Structural dynamics
Q 1) Differentiate Static analysis and Dynamic analysis with proper representing pictures.
Structural analysis is mainly concerned with finding out the behavior of a physical structure when subjected to force. This action can be in the form of load due to the weight of things such as people, furniture, wind, snow, etc. or some other kind of excitation such as an earthquake, shaking of the ground due to a blast nearby, etc. In essence all these loads are dynamic, including the self-weight of the structure because at some point in time these loads were not there. The distinction is made between the dynamic and the static analysis on the basis of whether the applied action has enough acceleration in comparison to the structure's natural frequency. If a load is applied sufficiently slowly, the inertia forces (Newton's first law of motion) can be ignored and the analysis can be simplified as static analysis. Structural dynamics, therefore, is a type of structural analysis which covers the behavior of structures subjected to dynamic (actions having high acceleration) loading. Dynamic loads include people, wind, waves, traffic, earthquakes, and blasts. Any structure can be subjected to dynamic loading. Dynamic analysis can be used to find dynamic displacements, time history, and modal analysis.
A dynamic analysis is also related to the inertia forces developed by a structure when it is excited by means of dynamic loads applied suddenly (e.g., wind blasts, explosion, earthquake).
A static load is one which varies very slowly. A dynamic load is one which changes with time fairly quickly in comparison to the structure's natural frequency. If it changes slowly, the structure's response may be determined with static analysis, but if it varies quickly (relative to the structure's ability to respond), the response must be determined with a dynamic analysis.
Dynamic analysis for simple structures can be carried out manually, but for complex structures finite element analysis can be used to calculate the mode shapes and frequencies.
Q.2. Explain the following with relevant force-displacement graph.
Elastic behavior
Inelastic behavior
Plastic behavior
Non-linear Inelastic behavior
- Elastic Behavior:-
Elastic behavior is the property of the material upto which the material can retain it's shape. From the aforementioned graph it is clearly mentioned that upto a certain point from "O" the graph is linear and shown its elastic properties.
- Inelastic Behavior:-
Inelastic behavior is the property of the material when the material can't retain it's previous shape after a certain deformation. In the aforementioned graph inelastic behavior has been shown in the upper shape of the curve upto point "a".
- Plastic Behavior:-
Plastic behavior occurs when the material completely lost it's ductility. In the aforementioned graph plastic behavior occurs during unloading after point "a".
- Non-linear Inelastic Behavior:-
Non-linear inelastic behavior occurs after the line from "O" tends to bend towards point"a".
Q.3. Explain Mass, Stiffness & Damping components in the equation of motion.
Q.4. Provide relationship between Natural period (Tn) & Natural frequency (f) and provide their definitions.
Natural frequency (f) =√stiffness/√Mass of structure.
Take the case of a very tall building which is susceptible to damage whan earthquake occur will have higher group and hence lower natural frequency.
Thereby, it is desirable to have higher natural frequencies. Also, at low natural frequencies, the structure can resonate easier and hence lead to amplification.
I do not know enough about building dynamics to comment about this mathematically, but this is a plausible argument.
mply put, the time period of a building is it’s natural period of oscillation when subjected to ground shaking in the event of an earthquake.
The building is modelled to be under harmonic oscillation and the time period is calculated in a similar way as in harmonic oscillation
T = 2π√(k/m)
where k is the total stiffness and m is the total mass.
k is calculated as the sum of the lateral stiffness of all stiffness providing and moment resisting vertical members (colomns, moment resisting frames, sheer walls, etc.) m is calculated as the sum of masses of all members on the storey
Q.5. Explain in detail about Response spectrum & its Graph.
A response spectrum is a graphical plot of the frequency of an oscillator and its damping. The response spectrum plot represents the peak or steady-state response (velocity, displacement, or acceleration) of a series of oscillators of varying natural frequency. In vibration analysis of any system, the response spectrum is very useful as the resulting plot can provide the response of any linear system with respect to its natural frequency. The response spectrum finds its usage in interpreting seismic or earthquake events and slug flow events.
Response Spectrum Analysis is a scientific method for estimating the structural response of dynamic vibration events. To perform the response spectrum analysis, the first job is to define the response spectrum of the system. In this article, we will explore the basics of the response spectrum and learn the steps for performing seismic/earthquake analysis using the response spectrum analysis method.