1 Introduction - WIT Press · 2014-05-20 · 3.3 Simulation analysis Tests results were simulated analytically by using a nonlinear finite element method (FEM). The analytical code

Experimental studies on the inelastic behavior

of reinforced concrete panels under high-speed

loading Part 1. Effects of dynamic loading

Haruji Tsubota, Jun Mizuno, Kazuhiro Kusama,

and Takahiro MommaKobori Research Complex Inc., 6-5-30, Akasaka, Minato-ku,Tokyo 107, Japan E-mail:[email protected] Brandes, Jurgen Herter and Ernst Limberger

5AM, Berlin, GermanyToshio Yamashita and Tomohiro FujitaTokyo Electric Power Co., Tokyo, JapanYasuo Sugimoto, Japan Nuclear Fuel Ltd., Tokyo, Japan

Abstract

When designing the nuclear related reinforced concrete (RC) structuressubjected to an aircraft impact, it is important to reliably evaluate the inelasticbehavior of RC panels, taking into account the deformation rate of RC members.The objectives of the present study are to experimentally investigate the inelasticbehavior of RC panels under high-speed loading using 1/6 scale specimens,focusing on the effects of rebar ratio and the applicability of rebar lap splices.This study consists of two parts; Part 1 describes the detailed test conditions, theresults of static and high-speed loading tests of reference specimens with atypical reinforcement ratio and no lap splices as is normal in practice. It alsopresents the results of finite element (FE) simulation analyses. Part 2 presentsthe results of high-speed and static loading tests on panel specimens withreduced rebar ratio and with lap splices, and evaluates those effects on theinelastic behavior of RC panels.

Transactions on the Built Environment vol 32, © 1998 WIT Press, www.witpress.com, ISSN 1743-3509

744 Structures Under Shock and Impact

1 Introduction

The reliable evaluation of inelastic behavior of reinforced concrete (RC)members, taking into account their deformation rate, is important to ensurethe safety of the nuclear related RC structures subjected to an aircraftimpact. When designing such RC structures, some critical designparameters must be considered, i.e. panel thickness, reinforcement ratio,rebar joint details, etc. Of these, the effects of rebar ratio and adoption of

lap splices are the main interests in the present study.Uchida et al.fl] conducted high-speed and static out-of-plane loading

tests using 1m x 1m square RC panels with reinforcement only at thebottom, and confirmed that the bearing capacity and the ductile behavior ofthe panels are increased in dynamic cases when the rebar ratio is 0.5% orgreater. Saito et al.[2] extended those experiments and the similar resultswere reported for the RC panel with 0.2% reinforcement at the top and thebottom. Such inelastic behavior of an RC panel under high-speed loading,however, depends not only on the rebar ratio but also on the geometricconfiguration of the panel and loading as shown by Herter et al.[3] andLimberger et al.[4]. It is, therefore, desirable to evaluate the performanceof the RC panel with variation of the rebar ratio by conducting experiments

under realistic conditions.On the other hand, there have not been many studies on the

performance of rebar joints in RC structures against impact loads.Limberger and Brandes[5] conducted high-speed loading experiments onlap splices of rebars in RC beam specimens and reported that theperformance of the lap splices is improved in dynamic cases when the laplength is sufficiently long. It would be preferable, however, to investigatethe inelastic behavior of the lap splices by using panel specimens, since theRC member against an impact load is generally in the shape of a twodimensional panel in reality.

Both the rebar ratio and rebar joints discussed above are of practicalimportance in improving design methods for RC members against impactloads. The objectives of the present study are to experimentallyinvestigate the effects of rebar ratio and lap splices on the inelasticbehavior of 1/6 scale RC panels under high-speed loading. The loadingrate was determined such that the displacement rate of the center of aspecimen becomes similar to that of real RC panels.

