WO2002013071A1 - System and method for analyzing structures subjected to catastrophic events - Google Patents
System and method for analyzing structures subjected to catastrophic events Download PDFInfo
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- WO2002013071A1 WO2002013071A1 PCT/US2001/001218 US0101218W WO0213071A1 WO 2002013071 A1 WO2002013071 A1 WO 2002013071A1 US 0101218 W US0101218 W US 0101218W WO 0213071 A1 WO0213071 A1 WO 0213071A1
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- damage
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Classifications
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01V—GEOPHYSICS; GRAVITATIONAL MEASUREMENTS; DETECTING MASSES OR OBJECTS; TAGS
- G01V1/00—Seismology; Seismic or acoustic prospecting or detecting
- G01V1/01—Measuring or predicting earthquakes
Definitions
- the present invention relates to. structure analysis systems, and in particular to a system for analyzing structures subjected to catastrophic events such as earthquakes, hurricanes, tornadoes, and man-made hazards .
- the Eastern Coast of the U.S. from Florida to Rhode Island is also susceptible to hurricanes.
- the hurricane season typically lasts from June through November each year.
- 12 to 14 hurricanes are generated in the Gulf each year. Losses from these hurricanes are also estimated at hundreds of billions of dollars.
- UBC Uniform Building Code
- the basic design procedure recommended by the Code assumes that the structure will undergo inelastic behavior and will sustain damage, i.e., may be permanently deformed or broken, during a design level earthquake. This is implied by the use of the R-factor in the 1997 UBC, (i.e., "numerical coefficient representative of the inherent overstrength and global ductility capacity of lateral-force-resisting systems '' ) to reduce the design lateral forces on a structure.
- a typical design procedure is as follows: 1. selection of a design level earthquake intensity; 2. reduction of the applied forces (e.g., base shear) computed from the design earthquake by a Code recommended R-factor; and 3.
- a value of the reduction factor, R, greater than approximately 1.5 implies that the system will undergo inelastic behavior and will be damaged if a ground motion of design intensity is observed at the site.
- the coefficient of 1.5 represents the average factor, which is used in design to either factor the loads in load factor design or factor the yield strength of materials in working stress design.
- the R-factor is intended to refer to an acceptable level of damage via a global ductility response measure.
- Global ductility is a measure of damage. Typically for a building subjected to earthquake motions, it is defined as the ratio of the maximum building roof displacement and the roof displacement at which the first significant damage occurs anywhere in the building.
- Such assumed ductilities used in design can only be confirmed by a nonlinear analysis (or experimental testing) .
- the building codes do not require such a state-of-the-art nonlinear analysis to confirm that the assumed global ductilities can be achieved in the adopted design.
- a computer-implemented system and method for analyzing a structure subjected to a catastrophic event are provided. Based on linear elastic input data, the system automatically determines non-linear hysteretic behaviors without extensive manual intervention. The nonlinear models are then analyzed through any one of a number of nonlinear analysis techniques. Processing load of a computer is substantially reduced through various mathematical techniques which allow an ordinary server or workstation computer to conduct the analysis without requiring the power of a mainframe or super computer.
- FIG. 1 is a functional block diagram of a system for analyzing structures according to an exemplary embodiment of the present invention.
- FIG. 2 is a flow diagram of a method of performing a nonlinear analysis.
- FIG. 3 is a graph of an exemplary cyclic degradation/deterioration in strength and stiffness of a truss-type post-buckling type element.
- FIG. 4 is a graph of an exemplary envelope curve of a beam-column element.
- FIG. 5 is a graph of an exemplary failure behavior of a beam-column element.
- FIG. 9 is a plot of the number of damaged members as a function of a spectral acceleration from three different exemplary earthquake records .
- FIG. 10 is a flow diagram of a method of rating a structure for risk assessment.
- FIG. 11 is a flow diagram of a method determining damage functions.
