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12. Earthquake Damage Mitigation Strategies Informed by Rupture-to-Rafters Simulations

11. 3-D Modeling of Precariously Balanced Rocks

10. Quantifying the Risk Posed to Tall Steel Frame Buildings in Southern California from Earthquakes on the San Andreas Fault

9. On the Elastic and Inelastic, Critical and Post-Buckling Behavior of Slender Columns and Braces

8. On the Mechanism of Collapse of Tall Steel Moment Frame Buildings

7. Tall Steel Building Response to the SHAKEOUT Scenario Earthquake

6. The Caltech Virtual Shaker

5. 1857-like San Andreas Earthquake End-to-End Simulation

4. PFRAME3D & FRAME3D

3. Behavior of Tall Steel Moment Frame Buildings Under Near-Source Ground Motion (PhD Thesis)

2. System Identification of Dynamic Struct. Systems Using Continuous-Time Domain Methods (MS Thesis)

1. Long-Span Cable-Supported Bridges (B.Tech Thesis)

 


12. Earthquake Damage Mitigation Strategies Informed by Rupture-to-Rafters Simulations

Funding Source: US Geological Survey (USGS)

To reduce the collapse potential of existing structures, retrofitting measures must be taken. These measures must realize a lower probability of collapse for the structure at a given intensity of ground shaking when compared to the existing version. At the same time, they need to be economically feasible and, to the extent possible, must preserve the architectural integrity and functionality of the building. Rupture-to-rafters simulations provide a convenient platform for generating fragility curves (probability of failure at a given intensity of ground motion) and comparing alternative retrofitting schemes on such metrics as reduction in collapse probability, cost of retrofit, and impact on architecture as measured by the lease rate. This research aims to reduce the potential for an existing 18-story steel moment frame building to collapse under an 1857-like earthquake on the San Andreas fault through retrofitting measures that are targeted to reducing the P−∆ effects and are conceived with the goal of minimum intervention to preserve the architectural integrity.

GROUP MEMBERS

Arnar Bjorn Bjornsson, Graduate Student

COLLABORATORS

Dr. Rob Graves, USGS

REFERENCES

Bjornsson, A.B. and Krishnan, S., 2012.  "A Retrofitting Framework for Pre-Northridge Steel Moment-Frame Buildings", 15th World Conference in Earthquake Engineering, Lisbon, Portugal, September 24-28, 2012 (submitted).  [PDF]


11. 3-D Modeling of Precariously Balanced Rocks

Funding Source: Southern California Earthquake Center (SCEC), US Geological Survey (USGS)

This research aims establish a rigorous framework for constraining peak ground motion at the locations of precariously balanced rocks (PBR) through 3-D finite element analysis of high-fidelity computational models with due consideration to in-situ rock-pedestal geometry as well as uncertainty in rock properties and rockpedestal contact interface. The proof of concept will be established through a prototype study of the recently imaged Echo Cliffs PBR. The success of the prototype study will provide an impetus to 3-D imaging and analysis of hundreds of PBRs identified and cataloged by Brune et al. The ultimate goal is to arrive at probabilistic constraints on region-wide ground shaking intensity by combining the results of this study with cosmogenic dating of these rocks.

GROUP MEMBERS

Swetha Veeraraghavan, Graduate Student

COLLABORATORS

Dr. Ken Hudnut, USGS

REFERENCES

Veeraraghavan, S. and Krishnan, S., 2012.  "3-D Dynamic Analysis of Precariously Balanced Rocks Under Earthquake Excitation", 15th World Conference in Earthquake Engineering, Lisbon, Portugal, September 24-28, 2012 (submitted).  [PDF]


10. Quantifying the Risk Posed to Tall Steel Frame Buildings in Southern California from Earthquakes on the San Andreas Fault

Funding Source: National Science Foundation (NSF)

