Behavior of Ultrahigh-Strength Prestressed Concrete Panels Subjected to Blast Loading

Behavior of Ultrahigh-Strength Prestressed Concrete PanelsSubjected to Blast Loading

Tuan Ngo1; Priyan Mendis2; and Ted Krauthammer3

Abstract: This paper presents the results of an experimental investigation conducted in Woomera, South Australia in May 2004 on theblast-resistance of concrete panels made of ultrahigh-strength concrete �UHSC� material. A special concrete supporting frame wasdesigned for testing concrete panel targets against blast loading. Four 2 m�1 m panels with various thicknesses and reinforcement detailswere tested under a 6 t TNT equivalent explosion at standoff distances of 30 and 40 m. Data collected from each specimen included blastpressures and deflections of panels. The test data were analyzed to assess the performance of UHSC and normal-strength concrete �NSC�panels. The test results and observations showed that the 100-mm-thick UHSC panels performed extremely well surviving the blast withminor cracks. The 75-mm-thick UHSC panel suffered moderate damage while the 100-mm-thick NSC panel was breached. Test resultsfrom this experimental program were used to validate a finite-element computer code that was developed by the writers to analyzeconcrete structures subjected to blast and impact loading.

DOI: 10.1061/�ASCE�0733-9445�2007�133:11�1582�

CE Database subject headings: Concrete, prestressed; Panels; Blasting; High strength concretes; Finite element method.

Introduction

Around the world, almost all concrete high-rise and medium-risebuilding projects utilize high-strength concrete �HSC� for majorstructural elements. The technology for producing HSC has suf-ficiently advanced such that concretes with compressive strengthsup to about 120 MPa are commercially available. HSC offers sig-nificantly better structural engineering properties, such as highercompressive and tensile strengths, higher stiffness, and better du-rability, in comparison to the conventional normal-strength con-crete �NSC�. Despite being widely used, the performance of HSCunder severe impulsive loading has not been investigated in depthbefore.

The main aim of this study is to investigate the blast resistanceof ultrahigh-strength concrete �UHSC� panels made of reactivepowder concrete �RPC�. RPC is an UHSC material consisting ofcement, sand, silica fume, silica flour, steel fibers, admixture, andwater which can have strengths up to about 200 MPa. This aim isviewed within the wider context of developing an efficient pro-tective material for new structures and a retrofitting scheme that

1Lecturer, Dept. of Civil and Environmental Engineering, Univ. ofMelbourne, Parkville, VIC 3052, Australia. E-mail: [email protected]

2Professor, Dept. of Civil and Environmental Engineering, Univ. ofMelbourne, Parkville, VIC 3052, Australia �corresponding author�.E-mail: [email protected]

3Professor, Dept. of Civil and Coastal Engineering, Univ. of Florida,Gainesville, FL32611-6580; formerly, Protective Technology Center,Penn State Univ., University Park, PA 16802. E-mail: [email protected]

Note. Associate Editor: Yahya C. Kurama. Discussion open untilApril 1, 2008. Separate discussions must be submitted for individualpapers. To extend the closing date by one month, a written request mustbe filed with the ASCE Managing Editor. The manuscript for this paperwas submitted for review and possible publication on March 13, 2006;approved on May 15, 2006. This paper is part of the Journal of Struc-tural Engineering, Vol. 133, No. 11, November 1, 2007. ©ASCE, ISSN
0733-9445/2007/11-1582–1590/$25.00.
1582 / JOURNAL OF STRUCTURAL ENGINEERING © ASCE / NOVEMBER

can be easily applied to target structures. In addition to increasingthe structural integrity, it is envisaged that, in using UHSC, theproposed scheme will obtain a high-strength/weight ratio and re-duce damage resulting from fragmented projectiles. In Woomera,South Australia, four concrete panels of 2 m�1 m, with thick-nesses of 75 and 100 mm, were tested against an explosion of 5 t�5,000 kg� Hexoline �equivalent to 6 t of TNT� at the standoffdistances of 30 and 40 m. Three of the panels were made ofUHSC. These UHSC panels were especially designed for blastresistance, and were prestressed using high-strength steel tendons.The fourth panel was made of NSC for comparison. The blastwave characteristics, including reflected pressures and impulses,were measured. The central deflection and postblast damage ofeach panel was recorded and observed. The experimental resultswere used to validate the computer code developed in this study.