The present study consists of two parts; Part 1 describes the detailedconditions of the experiments and the results of static and high-speedloading tests using reference specimens. The specimens are denoted asstandard specimens and have a typical reinforcement ratio with no lap


Structures Under Shock and Impact 745

splices, similar to RC members in practice. It also presents the results offinite element (FE) simulation analyses accounting for the strain rate

effects on the material properties. Part 2[6] presents the results of high-speed and static loading tests on specimens with the reduced rebar ratiosand lap splices, and evaluates those effects on the failure modes and the

load deflection relationships of RC panels.

2 Experiments

2.1 Test cases

Table 1 shows the test parameters and test cases. The loading rate was200cm/s for the dynamic test, which corresponds almost similar to adisplacement rate of real RC panels which is analytically estimated againstan aircraft impact load in Japan. The results of the standard specimens

are also referred in Part 2.

2.2 Specimens

The dimensions of the specimen are shown in Fig. 1. The specimens were240cm x 210cm x 20cm rectangular RC panels with supporting span of200cm x 170cm. The scale of the specimen was 1/6 of the full scale RCstructure. The rebar ratio in the present paper is defined as the ratio ofthe total area of nominal rebar sections for one way in one layer, i.e. in atop or bottom layer, to the entire concrete section.

Normal concrete with 30MPa design compressive strength and D10deformed rebars (JIS SD345, nominal diameter 10mm and area 0.71cm')were used in both specimens. Table 2 shows the material properties forboth concrete and rebars, and Fig. 2 shows an example of rebar stressstrain curve. The static compressive strengths of concrete on the test daywere 33.9MPa and 29.8MPa for STDn and STDs, respectively. Staticyield strength of D10 rebar was 382MPa.

2.3 Apparatus

The servo-hydraulic impact testing machine of BAM ( Bundesanstalt furMaterialforschung und -prufung, Berlin, Germany) [7] used for bothdynamic and static tests is shown in Fig. 3. Its main components are a



reaction frame, accumulators, a hydraulic actuator, a load cell, foursupporting columns for the specimen, and data acquisition system. Thecapacity of the hydraulic actuator is lOOOkN for the static test and themaximum of 800kN at the loading rate of 200cm/s for the dynamic test.

The loading was controlled by a closed loop displacement control systemusing a preset function. The deflection stroke limit was determined to180mm to observe the inelastic behavior of the RC panel well beyond thedesign level against an aircraft impact load in practice.

The specimens were located on the four simple supports at each corneron top of the four supporting columns. A steel circular load introductionplate (diameter: 43cm) with a thin layer of mortar was installed betweenthe load cell and the top surface of the specimen to provide smooth contactand even load application. The loading was initiated after the weakpreliminary load, less than 5kN, to ensure the even contact between theload cell and the specimen was applied.

2.4 Measurements

Figure 4 shows the measurement items and their locations. Rebar andconcrete strains were measured by using the strain gauges. Thedeflections of the panel were measured by linear valuable displacementtransducer (LVDT). High-speed films and videos were taken to observethe behavior of the specimen during the high-speed loading from the side ofthe specimen at a rate of approximately 500 frames/s and 4500 frames/s,respectively.

3 Results and discussion

3.1 Failure modes of RC panels

Some photographs from the high-speed video during the dynamic loadingof STDnis shown in Fig. 5. The failure process of the panel is explainedin the figure. Figure 6 shows top, bottom and side views of the damagedRC panels after the loading for both STDn and STD%. Both tests wereconducted up to the preset deflection limit of 180mm, which is well beyondthe design level of an RC panel against an aircraft impact load in practice.

Based on the observation of Fig. 5 and 6, it is certain that the finalfailure mode of all panels was flexural failure accompanied by the



compressive failure of the cover concrete on the top surface of the panelsalong the yield line at the center of the long span, although local

penetrations at the edge of the load introduction plate were observed.

3.2 Effects of dynamic loading

The experimental results were summarized in Table 3, i.e. loads P,deflections 5, rebar strains e and ductility factors 5/5, , at the point of themaximum load and unloading. The ductility factors 5/5, are defined as aratio of a deflection at a corresponding point to the deflection at the initialrebar yield, that was defined as a point where the rebar strain gauge recordreached the static yield point of a rebar (2085|H) for the first time in eachtest. The results at the unloading point may be referred to evaluate theductile behavior of each panel beyond the point of the maximum load.