The recently released Uniform California Earthquake Rupture Forecast by the Working Group on California Earthquake Probabilities concludes that there is a high probability that an earthquake of magnitude 6 or larger will occur on the southern section of the San Andreas fault in the next 30 years. The research objective of this award is to do a region-wide quantitative risk analysis of six steel buildings in the 20-story class for the hazard posed by the San Andreas fault. For this, rupture-to-rafters simulations of ground motion from 36 earthquakes and damage to the six buildings will be carried out. The earthquakes vary in magnitudes from 6.0 to 8.0 and originate at three hypocenter locations on the fault. Two rupture propagation directions will be considered. The Los Angeles metropolitan region will be divided into 636 analysis sites on a uniform grid of about 3.5km spacing. Three steel moment frame and three steel braced frame building models will be analyzed at each site for damage caused by the 3-component motion of the 36 scenario earthquakes. The results will be probabilistically analyzed to quantify the expected annualized economic loss for each building at each of the sites. Remedial measures that prevent collapse of the buildings will be investigated. The study will resolve long-standing questions related to failure modes, degradation characteristics, and collapse mechanisms of steel moment frame and braced frame buildings. This will also provide a quantitative measure of the economic risk due to the seismic activity on the San Andreas fault to the hundreds of high-rise buildings that exist in Southern California.

GROUP MEMBERS

Ramses Mourhatch, Graduate Student; Hemanth Siriki, Graduate Student

COLLABORATORS

Dr. James L. Beck, Caltech

Dr. Chen Ji, University of California, Santa Barbara

Dr. Hiroo Kanamori, Caltech

Dr. Dimitri Komatitsch, University of Pau, France

Dr. Marco Stupazzini, Politecnico di Milano

Dr. Jeroen Tromp, Princeton University

REFERENCES

Siriki, H., Bhat, H., Lu, X., Rosakis, A.J., and Krishnan, S., 2012.  "A Recursive Division Stochastic Strike-Slip Seismic Source Algorithm Using Insights from Laboratory Earthquakes", 15th World Conference in Earthquake Engineering, Lisbon, Portugal, September 24-28, 2012 (submitted).  [PDF]

Mourhatch, R. and Krishnan, S., 2012.  "High-Frequency Ground Motion Simulation Using a Source- and Site-Specific Empirical Green's Function Approach", 15th World Conference in Earthquake Engineering, Lisbon, Portugal, September 24-28, 2012 (submitted).  [PDF]


9. On the Elastic and Inelastic, Critical and Post-Buckling Behavior of Slender Columns and Braces

Funding Source: Southern California Earthquake Center (SCEC)

An efficient beam element, the modified elastofiber (MEF) element, has been developed to capture the overall features of the elastic and inelastic response of slender columns and braces under axial cyclic loading without unduly heavy discretization. In the first half of this two-part paper, MEF element theory and calibration are presented. The ability of the element to capture elastic buckling of columns is illustrated. The MEF element consists of three fiber segments, two at the member ends and one at mid-span, with two elastic segments sandwiched in between. The segments are demarcated by two exterior nodes and four interior nodes. The fiber segments are divided into 20 fibers in the cross-section that run the length of the segment. The fibers exhibit nonlinear axial stress-strain behavior akin to that observed in a standard tension test of a rod in the laboratory, with a linear elastic portion, a yield plateau, and a strain hardening portion consisting of a segment of an ellipse. All the control points on the stress-strain law are user-defined. The elastic buckling of a member is tracked by updating both exterior and interior nodal coordinates at each iteration of a time step, and checking force equilibrium in the updated configuration. Inelastic post-buckling response is captured by fiber yielding, fracturing, and/or rupturing in the nonlinear segments. The element is calibrated to accurately predict the Euler critical buckling load of box and I-sections with a wide range of slenderness ratios (L/r = 40, 80, 120, 160, and 200) and support conditions (pinned-pinned, pinned-fixed, and fixed-fixed). Elastic post-buckling of the Koiter-Roorda L-frame (tubes and I-sections) with various member slenderness ratios (L/r = 40, 80, 120, 160, and 200) is simulated and shown to compare well against second-order analytical approximations to the solution, even when using a single MEF element to model each leg of the frame. the inelastic behavior of struts under cyclic loading observed in the Black et al., Fell et al., and Tremblay et al. experiments is shown to be accurately captured by single MEF element models. A FRAME3D model (using MEF elements for braces) of a full-scale 6-story braced frame structure that was pseudodynamically tested by the Building Research Institute of Japan subjected to the 1978 Miyagi-Ken-Oki earthquake record, is analyzed and shown to closely mimic the experimentally observed behavior. To aid in the evaluation of the collapse-prediction capability of competing methodologies, a benchmark problem of a water-tank subjected to the Takatori nearsource record from the 1995 Kobe earthquake, scaled down by a factor of 0.32, is proposed. The water-tank is so configured as to have a unique collapse mechanism (under all forms of ground motion), of overturning due to P−D instability resulting from column and brace buckling at the base.