Woomera Blast Trial, May 2004

Background

The Woomera trial in May 2004 was sponsored by the UnitedKingdom Ministry of Defence. There were two detonations, eachconsisting of a bare charge of 5 t of Hexolite—RDX/TNT�60:40�, which is equivalent to approximately 6 t of TNT. Thetargets were typical commercial and residential structures. Theexplosives were in solid blocks of 250 and 100 kg. The incidentand reflected blast pressures were recorded by various pressuregauges. The aim of all these tests was to assess the efficiency ofprotective barriers, storage structures, and adjacent structures inthe event of an explosion, and the lethality and destructive effectsof high-speed fragmentation and other missiles �debris� generatedby large-scale explosions. This trial attempted to approximate a
hemispherical blast wave as closely as possible.
2007

Design and Fabrication of Test Specimens

A total of four concrete panels were prepared for the first trial.Each panel had the dimensions of 1,000�2000 mm. The panel

thicknesses were 75 and 100 mm. The first three panels weremade of UHSC �unconfined compressive strength of 164.2 MPa�and the fourth panel was made of NSC �unconfined compressivestrength of 39.8 MPa�. The UHSC panels �UHSC-1–UHSC-3�only have prestressed tendons one way in the long direction�2 m�. The tendons were located at the center of these panels andwere prestressed to 20% of the ultimate strength of the tendons.The NSC panel had normal passive reinforcement both ways lo-cated at the tension face. Panel dimensions and reinforcementdetails are given in Table 1.

Before the Woomera blast trial, static tests were carried out atthe University of Melbourne to obtain the mechanical propertiesof UHSC material under quasi-static loading. UHSC has a com-pressive strength, fc� of 164.2 MPa, a tensile strength of22.28 MPa, and a modulus of elasticity of 44 GPa. The staticstress-strain curve of UHSC is shown in Fig. 1.

Instrumentation

Various pressure gauges were installed to measure incident �side-on� pressure and reflected pressure. The piezoelectric gauge mea-sured dynamic and short-term pressures up to 1,513 kPa, at a risetime of 5 �s. The free-field incident pressures were also mea-sured. Prior to the test, gauge distances were checked. Mechanicaldisplacement measurement devices were mounted on the hollow

Table 1. Details of Test Panels

Panelnumber

PanelID Type of panels

1 UHSC-1 Prestressed15.2 mm tendons at 100



4 NSC-1 Normal reinforcement�N16 at 200 both ways on

tension face, yield strength 500

Fig. 1. Static stress-strain curve of UHSC

JOURNAL O

steel bar inside the test frame to measure the deflection of the

panels. These devices can record the maximum inward and out-ward deflections of the panels at the center point.

Test Frames

The panels were installed on site into a box-like concrete frame.The size in plan was 2.28 m�2 m, with the 2.28 m face turnedtowards the blast. The height of the test frame was 1.5 m, includ-ing a 300-mm-thick concrete base. The vertical edges of the pan-els were simply supported and the other edges were free. Withthis setup, the tests panels were acting as one-way slabs with aspan of 2 m. Within the box structure, all the wiring connectionand displacement measurement devices can be placed inside theburied boxes without being damaged during the blast tests.

MaterialThickness

�mm�

Standoffdistance

�m�

UHSCfc�=164.2 MPa

100 30

UHSCfc�=164.2 MPa

100 40

UHSCfc�=164.2 MPa

75 40

NSCfc�=39.8 MPa

100 40

Fig. 2. UHSC Panel 1—before and after explosion

theMPa�

F STRUCTURAL ENGINEERING © ASCE / NOVEMBER 2007 / 1583

Test Results

The results of the blast trial include recorded measurements ofreflected blast pressures and midspan deflections of test panels.Failure modes of concrete, i.e., spalling or crushing, and crackpropagation, were observed and recorded. A summary of the testresults is tabulated at the end of this section.

UHSC Panel 1

Panel 1 is a 100-mm-thick prestressed UHSC panel located at a30 m standoff distance. Details of the prestressed tendons aregiven in Table 1. The blast resulted in an average reflected im-pulse at the panel surface equal to 3,771 kPa ms, with an averagereflected pressure of 1,513 kPa �Table 2�. UHSC Panel 1 per-formed very well against the blast, with only minor damage.There was no concrete spalling of either the front or back surface�Fig. 2�. No permanent deflection was recorded. There were onlyvertical hairline cracks of 0.1–0.2 mm width. The maximum mid-span inward and outward deflections were measured as 50.4 and37.0 mm, respectively. It can be observed that Panel 1 experi-enced significant deformation �deflection�span/40� without anymajor damage. The high tensile strength and ductility of theUHSC material and the prestress of the tendons can explain this.

