ACI Structural Journal/July-August 2009 523

ACI Structural Journal, V. 106, No. 4, July-August 2009.MS No. S-2008-038.R1 received February 2, 2008, and reviewed under Institute

publication policies. Copyright © 2009, American Concrete Institute. All rights reserved,including the making of copies unless permission is obtained from the copyright proprietors.Pertinent discussion including author’s closure, if any, will be published in the May-June2010 ACI Structural Journal if the discussion is received by January 1, 2010.

ACI STRUCTURAL JOURNAL TECHNICAL PAPER

As part of a research project focusing on the blast assessment ofbridges, a dynamic characterization was carried out on reinforcingsteel belonging to an existing structure. The steel was from a reinforcedconcrete (RC) arch bridge, namely, the Tenza Bridge, built in the1960s in southern Italy. The behavior of both concrete andreinforcing steel under dynamic loading rates was investigated;the results of a test campaign on reinforcing steel are presentedherein. Tensile failure tests were performed on steel specimens atdifferent strain rates using a modified Hopkinson bar device. Datafrom the tests were processed to obtain stress-strain relationships underdifferent strain-rate conditions, and the results were compared withexisting formulations, providing the dynamic properties ofreinforcing steel.

Keywords: dynamic behavior; dynamic increase factor; reinforcing steel;strain rate.

INTRODUCTIONStructural designers of civil infrastructures have to consider

the possibility that particular extreme loading could act onstructures during their lifetime. Particular events, such as severeearthquakes and accidental or deliberate explosions should beconsidered as current design loads; these design loads need aspecific scientific background to be correctly managed.

While it is obviously fundamental to analyze the forcesacting on the structure in the case of such events, this taskmay be somewhat arduous because of uncertainty related toload definition, especially for blast actions. A second criticalissue for structural design under extreme events is undoubtedly thebehavior of materials: mechanical properties under severedynamic loads can be very different from those exhibited understatic actions and specific investigations become necessary.

Dynamic characterization of the reinforcing steel of theTenza Bridge under high strain-rate conditions is presentedherein. The activity is part of a wider research project,namely, the Tenza project, whose objective is to perform ablast assessment of the structure. The Tenza Bridge is a reinforcedconcrete (RC) superior way arch bridge (Fig. 1) in southernItaly, once part of a highway section and now disused. Thebridge consists of a full section arch and a ribbed superiorslab, linked to the arch through piers of different heights. Thespan of the bridge is 120 m (393.7 ft) and the maximumheight above the valley bottom is 40 m (131.2 ft). It was builtin the 1960s and lightly ribbed bars were used as reinforcingsteel. Further information about the bridge and the projectare presented in References 1 and 2. The results of a similaractivity investigating the dynamic properties of concretefrom the bridge are presented in Reference 3.

Data obtained from the experimental activities played afundamental role in defining appropriate models of the structuralbehavior of the bridge under extreme dynamic loads. Therole of reinforcing steel in RC behavior under such dynamic

conditions is absolutely fundamental. Indeed, energy dissipationmechanisms are essential under such loading patterns and thecontribution of ductility provided by steel must be correctlyinvestigated and considered in assessing an RC structureunder extreme dynamic loads. Therefore, analyzing howsteel mechanical properties change from static to dynamicconditions is essential to correctly evaluate the plasticitycapabilities of RC members under extreme dynamic loads.

As experienced with many other metallic materials, thedynamic mechanical behavior of steel is significantlydifferent from that exhibited under static load conditions.This is due to several phenomena involved in steel strain-ratesensitivity, although the main reason for such differenceslies in the evolution of dynamic dislocations affecting themicroscopic scale.4-6 Available scientific data indicate that,as the strain rates increase, the following changes in mechanicalproperties of reinforcing steel can be observed:4-8

• An increase in yield stress fy;• An increase in ultimate tensile stress ft; and• An increase in ultimate tensile strain εt.

By contrast, no changes are experienced in terms ofYoung’s modulus.

Unfortunately, the available literature focuses on dynamicproperties of several steel alloys, mainly for industrialapplications,9-19 whereas little is known of reinforcing steelproperties.7,8,20 Therefore, further investigations on reinforcingsteel appear necessary to evaluate the real dynamic behaviorof RC members in the event of impact or blast loads.

