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Linear Time History Analysis of Building due to Earthquake
Ground Motion using SANSPRO V.5.30
(LTHA using SANSPRO V.5.30)
by Nathan Madutujuh, ESRC, 2024
E-mail: esrc.nathan@gmail.com, WA: 0878-25670070
Step by Step:
1. Introduction
2. Preparing Ground Motion Data
3. Select Ground Motion dataset for Time History Analysis
4. Select Analysis Method : Linear Time History Analysis (Dynamic Direct Integration)
5. Select Time History Analysis Integration Method
6. Run Linear Time History Analysis
7. View Linear Time History Analysis Result
8. Get Envelope from Several Ground Motion
9. Use Envelope for Final Design
Engineering Software Research Center (www.esrcen.com)
2024
1. Introduction
Linear Time History Analysis is a linear dynamic analysis method useful for analyzing response of a
structure for dynamic load, such as impact load, harmonic load, dynamic wind gust, blasting load, or
ground motion caused by earthquake.
Advantages of Linear Time History Analysis (LTHA)
LTHA calculate dynamic response of a structure for every time step for a certain duration.
If the right parameter is used and the time step is small enough, LTHA will give good accuracy and
correct sign of the response of the structure due to the applied dynamic load.
Difficulties in Linear Time History Analysis
Several difficulties are found when conducting LTHA, includes:
1. Preparing several appropriate ground motion data (3-5 GM data set will be required)
2. Matching the ground motion data to design spectra
3. Longer Running time compared to Modal Spectrum Response Analysis
4. Large output file size to analyze and process
LTHA output will be used to design of structural component and for checking drift and vibration pattern.
Mass Distribution :
To include the effects of accidental torsion, we can use several methods as follows:
Building : Use 5% offset for center of mass (Accidental torsion)
General : Use several LL distribution pattern (run several times using different LL pattern)
Modelling for damping:
Damping in a structure is very difficult to model accurately. Several methods can be used to approximate
the damping effects of the structure:
1. Artificial damping (using Hilber-Hughes-Alpha method, only for small damping)
2. Raleygh damping (using a*K + b*M), need 2 first eigen values, for small, large damping)
3. Using Damper link (for viscous damping, seismic damper, seismic bearing, large linear /
nonlinear damping)
2. Preparing Ground Motion Data
LTHA requires 3-5 appropriate Ground motion data sets. Each data set contains 2-3 ground motion data for
X,Y,Z directions for an earthquake event accordingly. Each data set must have same time step and
duration, and normalized to g value.
a. Select Target Spectra
Based on : Coordinate, Soil Class, Return Period, EQ Map (PGA, Ss, S1)
Ss,S1 values must be checked also for constant acceleration region (near fault zone).
In near fault zone area (NFZ), use Ss >= 1.5 and S1 >= 0.6.
Use Horizontal Target Spectra : MCEr (no need to multiply by 2/3)
For Vertical Target Spectra, take av from 0.2*Sds and check for av,max from actual earthquake recorded
data from near fault zone, and take the maximum value from both.
b. Using Deaggregation Map, select right Ground Motion
Selected GM must cover : Mega Thrust, Shallow Crustal, Benioff
Selected GM must have : 2 directions
Spectra is matched using individual and 100Rot spectra (combined 2 directions)
Jakarta site:
Deaggregation, T = 6 sec
Mega Thrust : 60%, 8.3M, 200km
Shallow Crustal : 38%, 7.5M, 180km
Benioff : 2%, 6.3M, 30km
LTHA : 3 or 5 Ground Motions
Several sources for Ground Motion : BMKG, PusGeN, Local University, PEER, Taiwan, Japan, Europe
Ground Motion data requirements:
- From the same station and time, and pairs of X,Y,Z directions
- Find station with distance similar with the project distance to estimated epicenter
- Use GM data for area closest to the project's location
- Every component in X,Y,Z directions must have same time step and duration
c. Modify Selected Ground Motion
Before used in LTHA analysis, a GM data must be matched to the target design spectra as follows:
LTHA : Match to 0.9 MCEr (Amplitude matching for 100Rot), 2/3 MCEr for each direction
NLTHA : Match to 1.1 MCEr (Spectral Matching for 100Rot)
Near Fault : Use Amplitude Matching
Scale Factor : 0.25 - 4.0
CMS : >= 75% MCEr for 100Rot
Period to match:
T90% EMF - 2*T1max
0.8*T1min - 2*T1max
0.2*T1min - 2*T1max
> 0.1 s if av considered
Spectral matching can be done using several software tools : NSPECTRA, SeismoMatch, etc.