REFERENCES

Krishnan, S., 2010.  "Case Study of the Collapse of a Water Tank", Technical Report - CaltechEERL:EERL-2010-01, California Institute of Technology, Pasadena, California, 2010. [PDF]

Krishnan, S..  "The Modified Elastofiber Element for Steel Slender Column and Brace Modeling", vol. 136(11), November 2010, Journal of Structural Engineering. [PDF]

Krishnan, S., 2009.  "On the Modeling of Elastic and Inelastic, Critical- And Post-Buckling Behavior of Slender Columns and Bracing Members", Technical Report - CaltechEERL:EERL-2009-03, California Institute of Technology, Pasadena, California, 2009. [PDF]


8. On the Mechanism of Collapse of Tall Steel Moment Frame Buildings

Funding Source: National Earthquake Hazard Reduction Program (NEHRP)

We explore the behavior of two tall steel moment frame buildings and their variants under strong earthquake ground shaking through parametric analysis using idealized ground motion waveforms. Both fracture-susceptible as well as perfect-connection conditions are investigated. Ground motion velocity waveforms are parameterized using triangular (sawtooth-like) wave-trains with a characteristic period (T), amplitude (peak ground velocity, PGV ), and duration (number of cycles, N). This idealized representation has the desirable feature that the response of the target buildings under the idealized waveforms closely mimics their response under the emulated true ground motion waveforms. A suite of nonlinear analyses are performed on four tall building models subjected to these idealized wave-trains, with T varying from 0.5s to 6.0s, PGV varying from 0.125 m/s to 2.5 m/s, and N taking the values of 1 to 5, and 10. Severe dynamic response is induced only in the long-period, large-amplitude excitation regime. Through a simple examination of the energy balance during earthquake shaking, it can be shown that the input excitation energy is small for excitation with periods shorter than the structural period, whereas it is proportional to the square of the ground velocity if the excitation periods are much longer than the structural periods. Thus, collapse-level response can be induced only by long-period, moderate to large PGV ground excitation. The collapse initiation regime expands to lower ground motion periods and amplitudes with increasing number of ground motion cycles. The close examination of one instance of collapse shows the formation of plastic hinges at the top of all columns in an upper story, at the bottom of all columns in a lower story, and at both ends of all beams in the intermediate stories. Such a pattern of hinging results in shear-like deformation in these stories, resembling plastic shear bands in ductile solids. Most of the lateral deformation due to seismic shaking is concentrated in this "quasi-shear" band (QSB). When the overturning 1st-order and 2nd-order (P-Δ) moments from the inertia of the overriding block of stories exceed the moment-carrying capacity of the quasi-shear band, it loses stability and collapses. This puts the overriding block of stories in free fall, progressive collapse is initiated, and gravity takes over. Thus, the collapse mechanism initiates as a sidesway mechanism that is taken over by gravity once the quasi-shear band is destabilized. There are Ns(Ns+1)/2 possible quasi-shear bands (and an equal number of sidesway collapse mechanisms) in either principal direction of an Ns-story moment frame building. More than one quasi-shear bands could occur during the entire duration of strong earthquake shaking. The band exhibiting the greatest distress (termed the “primary” quasi-shear band) ultimately evolves into a sidesway collapse mechanism. The location of the primary quasi-shear band (the shear band with the greatest plastic strains) as a function of the input excitation period largely follows that of the region of greatest yield in a uniform shear-beam. Greater the period of input excitation, lower the location of the band. However, because the buildings are non-uniform in strength, the downward migration of the primary QSB with increasing pulse period is arrested a few stories above the base. In the uniform shear beam, yielding would migrate all the way to the base for pulse periods exceeding the beam period. Combined with the fact that collapse can occur only under long-period motions, this implies that there must exist a characteristic mechanism of collapse or a few preferred mechanisms of collapse for these buildings– sidesway collapse initiated by shear instability in the primary quasi-shear band a few stories above the base. The Principle of Virtual Work is applied to to all possible quasi-shear bands in the building. The band whose capacity is exceeded under the smallest absolute acceleration (acr) of the over-riding block of stories is identified as the characteristic collapse mechanism. If one or more mechanisms have an acr very close (say within 5%) to the minimum acr, the characteristic collapse mechanism may be non-unique. Collapse may occur in one of these preferred mechanisms. The results from this approach agree well with the simulations of all four building models under idealized ground motion waveforms where collapse occurs. These simulations do not show the formation of a single (unique) collapse mechanism. However, in each model only one to five collapse mechanisms occur out of a possible 153 mechanisms in each principal direction of the building. Furthermore, if two or more preferred mechanisms do exist, they have significant story-overlap, typically separated by just one story. For example, the strongly preferred collapse mechanisms in the existing building model (perfect connections) under X direction excitation occur between floors 3 and 9, and floors 4 and 9, while the weakly preferred mechanisms occur between floors 3 and 8, and floors 4 and 8 (four preferred mechanisms out of 153 possible mechanisms, all clustered together within a narrow story zone; two of these mechanisms are in fact a subset of the other two mechanisms).