Title no. 106-S50

Tensile High Strain-Rate Behavior of Reinforcing Steelfrom an Existing Bridgeby Domenico Asprone, Ezio Cadoni, and Andrea Prota

Fig. 1—Tenza Bridge.

ACI Structural Journal/July-August 2009524

RESEARCH SIGNIFICANCEThe dynamic behavior of civil infrastructures is becoming

a very important issue for structural engineers. This topiccannot be investigated while ignoring the dynamic properties ofthe constituent materials. Even if attention has been widelyfocused on dynamic behavior of steel alloys, little is knownof the dynamic properties of reinforcing steel used forcommon RC structures. The significance of this research isthe assessment of the dynamic properties of reinforcing steelfrom an existing structure; furthermore, the data obtained arecompared with existing formulations providing the dynamicproperties of reinforcing steel.

EXPERIMENTAL ACTIVITYDuring a dynamic tensile failure test campaign on steel

from the Tenza Bridge, steel bars 18 mm (0.71 in.) in diameterwere collected at the base of the arch and specimens wereobtained using an automatic lathe. The geometry of thespecimens is depicted in Fig. 2. In all, 10 dynamic tensilefailure tests were carried out, with a strain rates ranging fromapproximately 150 to 600 s–1; such values are typicallyexperienced in the case of impact or blast loading.7 To

conduct these tests, a modified Hopkinson Bar21 was used atthe DynaMat Laboratory22 of the University of AppliedSciences of Southern Switzerland. Three static tensile failuretests were also conducted on the same types of specimens tocompare dynamic and static results; to carry out these tests,a universal electromechanical device was used and a speeddisplacement control of 6 × 10–3 mm/s (0.24 × 10–3 in./s)was applied (Fig. 3).

Dynamic test setupThe Hopkinson Bar equipment consisted of three

longitudinally aligned bars: prestressed bar, input bar, andoutput bar (Fig. 4 and 5). The test was conducted introducingthe specimen between the input bar and the output bar.Elastic energy is stored in the prestressed bar by staticallypulling it at a stress value lower than its yielding strength; inparticular, one end of the prestressed bar is blocked by abrittle intermediate piece and the other end is pulled bymeans of a hydraulic actuator of a maximum loadingcapacity of 600 kN (134.8 × 103 lb). Once the elasticmechanical energy has been stored in the prestressed bar, theintermediate piece fails and a tension wave with a rise timeof approximately 30 μs is generated and transmitted alongthe input bar. The generated tension wave reaches the specimen,causing its fracture, and propagates in the output bar. Thetension wave remains uniaxial because the pulse wave length,equal to 12 m (39.4 ft), is much higher than the bar diameter(10 mm [0.39 in.]). The prestressed bar, the input bar, and theoutput bar are 6, 3, and 6 m (19.7, 9.8, and 19.7 ft) long,respectively. The steel specimen, with a diameter of 3 mm(0.12 in.), is screwed to the input and output bars. Both inputand output bars were instrumented with semiconductor straingauges, measuring incident, reflected, and transmitted pulsesacting on the cross section of the specimen.

When a fragile bolt in the blocking device fails, the pretensionis transmitted into the input bar through a tensile mechanicalpulse of 1200 μs duration, characterized by a linear loadingrate during the rise time. The pulse is then transmitted to the

Domenico Asprone is a PhD Student at the University of Naples Federico II, Naples,Italy, where he received his MS in civil engineering. His research interests include thebehavior of structures under high dynamic loads and related retrofitting techniques.

Ezio Cadoni is a Professor at the University of Applied Sciences of Southern Switzerland.He received his MS in Civil Engineering from the University of Cagliari, Cagliari,Italy, and his PhD from Turin Polytechnic, Turin, Italy. His research interestsinclude impact and dynamic behavior of materials and structures, durability, andnondestructive techniques.

Andrea Prota is an Assistant Professor of Structural Engineering at the University ofNaples Federico II. He received his Master of Science in civil engineering at theUniversity of Missouri-Rolla, Rolla, MO, and his PhD in structural engineering at theUniversity of Naples Federico II. His research interests include behavior of reinforcedconcrete and masonry structures under man-made and natural extreme loads, the useof advanced materials for new construction, and the retrofit of existing structuresusing innovative techniques.

