methods of dynamic analysis
TRANSCRIPT
Methods of Dynamic Analysis
Dr. S. K. Prasad
Professor of Civil Engineering
S. J. College of Engineering, Mysore
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.
ANALYSIS TYPE
2D 3D
Seismic Analysis
Linear
Equivalent Static
Response Spectrum
Time History
Non-Linear
Pushover Analysis
Time History
Classification of Dynamic Analysis
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
Equivalent static force method
• The equivalent static lateral force method is asimplified technique to substitute the effect ofdynamic loading of an expected earthquake by astatic force distributed laterally on a structure fordesign purposes.
• The total applied seismic force V is generallyevaluated in horizontal directions parallel to themain axes of the building.
• It assumes that the building responds in itsfundamental lateral mode. For this to be true, thebuilding must be low rise and must be fairlysymmetric to avoid torsional movement underground motions.
• The structure must be able to resist effectscaused 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
Equivalent lateral shear force along two orthogonal axis
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
ZIA ah
2
When to use Equivalent static method?
• All design against earthquake effects must considerthe dynamic nature of the load. However, for simpleregular structures, analysis by equivalent linearstatic methods is often sufficient.
• This is permitted in most codes of practice forregular, low- to medium-rise buildings.
• Tall buildings (over, say, 75 m), where second andhigher modes can be important, or buildings withtorsional effects, are much less suitable for themethod.
• Regular buildings up to around 15 storey's in heightcan usually be designed using equivalent staticanalysis.
Response Spectrum Method
Response Spectrum
Response spectrum is a plot of peak orsteady state response (displacement,velocity or acceleration) of a series ofoscillators (SDoF systems) of varyingnatural frequency at a given damping andforced in to motion by the same basevibration.
• The method involves the calculation of only themaximum values of the displacements and forces ineach mode of vibration.
• Response spectra are curves plotted betweenmaximum response of SDOF system and timeperiod (or frequency).
• Response spectrum can be interpreted as the locusof maximum response of a SDOF system for givendamping ratio.
• Response spectra helps in obtaining the peakstructural responses under linear range.
Response Spectrum Method
• Response of a SDOF system is determined by timedomain or frequency domain analysis, and for agiven time period of system, maximum response ispicked.
• This process is continued for all range of possibletime periods of SDOF system.
• Final plot with system time period on x-axis andresponse quantity on y-axis is the requiredresponse spectra.
• Same process is carried out with differentdamping ratios to obtain overall response spectra.
Response Spectrum Method
Response Spectrum Method
Response spectrum for El Centro ground motion plotted with normalized scale for damping ratios of 0, 2, 5 & 10%
Design spectra for earthquakes originating from two different faults
0 1 2 3 4 50.0
0.5
1.0
1.5
2.0
2.5 Rock or Hard Soil
Medium Soil
Soft Soil
Sa/g
Time Period (secs)
Response Spectrum IS : 1893 :2002
R
I
g
SZA
WAV
ah
hB
..2
Structural Response Factor, Sa/g
The advantages of RSA, compared with time-history analysis
• The size of the problem is reduced to finding onlythe maximum response of a limited number ofmodes of the structure, rather than calculating theentire time history of responses during theearthquake.
• The use of smoothed envelope spectra makes theanalysis independent of the characteristics of aparticular earthquake record.
• RSA can very often be useful as a preliminaryanalysis, to check the reasonableness of resultsproduced by time-history analyses.
Disadvantages of RSA
• RSA is essentially linear and can make onlyapproximate allowance for nonlinearbehavior.
• The results are in terms of peak responseonly, with a loss of information onfrequency content, phase and number ofdamaging cycles, which have importantconsequences for low-cycle fatigue effects.
Time history analysis• To perform such an analysis, a representative
earthquake time history is required for a structurebeing evaluated.
• In this method, the mathematical model of thebuilding is subjected to accelerations fromearthquake records that represent the expectedearthquake at the base of the structure.
• The method consists of a step- by- step directintegration over a time interval.
• The time-history method is applicable to bothelastic and inelastic analysis.
• In elastic analysis the stiffness characteristics of thestructure are assumed to be constant for the wholeduration of the earthquake.
• In the inelastic analysis, however, the stiffness isassumed to be constant through the incrementaltime only.
• The method involves significantly greatercomputational effort than the corresponding RSAwhich gives precise results.
• Performance based design – better means toevaluate and understand different performancelevels.
Time history analysis
Time history analysis
What is Pushover Analysis?
VB
Δroof
Δroof
VB
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 plastichinge at potential location.
Lateral load is increased in step and sequence ofcracking, yielding, and failure of component isrecorded.
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
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)
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
