Dynamic Collapse Simulation of 3-Bay RC Frame Under Extreme Earthquake Loadings

8/6/2019 Dynamic Collapse Simulation of 3-Bay RC Frame Under Extreme Earthquake Loadings

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Dynamic Collapse Simulation of 3-Bay RC Frame under

Extreme Earthquake Loadings

Authors:

Chiun-lin Wu, National Center for Research on Earthquake Engineering, Taipei 106,Taiwan, [email protected]

Wu-Wei Kuo, Department of Construction Engineering, National Taiwan Univeristy of

Science and Technology, Taipei 106, Taiwan, [email protected] Yang, National Center for Research on Earthquake Engineering, Taipei 106,

Taiwan, [email protected] Hwang, Department of Civil Engineering, National Taiwan Univeristy, and

National Center for Research on Earthquake Engineering, Taipei 106, Taiwan,

[email protected] Loh, Department of Civil Engineering, National Taiwan Univeristy, Taipei

106, Taiwan, [email protected]

ABSTRACT

Collapse experiments are found very helpful in facilitating collapse analysis of new buildings and

identification of older buildings that are at high risk of structural collapse during severe earthquake events.

Experimental observations from dynamic global collapse of a single story 3-bay RC frame are presented in

this paper. The frame is composed of shear-critical columns and ductile columns to allow for load

redistribution. A near-fault record from the September 21 (local time) 1999 Chi-Chi Taiwan earthquake

was employed. Preliminary investigation shows that existing empirical equations are able to predict

hysteretic backbone until the point of structural collapse with satisfaction.

INTRODUCTION

During the past two decades, several severe earthquake attacks caused tremendous

damage to populated urban cities, such as the 1985 Mexico, the 1989 Lomo Prieta (USA),

the 1994 Northridge (USA), the 1995 Kobe (Japan), and the 1999 Chi-Chi (Taiwan)earthquakes. The past experience showed that buildings were vulnerable to extreme

earthquake events and did not demonstrate satisfactory seimsic performance as originallyexpected. To respond to the observed shortcomings, improved detailing schemes were

introduced for new buildings and retrofitting schemes were proposed for older existing buildings, especially those in the category of essential facilties, to ensure acceptableresilience in probable future earthquake attacks. These measures need to be done early

because of an increase in the required seismic lateral force in the new code documentsrevised based on the most recently known facts about seismicity or because of

insufficient ductility and/or strength capability observed of building performance during

past extreme earthquake events. As such, performance-based design framework wasproposed and collapse analysis is one of the key components to realize such innovative

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concepts. Collapse simulation in both experimental and analytical aspects is getting much

more attention than before worldwide to facilitate introduction of perforamnce-baseddesign in view of the following important facts:

To ensure energy dissipation capacity and collapse prevention: Previous seismicdesign code documents considered only 10%/50yrs. earthquakes (i.e. an average

return period of some 500 years) and a performance objective of life safety was setaccordingly, which imposed a single control point over the structural nonlinear

skeleton curve. This arrangement considerably lessened computational efforts andeffectively simplified seismic design procedures, but as a tradeoff it could not ensure

sufficient structural ductility during extreme earthquake events. To eliminate thisdrawback, performance-based design adds an extra control point at 2%/50yrs.

earthquake level to ensure the ultimate performance objective of collapse prevention

shall be satisfied. Collapse analysis, therefore, should provide the designer and clientwith the guarantee that, during such extreme events, local collapse (or, component

failure) may take place, but system collapse should be avoided with confidence.

To offer house owners an option for custom-made buildings: Performance-baseddesign framework enables a building structure performs according to owner-specifiedobjectives under 10%/50yrs. and 2%/50yrs intensity levels. An enterpriser may

specify a higher seismic standard for his/her headquarter to alleviate earthquake-induced loss due to interrupted operation.

To reduce probability of casualties: A return period of 2500 years earthquakeindicates an occurrence rate of 2% in 50 years. If collapse prevention can not be

guaranteed at this hazard level, then it means a 2% probability in 50 years thatresidents could lose their lives in extreme earthquake attacks.

