Structural dynamics
1) In general , static means stationary and dynamic means constant movement. It is important to perform analysis on a building to find the response of the structure when its subjected to loads. There are two types of analysis done on structures, for designing a building with all safety measures, to find its all safety parameters and finally getting an economical design. they are:
STATIC ANALYSIS
DYNAMIC ANALYSIS
Static analysis - This analysis is done taking into consideration all the static loads of the structure , for eg., self weight of the structure, dead loads, etc. These loads do not change with time. This can be done before execution when structure has external displacements. This may give a lot of errors as it ignores all the inertia and damping effects on the structure. Therefore, only gives data about the steady loading conditions. If time varying loads are applied this analysis assumes them to be constant.
Dynamic analysis - This analysis is done taking into consideration all the dynamic loads acting on the structure , for eg. wind load, earthquake load, etc. As our earth is divided into various seismic zones , it becomes important to test our structure with seismic aspect. These changes with time and these changes are very high in frequency and intensity. It is done in runtime after execution of the building. This may give a high deflection.
Methods carried out to perforrm these analysis are:
Push over method
Time history method
Response spectrum method
These analysis are done on the various softwares nowadays like STADDPRO. It helps to calculate internal forces, reactions, stresses , moment etc.
It is advisable to do a hybrid analysis for a building to get all the calculations correct.
2) a. Elastic behavior - This is the property of a material , substance or a structure to get back to its original position after deformation under the application of load.The same behaviour when a spring comes back to its original position after load is removed from its ends. A structure behaving elastically means zero displacement from its position after the load is removed. It is essential for structure to behave elastically so as to prevent collapse of the structure after the application of forces or loads.
b. Inelastic behavior - This is the property of a material , substance or a structure in which it do not come back to its original position after deformation under the application of load and leaves a permanent displacement in the structure. It usually seen when structure exceeds its elastic limit.
c. Plastic behavior - This is the property of a material , substance or a structure in which it do not come back to its original position after deformation under the application of load , this occurs beyong elastic limit. It is not same as of inelastic behavior as this is nonlinear. In this phase actual failure of the structure is calculated, all the loads which cause the structure to fail , falls in this region.
d. Non linear inelastic behavior- This is the property of the substance, material or structure where it deforms or displaces non uniformly and irreversibly after the application and removal of loads or forces.
3)Mass - It is the total self weight and cumulated load concentrated at the centre in a building. In motion, mass plays a great role, less mass means high frequency in buildings to displace and vice versa.
Whereas stiffness refers to no movement in buildings, how much steady a building can be. Stiffness is function of height , area and cross sectional shape of column in the building. Both of these factors are used to calculate buildings responses when in motion due to loads and forces. Dampness is the component added to a structure to reduce frequency of oscillations caused due to forces.
All these three factors are considered in non linear dynamic analysis of the building and hence becomes a SDOF system.
Stiffness component- It is the frame without mass and damping. It is related to displacement.
Mass component - It is independent component without stiffness and damping. In this frame external mass is related to acceleration.
Damping component- It is the frame with damping property and independent without stiffness or mass. Here external force is related to velocity.
4) Vibrations are the oscillation produced due to any external force applied on the member. Undamped are the vibrations with one degree of freedom, and the simplest to analyse in the system. In these movements no energy is lost in the system.
Natural period of vibration - (Tn) As the name suggests it is the time period for the undamped system to complete one cycle of vibration. It is measured in seconds. Whereas Natural frequency (f) - is defined as the number of vibrations occuring in that period or amount of time. It is calculated in no. of cycles or no. of revolutions occuring when it occurs in cyclic motion. It is measured in hertz.
[ f=1/Tn ]
also cyclic frequency is [ Tn=2 π /w ]
Both these functions depends on mass as well as stiffness structure [ k=mw^2 ] .This means when two systems are defined , the one with less mass at same stiffness will have less natural period and high natural frequency , whereas the one with high stiffness of the two with same mass will have less natural periods and high natural frequency.
5) Different structures behaves differently under earthquake conditions. Therefore to read various outcomes , a concept is build called reesponse spectrum. It is a study of characterizing ground motions and its effects on the structures under different natural periods. It gives an overview of how the structure can behave under seismic and earthquake loads , so a better design could come up with all safety factors considered. It can be used for large intensity of ground motions. The peak value achieved for any function under a natural period is called the response spectrum of that function. There are three types of response spectrum:
Deformation spectrum
Relative velocity spectrum
Accleraton spectrum
Vibrations are recorded and plotted against displacement with time graph
Steps to construct a response spectrum are:
a) Measure the ground motion ordinates in the interval of 0.02 sec , numerically.
b) Select the natural time period Tn and damping ratio.
c) Calculate displacement due to ground motion.
d) Find spectrum fucntions.