Fig. 2—Specimen geometry (dimensions in mm; 1 mm =0.0394 in.).

Fig. 3—Quasi-static test.

Fig. 4—Modified Hopkinson bar (MHB) machine.

ACI Structural Journal/July-August 2009 525

output bar through the specimen, which is consequentlybrought to failure. During this phase, the strain gauge on theinput bar records the incident pulse εI and the reflected pulseεR, whereas the strain gauge on the output bar measures thetransmitted pulse εT. The relative amplitudes of the incident,reflected, and transmitted pulses are related to the mechanicalproperties of the specimen through relationships defined bythe application of the well-founded uniaxial elastic stresswave propagation theory.23,24

On the basis of the record of εI, εR, and εT presented inFigure 6 in terms of acquired signals, it is then possible tocalculate the engineering stress, engineering strain, andstrain-rate curves using the following equations

(1)

(2)

(3)

where σ(t) represents the engineering stress in the specimen;ε(t) represents the engineering strain in the specimen; (t)represents the strain rates in the specimen; E0 is the elasticmodulus of the bars; A0 is the cross-sectional area of thebars; A is the specimen cross-sectional area; L is specimenlength; and C0 is the sound velocity of the bar material.

Then the engineering stress-versus-strain curves in tensionwere transformed into true stress versus true strain curves bythe application of the following relationships

σtrue = σ(1 + ε) (4)

εtrue = ln(1 + ε) (5)

σ t( ) E0A0

A-----εT t( )=

ε t( )2C0

L--------- εR

0

t

∫ t( )dt=

ε· t( )2C0

L---------εR t( )–=

ε·

True stress versus true strain relationships provide usefuldata to predict the behavior of the investigated steel in the caseof stress conditions other than those induced by uniaxialtensile loading. It must be pointed out that engineering stressdoes not represent the actual stress in the material during thetensile test because it is calculated as the ratio between theapplied load and the initial area, which differs from the realarea during the test. Also, engineering strain is inadequate todescribe the actual strain of the material, in particular in theplastic range, where large deformations occur. Thus, truestress versus true strain curves are more informative instudying plastic behavior and are useful in conductingresearch on material and in developing a constitutive law forfinite element codes. By contrast, engineering curves providesatisfactory information for structural design. True stressversus true strain relationships, however, can be consideredsignificant up to the maximum stress point where neckingbegins; after this point, localization and fracture propagationgovern the flow curve, which is no longer representative of thehomogeneous mechanical properties of the materials.

An image was also acquired after the test to observe thefailure mechanism in the necking zone. Figure 7 depicts thespecimen during the test, while Fig. 8 presents a microscopicview of the specimen after the test, revealing the fracturezone. Further details about the Hopkinson bar may be foundin a separate study.3

Test resultsResults of static tensile tests on steel specimens are

presented in Table 1, while Fig. 9 presents the stress-strainrelationships obtained for the three tests. A mean yield stressof 388 MPa (56.3 ksi) was determined as the mean value ofthe yield stresses obtained in the three tests; this is in

Fig. 5—MHB working scheme.

Fig. 7—Specimen during high strain-rate test.

Fig. 6—Measurements obtained by MHB.

Fig. 8—Specimen after failure.

526 ACI Structural Journal/July-August 2009

agreement with original design documents, which gave avalue of 320 MPa (46.4 ksi) for the characteristic yield stressof concrete reinforcing bars. An average ultimate tensilestress of 708 MPa (102.7 ksi) was also obtained.

Data from static tensile failure tests conducted on steelbars are also available. Such tests were conducted on bars18 mm (0.71 in.) in diameter and 500 mm (19.69 in.) inlength and revealed an average yield stress and an averageultimate tensile stress of 400 MPa and 593 MPa (58.0 ksi and86.0 ksi), respectively. Comparing these data with thoseobtained on steel specimens reveals some differences,especially for ultimate tensile stress. This is probably due tosome disturbance introduced in the steel during the lathephase and needs to be examined in depth in furtherexperimental investigations.

