Structural dynamics

Q.1 DIFFERENTIATE STATIC ANALYSIS AND DYNAMIC ANALYSIS WITH PROPER REPRESENTING PICTURE

ANS:

1. STATIC ANALYSIS:

1. A static structural analysis is the calculation of the effect of steady loading condition on a structure while ignoring inertia and damping effects such as those caused by time varying loads
2. A static analysis can include steady inertia loads such as gravity and rotational velocity and accelerations and time varying loads that can be approximated as static equivalent loads
3. Static analysis is =Internal forces + applied forces = 0
4. Dead load of the building is the example of static load which does not change with respect to the time

2. DYNAMIC ANALYSIS OF STURCTURE:
3. A dynamic structural analysis is the calculation of the effect of the varying loading condition on structure while considering the inertia and damping effect such as those caused by time varying load
4. A dynamic structure analysis loads such as wind load, seismic load are the dynamic loads
5. Dynamic analysis is =Internal forces + applied forces + inertia forces = 0

Q.2 EXPLAIN THE FOLLOWING WITH RELEVANT FORCE-DISPLACEMENT GRAPH

1. ELASTIC BEHAVIOR
2. INELASTIC BEHAVIOR
3. PLASTIC BEHAVIOR
4. NON-LINEAR INELASTIC BEHAVIOR

ANS:

1. ELASTIC BEHAVIOUR:
2. Elastic behaviour can be defined as the ability of a component to return to its original shape when an application of external loading is removed
3. The explanation is that any component under loading like compression or tension loses its original shape and tends act according to the load and when the load is removed the component restored to its original shape when loading is removed
4. For linear system force can be expressed as fs=ku where k is lateral stiffness constant

1. INELASTIC BEHAVIOR:
2. Inelastic behaviour of material is defined as the inability of the material to return to its original shape when the load is removed and tend to be in the deformed shape
3. The material undergone deformation act opposite to elastic behaviour hence, called as inelastic behaviour

1. PLASTIC BEHAVIOUR:
2. The property of the material which has the deformed shape and permanent strain in it when the loading is removed is called the plastic behaviour of structure
3. The plastic behaviour of the structure occurs beyond point ‘a’ after unloading as represented in the curve

4. NON-LINEAT INELASTIC BEHAVIOUR:
5. When large deformation occur at the material the force displacement relationship of the material becomes non linear
6. Force corresponding to displacement is not single valued in non linear behaviour and depends on the history of deformation of the material
7. For non linear system force can be expressed as fs=fs(u,v)
8. The bend from O to represent the non linear

Q.3 EXPLAIN MASS, STIFFNESS & DAMPING COMPONENTS IN THE EQUATION OF MOTION.

ANS:

1. Mass component:
2. The mass component in equation of motion considers only the mass of the frame and stiffness and damping are considered to neglected.
3. The force is related with mass component with the equation of fi=mu

1. Stiffness component:
2. The rigidity of the material to resist deformation is called as the stiffness and in this component only stiffness is considered in the frame and other mass and damping components are neglected.
3. The force is related with stiffness component with the equation of fs=ku

1. Damping component:
2. Damping is the dissipation of energy due to vibration over time and distances.
3. It occurs due to the friction between and non-structural elements.
4. The force is relate with damping component with the mu+fd+fs = p(t) that is mu+cu+ku=p(t) where p(t) is external force

Q.4 PROVIDE RELATIONSHIP BETWEEN NATURAL PERIOD (Tn) & NATURAL FREQUENCY (F) AND PROVIDE THEIR DEFINITION

ANS:

1. Natural period:
2. The time taken for undamped system to complete on cycle of free vibration is called as the natural period of vibration and it is demoted by the formula Tn=2π/wn and the unit is seconds

1. Natural frequency:
2. The natural frequency is defined as the number of cycles i.e one full cycle free vibration completed in one second. It is denoted in radians/sec
3. The relation between and natural period and natural frequency Is inversely proportional to the period of vibration fn=1/Tn

Q.5 EXPLAIN IN DETAIL ABOUT RESPONSE SPECTRUM & ITS GRAPH

ANS:

1. It is a concept of characterizing the ground motion and their effect on structure of different time period Tn. A plot of the peak value of a response activity (u,v,a) as a function of natural vibration period Tn of the system is called the response spectra
2. The peak response of all linear single degree of freedom system can be computed by response spectra plot.
3. Three types of plots are generally plotted with u and Tn as deformation response spectra and a similar plot is don with u* as relative velocity spectrum and with u** as acceleration response spectrum. Each plot is done with fixed damping ratio and several such plots with different damping ratio are created for the range of damping values encountered in the structure

1. The above image contains the plot with deformation with respect to time. The 1^st plot (a) represents the ground acceleration recorded during a earthquake
2. The second plot (b) represent the plots of deformation response of three independent SDF system in each plots of b has been done with fixed damping ratio as 2% and variation in natural time period as 0.5s,1s,2s and the corresponding deformation are obtained with respect to time period of vibration the deformation of the system can be obtained which can be multiplied with stiffness to obtained which can be multiplied with stiffness to obtain equivalent static force which can be further used for the analysis of the structure
3. Pseudo acceleration response spectrum:Pseudo acceleration for an single degree of freedom system with natural frequency wn is related to its peak deformation d = uo, due to earthquake ground motion A=(wn^2)*D = ((2 π/Tn)^2)*D the D here represents relative deformation and not total deformation hence the acceleration obtained is relative so it is called as pseudo acceleration. The quantity a has units of acceleration and it is related with base shear Vbo.Vbo=fso= m A OR Vbo = (A/g)*w.
4. In this formula A/g is base shear coefficient which is acceleration divided by gravitational force. So multiplying this with total mass of the structure provided total base shear or equivalent static force which can be used for analysis of the structure
5. The below image represents the graphical difference between deformation spectra and pseudo-acceleration can be calculated by multiplying deformation with natural circular frequency of vibration at any instant of time