Figure 7 shows the comparison of the load deflection curves of STDnand STDs. The load record of the dynamic case in Fig. 7 had beenalready compensated and smoothed to extract only the bearing capacities ofthe specimens without the inertial effects of the panel. The detailedmethods are given in Appendix. The initial crack point of the concrete forthe dynamic test of STDH was judged from the high-speed video and thepoint of the cover concrete compressive failure was determined from theconcrete strain gauge. As shown in Table 3 and Fig. 7, the maximumload and the corresponding deflection of STD are about 15% and 10%higher than those of STDs. This is considered to be due to the dynamicincrease effects of material strengths of both rebars and concrete. Theload reduction ratio of STD at the unloading point, 0.81, is also higherthan 0.69 of the STDs. Consequently, the RC panel shows higher bearingcapacity and ductility under the high-speed loading than those of the static

case.Concrete and rebar strains for STD and STDs are shown in Fig. 8 and

Fig. 9. The maximum concrete strain records occurred at the maximumload point and are approximately 5000|i and 6500 |i for STDn and STDs,respectively. The maximum rebar strains at the bottom surface for STDsare about 35000|i at the maximum load point and about 57000 at theunloading point. Those for STD« are about 37000|i and 78000|i,respectively and higher than those of the STDs.



3.3 Simulation analysis

Tests results were simulated analytically by using a nonlinear finite elementmethod (FEM). The analytical code used in the simulation is CARC-SHELL-DYN [8]. The FEM model for both the dynamic and static test isshown in Fig. 10. It is a 1/4 model of the actual specimen considering theaxi-symmetric conditions and consists of laminate shell elementsrepresenting concrete and rebar layers. The boundary and supportconditions of the model are determined so as to present the actualconditions of the experiments. The material properties assumed for bothconcrete and rebars are shown in Fig. 11. The dynamic increase factorsshown in Table 4 were used for the material strength in the dynamicanalysis [9]. In the dynamic analysis for STDn, the load time historymeasured in the test was simplified by a tri-linear curve as shown in Fig. 12and applied to the model. The deflection time histories and the loaddeflection curves from the analyses and the experiments are shown in Fig.13 and Fig. 14, respectively. The analytical results of both dynamic andstatic analyses agree well with those of experiments. Figure 15 shows themaximum rebar strains at the bottom layer obtained from the analyses andthe experiments. The rebar strain distributions estimated by analysesagree well with experimental results.

4 Concluding remarks

The dynamic and static loading experiments were conducted to evaluate theeffects of high-speed loading on the inelastic behaviors of reinforcedconcrete panels subjected to an aircraft impact load. Simulation analyseswere also conducted by using the nonlinear finite element analyses.

Based on the experimental and analytical studies, the following

conclusions are obtained.(1) The maximum load of the specimen under high-speed loading increases

by 15% from that of the static case. The RC panel (reinforcementratio: 0.47%) shows more ductile behavior under dynamic loading thanthat of the static loading.

(2) The test results can be simulated well by the dynamic nonlinear FEM

analyses, taking into account the dynamic increase factor in material

strengths.



References

[1] Takahashi, Y., Tsujimoto, M., Yamada, I., Ohno, T. and Uchida. T, AnExperimental Study on Ultimate Limit State Capacity of Reinforced

Concrete Members under High-speed Loading (in Japanese), Proc. of

JCI colloquium on ductility of concrete structures and its evaluation,

March 1988.[2] Saito, H., Imamura, A., Takeuchi, M., Kasai, Y., Okamoto, S. and

Yoshimura, M., Loading tests and analyses of various types ofreinforced concrete slabs under different deformation speeds,

Earthquake Engineering, Tenth World Conference, 1992[3] Herter, J., Brandes, K., Limberger, E., Kinetic Load Bearing Capacity

on Impulsively Loaded Reinforced Concrete Members, Test onReinforced Concrete Slabs, Part 1 (in German), Forschungsbericht der