UHSC Panel 2

Panel 2 has the same properties and prestressed tendons as Panel1, but was located at a 40 m standoff distance. The average re-flected impulse at the panel surface was 2,867 kPa ms, with anaverage reflected pressure of 735 kPa �Table 2�. The observeddamage of Panel 2 was less than that observed in Panel 1. Bothtop and bottom surfaces showed neither concrete spalling norcrushing �Fig. 3�. Only minor vertical cracks of 0.1 mm widthwere observed. No permanent deflections were recorded. It wasconcluded from visual inspection and measurement of crackwidth that the blast resulted in only minor damage to Panel 2. Themaximum midspan inward and outward deflections were mea-sured as 27.1 and 20.7 mm, respectively.

Table 2. Summary of Blast Pressure Histories

Standoffdistance�m�

Peakreflectedpressure

�kPa�

Reflectedimpulse�kPa ms�

30 1,513 3,771

40 735 2,867

Fig. 3. UHSC Panel 2 after explosion


UHSC Panel 3

Panel 3 is a 75-mm-thick prestressed UHSC panel located at a40 m standoff distance. This panel was prestressed by 15.2 mmtendons at 200 mm center-to-center. The average reflected im-pulse and average reflected pressure were 2,876 kPa ms and735 kPa, respectively �Table 2�. On the front face, a severe ver-tical crack at the midspan and concrete crushing were observed�Fig. 4�. Tensile cracks and minor concrete spalling were alsonoticed at the back face. The maximum midspan inward and out-ward deflections were measured as 72.6 and 54.8 mm, respec-tively. A permanent inward deflection of 32 mm was recorded.

NSC Panel 4

Panel 4 is a 100-mm-thick NSC panel located at a 40 m standoffdistance. The panel was reinforced with N16 bars at 200 mmcenter-to-center. The average reflected impulse and average re-flected pressure was 2,876 kPa ms and 735 kPa, respectively�Table 2�. Panel failure due to concrete breach was observed. Atthe front surface, concrete was crushed and a cavity of 100 mmwidth and 30 mm depth was formed vertically at the midspan. Apermanent deflection of 142 mm was measured. At the rear sur-face, an approximately 8-mm-wide crack at the midspan was ob-served. The concrete cover at the rear surface and front surfacespalled off with wide visible cracks. Fig. 5 shows the failuremode of Panel 4. No displacement measurement device wasplaced for Panel 4, so the deflection history of this panel was notrecorded.

Fig. 4. Panel 3 after explosion

Fig. 5. NSC Panel 4—after explosion

2007

Summary of Blast Pressure Histories and PanelDeflections

The reflected pressure and impulse time histories recorded bypressure transducers at 30 and 40 m are shown in Figs. 6 and 7,and Table 2. Midspan deflections of test panels recorded by dis-placement measurement devices are given in Table 3.

This experimental program investigated the performance ofUHSC panels under blast loading. The following conclusions aredrawn:1. The test results and observations showed that the 100-mm-

thick UHSC panels performed extremely well, surviving theblast with minor cracks. The 75-mm-thick UHSC panel suf-fered moderate damage while the panel made of NSC wasbreached;

2. The prestressed panels were able to sustain considerable de-flection under a very high loading rate; and

Fig. 6. Reflected

Fig. 7. Reflected

3. UHSC panels eliminate the risk of injury or damage caused

JOURNAL O

Table 3. Summary of Panel Deflections and Damages

Panelnumber

PanelID

Inwarddeflection

�mm�

Outwarddeflection

�mm�Damage

level Observation

1 UHSC-1 50.4 37.0 Minor Hairline cracks

2 UHSC-2 27.1 20.7 Minor Hairline cracks

3 UHSC-3 72.6 54.8 Heavy Wide cracks,permanent

deformation

4 NSC — — Severe Concretebreach

pressure history at 30 m

pressure history at 40 m


by concrete debris as they do not break into fragments whensubjected to blast loading.

Constitutive Model for Concrete at High StrainRates

For concrete structures subjected to blast or impact effects, a re-sponse at very high strain rates is often sought. At these highstrain rates, the strength of concrete can increase significantly. Aseries of impact tests were carried out by Ngo �2005�, based onthe split Hopkinson pressure bar �SHPB� setup, using large-diameter concrete cylinders to achieve a range of loading ratesand hydrostatic pressures. Concrete specimens with differentstrengths were tested.