REFERENCES

Krishnan, S. and Muto, M., 2012.  "Mechanism of Collapse of Tall Steel Moment Frame Buildings Under Earthquake Excitation", Journal of Structural Engineering (in print).  [PDF]

Krishnan, S. and Muto, M., 2012.  "Sensitivity of the Earthquake Response of Tall Steel Moment Frame Buildings to Ground Motion Features", in Revision, Journal of Earthquake Engineering. PDF draft available upon request.

Krishnan, S., Casarotti, E., Goltz, J., Ji. C., Komatitsch, D., Mourhatch, R., Muto, M., Shaw, J. H., Tape, C., and Tromp, J., 2012.  "Rapid Estimation of Damage to Tall Buildings Using Near Real-Time Earthquake and Archived Structural Simulations", Bulletin of the Seismological Society of America (in print). [PDF]

Krishnan, S., and Muto, M., 2011.  "Mechanism of collapse, sensitivity to ground motion features, and rapid estimation of the response of tall steel moment frame buildings to earthquake excitation", Technical Report - CaltechEERL:EERL-2011-02, California Institute of Technology, Pasadena, California, 2011. [PDF]

GROUP MEMBERS

Dr. Matthew Muto, Post-Doctoral Scholar


7. Tall Steel Building Response to the SHAKEOUT Scenario Earthquake

Funding Source: Multi-Hazard Demonstration Project, US Geological Survey

In order to prepare for the next big earthquake on the San Andreas fault, the US Geological Survey (USGS) conducted a year-long "DARE TO PREPARE" campaign that culminated in the Great Southern California Shakeout Scenario in 2008 (Porter et al. 2009). The scenario earthquake, chosen based on a wide variety of observations and constraints, was a magnitude 7.8 earthquake on the San Andreas fault with rupture initiating at Bombay Beach and propagating northwest through the San Gorgonio Pass a distance of roughly 304 km, terminating at Lake Hughes near Palmdale, sections of the San Andreas fault that last broke in 1680, 1812, and 1857. Through community participation in two Southern San Andreas Fault Evaluation (SoSAFE) workshops organized by the Southern California Earthquake Center (SCEC), a source model specific to the southern San Andreas fault was constructed with constraints from geologic, geodetic, paleoseismic, and seismological observations. Using this source model, Rob Graves of URS Corporation simulated 3-component seismic waveforms on a uniform grid covering southern California (Graves et al. 2008). Peak velocities of the synthetic ground motion were in the range of 0-100 cm/s in the San Fernando valley, and 60-180 cm/s in the Los Angeles basin. Corresponding peak displacement ranges were 0-100 cm and 50-150 cm. For the shakeout drill, USGS commissioned us to provide a realistic picture of the impact of such an earthquake on the tall steel buildings in southern California. We selected 784 sites across southern California to place 3-D computer models of three steel moment frame buildings in the 20-story class (an existing building designed according to the 1982 UBC, the same building redesigned using the 1997 UBC, and a hypothetical L-shaped building also designed according to the 1997 UBC), and analyzed these models subject to the simulated 3-component ground motion, orienting them in two different directions, considering perfect and imperfect realizations of beam-to-column connection behavior. We averaged the response from these 12 cases (3 buildings x 2 orientations x 2 connection susceptibility realizations), and combined this with the observed response of tall steel buildings in past earthquakes to provide a qualitative picture of one plausible outcome in the event of the big one striking southern California.