To distinguish unique characteristics of innovative structural systems fromconventional systems: In current engineering practice, the seismic performance of a building is evaluated through its strength capacity and maximum interstory drift

under design earthquakes. These years, innovative structural systems adopt smartmaterial and advanced design concept to be equipped with cutting edge self-centeringdevices to reach the goal of seismic isolation and/or energy dissipation to minimize

residual deformation. These structural systems may have comparable maximum driftas traditional buildings, but permanent deformation is significantly reduced. To

classify substantial difference from conventional structural systems in seismic

performance, a combined consideration of permanent deformation together withmaximum drift may be preferential in the future evaluation framework. In this regard,

consideration of collapse or post-peak behavior will help advance accurate predictionof these indices.

Retrofit of older essential facilities such as schools, fire and police stations, etc.:During the September 21 (local time) 1999 Chi-Chi Taiwan earthquake, a largenumber of older buildings built before 1982 sustained severe damage and many

others suffered from complete failure. Older structures are prone to shear type of

failure in a low ductility manner. A large portion of the elementary and high school

buildings falls into this category. The Chi-Chi earthquake hit the central part ofTaiwan at 1:47am, so these collapsed school buildings did not cause tremendous

tragedy of students death. However, it becomes main concerns of Taiwansgovernment how to retrofit old school buildings that are identified as high risk of




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structural collapse in future earthquakes. To reach this goal, dynamic nonlinear

behaviors of these low ductility columns must be first thoroughly understood.Strictly speaking, the idea of collapse tests is not new as it has been widely adopted in

many industrial products, especially in car industry. A new car model always goesthrough various types of collision tests before mass production for market sale to ensure

life safety of its driver and passengers. On the other hand, buildings are usually custom-designed and built such that individual collapse tests are infeasible. The major technicaldifficulties in building design would be to incorporate the same concept into code

documents through a uniform and simplified standard procedure.

DRIFT

STRENGTH

Gravity Collapse

Shear Failure

DRIFT

STRENGTH

Gravity Collapse

Shear Failure

-5 0 5 10 15

Interstory Drift Ratio (%)

-40

-20

0

20

40

N.

Co

lumn

Shear

(kN)

15.9s

18.3s

18.2s

Source: Wu et al. [2]

/L

Source: Elwood [1]

(a) without System Redundancy (b) with Sufficient System Redundancy

FIGURE 1IDEALIZED BACKBONE CURVE (UPPERROW) AND EXPERIMENTAL DATA (LOWERROW) OF SHEAR-CRITICAL

COLUMNS.

To illustrate the general progress of collapse, Figure 1 gives the idealized backbonecurves of shear-critical columns. Figure 1(a) illustrates that a shear-critical column will

go through the progress of flexural yield (i.e., the 1st

yield point of the idealized backbonecurve), and then its lateral drift at shear failure and finally the envelope starts to descend

toward the limit-sate of gravity collapse at which its lateral strength is completely lost.

Figure 1(b) illustrates that a shear-critical column will keep a certain level of residual

strength if system redundancy provides an alternative path for gravity load redistribution.This residual strength may result from dowel action from longitudinal reinforcement bars




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restrained by concrete above and below the failure planes, and/or frictional resistance

between concrete fracture surfaces. Columns with different types of failure modes (e.g., pure flexural failure, pure shear failure) may show a similar tendency if system

redundancy can provide an alternative path for load redistribution. A superposition ofindividual backbone curves constitutes the system backbone as shown in Figure 2. The

system failure can be defined as a significant loss of its lateral seismic resistance capacity(say, 50%) such that the repair cost is larger than its initial construction cost.

Elwood [1] tested 3-column frames with perfect redundancy. The side columns atboth ends provide a perfect alternative path for gravity load redistribution after the central

shear-critical column completely failed. Residual strength was observed on lateral and

axial load carrying capacity even though the local tangent stiffness almost reached zero.

To the contrary, 2-column portal frames tested by Wu et al. [2] had no redundancy at alland the time instant of component failure coincides with tha of system failure, in whichsystem collapse can be fully determined from component failure.

