seismic analysis
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This document gives details of seismic analysis and non linear methods to do seismic analysisTRANSCRIPT
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First and second modes ofbuilding seismic response
Seismic analysisFrom Wikipedia, the free encyclopedia
Seismic analysis is a subset of structural analysis and is the calculationof the response of a building (or nonbuilding) structure to earthquakes.It is part of the process of structural design, earthquake engineering orstructural assessment and retrofit (see structural engineering) in regionswhere earthquakes are prevalent.
As seen in the figure, a building has the potential to ‘wave’ back andforth during an earthquake (or even a severe wind storm). This is calledthe ‘fundamental mode’, and is the lowest frequency of buildingresponse. Most buildings, however, have higher modes of response,which are uniquely activated during earthquakes. The figure just showsthe second mode, but there are higher ‘shimmy’ (abnormal vibration)modes. Nevertheless, the first and second modes tend to cause the mostdamage in most cases.
The earliest provisions for seismic resistance were the requirement to design for a lateral force equal to aproportion of the building weight (applied at each floor level). This approach was adopted in the appendixof the 1927 Uniform Building Code (UBC), which was used on the west coast of the USA. It later becameclear that the dynamic properties of the structure affected the loads generated during an earthquake. In theLos Angeles County Building Code of 1943 a provision to vary the load based on the number of floor levelswas adopted (based on research carried out at Caltech in collaboration with Stanford University and theU.S. Coast and Geodetic Survey, which started in 1937). The concept of "response spectra" was developedin the 1930s, but it wasn't until 1952 that a joint committee of the San Francisco Section of the ASCE andthe Structural Engineers Association of Northern California (SEAONC) proposed using the building period(the inverse of the frequency) to determine lateral forces.[1]
The University of California, Berkeley was an early base for computerbased seismic analysis of structures,led by Professor Ray Clough (who coined the term finite element[2]). Students included Ed Wilson, whowent on to write the program SAP in 1970,[3] an early "Finite Element Analysis" program.
Earthquake engineering has developed a lot since the early days, and some of the more complex designsnow use special earthquake protective elements either just in the foundation (base isolation) or distributedthroughout the structure. Analyzing these types of structures requires specialized explicit finite elementcomputer code, which divides time into very small slices and models the actual physics, much like commonvideo games often have "physics engines". Very large and complex buildings can be modeled in this way(such as the Osaka International Convention Center).
Structural analysis methods can be divided into the following five categories.
Contents
1 Equivalent static analysis
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2 Response spectrum analysis3 Linear dynamic analysis4 Nonlinear static analysis5 Nonlinear dynamic analysis6 See also7 References
Equivalent static analysis
This approach defines a series of forces acting on a building to represent the effect of earthquake groundmotion, typically defined by a seismic design response spectrum. It assumes that the building responds inits fundamental mode. For this to be true, the building must be lowrise and must not twist significantlywhen the ground moves. The response is read from a design response spectrum, given the natural frequencyof the building (either calculated or defined by the building code). The applicability of this method isextended in many building codes by applying factors to account for higher buildings with some highermodes, and for low levels of twisting. To account for effects due to "yielding" of the structure, many codesapply modification factors that reduce the design forces (e.g. force reduction factors).
Response spectrum analysis
This approach permits the multiple modes of response of a building to be taken into account (in thefrequency domain). This is required in many building codes for all except for very simple or very complexstructures. The response of a structure can be defined as a combination of many special shapes (modes) thatin a vibrating string correspond to the "harmonics". Computer analysis can be used to determine thesemodes for a structure. For each mode, a response is read from the design spectrum, based on the modalfrequency and the modal mass, and they are then combined to provide an estimate of the total response ofthe structure. In this we have to calculate the magnitude of forces in all directions i.e. X, Y & Z and thensee the effects on the building.. Combination methods include the following:
absolute peak values are added togethersquare root of the sum of the squares (SRSS)complete quadratic combination (CQC) a method that is an improvement on SRSS for closelyspaced modes
The result of a response spectrum analysis using the response spectrum from a ground motion is typicallydifferent from that which would be calculated directly from a linear dynamic analysis using that groundmotion directly, since phase information is lost in the process of generating the response spectrum.
In cases where structures are either too irregular, too tall or of significance to a community in disasterresponse, the response spectrum approach is no longer appropriate, and more complex analysis is oftenrequired, such as nonlinear static analysis or dynamic analysis.
