Computer Modeling of Structure to Earthquake Load By John Li (
[email protected]) Solutions Research Centre
How Do Earthquake Affect Buildings z z z z z
Earthquake Seismic waves Site/soil effects Soil-structure interaction Structural response
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Ground Motion Parameters For engineering purposes, three characteristics of earthquake motion are of primary significance: Amplitude z Frequency content z Duration of the motion z
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Newton Equation of Motion F (t ) = Ma F (t ) = [K ]{x}+ [C ]{x&}+ [M ]{&x&} Building codes provide guidelines for: F(t) z Computation method to solve equation z Solution interpretation and design z
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Earthquake Analysis Procedure z Modal/Ritz
Vectors Analysis
z Equivalent
Lateral Load
z Static
Pushover
z Response z Linear
Spectrum
Time History
z Nonlinear
Time History
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Energy Conservation Work Done Mechanical Energy z z z
Kinetic Strain Damped = + + Energy Energy Energy Kinetic Strain = + Energy Energy
Energy is the fundamental in dynamic analysis. For earthquake resistant design, try to minimize the mechanical energy. Use to evaluate the accuracy of the solution. Solutions Research Centre
P-Delta Parameters z Non-iterative
– Based on Mass z Iterative – Based on Load Combination
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Modal Vs Ritz Vectors
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Equivalent Lateral Force Method Fi =
Wi H i
Fek (1 − δ n )
n
∑W H j =1
j
j
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Response Spectrum Analysis
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Time History Record 24538-S2486-94020.06 SANTA MONICA - CITY HALL GROUNDS AT 90 DEG 3000 POINTS OF ACCEL DATA EQUALLY SPACED AT .020 SEC. (UNITS: CM/SEC/SEC) 2.321 1.647 .854 -.188 -1.492 -.155 1.559 1.468 1.468 .234 -1.725 -.507 .331 .014 1.031 1.911 1.272 -1.191 -.432 .994 1.705 1.341 -1.266 -1.638 -.495 3.286 4.705 -.057 -2.141 .031 2.391 3.937 3.209 -1.892 -4.787 -.361 4.965 2.778 -.768 -1.933 -3.859 -1.514 .460 -.759 -3.399 -1.470 5.361 .499 -3.190 -2.014 -6.361 -.327 5.597 -.284 -6.629 -1.982 3.192 -3.786 -5.605 -3.604 -3.588 1.536 1.673 .285 -2.091 -4.786 .461 1.878 6.096 6.154 -.362 -.090 8.028 15.086 9.537 2.588 -3.574 -1.133 2.995 -5.163 -12.471 -9.782 -4.950 -5.719 -9.039 -8.594 -7.362 -5.799 .590 6.948 5.881 1.054 5.206 7.877 .808 -8.184 -11.273 -6.557 -4.386 -5.915 -8.621 -6.395 4.616 11.018 7.740 4.030 7.361 13.319 14.179 13.029 12.126 7.768 1.784 -4.704 -10.645 -15.894 -16.559 -9.928 -4.541 3.332 10.073 5.642 1.994 5.629 6.987 3.263 -6.605 -14.153 -9.129 .915 .638 -7.667 -9.769 -11.986 -8.324 -4.435 -7.603 -8.013 -5.754 3.932 17.271 17.645 5.381 2.855 5.636 6.088 3.796 2.630 6.783 8.365 5.489 2.831
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Time History Function
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Time History Analysis
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Time History Trace
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Time History Video
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Nonlinear Time History Analysis Full nonlinear behavior may be considered in a timehistory analysis using direct integration. P-delta effects, large-displacements, and material nonlinearity are available. Arbitrary loading may be applied. Applications include seismic loading, dynamic pushover, and instability analysis. Most commonly used implicit integration schemes are available, as well as high-speed explicit integration for wave propagation, blast, and collapse problems. Nonlinear direct-integration timehistory analysis cases can be chained together with other nonlinear time-history or static cases (including staged construction), to address a wide range of applications.
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Nonlinear NLLink Element z Linear z Damper z Gap z Hook z Plasitc1 z Isolator1 z Isolator2 Solutions Research Centre
Nonlinear Time History
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Energy Plots
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Pushover Curve M3 Major Moment z P Axial z PMM Axial & Bi-Axial Moments z S Shear z
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Pushover Hinge Types z M3
Major Moment z P Axial z PMM Axial & Bi-Axial Moments z S Shear
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Pushover Analysis Case
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Hinge Formation
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Pushover Curve
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The Reality!! Dynamic Testing and Modelling of Existing Buildings in Hong Kong by Dr Ray Su, Prof Adrian Chandler, Prof Peter Lee, Dr Alex To & Mr J H Li. Vibration Period (second) Vibration Mode
Bare Frame
Modifications 2
3
Test Result
0.727
0.661
0.578
1.148
0.860
1.789
1.540
1 TTT Building
Y Trans
1.622
1.287
BSB Building Y Trans
1.588
1.302
1.401
TRB Building Torsion
2.835
2.336
2.123
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Power Spectral Density Analysis Power-spectral-density analysis is available to determine the probabilistic response of a structure due to cyclic (harmonic, sinusoidal) loading over a range of frequencies. This is useful for fatigue studies, random response due to earthquakes, and other applications. Multiple loads may be applied at different phase angles, and may be correlated or uncorrelated. The structure may be damped or undamped. Frequency-dependent stiffness and damping (complex impedance) properties may be included for modeling foundations and far-field effects, including radiation damping. Power-spectraldensity curves may be plotted for any response quantity, and the integrated expected value is automatically computed. Solutions Research Centre