Using the Hopkinson bar apparatus, 10 failure tests wereperformed. Details about the results-acquisition techniqueand data-processing procedures are presented in References 2and 3. Table 2 provides the main results from such tests, inparticular the dynamic values for the yield stress fy, the ultimatetensile stress ft , and ultimate tensile strain εt. It must bepointed out that the exact strain-rates level cannot be definedbefore the test starts but can be evaluated only after the test.Therefore, depending on the strain-rates value reachedduring the tests, specimens are divided into two groups,Group A and Group B, characterized by average strain ratesof 174 s–1 and 562 s–1, respectively. Hence, in Group A tests, an

average yield stress of 547 MPa (79.3 ksi) and an average ultimatestress of 789 MPa (114.4 ksi) were obtained, whereas in Group B,characterized by higher stress values, an average yield stress of626 MPa (90.8 ksi) and an average ultimate stress of 830 MPa(120.4 ksi) were obtained. It should be pointed out that suchyield stress values were evaluated as the stresses correspondingto a 0.2% permanent strain. Moreover, average ultimate strainsof 11% and 15% were obtained for Group A and Group B,respectively. Figures 10 and 11 represent the stress-versus-strain curves of Group A and Group B, respectively.

Such data were then processed in terms of the dynamicincrease factor (DIF), defined as the ratio of the dynamic tostatic value, for each of the analyzed properties. To perform

Fig. 9—Quasi-static stress-strain relationships.

Table 1—Static tensile failure test results*

Specimenno.

fy ,MPa (ksi)

fy,ave,MPa (ksi)

ft ,MPa (ksi)

ft,ave,MPa (ksi) εt , % εt,ave, %

1 390 (56.6)

388 (56.3)

[4 (0.6)]

688 (99.8)

708 (102.7)

[18 (2.6)]

9.3

10 [1]2 384 (55.7)

713 (103.4) 9.9

3 391 (56.7)

723 (104.9) 10.7

*Suffix “ave” indicates average value; standard deviation is given in square brackets.

Table 2—Dynamic tensile failure test results*

Specimenno.

,

s–1

ave,

s–1

fy,dyn, MPa (ksi)

fy,dyn,ave, MPa (ksi)

ft,dyn, MPa (ksi)

ft,dyn,ave, MPa (ksi)

εt,dyn, %

εt,dyn,ave, %

4 155

174[18]

(Group A)

579 (84.0)

547 (79.3)

[43 (6.2)]

811 (117.6)

789 (114.4)

[43 (6.2)]

12

11[1]

5 160 575 (83.4)

793 (115.0) 10

6 172 533 (77.3)

809 (117.3) 9

7 184 571 (82.8)

819 (118.8) 12

8 198 478 (69.3)

715 (103.7) 11

9 486

562[55]

(Group B)

636 (92.2)

626 (90.8)

[10 (1.4)]

824 (119.5)

830 (120.4)[8 (1.2)]

16

15[1]

10 529 620 (89.9)

823 (119.4) 15

11 579 614 (89.1)

831 (120.5) 16

12 585 635 (92.1)

843 (122.3) 14

13 629 627 (90.9)

827 (119.9) 15

*Suffix “ave” indicates average value; standard deviation is given in square brackets.

ε·

ε·

Fig. 10—Stress-strain relationships from Group A tests( = 174 s–1).ε· ave

Fig. 11—Stress-strain relationships from Group B tests( = 562 s–1).ε· ave

ACI Structural Journal/July-August 2009 527

this process, the mean values from Table 1 were used asreference static values. The experimental DIF for the yieldstress fy, the ultimate tensile stress ft , and the ultimate tensilestrain εt were determined for each specimen (Table 3). It canbe observed that DIF grows as the strain rate increases, forall three properties. Moreover, yield stress exhibits higher valuesof DIF compared with those related to ultimate tensile stress.

Figures 12 to 14 present the true stress versus true straincurves for the three strain-rate regimes. It should be notedthat the true stress versus true strain curves are considered upto the point of maximum stress where necking begins; after thispoint, localization and fracture propagation govern the flow curve,which is no longer representative of the material’s homogeneousmechanical properties. Moreover, using microscopymeasurements, the reduction in the area (RA) at fracture was

(6)

where A0 is the initial cross-sectional area, and AF is thecross-sectional area of the fractured section. The fracturestrain εt,Fracture and fracture stress st,Fracture were thencalculated measuring the outside radius of the cross sectionof the neck and the radius of curvature at the neck accordingto the Bridgeman correction,25 which considers the triaxiality inthe necking zone. Tables 4 and 5 report the main data fromthe true stress versus true strain curves; in particular, σt,TRUE

RAA0 AF–( )

A0

-----------------------=

represents the ultimate tensile true stress and εt,TRUErepresents the corresponding true strain.