Linear dynamic analysis
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Static procedures are appropriate when higher mode effects are not significant. This is generally true forshort, regular buildings. Therefore, for tall buildings, buildings with torsional irregularities, or nonorthogonal systems, a dynamic procedure is required. In the linear dynamic procedure, the building ismodelled as a multidegreeoffreedom (MDOF) system with a linear elastic stiffness matrix and anequivalent viscous damping matrix.
The seismic input is modelled using either modal spectral analysis or time history analysis but in bothcases, the corresponding internal forces and displacements are determined using linear elastic analysis. Theadvantage of these linear dynamic procedures with respect to linear static procedures is that higher modescan be considered. However, they are based on linear elastic response and hence the applicability decreaseswith increasing nonlinear behaviour, which is approximated by global force reduction factors.
In linear dynamic analysis, the response of the structure to ground motion is calculated in the time domain,and all phase information is therefore maintained. Only linear properties are assumed. The analyticalmethod can use modal decomposition as a means of reducing the degrees of freedom in the analysis.
Nonlinear static analysis
In general, linear procedures are applicable when the structure is expected to remain nearly elastic for thelevel of ground motion or when the design results in nearly uniform distribution of nonlinear responsethroughout the structure. As the performance objective of the structure implies greater inelastic demands,the uncertainty with linear procedures increases to a point that requires a high level of conservatism indemand assumptions and acceptability criteria to avoid unintended performance. Therefore, proceduresincorporating inelastic analysis can reduce the uncertainty and conservatism.
This approach is also known as "pushover" analysis. A pattern of forces is applied to a structural model thatincludes nonlinear properties (such as steel yield), and the total force is plotted against a referencedisplacement to define a capacity curve. This can then be combined with a demand curve (typically in theform of an accelerationdisplacement response spectrum (ADRS)). This essentially reduces the problem toa single degree of freedom (SDOF) system.
Nonlinear static procedures use equivalent SDOF structural models and represent seismic ground motionwith response spectra. Story drifts and component actions are related subsequently to the global demandparameter by the pushover or capacity curves that are the basis of the nonlinear static procedures.
Nonlinear dynamic analysis
Nonlinear dynamic analysis utilizes the combination of ground motion records with a detailed structuralmodel, therefore is capable of producing results with relatively low uncertainty. In nonlinear dynamicanalyses, the detailed structural model subjected to a groundmotion record produces estimates ofcomponent deformations for each degree of freedom in the model and the modal responses are combinedusing schemes such as the squarerootsumofsquares.
In nonlinear dynamic analysis, the nonlinear properties of the structure are considered as part of a timedomain analysis. This approach is the most rigorous, and is required by some building codes for buildingsof unusual configuration or of special importance. However, the calculated response can be very sensitiveto the characteristics of the individual ground motion used as seismic input; therefore, several analyses arerequired using different ground motion records to achieve a reliable estimation of the probabilistic
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distribution of structural response. Since the properties of the seismic response depend on the intensity, orseverity, of the seismic shaking, a comprehensive assessment calls for numerous nonlinear dynamicanalyses at various levels of intensity to represent different possible earthquake scenarios. This has led tothe emergence of methods like the Incremental Dynamic Analysis.[4]
See also
Modal Analysis using FEMStructural DynamicsOpenSees Analysis SoftwareVibration controlEarthquake simulationApplied element methodExtreme Loading for Structures Seismic Analysis Software
References
1. ^ ASCE. (2000). Prestandard and Commentary for the Seismic Rehabilitation of Buildings (FEMA356) (Report No. FEMA 356). Reston, VA: American Society of Civil Engineers prepared for theFederal Emergency Management Agency.
2. ^ ATC. (1985). Earthquake Damage Evaluation Data for California (ATC13) (Report). Redwood,CA: Applied Technology Council.
3. ^ Bozorgnia, Y, Bertero, V, "Earthquake Engineering: From Engineering Seismology toPerformanceBased Engineering", CRC Press, 2004.
4. ^ "Early Finite Element Research at Berkeley" (http://www.edwilson.org/History/fehistory.pdf),Wilson, E. and Clough R., presented at the Fifth U.S. National Conference on ComputationalMechanics, Aug. 46, 1999
5. ^ "Historic Developments in the Evolution of Earthquake Engineering"(http://www.curee.org/image_gallery/calendar/essays/1998CUREE_excerpt.pdf), illustrated essaysby Robert Reitherman, CUREE, 1997, p12.
6. ^ Vamvatsikos D., Cornell C.A. (2002). Incremental Dynamic Analysis. Earthquake Engineering andStructural Dynamics, 31(3): 491–514.
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Categories: Earthquake and seismic risk mitigation Structural analysis Earthquake engineering
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