computer modeling of structure to earthquake load

Computer Modeling ofStructure to Earthquake Load

ByJohn Li (johnli@src-asia.com)Solutions Research Centre

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How Do Earthquake Affect Buildings

EarthquakeSeismic wavesSite/soil effectsSoil-structureinteractionStructuralresponse

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Ground Motion Parameters

For engineering purposes, threecharacteristics of earthquake motion are ofprimary significance:

AmplitudeFrequency contentDuration of the motion

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Newton Equation of Motion

Building codes provide guidelines for:F(t)Computation method to solve equationSolution interpretation and design

[ ]{ } [ ]{ } [ ]{ }xMxCxKtFMatF

&&& ++==

)()(

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Earthquake Analysis Procedure

Modal/Ritz Vectors Analysis

Equivalent Lateral Load

Static Pushover

Response Spectrum

Linear Time History

Nonlinear Time History

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Energy Conservation

Energy is the fundamental in dynamic analysis.For earthquake resistant design, try tominimize the mechanical energy.Use to evaluate the accuracy of the solution.

StrainEnergy+Kinetic

Energy=MechanicalEnergy

DampedEnergy+Strain

Energy+KineticEnergy=Work

Done

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P-Delta Parameters

Non-iterative –Based on MassIterative – Basedon LoadCombination

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Modal Vs Ritz Vectors

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Equivalent Lateral Force Method

)1(

1

nekn

jjj

iii F

HW

HWF δ−=

∑=

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Response Spectrum Analysis

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Time History Record24538-S2486-94020.06 SANTA MONICA - CITY HALL GROUNDS AT 90 DEG3000 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 time-history analysis using direct integration. P-delta effects,large-displacements, and material nonlinearity areavailable. Arbitrary loading may be applied. Applicationsinclude seismic loading, dynamic pushover, andinstability analysis. Most commonly used implicitintegration schemes are available, as well as high-speedexplicit integration for wave propagation, blast, andcollapse problems. Nonlinear direct-integration time-history analysis cases can be chained together with othernonlinear time-history or static cases (including stagedconstruction), to address a wide range of applications.

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Nonlinear NLLink Element

LinearDamperGapHookPlasitc1Isolator1Isolator2

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Nonlinear Time History

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Energy Plots

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Pushover Curve

M3 Major MomentP AxialPMM Axial & Bi-Axial MomentsS Shear

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Pushover Hinge Types

M3 Major MomentP AxialPMM Axial & Bi-Axial MomentsS 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 DrRay Su, Prof Adrian Chandler, Prof Peter Lee, Dr Alex To & Mr J H Li.

1.5401.7892.1232.3362.835Torsion

TRB Building

0.8601.1481.4011.3021.588Y Trans

BSB Building

0.5780.6610.7271.2871.622Y Trans

TTT Building

321

TestResult

ModificationsBareFrame

Vibration Period (second)Vibration

Mode

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Power Spectral Density Analysis

Power-spectral-density analysis is available to determinethe probabilistic response of a structure due to cyclic(harmonic, sinusoidal) loading over a range offrequencies. This is useful for fatigue studies, randomresponse due to earthquakes, and other applications.Multiple loads may be applied at different phase angles,and may be correlated or uncorrelated. The structuremay be damped or undamped. Frequency-dependentstiffness and damping (complex impedance) propertiesmay be included for modeling foundations and far-fieldeffects, including radiation damping. Power-spectral-density curves may be plotted for any response quantity,and the integrated expected value is automaticallycomputed.