04-Dynamic-Analysis-Methods jdsud cak.pdf
- 1. Methods of Dynamic Analysis Dr. S. K. Prasad Professor of Civil Engineering S. J. College of Engineering, Mysore prasad_s_k@hotmail.com
- 2. Seismic shaking of structures - COMPLEX!!!! Different structures behave differently during different earthquakes. Material of structure, height of structure, seismic weight, overburden soil, characteristics of earthquake force have varied influence on shaking.
- 5. Analysis Type Depends Information needed Complexity of the structure Resources available e.g. time, money, skill etc. Expected force level on the structure Expected behaviour of the structure
- 6. Equivalent static force method • The equivalent static lateral force method is a simplified technique to substitute the effect of dynamic loading of an expected earthquake by a static force distributed laterally on a structure for design purposes. • The total applied seismic force V is generally evaluated in horizontal directions parallel to the main axes of the building. • It assumes that the building responds in its fundamental lateral mode. For this to be true, the building must be low rise and must be fairly symmetric to avoid torsional movement under ground motions.
- 7. • The structure must be able to resist effects caused by seismic forces in either direction, but not in both directions simultaneously. V = W * A V = Base shear W = Total weight of the structure A = Basic horizontal seismic coefficient • Also called Seismic Coefficient Method Equivalent static force method
- 8. Equivalent lateral shear force along two orthogonal axis
- 9. W H H = W * Ah Pseudo Static or Seismic Coefficient Method Zone Designation Zone Factor Z Zone II 0.10 Zone III 0.16 Zone IV 0.24 Zone V 0.36 g S R ZI A a h 2
- 10. When to use Equivalent static method? • All design against earthquake effects must consider the dynamic nature of the load. However, for simple regular structures, analysis by equivalent linear static methods is often sufficient. • This is permitted in most codes of practice for regular, low- to medium-rise buildings. • Tall buildings (over, say, 75 m), where second and higher modes can be important, or buildings with torsional effects, are much less suitable for the method. • Regular buildings up to around 15 storey's in height can usually be designed using equivalent static analysis.
- 12. Response Spectrum Response spectrum is a plot of peak or steady state response (displacement, velocity or acceleration) of a series of oscillators (SDoF systems) of varying natural frequency at a given damping and forced in to motion by the same base vibration.
- 13. • The method involves the calculation of only the maximum values of the displacements and forces in each mode of vibration. • Response spectra are curves plotted between maximum response of SDOF system and time period (or frequency). • Response spectrum can be interpreted as the locus of maximum response of a SDOF system for given damping ratio. • Response spectra helps in obtaining the peak structural responses under linear range. Response Spectrum Method
- 14. • Response of a SDOF system is determined by time domain or frequency domain analysis, and for a given time period of system, maximum response is picked. • This process is continued for all range of possible time periods of SDOF system. • Final plot with system time period on x-axis and response quantity on y-axis is the required response spectra. • Same process is carried out with different damping ratios to obtain overall response spectra. Response Spectrum Method
- 16. Response spectrum for El Centro ground motion plotted with normalized scale for damping ratios of 0, 2, 5 & 10%
- 17. Design spectra for earthquakes originating from two different faults
- 18. 0 1 2 3 4 5 0.0 0.5 1.0 1.5 2.0 2.5 Rock or Hard Soil MediumSoil Soft Soil Sa/g Time Period (secs) Response Spectrum IS : 1893 :2002 R I g S Z A W A V a h h B . . 2 Structural Response Factor, Sa/g
- 19. The advantages of RSA, compared with time-history analysis • The size of the problem is reduced to finding only the maximum response of a limited number of modes of the structure, rather than calculating the entire time history of responses during the earthquake. • The use of smoothed envelope spectra makes the analysis independent of the characteristics of a particular earthquake record. • RSA can very often be useful as a preliminary analysis, to check the reasonableness of results produced by time-history analyses.
- 20. Disadvantages of RSA • RSA is essentially linear and can make only approximate allowance for nonlinear behavior. • The results are in terms of peak response only, with a loss of information on frequency content, phase and number of damaging cycles, which have important consequences for low-cycle fatigue effects.
- 21. Time history analysis • To perform such an analysis, a representative earthquake time history is required for a structure being evaluated. • In this method, the mathematical model of the building is subjected to accelerations from earthquake records that represent the expected earthquake at the base of the structure. • The method consists of a step- by- step direct integration over a time interval. • The time-history method is applicable to both elastic and inelastic analysis.
- 22. • In elastic analysis the stiffness characteristics of the structure are assumed to be constant for the whole duration of the earthquake. • In the inelastic analysis, however, the stiffness is assumed to be constant through the incremental time only. • The method involves significantly greater computational effort than the corresponding RSA which gives precise results. • Performance based design – better means to evaluate and understand different performance levels. Time history analysis
- 24. What is Pushover Analysis? VB Δroof Δroof VB
- 25. What is Pushover Analysis? Building is pushed in one horizontal direction. Proportion of applied force on each floor is constant, only its magnitude is increased gradually. Load pattern may be 1st mode shape, parabolic, uniform, inverted triangular etc. Material nonlinearity is modeled by inserting plastic hinge at potential location. Lateral load is increased in step and sequence of cracking, yielding, and failure of component is recorded.
- 26. Why Pushover Analysis? More accurate prediction of Global displacement Demand on individual members Weakest link (“bad actors”) Building do not respond as linearly elastic during strong ground motion
- 27. How much information is needed? Forces & displacement Linear static Modal properties & dynamic effects (Elevation and plan irregularity) Linear Dynamic Post yield behavior & performance of structure Nonlinear Static (Pushover)
- 28. It is impossible to stop or predict earthquake. As engineers, let us all unite and move forward & work for reducing calamities due to natural and man made hazards