- a structure analysis program 114 is maintained in an exemplary computer system 100, such as a WINDOWS-based or UNIX-based personal computer, server, workstation or a mainframe.
- the structure analysis system 100 of the present invention includes simplified input data to the computer programs used in the industry on large-scale projects. Seismic retrofit of the Golden Gate Bridge is one example of a large-scale project.
- the present invention simplifies input data to an extent that the input data structure mimics the typical linear elastic analyses data structure .
- structure data input includes the geometry data for each element or member in the structure.
- the linear elastic input data would define the geometry of columns and beams in terms of their section sizes, i.e., W12x24 , etc. This data is sufficient to calculate the stiffness and mass of the member. Given the spatial distribution of members within a building, the total structure stiffness and mass can be calculated.
- the present invention overcomes this problem by having the user define the member inputs for the linear elastic model, i.e., element geometry is defined via section size specification. Additional linear input data required are the material type, and its yield stress to calculate overstress ratios. With the linear elastic input data, the program automatically calculates the complex hysteretic behavior internally.
- nonlinear dynamic time history analyses require numerical solution of a large system of equations during each step of integration.
- the number of steps may vary from 1000 to 5000.
- the number of steps may vary from a few hundred to a few thousand.
- more solutions may be needed to achieve equilibrium, i.e., several iterations within a time step. The iterations may be due to element nonlinear behavior or large displacement effects or both.
- linear analyses require such solution once only in dynamic analyses.
- traditional numerical methods are utilized, they require tremendous computing power.
- the present invention overcomes this problem by developing numerical schemes and methods to substantially reduce computation time required in solving the system of equations.
- results are conveniently summarized in tabular and graphical form.
- the user also receives a color-coded picture of the structure in which damaged areas with varying damage levels are shown.
- a 3-D photo-realistic movie showing real-time dynamic responses may also be generated.
- the program 114 provides an engineering based structure rating system which identifies the potential risk due to catastrophic events for use by, for example, the financial institutions, engineering communities and insurance companies, corporate and other institutions to assess and manage their risks.
- Structures can be of any material and type (e.g., residential, non-residential, transportation infra-structure, etc.).
- FIG. 2 illustrates a nonlinear analysis routine 200 which is a part of the structure analysis program 114.
- Non-linear analysis types include, but are not limited to, time history analysis, static pushover, modal analyses, and fatigue analysis.
- linear elastic input data is received by the system 100.
- the linear elastic input data for analyses includes: (a) geometry (nodal coordinates, boundary conditions, nodal masses, etc); (b) member connectivity/properties (section properties, material properties, etc) ; (c) load data (earthquake, wind, waves, currents, etc.).
- the input data may be provided as an ASCII data file conforming to the software's input specifications, or it could be generated interactively through a graphical user interface of the present invention.
- filters in the present invention can be used to convert data from a suite of existing programs used in the industry to generate an ASCII data file that conforms to the present invention's software input specifications.
- the linear input data to be received in step 202 includes global definitions of material properties, section properties for stiffness calculations, section properties for Building Codes and Other Code checks, wave properties, miscellaneous data, group properties, eccentricities and local fixed end forces. Access to AISC and other standard rolled sections is achieved in the global section library.
- nonlinear hysteretic member behavior comprises a definition of three components: (a) envelope behavior or curve; (b) cyclic degradation/deterioration in strength and stiffness (or simply degradation behavior) ; and (c) failure behavior.
- envelope behavior or curve a definition of envelope behavior or curve
- cyclic degradation/deterioration in strength and stiffness or simply degradation behavior
- failure behavior e.g., failure behavior
- these components may be defined from databases and or lookup tables created from experimental observations, analytical formulae, empirical formulae, and/or any combination of the above. Interpolation and/or extrapolation formulae may be used wherever appropriate. In the present invention, all of the above methods are used wherever appropriate.
- One of the more difficult tasks in any nonlinear analysis procedure is the selection of the appropriate element type to model a member in the structure . Once an element type is selected, the corresponding material, section and element properties are required to adequately define the physical behavior of that member. Selection of such properties can be tedious and requires considerable experience.