Fig. 8 shows the stress strain curves at different strain rates of50-mm-diameter RPC cylinders. It can be seen that the compres-sive strength increases up to 1.5 times at the strain rate of about267.4/s. This corresponds to a strength dynamic increase factor

Fig. 8. Stress-strain curves of RPC at different strain rates

Fig. 9. Proposed D


�DIF� of 1.5. Table 4 summarizes the test results of three RPCspecimens. It was found that RPC is less rate sensitive comparedto both NSC and HSC �Ngo 2005�.

Based on the results of the experimental program using Hop-kinson bar apparatus, and through a rigorous calibration process,a new strain rate dependent constitutive model is proposed by thewriters. This applies to concrete under a dynamic load, and takesinto account the strain rate effect by incorporating multiplyingfactors for increases in the peak stress and strain at peak strength.This model is applicable to concrete strengths varying from 32 to160 MPa with a strain rate up to 300 s−1.

In this model, the rate dependent peak stress �fcd� � can be ex-pressed as

DIF =fcd�

fcs�= � �̇

�̇s�1.026�

for �̇ � �̇1 �1�

DIF =fcd�

fcs�= A1 ln��̇� − A2 for �̇ � �̇1 �2�

where fcd� �dynamic peak stress �MPa�; fcs� �static compressivestrength �MPa�; �̇�strain rate; �̇s=3�10−5 s−1 �quasi-static strainrate�; �=1/ �20+ fcs� /2�; �̇1=0.0022fcs�

2−0.1989fcs� +46.137;A1=−0.0044fcs� +0.9866; and A2=−0.0128fcs� +2.1396.

Fig. 9 shows the DIF curves plotted using the proposed model

Table 4. Dynamic Compressive Strength of RPC

Concretespecimen

Velocity�m/s�

Averagestrain rate

�̇�1/sec�

Ultimatestrength�MPa� DIF

Static test — — 159.8 —

RPC-1 11.6 80.7 187.2 1.17

RPC-2 16 187.3 226.1 1.41

RPC-3 20 267.4 240.9 1.50

del for peak stress
IF mo
2007

3

for three concrete groups: NSC, HSC, and RPC. Test results arealso plotted to compare with the proposed model. It should benoted that in the above formulas, the turning point strain rate, �̇1,is a function of the static compressive strength fcs� . This is differ-ent from the CEB-FIP model �CEB-FIP 1990� where �̇1 is fixed at30 s−1 for all concrete strengths.

Finite-Element Model for RC Structures Subjectedto Impulsive Loading

The analytical prediction of failure modes of reinforced concrete�RC� structures under severe impulsive loads is very difficult, dueto the complexity of concrete behavior in the high strain ratedomain. Most current design and analysis methods are based onsimplified equivalent static forces or single degree of freedomsystems. Although this approach may be suitable for preliminaryanalysis, it contains inherent inconsistencies. The finite-elementmethod provides an effective numerical approach for the model-ing of structural problems involving severe impulsive loading.

As a result of the impulsive loads reaching their peak intensityin extremely short durations of time, material nonlinearities andstrain rate effects play an important role in the analysis. Majorsources of nonlinearities in reinforced concrete structures need tobe taken into consideration, such as the progressive cracking ofconcrete in tension, the inelastic response in compression, theyielding of reinforcing steel, and strain rate sensitivity of concreteand steel reinforcement. The finite-element method has enabledthe solution of the complicated problems represented by the non-linear behavior of reinforced concrete.

Fig. 10. Lattice model

Fig. 11. Finite-elemen

JOURNAL O

A finite-element code was developed in this study to modeland predict the nonlinear structural response of two-dimensionalconcrete structures subject to severe blast or impact. A numericalapproach based on an explicit finite-element formulation was de-veloped in this project to solve two-dimensional planar structuralproblems involving direct impact or blast loading.

A rate dependent lattice model �RDLM� was developed for thecompressive and tensile behavior of concrete. In tension, concreteis modeled as a linear elastic strain-softening material where thetensile cracking is monitored by a strain rate criterion. Concretecracking phenomenon is modeled by the smeared approach andtension stiffening, and shear transfer across the cracks are ac-counted for. Upon crack initiation at a sampling point, represent-ing average behavior of some tributary area around that point, theconstitutive matrix is modified to take into account the damagedue to cracking which induces anisotropy. After cracking, con-crete is assumed to become orthotropic. Using the smearedapproach, cracks in different directions can be generated auto-matically without the need for redefining the initial finite-elementmesh. Details of the implementation of the smeared approach canbe found elsewhere �Ngo 2005�. Steel is modeled as a strainrate sensitive uniaxial elasto-viscoplastic material with linearhardening.