According to solid mechanics theory, development of negative structural stiffness

may stem from P-

effects and/or material fractures. Although in the literature there areplenty of studies on how to incorporate P- effects in response analysis, few are capable

of successfully simulating fracture-induced collapse, especially in brittle shear failure.Accurate fracture-based numerical approach is technically sophisticated and might beeconomically unaffordable to most design firms. As such, collection of experimental data

on structural collapse, in global and local manner, becomes very informative in

developing computationally affordable macroscopic models. This study, by performing

shake table tests on typical building columns designed according to past Taiwanese practice, expects to validate a reliable phenomenon-based hysteretic model with

consideration of material post-peak behavior. This model, when combined with P-

effects, will be capable of predicting structural dynamic response under code-defined

maximum considered earthquakes.

DRIFT

STRENGTH

System Collapse

FIGURE 2IDEALIZED BACKBONE CURVE OF STRUCTURAL SYSTEM




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FIGURE 3TYPICAL COMMERCIAL-RESIDENT COMPLEX WITH OPEN-FRONT PEDESTRIAN CORRIDOR IN TAIWAN

DESIGN OF SHAKE TABLE TEST

FIGURE 4REINFORCEMENT DETAILS OF SPECIMEN FRAME,DUCTILE COLUMNS C1,C2 ANDNON-DUCTILE COLUMNS

C3,C4.

The single-story 4-column frame tested in this study contains 2 ductile columns and 2

non-ductile columns. This frame can serve as an example for demonstrating progressivecollapse in case that limited redundancy is found in the structural system. It can be

foreseen that due to the limited redundancy there would be trivial time lag between thefirst local failure of non-ductile columns and the subsequent failure of ductile columns

when global collapse occurred. This type of structures does exist in Taiwan as

commercial-resident complex with open-front pedestrian corridor (Figure 3) which




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imposes a shortcoming of soft 1st

story onto the structural system. The commercial-

resident complex is comprised of individual town houses joined by common sidewalls.These town houses oftentimes belong to different owners and were usually built in

different years, and therefore incorporated different versions of seismic design codes thathad different seismic requirements and detailing schemes. This can be easily seen from

different appearance of the faade in Figure 3.

Specimen Specifications

The test specimen was composed of four columns (Figure 4). They were fixed at their

bases and interconnected by a beam at the upper level. The columns were constructed at

1/3 scale. Columns C1 and C2 were designed and detailed to satisfy most current design

codes for a high seismic zone, with a transverse reinforcement ratio of =1.5% in the plastic hinge zone. In contrast, Columns C3 and C4, with =0.2%, were typical ofcolumns designed without seismic considerations, and hence were considered vulnerable

to shear failure and subsequent axial load failure during testing. The connecting beam and

footings were made relatively stiff and strong to remain elastic during testing. Through30gal white noise excitation before the collapse test, the natural period of the frame wasidentified as 0.41sec and 3% damping critical.

FIGURE 5PHOTOGRAPHICAL VIEW OF THE SINGLE-STORY 4-COLUMN SPECIMEN FRAME.

Lead Packet Stacks Beam Columns Footings Total

Weight

(metric tons)17 5.72 0.22 1.12 24.06

TABLE 1WEIGHT OF SPECIMEN FRAME AND ITS PAYLOAD

Loadings

A total weight of 17 metric ton lead ballast was added to reproduce axial loads (

0.1 'g cA f ) at columns as shown in Figure 5. The weights of beam, columns and footings

are listed in Table 1.




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Material Properties

The frame specimen was constructed in two steps. The first step was to construct 4 sub-

assemblages that contained columns and footings in a lay-down position to have uniformconcrete strength over the entire height of the column. The second step was to place these

4 sub-assemblages in an upright position and then build the connecting beam. The framespecimen was then moved into NCREE laboratory for storage 6 weeks after construction

job was complete. The concrete mix was cast in two lifts, footings and columns, and then beams with a 1-week interval in between. After the construction was complete, wet

curing was continued for another 2 weeks. Standard concrete cylinders (15cm diameter by 30cm high) were cast at the days of concrete pour, and then cured in the same

condition as the frame specimen. Compressive strength tests of concrete cylinders were

conducted at the same day of the test. The average concrete compressive strength at testdate was 329 kgf/cm2. Tensile strength test results of longitudinal bars (#2, #3) andtransverse reinforcement (D5 & D3.2 steel wire) are also shown in Table 2. D5 and D3.2

steel wires were made through cold-rolling operation on bars of a slightly larger diameter,

with a consequence of an increase in its yield strength and a significant ductility lossbecause appropriate heat treatment (anealing) was not performed. The stress strain curves

of longitudinal bars are shown in Figure 6.

