Structural dynamics

1. Differentiate Static analysis and Dynamic analysis with proper representing pictures (30 marks)

    STATIC ANALYSIS

•  Static analysis primarliy concerned with assessing the response of structures under static loads.Static loads are those that do not change over time,such as weight of building itself,occupants and stationary objects
• Engineer's use static analysis to determine how a structure will deform and distribute stress under these steady loads.Common technique includes finite element methodsand manual calculations.
• It is essential for design of buildings and structuresto ensure that they can support their own weight and expected loads without expected deformation or failure.

  DYNAMIC ANALYSIS

• Dynamic analysis focuses on how the structures respond to dynamic or time - varying loads.These loads can include forces from wind,earthquake or traffic, or machinery.
• Engineers employ the dynamic analysis to study how a structure vibrates , oscillates or moves when subjected to dynamic loads.Ttechniques are finite element methods and modal analysis are used for the understanding a structures natural frequencies and rensponse to external forces
• It is crucial for ensuring that structures can withstand forces like earthquakes ,wind gusts and vibrations from nearby sources like heavenly machinery

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

    

    

3. Explain Mass, Stiffness & Damping components in the equation of motion (30 marks)

MASS (M) : Represents the physical mass of an object.It quantifies how much inertia an object has,resisting changes in velocity in responce to external forces

In Equation of motion mass M represents coefficient of acceleration and is expressed as M*(d^x/dt^2) where x is the displacement.

STIFFNESS (K) : Measures how a system is resistent to deformation when subjected to external forceIt characterises the systems ability to return it's equilibriium position.

In equation of motion it is typically represented as -Kx signifying that the force is proportional to the displacement.

DAMPING (C) : Represents the dissipation of energy within the system due to friction,internal friction and other sources of resistence.It regulates how the system comes to rest quickly after being perturbed.

In general the Equation of motion for dynamic system is 

M*(d^2x/dt^2) + C(dx/dt) + Kx = F(t)

where M is the mass of electron

          Cis the damping coefficient

          Kis the stiffness of the system

          x is the displacement of the system

          t is time 

          F(t) represents the applied external force as a function of time

4. Provide relationship between Natural period (Tn) & Natural frequency (f) and provide their definitions (25 marks)

Natural Frequency (f) : It is the number of oscillationsor cycles that a system undergoes in one second and measures in Hertz(Hz).

Natural Period (T) : is the time takes for a dynamic system to complete one full oscillation or cycle and measured in seconds

The relation ship between natura period and natural frequency is given by

f = 1/T

conversely

T = 1/f

5. Explain in detail about Response spectrum & its Graph (25 marks)

A Response spectrum is a typical representation of maximum responses(displacements,velocities and accelerations) that is a linear dynamic system is expected to undergo when subjected to change of ground motion acceleration over a range of frequencies and commonly used in stryctural engineering and earth quake engineering to assess how the structure will behave in response to the siesmic forces.