- step 204 of FIG. 2 complex member hysteretic behaviors are automatically generated. Specifically, step 204 automatically generates the nonlinear physical properties for various element types used to model tubular members, general AISC and other standard rolled sections, built-up sections, general sections, and user-defined sections. Materials may be steel, concrete, asonary, reinforced concrete, or user defined materials. Element types can be grouped as beam-column type, truss-type, foundation-type, and general/special type. Thus if a truss-type post-buckling type element is selected to model tubular braces of an offshore structure, the user needs to specify only the member name, its connectivity, its diameter and thickness, its yield stress and the effective length factor as part of inputting the linear elastic input data in step 202.
- Step 204 of the routine 200 automatically generates the nonlinear envelope curve needed to define the member's physical behavior and selects an appropriate stiffness and strength deterioration algorithm for cyclic loads as shown in FIG. 3.
- the algorithms for generation of these properties have been derived and compiled from an extensive experimental database.
- EIy4 FAC3 * EIy3 (4)
- FACl, FAC2, FAC3 are factors.
- FACl may be 0.428
- FAC3 0.001.
- FAC4, FAC5, FAC6 are factors.
- Torsion behavior is assumed linear while the axial behavior may be calculated using the Load Factor Resistant Design (LRFD Buckling equation) or any other appropriate equation or experimental data.
- LRFD Buckling equation Load Factor Resistant Design
- the failure behavior (third type of the non-linear input data) for the beam-column element may be defined in terms of critical cumulative rotational ductility and critical cumulative axial ductility.
- critical cumulative rotational ductility when the critical cumulative resultant rotational ductility from the in-plane and out-of-plane bending exceeds a threshold value, member failure is initiated.
- the subsequent failure behavior is characterized by the equation shown in FIG. 5.
- Bridges especially older steel bridges such as the Golden Gate Bridge of San Francisco, CA, comprise built- up sections.
- the present invention can handle almost any kind of a steel bridge built-up section.
- a typical section shown in FIG. 6 comprising external and internal plates, external and internal angles, and lacing, the user specifies the information shown in the figure.
- the present invention automatically calculates the nonlinear hysteretic bending and axial behavior.
- the user For a masonary infill wall, the user needs to specify the panel's geometry (panel width, height, thickness) , yield stress (to calculate overstress factors) and modulus of elasticity as part of the linear elastic data input .
- the panel hysteretic behavior is automatically defined as two diagonal struts .
- the strut properties are based on experimental and analytical data. Similar procedure defines properties of shear wall elements.
- Foundation comprises the foundation elements and soil.
- the foundation elements may be piles driven in soil to appropriate depths . They may be steel , wood or concrete piles.
- the soil type characterizes soil elements.
- the soil may be specified by its type (e.g., clay, sand, sand etc.) and its other basic properties readily available from literature or specific soil boring laboratory tests.
- the soil layer at the depth is modeled with three- orthogonal truss-type elements: two lateral and one axial. The nonlinear hysteretic behavior of each of these truss-type elements is automatically generated.
- Loads may be static and/or dynamic.
- the present invention in step 204 automatically generates static load pushover profiles for earthquake loads and wave/wind/current loads in addition to the nonlinear hysteretic member behaviors .
- Step 204 then automatically generates a static pushover profile by performing the eigen solution, combining the modal forces from modes capturing up to at least 90% of the mass, and correcting the pushover profile to match the story shears and overturning moments.
- the wave/current/wind is passed through the mathematical model and the snap-shot profile defining the largest base shear in the time history is selected as the load profile.
- the analysis is performed automatically where only the load analysis is performed without the accompanying structural response calculations. Input for these loads is minimal and standard.
