram that is non-linear and that retains a permanent strain or returns to an unstrained state on complete unloading.

Plastic behaviour

• It is the ability of a solid material to undergo permanent deformation, a non-reversible change of shape in response to applied forces.

Non-linear Inelastic behaviour

• Materials have elastic behaviour usually only upto a certain point after that deformation are plastic and relation in this is not linaer i.e. non linear elsatic behaviour.

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

Mass component:

• 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 = mű

mü + fD + fs = p(t) → mü + cὺ + ku = p(t)

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

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

NATURAL PERIOD:

• Natural Period Tn of a building is the time taken by it to undergo one complete cycle of oscillation. It is an inherent property of a building controlled by its mass m and stiffness k. These three quantities are related by its units are seconds (s).

Tn = 2 π √ (m/k)

Natural frequency:

• The reciprocal (1/Tn) of natural period of a building is called the Natural Frequency fn; its unit is Hertz (Hz).

5.Explain in detail about Response spectrum & its Graph

• Response spectrum is a practical means of characterizing ground motions and their effects on structures for different time period 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 of structures and development of lateral force requirements in building codes.
• Each such plot is for SDF systems having a fixed damping ratio ᶗ and several such plots for different values of ᶗ 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 ᶗ.