Concrete Steel

Column & Footing Beam #2 #3 5 mm 3.2 mm

Age cf'

Age cf'

Age cf' yf , uf yf , uf yf , uf yf , uf

Day kgf/cm2 Day kgf/cm2 Day kgf/cm2 kgf/cm2 kgf/cm2 kgf/cm2 kgf/cm2

7 198 89 329 54 361 2363 4803 6755 5594

28 303 147 345 2891 7220 7058 5897

TABLE 2PROPERTIES OF CONCRETE AND STEEL FROM MATERIAL TESTS

0

1

2

3

4

5

6

7

8

0 0.05 0.1 0.15 0.2

FIGURE 6STRESS STRAIN CURVES OF LONGITUDINAL REBARS




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Instrumentation

Figure 5 shows the experimental setup of the specimen frame on the shake table. A

supporting steel frame system was provided inside the table to prevent unfavorable out-of-plane movement of the frame specimen. In addition, a protective system was installed

outside the table to catch the frame from hitting the shake table when global collapseoccurred. The experimental setup aims for instrumented observation of global dynamic

collapse of RC columns. To do so, load cells, accelerometers, Temposonics lineardisplacement transducers (LDTs), inclinometers, and strain gages were employed to

collect experimental data of engineering interest, which were helpful in finding hownegative stiffness took place and how specimen was capable of remaining in stability

when negative stiffness did occur. All these observations are very helpful in finding

numerical solution methods related to dynamic stability problems to solicit theintroduction of performance-based earthquake engineering.

FIGURE 7LOCATION OF LOAD CELLS,ACCELEROMETERS AND TEMPOSONICS LDTS.

Input Table Motions

Because a 1:3 geometric scale factor was taken for the test specimen, input ground

motions should then be adjusted using a time compression factor of 1/ 3 on the basis of

keeping unchanged acceleration scale factor (= 1). In the test, the EW component of

TCU082 accelerogram from the 1999 Chi-Chi Taiwan earthquake was applied as the

input ground motion based on the following considerations:

Representative of main characteristics of near-fault earthquake motions in Taiwan. In particular, Station TCU082 is located in central Taiwan, and is close to typical

buildings studied herein. Frequency content of the record consists of dynamicvelocity pulses; however, its waveforms do not contain static fling step pulses, which

are not in the consideration of this study.

In addition to intermediate-period velocity pulses, the frequency content also consistsof short period strong motions as shown in Figure 8. This non-stationary evolution of

frequency contents as observed in ordinary earthquake motions could be then put into

consideration.




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0.0 0.5 1.0 1.5 2.0 2.5 3.0

Period (sec)

0

1

2

3

4

5

6

Spec

tra

lA

cce

lera

tion

(g)

1st Table Motion (Pre-collapse)

2nd Table Motion (Collapse)

FIGURE 8

RESPONSE SPECTRUM OF 1ST&2NDINPUT MOTIONS AFTERTIME COMPRESSION FACTOR 1/ 3 .

The response spectra of achieved table motions are shown in Figure 8. The spectral

values of selected ground motions have to meet the capacity limitation of the shake table.The selected ground motion, after modulated with a trapezoidal frequency domain filter

from 0.2Hz to 20Hz, was scaled to 1.57g and 1.87g PGA levels for the 1st

and 2nd

table

input motions, respectively.