Lattice Concrete Model

The discrete lattice model was initially developed by Niwa et al.�1994�. This model has been successfully used to model RC struc-tures under cyclic loading �Itoh et al. 2000�. The discrete latticemodel was extended by Tanabe and others �Tanabe and Ishtiaq1999; Itoh et al. 2000�, so as to be able to model continuum RCstructures using a finite-element method. In the equivalent con-tinua lattice model �ECLM� �Tanabe and Ishtiaq 1999� a RCstructure can be modeled as parallel layers of concrete and rein-

Table 5. Material Properties of UHSC Panels Modeled withRC-IMPULSIVE

Properties Notation Value

Static compressive strength of concrete fcs� 164.2 MPa

Static tensile strength of concrete f ts 22.8 MPa

Static elastic modulus of concrete Ecs� 44.1 GPa

Fracture energy GF 325 N/m

Maximum aggregate size dmax 1 mm

Density of concrete � 2,412 kg/m

Roughness angle of the crack surface /6

Static yield strength of steel �prestressed tendon� fys 1,680 MPa

Elastic modulus of steel reinforcement Es 198 GPa

Hardening modulus of steel reinforcement Eh 2.1 GPa

eling of UHSC panel
t mod

https://www.researchgate.net/publication/270430642_Evaluation_of_Ultimate_Deformation_of_RC_Columns_Subjected_to_Cyclic_Loading_Based_on_the_Lattice_Model?el=1_x_8&enrichId=rgreq-a01955be329a1154638d277404480013-XXX&enrichSource=Y292ZXJQYWdlOzI0NTMwNTM1OTtBUzoyMDQzNDkwOTI0MzgwMTZAMTQyNTczMjAyODQyMw==

forcement lattices, as shown in Fig. 10. This model can be ex-pressed using the finite-element �FE� formulation, by smearingout concrete and reinforcement lattices into a continuum. Theequivalent continua lattice model has been used successfully inmodeling RC columns subject to quasi-static and cyclic loadings�Itoh and Tanabe 2002�.

In this study, the ECLM was further improved to model RCstructures subjected to impulsive loading, such as blasts or im-pacts. The new model, called the RDLM, incorporates a strainrate sensitive lattice model for both the compressive and tensilebehavior of concrete. The FE formulation of the proposed modelis described in detail by Ngo �2005�.

Computer Implementation and NumericalApplications

A computer program, named RC-IMPULSIVE, has been devel-oped for the finite-element linear and nonlinear dynamic analyses

Fig. 12. Midspan deflection history of 100-mm-thick UHSC Panel 1

Fig. 13. Comparison of deflection histories of Pan


of two-dimensional reinforced concrete structures subjected toimpulsive loading. The program is written in FORTRAN inmodular form, and possesses sufficient flexibility to add new op-tions resulting from further research. For time integration the pro-gram uses the central difference scheme. The explicit algorithmwas optimized to reduce the computational time �see details inNgo 2005�.

The program implements the rate-dependent continuum latticemodel described above, combined with a tensile crack-monitoringalgorithm. The algorithm, which traces the opening of new cracksas well as the closing and reopening of existing ones, is activatedafter total and elastic evaluation for each sampling point at eachtime step.

From testing on UHSC panels during the Woomera blast trial,experimental results were used to validate the computer code RC-IMPULSIVE. The results from the blast trial are presented indetail in Ngo �2005�. Finite-element modeling of these panelsusing RC-IMPULSIVE is presented in this section.

predicted by RC-IMPULSIVE compared with Woomera test results

redicted using elastic model and proposed RDLM

at 30 m

el 1 p

2007

Description of Structure and Material Properties

The finite-element mesh and the boundary conditions are shownin Fig. 11. The main material properties of concrete and steelemployed in the analysis are listed in Table 5. The proposed ratedependent lattice model �RDLM� described above was used forthe analysis. Because the UHSC Panels 1-3 are one-way panelssupported only on two vertical sides, they can be modeled assimply supported beams with a span of 2 m.