- the present invention optimizes the solution by (a) minimizing storage of the stiffness matrix utilizing minimization procedures such as bandwidth minimization, profile frontal method, etc.; (b) utilizing numerical solution methods that require only one copy of the stiffness matrix; (c) utilizing storage and solution schemes where only the portion of stiffness matrix that has changed due to change in member state and/or large displacement effects is reformulated and reduced; (d) utilizing higher order numerical integration schemes which allow increase in step size and hence reduction in the total steps required for analysis; and (e) utilizing hardware specific available accelerations.
- the first option is to print a summary of inelastic sequence of events for members, an exemplary summary of which is shown in FIG. 7.
- the summary includes an event sequence number, static increment number and load step within the increment when the member becomes inelastic, the total load step or dynamic time step, member name experiencing the inelastic behavior, member type, member group number, nodes I and J, D/C ratio, and group title.
- Each nonlinear member's maximum ductilities are also available in terms of resultant bending, axial tension, axial compression and axial total.
- a list in order of inelastic event sequence is available, followed by the sorted list of members experiencing maximum to minimum damage. Further sorting is available for different member types. Other information may also be available .
- a second option' is to generate one or more of at least two forms of graphical output: (a) a color-coded picture of the structure depicting all damaged members from maximum to minimum (a gray scale version of the color-coded picture is shown in FIG. 8) ; and (b) a color-coded animation of the structure response.
- the color or the gray scale codes the damage in the braces summarized in FIG. 7.
- the upper panel braces LX1 and LX2 have maximum axial ductilities of approximately 15 and are shown in dark shade (red in actual application) .
- the lower panel braces LX3 and LX4 are in light shade (blue in actual application) since their maximum ductilities are approximately 4.0.
- the present invention provides a mechanism to quantify local, regional and global damage and maps these quantities to Building and Other Code Requirements.
- the user needs to specify the following information only; (a) number of stories in the building where damage is to be monitored; and (b) the nodes at each story which are used to calculate average story motions and displacements.
- the present invention automatically calculates global damage measure, regional damage measure and local damage measure.
- Global damage measure is defined in terms of global displacement ductility.
- Regional and local damage is defined in terms of inter- story drifts, inter-story shears, number of damaged members, their maximum and cumulative ductilities, and their number of equivalent full plastic cycles. Other measures may be included. The methods used to calculate these quantities are widely known and available in public literature, standard text books.
- the analysis step 206 is repeated for multiple load conditions.
- the building is analyzed for a series of seismic loads representing different earthquake intensities.
- the selection of earthquakes and the analyses can be extremely time consuming, cumbersome and complex.
- the present invention simplifies the process.
- a single input data stream can be utilized to perform multiple analyses using a single set of ground motions.
- Each execution run scales the single set of ground motions by user defined scale factors.
- the first scale factor is selected such that damage initiates in the structure when subjected to this scaled ground motion.
- the user may specify different target spectral accelerations. Again, the first target spectral acceleration is selected such that damage initiates in the structure when subjected to this scaled ground motion.
- Scale factors for ground motions are automatically calculated to match the user specified target spectral accelerations.
- the user may be notified by e-mail to download the print-out of analyses results and associated information in graphical form.
- These may be pictures of their structure models, pictures of their structure depicting color-coded damaged areas, and real-time animation of their structure response. Any support is provided through a 1-900-number with costs billed through the telephone company.
- the routine 150 receives from the user the location and properties information of the structure to be rated. For example, for a house in California, the user would supply the location address, the type of structure (e.g., one, two-story wood frame), when it was built, information about any upgrades and the like.
- the structure's fundamental period is determined by either utilizing Building Code equations or other well-known methods. The reason for obtaining the structure's fundamental period will be discussed later herein in detail.
- step 154 the routine identifies all active faults around the structure to be rated.
- step 156 the routine identifies the fault (s) that likely cause the most damage to the structure with the earthquake magnitudes the identified fault (s) can generate and their probability. This information can be obtained from a seismic hazard analysis or publicly available databases.
- step 158 spectral accelerations for the structure from the identified fault in step 156 are obtained.