REFERENCES

Muto, M., and Krishnan, S., 2011.  "Hope for the Best, Prepare for the Worst: Response of Tall Steel Buildings to the ShakeOut Scenario Earthquake", vol. 27(2), May 2011, ShakeOut Special Issue, Earthquake Spectra. [PDF]

Muto, M., and Krishnan, S., 2008.  "Response of tall steel buildings in southern California to the magnitude 7.8 shakeout scenario earthquake", Inaugural International Conference of the Engineering Mechanics Institute, University of Minnesota, May 18-21 2008. [PDF]

GROUP MEMBERS

Dr. Matthew Muto, Post-Doctoral Scholar

COLLABORATORS

Dr. Rob Graves, USGS


6. The Caltech Virtual Shaker

The Caltech Virtual Shaker (CVS) is a publicly accessible online science gateway created to facilitate the analysis and visualization of structural models under various kinds of earthquake ground motion. It consists of a structural model database and a ground motion waveform database. Registered users can upload new structural models and ground motion time-histories, can select existing models from the database and analyze them under selected ground motion waveforms. The analyses are conducted on a high-performance computing cluster on the Caltech campus. Upon completion, results are emailed back to the user. Newly submitted models become available to all registered users. This is a community-driven venture that is expected to be self-sustaining in the long run, with models contributed by users and the software and CPU cycles being provided by CVS.

RELATED LINKS:

http://virtualshaker.caltech.edu


5. 1857-like San Andreas Earthquake End-to-End Simulation

What would happen to engineered highrise buildings in the Los Angeles and San Fernando basins if an 1857-like magnitude 7.9 earthquake were to occur on the San Andreas fault?

Two such earthquakes have been simulated and the nonlinear response of two 18-story steel moment-frame buildings has been modeled with the aid of high-performance computing.

Key information:

1.  Two scenarios - one with rupture initiating at Parkfield in central California and propagating north-to-south a distance of 290 km and the other with the slip distribution and rupture direction flipped such that rupture starts north of Los Angeles and proceeds south-to-north terminating at Parkfield.

2.  Both are magnitude 7.9 earthquakes.  Kinematic source model of the Denali (Alaska) fault earthquake of 2002 has been mapped on to the San Andreas fault.

3.  Domain of simulation includes a uniform grid of 636 analysis sites spaced at 3.5 km in each direction.

4.  3-D models of two 18-story steel moment-frame buildings (one existing building designed according to the 1982 Uniform Building Code, and the other being the same building redesigned according to the stricter 1997 UBC) have been analyzed subjected to 3-component ground motion from the two San Andreas fault earthquakes at each of the 636 sites.

5.  Building response summed up in the form of maps of peak interstory drift ratio.

Watch movies of the seismic wave propagation and building response.

MOVIES

NORTH-TO-SOUTH RUPTURE SCENARIO
Fault rupture and seismic wave propagation:  Play Movie (18 MB)

Movies of the shaking of existing and new 18-story steel moment-frame building models at various sites in Southern California.  Of these, the existing building models in Thousand Oaks and Northridge are seen collapsing, while there is significant permanent tilt in most other cases.