ANALYSIS OF TEST RESULTSThe data were compared with the theoretical prediction of

the dynamic properties of the investigated steel, conductedusing relationships found elsewhere. In particular, twodifferent formulations were considered: 1) the CEB InformationBulletin No. 187 formulation7; and 2) Malvar formulation.8

The CEB Bulletin presents several formulations fordifferent steel types, providing DIF for yield stress and ultimatestress. In the case of hot-rolled reinforcing steel, the followingexpressions are provided

(7)DIFfy

fy dyn,

fy

------------ 1 6.0fy

-------ln ε·

ε· 0

----+= =

Fig. 12—True stress versus true strain curves in statictests ( = 10–4 s–1).ε· ave

Fig. 13—True stress versus true strain curves from Group Atests ( = 174 s–1).ε· ave

Fig. 14—True stress versus true strain curves from Group Btests ( = 562 s–1).ε· ave

Table 3—Experimental dynamic increase factors*

Specimenno. , s–1 DIFfy DIFfy,ave DIFft DIFft,ave DIFεt DIFεt,ave

Gro

up A

4 155 1.49

1.41[0.11]

1.15

1.12[0.06]

1.2

1.1[0.1]

5 160 1.48 1.12 1.0

6 172 1.37 1.14 0.9

7 184 1.47 1.16 1.2

8 198 1.23 1.01 1.1

Gro

up B

9 486 1.64

1.61[0.03]

1.16

1.17[0.01]

1.6

1.5[0.1]

10 529 1.60 1.16 1.5

11 579 1.58 1.17 1.6

12 585 1.64 1.19 1.4

13 629 1.62 1.17 1.5*Suffix “ave” indicates average value; standard deviation is given in square brackets.

ε·

Table 4—True stress-true strain elaborations (a)*

Specimen no. , s–1

σt,TRUE,MPa (ksi)

σt,TRUE,ave,MPa (ksi)

εt,TRUE ,%

εt,TRUE,ave, %

4 155 874 (84.0)

890 (79.3)[55 (8.0)]

10

14[3]

5 160 916 (83.4) 12

6 172 803 (77.3) 13

7 184 946 (82.8) 19

8 198 911 (69.3) 15

9 486 973 (92.2)

973 (90.8)[10 (1.5)]

19

18[1]

10 529 985 (89.9) 16

11 579 959 (89.1) 18

12 585 969 (92.1) 18

13 629 982 (90.9) 18*Suffix “ave” indicates average value; standard deviation is given in square brackets.

ε·

528 ACI Structural Journal/July-August 2009

(8)

where DIFfy is the DIF for the yield stress; DIFfu

is the DIFfor the ultimate stress; fy,dyn is the dynamic yield stress; fy isthe static yield stress; ft,dyn is the dynamic ultimate tensile stress;fu is the static ultimate tensile stress; is the strain rates; and

is a constant equal to 5 × 10–5 s–1 and represents strain rates atquasi-static condition.

By contrast, Malvar’s work, presenting a review of availablestudies investigating strain-rate sensitivity of reinforcing steel,proposes the following formulations

DIFfu

fu dyn,

fu

------------ 1 7.0fu

-------ln ε·

ε· 0

----+= =

ε·ε· 0

(9)

(10)

where fy is required in ksi.Using such formulations, data in Table 6 were obtained. A

comparison between the numerically evaluated DIFs andthose obtained from the experimental results reveals that theCEB expression slightly underestimates yield stress DIF,whereas the Malvar formulation weakly overestimates it. Bycontrast, both expressions fit experimental DIFs well for theultimate stress.

The results are then plotted in Fig. 15 and 16, where thesecomparisons are well appreciable. It must be pointed out thatboth in the case of CEB and Malvar formulations, backgrounddata, used to build the numerical expressions, are from tensilefailure test campaigns, with strain-rate values up to 10 s–1. Theincongruence between experimental data and numericalevaluations could be addressed in this respect.