EXPERIMENTAL RESULTS AND COMPARISON WITH PREDICTIVE MODEL

Figure 9 shows the damage of column ends after the 1st

table motion. There was

minor flexural cracking in ductile columns, and severe shear cracking in non-ductile

columns. Minor cover concrete crushing at column ends was also found. The final shots

of Columns C3, C4 and frame collapse were given in Figure 10, which demonstrates

severe shear fractures of non-ductile columns during progressive collapse. Relationship

between axial load, shear force, vertical displacement, and lateral interstory drift of

Columns C3 and C4 are plotted in Figures 11-12. A low axial load ratio of 0.1g c

A f was

applied to columns, and due to dynamic effect of overturning moment, the axial forces in

columns fluctuated about their initial values during the progress of system collapse. Same

observation was obtained of vertical displacement at the top of columns. Black dots in

Figures 11-12 indicate failure points of columns. A failure point is taken herein as the last

initiation of negative slopes in a shear-critical column and the column was unable to

remain in stability. It should be noted that the failure point herein is defined in a dynamic

sense and may get slightly different if another earthquake record is applied as the input

table motion. Tremendous loss of shear capacity was observed of non-ductile columns C3

and C4 at collapse. Same observation was made of the loss of gravity load carryingcapacity of Column C3, but the same could not be said of Column C4. This is most likely

because X-shaped shear fractures were formed at Column C3, but frictional force along

the fracture surface of Column C4 still took effect at the instant of collapse such that the

loss of axial load capacity in Column C4 is trivial. However, this only lasted for less than

1sec. An 8mm vertical displacement at the column top of Column C4 was observed at

failure. Figure 13 indicates that there was significant redistribution of gravity load (18sec




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19sec) in columns at the initiation of failure even though the total gravity load carrying

capacity of the specimen frame was basically kept unchanged.

C2 top C3 top C4 top

C2 bottom C3 bottom C4 bottom

FIGURE 9DAMAGE OF DUCTILE COLUMN C2, ANDNON-DUCTILE COLUMNS C3&C4 AFTER1

STGROUND EXCITATION.

Column C3 top Column C4 top Frame Collapse

FIGURE 10SNAPSHOTS OF COLUMNS C3&C4 AT FAILURE AND FINAL STATUS OF FRAME COLLAPSE.

Shown in Figure 14 is the experimentally obtained hysteretic loop of the specimenframe, which imposes important implications on engineering practice; especially the

segment with negative slope will help in determining failure point of structuralcomponents and system. Plotted against the experimental curve is the phenomenon-based

drift capacity model developed by Elwood [1] and Zhu [3]. The lateral resisting strengthwas taken from the smaller value of base shear strength converted from nominal momentcapacity following ACI procedures and shear strength calculated according to Sezen [4].

In Figure 14, the plateau stands for the ACI nominal moment capacity because offlexural-shear type of failure. The lateral drift at the first yield of longitudinal

reinforcement can be considered as the sum of displacements due to flexure, shear and

bar lip at the bottom of the column. Secondly, median values were used to predict theirdrifts at shear and axial failure for non-ductile columns; P- effect was appropriately




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accounted for in the calculation of backbone curves of ductile columns. Theseindividually calculated backbone curves were then added up to stand for the resultant

backbone curve of the whole frame. The comparison shows that Elwood and Zhu proposed a reasonable backbone curve prediction, which at the current stage is very

helpful in promoting collapse consideration among engineering community. As for

rational numerical simulation using nonlinear dynamic analyses, further details can bereferred to the paper by Yavari et al. [5], in which the finite element program OpenSees,

developed by the Pacific Earthquake Engineering Research Centre, was employed toconduct the analyses with Limit State Material models for shear and axial failure.

0

20

40

60

80

100

-40 -20 0 20

0

20

40

60

80

100

-0.15 -0.1 -0.05 0 0.05

-60

-40

-20

0

20

40

60

-40 -20 0 20

-60

-40

-20

0

20

40

60

-0.15 -0.1 -0.05 0 0.05

FIGURE 11RELATIONS BETWEEN AXIAL LOAD,VERTICAL DISPLACEMENT,SHEARFORCE,LATERAL DRIFT OF COLUMN

C3.