Anaheim:  Play Movie (8 MB)
Baldwin Park:  Play Movie (8 MB)
Downtown Los Angeles:  Play Movie (8 MB)
Long Beach:  Play Movie (8 MB)
Northridge:  Play Movie (8 MB)
Santa Ana:  Play Movie (8 MB)
Thousand Oaks:  Play Movie (8 MB)
West Los Angeles:  Play Movie (8 MB)

SOUTH-TO-NORTH RUPTURE SCENARIO
Fault rupture and seismic wave propagation:  Play Movie (18 MB)

SOFTWARE USED

SPECFEM3D for the seismic wave propagation.

FRAME3D for the building analyses.

REFERENCES

Krishnan, S., Ji, C., Komatitsch, D., Tromp, J., Muto, M., Mitrani-Reiser, J., and Beck, J. L., 2008.  "Simulation of an 1857-like Mw 7.9 San Andreas fault earthquake and the response of tall steel moment frame buildings in southern California - A prototype study",  Proceedings of the 14th World Conference in Earthquake Engineering, Beijing, China, October 17-21, 2008.  [PDF]

Muto, M., Krishnan, S., Beck, J. L., Mitrani-Reiser, J., 2008.  "Seismic loss estimation based on end-to-end simulation", IALCCE08: First International Symposium on Life-Cycle Civil Engineering, Varenna, Lake Como, Italy, June 11-14, 2008.           [PDF]

Krishnan, S., Ji, C., Komatitsch, D., and Tromp, J., 2006.  "Performance of Two 18-Story Steel Moment-Frame Buildings in Southern California During Two Large Simulated San Andreas Earthquakes", vol. 22(4), November 2006, Earthquake Spectra. [PDF]

Krishnan, S., Ji, C., Komatitsch, D., and Tromp, J., 2006.  "Case Studies of Damage to Tall Steel Moment-Frame Buildings in Southern California During Large San Andreas Earthquakes", vol. 96(4), August 2006, Bulletin of the Seismological Society of America. [PDF]

Krishnan, S., Ji, C., Komatitsch, D., and Tromp, J., 2006.  "Impact of a Large San Andreas Fault Earthquake on Tall Buildings in Southern California", EERI's 8th U.S. National Conference on Earthquake Engineering, April 2006. [PDF]

Krishnan, S., Ji, C., Komatitsch, D., and Tromp, J., 2005.  "Performance of 18-Story Steel Moment-Frame Buildings During a Large San Andreas Earthquake - A Southern California-Wide End-to-End Simulation", Technical Report - CaltechEERL:EERL-2005-01, California Institute of Technology, Pasadena, California, 2005. [PDF]

COLLABORATORS

Dr. Jeroen Tromp, Princeton University

Dr. Chen Ji, University of California, Santa Barbara

Dr. Dimitri Komatitsch, University of Pau, France


4. P-FRAME3D & FRAME3D

FRAME3D is a program for the three-dimensional nonlinear analysis of steel buildings. It aims to overcome the computational challenges posed by full 3D analysis of buildings subject to earthquake ground motion. The element library consists of a plastic hinge beam element, an elastofiber beam element, a modified elastofiber element, a panel zone element, a 4-noded diaphragm element to model floor slabs, and an elastic translational/rotational spring element to model foundations and supports. The program utilizes a Netwon-Raphson iteration strategy applied to an implicit Newmark time-integration scheme to solve the nonlinear equations of motion at each time-step. Geometric nonlinearity and shear deformation are included in the formulation.

P-FRAME3D is the parallel version of FRAME3D currently under development.  Upon completion, P-FRAME3D can be executed on a parallel computer cluster to solve complex structural engineering problems such as the strong shaking of a super-highrise building or a long-span cable-supported bridge under a large earthquake occurring on a nearby fault.

REFERENCES

Krishnan, S., 2009.  "FRAME3D V2.0 - A Program for the Three-Dimensional Nonlinear Time-History Analysis of Steel Buildings: User Guide", Technical Report - CaltechEERL:EERL-2009-04, California Institute of Technology, Pasadena, California, 2009.  [PDF]

RELATED LINKS:

FRAME3D Program - http://www.frame3d.caltech.edu.