- the seismic hazard analysis and the structure fundamental period (s) provide the information on spectral accelerations for the structure under consideration .
- a damage function routine 300 will now be discussed.
- the routine 300 classifies all structures according to a predetermined structure types such as building code guidelines, FEMA guidelines or any rational means.
- step 304 further classification (sub-classification) of the structures within each classified type is done based on fundamental structure periods. This way, all structures within a classified structure type whose fundamental structure period falls within a predetermined range are considered to be similar structures for the purpose of structure analysis.
- This novel feature of sub-classifying structure types based on fundamental structure periods allows (a) creation of fewer damage functions that are applicable to a larger population and (b) a rational basis for interpolation/extrapolation of damage functions between periods.
- a damage function for each sub- classified structure is determined in the following way to create a database of damage functions.
- the damage functions database is created by performing nonlinear analyses of typical structures built under typical building codes and typical building materials.
- step 164 the routine determines an overall rating for the property from a scale of 1 to 10.
- the rating considers structural damage (global, regional, local) and non-structural damage information in conjunction with the hazard under consideration (e.g., earthquake) . Financial and other information may also be considered.
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Priority Applications (5)
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BR0107614-0A BR0107614A (en) | 2000-01-12 | 2001-01-12 | Computer-implemented process for analyzing a structure |
MXPA02006851A MXPA02006851A (en) | 2000-01-12 | 2001-01-12 | System and method for analyzing structures subjected to catastrophic events. |
JP2002518356A JP2004506214A (en) | 2000-01-12 | 2001-01-12 | Systems and methods for analyzing structures that undergo catastrophic events. |
EP01903068A EP1257940A4 (en) | 2000-01-12 | 2001-01-12 | System and method for analyzing structures subjected to catastrophic events |
AU30932/01A AU3093201A (en) | 2000-01-12 | 2001-01-13 | System and method for analyzing structures subjected to catastrophic events |
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US17576100P | 2000-01-12 | 2000-01-12 | |
US60/175,761 | 2000-01-12 |
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WO2002013071A1 true WO2002013071A1 (en) | 2002-02-14 |
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PCT/US2001/001218 WO2002013071A1 (en) | 2000-01-12 | 2001-01-12 | System and method for analyzing structures subjected to catastrophic events |
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EP (1) | EP1257940A4 (en) |
JP (1) | JP2004506214A (en) |
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BR (1) | BR0107614A (en) |
MX (1) | MXPA02006851A (en) |
WO (1) | WO2002013071A1 (en) |
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- 2001-01-12 US US09/759,962 patent/US7069158B2/en not_active Expired - Lifetime
- 2001-01-12 EP EP01903068A patent/EP1257940A4/en not_active Withdrawn
- 2001-01-12 WO PCT/US2001/001218 patent/WO2002013071A1/en not_active Application Discontinuation
- 2001-01-12 MX MXPA02006851A patent/MXPA02006851A/en unknown
- 2001-01-12 BR BR0107614-0A patent/BR0107614A/en not_active IP Right Cessation
- 2001-01-13 AU AU30932/01A patent/AU3093201A/en not_active Abandoned
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Cited By (2)
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WO2005073688A1 (en) * | 2004-01-21 | 2005-08-11 | California Institute Of Technology | Extreme event performance evaluation of a structure using real-time hystersis monitoring |
US8538734B2 (en) | 2004-01-21 | 2013-09-17 | California Institute Of Technology | Extreme event performance evaluation using real-time hysteresis monitoring |
Also Published As
Publication number | Publication date |
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EP1257940A4 (en) | 2004-08-04 |
MXPA02006851A (en) | 2004-04-05 |
BR0107614A (en) | 2004-01-13 |
JP2004506214A (en) | 2004-02-26 |
AU3093201A (en) | 2002-02-18 |
EP1257940A1 (en) | 2002-11-20 |
US20010029432A1 (en) | 2001-10-11 |
US7069158B2 (en) | 2006-06-27 |
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