d. Check for Matched Spectra
- Displacement, Velocity, Acceleration
- Arias Intensity
PEER Strong Ground Motion Database
Ground Motion data can be taken from PEER database or from other agencies.
SANSPRO only recognizes GM data using PEER GM Database format as belows:
Example for Kobe Earthquake Ground Motion Data :
PEER NGA STRONG MOTION DATABASE RECORD
Kobe Japan, 1/16/1995, Abeno, 0
ACCELERATION TIME SERIES IN UNITS OF G
NPTS= 14000, DT= .0100 SEC,
-.1177487E-02 .5157907E-03 -.3291613E-03 .2328733E-03 -.1878516E-03
.1479636E-03 -.1314313E-03 .1075423E-03 -.1010870E-03 .8382757E-04
-.8238669E-04 .6859885E-04 -.6955823E-04 .5726025E-04 -.6030227E-04
.4937064E-04 -.5325906E-04 .4297747E-04 -.4765998E-04 .3819707E-04
-.4337183E-04 .3377382E-04 -.4031573E-04 .3038846E-04 -.3695545E-04
.2806580E-04 -.3358656E-04 .2372362E-04 -.3219255E-04 .2343589E-04
…..
…..
…..
3. Select Ground Motion dataset for Time History Analysis
Input several Ground Motion data set
Each GM data set consists of 1-3 Ground motion data file in PEER format
Each data file in a GM Data set must have same time step and duration
Data should be normalized to g (values will be multiplied with g by program during analysis)
Selected Ground Motion dataset will be used for the current analysis.
To get output result with different name, before running a different GM dataset, Model must be renamed
accordingly.
4. Select Analysis Method : Linear Time History Analysis (Dynamic Direct Integration)
5. Select Time History Analysis Integration Method
Select Integration Method and Parameters : Gamma, Beta, Alpha, Theta
Parameters for Central Difference Method (Explicit Method, Stable for dt/Tmin < 0.3183)
Parameters for Newmark-Beta Method (Implicit Method, Stable for dt/Tmin < 0.5513)
Select Cut-off Frequency, Max Time Step, Max Analysis Time
Cut-off Frequency is around 10-100 Hz for typical building case.
Max Step is currently limited to 100,000 steps.
Max Time step typically is 0.01 for Newmark's family Methods, and <= 0.001 for Central Difference
Method. For Central Difference Method, dT <= dT,critical to get convergent results.
Select Mass and Damping Option
Currently only Lumped Mass option provided.
Damping can be zero or generated using Raleygh-Ritz procedure using 2 set of parameters:
psi1,f1,psi2,f2 to get C = a*K + b*M as the full damping matrix.
6. Run Linear Time History Analysis
After all parameters set, we can start the Linear Time History Analysis. For this 4 story building with 50
seconds duration and 0.01 secs time step (total = 5000 time steps), and using Newmark-Beta integration
method, the analysis can be finished in 43.67 seconds.
7. View Linear Time History Analysis Result
Central Difference Method, Time step = 0.001 sec, Duration = 50 secs
Newmark-Beta Best Parameters, Time step = 0.01, Duration = 50 secs
Newmark-Beta Best Parameters, Time step = 0.005, Duration = 50 secs