Concrete is modeled using plane stress elements with fournodes. The prestressed tendon is simulated as perfectly bondedtruss elements. The FE model includes 205 nodes, 160 four-nodeelements, and 40 truss elements. The numerical modeling of con-crete and steel is based on the proposed RDLM. The prestressedeffects were modeled by setting initial tensile stresses for steel

Fig. 14. Midspan deflection history of 100-mm-thick UHSC Panel 2 a

Fig. 15. Midspan deflection history of 75-mm-thick UHSC Panel 3 a

JOURNAL O

elements, as well as initial compressive stresses for concrete ele-ments. The time step length is chosen to be 2.5 �s for the centraldifference explicit time integration scheme.

Based on the recorded reflected pressure at a 30 and 40 mstandoff distance �Figs. 6 and 7�, the piecewise-linear loadingfunctions, which closely approximated the recorded blast loadfrom the Woomera trial, were used for the dynamic analysis.

Analytical Results of UHSC Panel 1

Time History Response of Panel at Midspan

The computed displacement-time history and experimental mea-surements at the midspan of UHSC Panel 1 are plotted for com-

predicted by RC- IMPULSIVE compared with Woomera test results

predicted by RC- IMPULSIVE compared with Woomera test results

t 40 m

t 40 m


parison in Fig. 12 which shows very good agreement. The peakinward deflection of 50.4 mm was recorded which agrees closelywith the analytical results, for which the computed peak inwarddisplacement of 48.6 mm is reached in 14.4 ms. Again there isgood agreement between the computed peak outward displace-ment of 35.3 mm reached at time t=37.9 ms, compared with therecorded deflection of 37.0 mm. A dynamic elastic analysis of thepanel was carried out and the elastic response is compared withresults from the nonlinear analysis using the proposed RDLM�Fig. 13�. It can be seen that the elastic analysis underestimatesthe peak inward deflection by 30% and the peak outward deflec-tion by 16%. Fig. 13 also indicates that the nonlinear effects dueto concrete cracking and nonlinear properties have doubled thenatural period of vibration of the panel.

Similar analyses were carried out for UHSC Panels 2 and 3.The computed displacement-time history and experimental mea-surements at midspan of these panels are plotted for comparisonin Figs. 14 and 15 which show very good agreement. Crack pat-terns and the stress, and strain rate histories were also comparedfor all the panels. The analytical predictions matched the experi-mental results very well. More details are given in Ngo �2005�.

Concluding Remarks

This experimental and theoretical study shows that RPC can be avery effective material for blast resistance. The computer programRC-IMPLUSIVE, which was developed in this study, was used tomodel the dynamic behavior of test panels. The results agreedwell with experimental measurements. The dynamic response ofthe test panels under blast loading, as predicted by RC-IMPULSIVE, shows that an accurate numerical simulation of theexperimental observations is possible using the present nonlinear


numerical method, despite the highly variable nature of the load-ing conditions.

Acknowledgments

The writers would like to thank the Australian Research Council�Discovery Grant No. DP0450212� for financial support with thisproject. They would also like to acknowledge VSL Pty. Ltd., es-pecially the Technical Manager, Mr. Brian Cavill, for his supportin setting up the panel tests at Woomera. Finally they would liketo thank Tahmina Hossain for helping with the formatting of thepaper.

References

Comité Euro-International du Béton �CEB-FIP�. �1990�. CEB-FIP modelcode 1990, Redwood Books, Trowbridge, Wiltshire, U.K.

Itoh, A., Niwa, J., and Tanabe, T. �2000�. “Evaluation by lattice model ofultimate deformation of RC columns subjected to cyclic loading.”Proc., JSCE, 641�46�.

Itoh, A., and Tanabe, T. �2002�. “Analysis of RC column experiments atUCSD by an equivalent lattice model.” Research Rep., Dept. of CivilEngineering, Nagoya Univ., Nagoya, Japan.

Ngo, T. �2005�. “Behaviour of high strength concrete subject to impulsiveloading.” Ph.D. thesis, Univ. of Melbourne, Australia.

Niwa, J., Choi, I. C., and Tanabe, T. �1994�. “Analytical study for shearresisting mechanism using lattice model.” Proc., JCI Int. Workshop onShear in Concrete Structures, 130–145.

Tanabe, T., and Ishtiaq, A. S. �1999�. “Development of lattice equivalentcontinuum model for analysis of cyclic behaviour of reinforced con-crete.” Proc., Seminar on Post-Peak Behaviour of RC Structures Sub-jected to Seismic Load, Vol. 2, 105–123.

2007




Behavior of Ultrahigh-Strength Prestressed Concrete Panels Subjected to Blast Loading

Documents

Transcript of Behavior of Ultrahigh-Strength Prestressed Concrete Panels Subjected to Blast Loading