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0

20

40

60

80

100

120

-40 -20 0 20

0

20

40

60

80

100

120

-0.15 -0.1 -0.05 0 0.05

-60

-40

-20

0

20

40

-40 -20 0 20

-60

-40

-20

0

20

40

-0.15 -0.1 -0.05 0 0.05

Co

lumn

Shear

(kN)

Interstory Drift Ratio (%)

No Collapse

Collapse

t =18.725sec

FIGURE 12RELATIONS BETWEEN AXIAL LOAD,VERTICAL DISPLACEMENT,SHEARFORCE,LATERAL DRIFT OF COLUMN

C4.

CONCLUSIONS

Global and local collapse and dynamic structural post-peak behaviors were presented

in this study using a single-story-3-bay frame containing both non-ductile and ductile RCcolumns as the test specimen. Near-fault record TCU082ew from the 1999 Chi-Chi

earthquake was used as the input motion. It is observed that a combination of lateral drift

and shear strength reduction should be promising in serving as performance indices forpredicting initial system collapse. Test results obtained herein provide a great database

for calibrating existing numerical simulation methods to account for post-peak behaviors.This type of shake table tests may be used as benchmark problems for developing

advanced numerical simulation methods. Comparison shows that Elwoods drift capacity

models predicted the experimental backbone curve with satisfactory accuracy.




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0

50

100

150

200

250

300

350

14 16 18 20 22 24

Axia

lLoa

d(kN)

Time (sec)

total

0

50

100

150

200

250

300

14 16 18 20 22 24

-50

0

50

100

150

200

14 16 18 20 22 24

FIGURE 13AXIAL LOAD TIME HISTORIES OF:(A)WHOLE FRAME,(B)DUCTILE COLUMNS,(C)NON-DUCTILE COLUMNS.




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-150

-100

-50

0

50

100

150

-200 -150 -100 -50 0 50 100

FIGURE 14EXPERIMENTALLY OBTAINED STRUCTURAL HYSTEREIS OF TOTAL BASE SHEAR VS.ROOF DRIFT RATIO IN

COMPARISON WITH IDEALIZED BACKBONE CURVE.

ACKNOWLEDGEMENT

This research is funded in part by the National Science Council of Taiwan under grant

number NSC94-2625-Z-492-005. This financial support is gratefully acknowledged.Experimental facilities and technical support from NCREE are much appreciated. Special

thanks are given to Cheng-Piao Cheng, Lu-Sheng Lee and Shin-Yuan Yu for their

assistance in conducting the shake table tests. All opinions expressed in this paper aresolely those of the authors, and, therefore, do not necessarily represent the views of thesponsor.

REFERENCES

[1] Elwood K., Shake Table Tests and Analytical Studies on the Gravity Load Collapse of Reinforced

Concrete Frames, PhD dissertation, Department of Civil and Environmental Engineering, Universityof California, Berkeley (adviser: J.P. Moehle), 2002.

[2] Wu C.L., Yang Y.S., Loh C.H., Dynamic Gravity Load Collapse of Non-ductile RC Frames I :

Experimental Approach, the 100th Anniversary Earthquake Conference Commemorating the 1906 San

Francisco Earthquake, San Francisco, Moscone Center, April 18-22 2006.

[3] Zhu L., Probabilistic Drift Capacity Models for Reinforced concrete frames, Masters Thesis,

Department of Civil Engineering, University of British Columbia, Canada (adviser: K. Elwood), 2005.

[4] Sezen, H., Seismic Behavior and Modeling of Reinforced Concrete Building Columns, PhD dissertation,

Department of Civil and Environmental Engineering, University of California, Berkeley (adviser: J.P.Moehle), 2000.

[5] Yavari S., Kuo W.W., Elwood K.J., Wu C.L., Hwang S.J., and Loh C.H., Analysis of Shake Table

Collapse Tests for RC Frames, Proceedings of the 4th International Conference on Earthquake

Engineering, Taipei, Taiwan, Oct. 12-13, 2006, Paper No. 280.

[6] OpenSees, Open System for Earthquake Engineering Simulation,opensees.berkeley.edu, Berkeley,

California: Pacific Earthquake Engineering Research Centre, University of California, 2005.


Dynamic Collapse Simulation of 3-Bay RC Frame Under Extreme Earthquake Loadings

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