3. Behavior of Tall Steel Moment Frame Buildings Under Near-Source Ground Motion

Strong ground motion from a nearby fault has frequency content in the same range as the natural frequencies of tall buildings. This may have serious repercussions and is the topic of my Ph.D. dissertation.  Buildings are designed per building code standards. But, are the code provisions adequate? Strong motion from large earthquakes has been recorded only in recent times in the near-source region. Have the current codes used this information to update tall structure design guidelines? Considerable damage has been observed in tall buildings from the Northridge, Kobe, Turkey, and Taiwan earthquakes. How will tall buildings designed per the latest code regulations perform if they were to be shaken by any of these earthquakes?  My thesis attempts to answer these questions.

Tall buildings by their nature are computationally intensive to analyze. They consist of thousands of degrees of freedom and when subjected to strong ground motion from a nearby source, exhibit inelastic response. Modeling this inelastic response requires an iterative approach that is computationally expensive. Furthermore, a large class of buildings, classified as irregular, exhibits complex behavior that can be studied only when the structures are modeled in their entirety. To this end, a three-dimensional analysis program, FRAME3D, has been developed incorporating two special beam-column elements -- the plastic hinge element and the elastofiber element that can model beams and columns in buildings accurately and efficiently, a beam-column joint element that can model inelastic joint deformation, and 4-noded elastic plane-stress elements to model floor slabs acting as diaphragms forcing the lateral force resisting frames in a building to act as one unit. The program is capable of performing time-history analyses of buildings in their entirety.

Six 19-story irregular steel moment frame buildings (with buildings 2A and 3A being variants of buildings 2 and 3, respectively) have been designed per the latest code (Uniform Building Code, 1997). Two of these buildings have reentrant corners and the other two have torsional irregularity. Their strength and ductility are assessed by performing pushover analyses on them. To assess their performance under strong shaking, FRAME3D models of these buildings are subjected to near-source strong motion records from the Iran earthquake (Mw = 7.3, Tabas Station) of 1978, the Northridge earthquake (Mw = 6.7, Sylmar Station) of 1994 and the Kobe earthquake (Mw = 6.9, Takatori Station) of 1995. None of the buildings collapsed under these strong events in the computer analyses. However, when compared against the acceptable limits for various performance levels in FEMA 356 document, the damage in terms of plastic deformation at the ends of beams and columns and at joints would render the buildings inadequate in terms of life safety in quite a few cases and would even indicate possible collapse in a couple of cases. Thus, in these terms, the code falls short of achieving its life safety objective, and the near-source factors introduced in the code in 1997 in recognition of the special features of near-source ground motion seem to be inadequate. The ductility demand, in terms of plastic rotation at the ends of beams and columns and in joints, on these buildings during this class of earthquakes is up to 6% of a radian, which is far greater than a typical limiting plastic rotation of 3% associated with fracture and consequent failure of large wide-flanged steel sections during experiments. Thus, if strength degradation due to fractures, local buckling, etc., were to be included in the analysis, then the results would likely to be worse, as far as the ability of these buildings to withstand these earthquakes without collapse is concerned.

Due to damage localization, the peak drifts observed in the structure far exceeded the inelastic drift limit in the code of 0.02 (in some cases up to 3 times). This points to serious non-structural damage to facades, interior dry wall, etc. Furthermore, large roof permanent offsets after the events indicate significant post-earthquake repair requiring considerable disruption and building closure. Column yielding was minimal thus validating the strong-column weak-beam criterion in the code. Redundancy factors used to assess the redundancy in the system need to take into account the case of torsionally sensitive structures where frames in both principal directions are simultaneously activated. Stress concentration was not observed at the reentrant corners in L-shaped buildings.

Finally, the data catalogued in my thesis could be useful for future code development and tall structure design guidelines.

REFERENCES

Krishnan, S., 2003.  "Three-Dimensional Nonlinear Analysis of Tall Irregular Steel Buildings Subject to Strong Ground Motion", Technical Report - CaltechEERL:EERL-2003-01, California Institute of Technology, Pasadena, California, 2003.           [PDF]

Krishnan, S., 2007.  "Case Studies of Damage to 19-Story Steel Moment-Frame Buildings Under Near-Source Ground Motion",  vol. 36(7), July 2007, Earthquake Engineering and Structural Dynamics. [PDF]

Krishnan, S. and Hall, J. F., 2006.  "Modeling Steel Frame Buildings in Three Dimensions - Part I: Panel Zone and Plastic Hinge Beam Elements", vol. 132(4), April 2006, Journal of Engineering Mechanics. [PDF]

Krishnan, S. and Hall, J. F., 2006.  "Modeling Steel Frame Buildings in Three Dimensions - Part II: Elastofiber Beam Element and Examples", vol. 132(4), April 2006, Journal of Engineering Mechanics. [PDF]

RELATED LINKS:

Building Animations - http://www.frame3d.caltech.edu/anim.html.