DIFfy

fy dyn,

fy

------------ ε·

10 4–----------⎝ ⎠⎛ ⎞

0.074 0.040fy

60------–

= =

DIFfu

fu dyn,

fu

------------ ε·

10 4–----------⎝ ⎠⎛ ⎞

0.019 0.009fy

60------–

= =

Table 6—Comparison between experimentaland numerical DIFs*

Speci-mens

ave,

s–1

Experimental CEB formulationsMalvar

formulations

DIFfy,ave DIFfu,ave DIFfy,ave DIFfu,ave DIFfy,ave DIFfu,ave

Group A 174 1.41 1.12 1.23 1.15 1.69 1.16

Group B 562 1.61 1.17 1.25 1.16 1.76 1.18*Suffix “ave” indicates average value; standard deviation is given in square brackets.

ε·

Fig. 15—DIF for yield stress.

Fig. 16—DIF for ultimate stress.

Table 5—True stress-true strain elaborations (b)*

Specimen no. , s–1RA, % RAave, % εt,Fracture, % εt,Fracture,ave, % σt,Fracture, MPa (ksi) σt,Fracture,ave, MPa (ksi)

4 155 52

55[5]

66

73[9]

1331 (193.0)

1478 (214.4)[89 (12.9)]

5 160 51 68 1464 (212.3)

6 172 64 88 1538 (223.1)

7 184 53 69 1511 (219.2)

8 198 55 76 1548 (224.5)

9 486 53

52 [1]

82

76[9]

1727 (250.5)

1666 (241.6)[141 (20.5)]

10 529 51 82 1749 (253.7)

11 579 51 67 1474 (213.8)

12 585 51 84 1813 (263.0)

13 629 53 67 1565 (227.0)*Suffix “ave” indicates average value; standard deviation is given in square brackets.

ε·

ACI Structural Journal/July-August 2009 529

CONCLUSIONSThis study addressed the dynamic properties of reinforcing

steel from an existing structure. In particular, the focus was onhigh strain-rate levels, ranging from 150 to 600 s–1, that couldbe induced by blast or impact loads. To perform thisinvestigation, tensile failure tests on steel specimens wereperformed using a modified Hopkinson bar (MHB) machineand results were compared with existing formulations,providing DIF of yield and ultimate stresses for reinforcing steel.The results allow the following conclusions to be drawn:

1. The reinforcing steel was found to be strain-rate sensitive interms of yield stress, ultimate stress, and ultimate strain;

2. As the strain rate increases, yield stress increases morethan ultimate stress. Indeed, yield stress assumes a maximumDIF value of 1.62 for a strain rate of 629 s–1, while ultimatestress reaches a DIF of 1.17, with the same strain-rate level;

3. Both CEB and Malvar numerical predictions sufficiently fitthe experimental data; in particular, the CEB expressionunderestimates the yield stress with a maximum percentdifference of –24%, whereas the Malvar expressionoverestimates it, presenting a maximum percent differenceof +38%. Furthermore, in the case of ultimate stress, bothexpressions reproduce the experimental data even more reliably,with percent differences of approximately 2%; and

4. In the present case, small specimens were used; somedifferences were experienced between static tests performedon such specimens and steel bar specimens, revealing thatsome disturbance was probably introduced in preparing thedynamic samples via an automatic lathe. The DIFs, however,were obtained by processing dynamic and static testsperformed on the same sample type. Yet it must be pointedout that the most significant differences were obtained in terms ofultimate stress, whereas yield stress, more useful for designcalculations, was only slightly affected by such dissimilarities.Nevertheless, further investigations on this issue appearnecessary to verify the reliability of the data obtained.

Finally, it can be observed that the experimental resultsrepresent interesting data on very high strain-rate behavior ofreinforcing steel that could be very useful to assess furthernumerical formulations, providing the dynamic mechanicalproperties of reinforcing steel. To do this, however, additionaltest campaigns appear crucial: more recent types of reinforcingsteel require investigation to provide reliable design formulationsfor prediction of dynamic mechanical properties of reinforcingsteel under severe dynamic load conditions.

ACKNOWLEDGMENTSThe authors would like to thank the research center AMRA (Analysis and

Monitoring of Environmental Risk) that supported the activities presentedin the paper. Help from M. Dotta and D. Forni in carrying out theexperiments and reducing data is gratefully acknowledged.

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