Key Analysis Results -  http://www.frame3d.caltech.edu/bldgdb.html.


2. System Identification of Dynamic Structural Systems Using Continuous-Time Domain Methods

Structural system identification is the process of deducing the properties of a structural system from its measured response to ambient vibration by fitting a mathematical model.  The objectives of my Masters research were to: (1) investigate the use of existing system identification methods, and (2) develop new system identification methods, in order to evaluate both loading and structural modal parameters of ambient excited structures for which the load process is difficult to measure.  An example is the case of offshore platforms subjected to sea waves.  The study considers the inverse problem from the viewpoint of continuous-time linear dynamic systems.  An existing structural identification technique defined for the deterministic case (when the loading is known) and based on sequences of modal minimizations (called modal sweeps) is formulated for the general case of multiple-input multiple-output (MIMO) systems.  A global minimization technique based upon the Levenberg-Marquardt algorithm for nonlinear least-squares problems is developed for the same case.  Both identification techniques are applied to a multi-degree-of-freedom (MDOF) shear building model and the results are shown to be consistent.  Using the framework of random vibration theory, these techniques are then converted to the stochastic case, namely when the loading process is known only statistically.  These identification methods, both individually and combined, were tested based on simulated cases of increasing complexity.  The results obtained are promising and indicate that under certain conditions, both load and structural parameters can be estimated from the measured response and the statistical properties of the loading process.  However, the load parameters are not as well estimated as the structural parameters, since the load process is further removed from the response process than the structural filter.  Although a generic shear building model has been used throughout this study to simulate the dynamic response of real structures, the results obtained are believed to apply to linear multi-degree-of-freedom systems in general.

REFERENCES

Krishnan, S., 1994.  "System Identification of Dynamic Structural Systems Using Continuous-Time Domain Methods",  Master of Science Thesis, Rice University, Houston, Texas, 1994. [PDF]

Conte, J. P., and Krishnan, S., 1995.  "Modal Identification Method for Structures Subjected to Unmeasured Random Excitation", Proceedings of the 10th ASCE Engineering Mechanics Specialty Conference, Boulder, Colorado, 1995. [PDF]


1. Long-Span Cable-Supported Bridges

Cable-supported bridge systems are distinguished from conventional bridge systems by their ability to span wide crossings efficiently and aesthetically. The need for long-span bridges may arise due to high foundation cost resulting from wide flood zones, channel instability, deep gorges, etc. Two basic types of cable-supported bridge systems have been commonly used: cable-stayed bridge systems and suspension bridge systems. It is well-established that cable-stayed bridges are suitable for main spans in the range of 250m-500m, and cable-suspended bridges for main spans beyond 1500m. In the intermediate span range of 500m-1500m, both systems are deficient and there is need for a third option. Using the fundamental concept of "cable beams" applied in suspended roof structures, a new cable-net system is proposed. Detailed designs of this system and a cable-stayed bridge system are carried out for a main-span of 800m. By means of a comprehensive comparative analysis of bending moments, axial forces, deflections, and amount of steel used, the paper demonstrates that the cable-net bridge system provides an economically, structurally, and asethetically viable alternative to the cable-stayed and cable-suspended bridge systems for intermediate spans.

REFERENCES

Krishnan, S., 1994. "Cable-Net Bridge System",  Submitted to the Student Paper Competition at the 11th Annual International Bridge Conference, 1994. [PDF]

Krishnan, S., 1992.  "Long-Span Cable-Supported Bridges", Bachelor of Technology Thesis, Department of Civil Engineering, Indian Institute of Technology, Madras, India, May 1992.

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