BAM 119, 1985.[4] Limberger, E., Brandes, K., Herter, J., Kinetic Load Bearing Capacity

on Impulsively Loaded Reinforced Concrete Members, Test onReinforced Concrete Slabs, Part 2 (in German), Forschungsbericht der

BAM 131, 1986.[5] Limberger, E. and Brandes, K., Versuche zum Verhalten von

Stahlbetonbalken mit UbergreifungsstoBen der Zugbewehrung unter

stoBartiger Belastung, Forschungsbericht der BAM 157, 1986.[6] Tsubota, H., Mizuno, J., Kusama, K., Momma, T., Brandes, K., Herter,

J., Limberger, E., Nakazawa, M., Matsumoto, H., Nukui, Y.,Experimental studies on the inelastic behavior of reinforced concretepanels under high-speed loading. Part 2. Effects of rebar ratio and lapsplices, Proc. of the 5th Int. Conf. on Structures Under Shock andImpact, Thessaloniki, Greece, 1998.

[7] Limberger, E. and Struck, W., Servohydraulic equipment for testingreinforced concrete structural members and components underimpulsive loading, Proc. of RILEM Symposium: Concrete structuresunder impact and impulsive loading, BAM, Berlin, June 2-4, 1982.

[8] Uchida. T, Tsubota. H, Yamada. T, Experimental Investigation onReinforced Concrete Slabs Subjected to Impact Loading, Transactionsof the 8th International Conference on Structural Mechanics in Reactor

Technology, J5/1 (Invited Lecture), 1985.[9] Stevenson. J. D et al, Structural Analysis and Design of Nuclear Plant

Facilities, Editing Board and Task Group of the Committee on NuclearStructures and Materials of Structural Division, ASCE, 1980 ASCE-Manuals and Reports on Engineering Practice - No. 58.



Table 1 Test cases

No

1

2

Test name

ST%,

STDg

Reinforcementratio

0.47%

0.47%

Loading rate

200cm/s(Dynamic)

0.1 mm/s(Static)

Remarks

Standard specimen

Standard specimen

Table 2 Material properties (Static)

Concrete

Test case

srq,

STD,

Compressive strength

(MPa)

319

29.8

Young's modulus

(x 10" MPa)

2.24

2.18

RebarDK)

SD345(JIS)

Nominal

diameter, area

10 mm, 0.71 cm'

Yield strength

(MPa)

382

Young's modulus

(x 10' MPa)

1.87

Table 3 Experimental results

Testname

STD.

STD,

Initial rebaryield

load

P(kN)

272

269

deflec.

8y

(mm)

7.9

8.6

Max. load

load

P(kN)

417

357

deflec.

8

(mm)

67.9

578

ductilityfactor

8 /8m y

9

7

max.bottomrebarstrainm

37430

34670

Unloading point due to the stroke limit

load

PU,(kN)

339

245

loadreduction

ratioP ,/Pul m

0.81

0.69

derlec.

8ul

(mm)

162.6

179.0

ductilityfactor

8 /8ul y

21

21

max.bottomrebarstrain(m

78480

56670



310Rebc

~

•

—

—

-SD345(JIS) (gir ratio : 0.47%) ~,_

2

75

-

-

-

.

-

00 20CX) 200. _ _ L _ 7 5

____.___^ _.____^.^ , ""%! T " " " * ""T TT""

-

-

:

=«

-

=|-

—

-

-

-

—

^

-—- - ^

rziL

1— w

— =- _ ^_

-^

:

-

-

-

--^

I

:

r=

~

=.

-- =- -

=-,=_=-=

- r

= = -r~ —--r- t- "

— — =

"

-^

E

-0

E=

-^

=

—}

--'

=-

-=

-

ir-/

-

=-

r™~

_ —

_ Load ir

/_ ^ _

„-„

_ .,

=—

-

.-_

Urc

"~

-

--

z

xlu

=

•V-t

-

Ctl

-

r %j%__

:_:;::

in plate -

-- rj-_ _ ^ i _

i=— -r-=r"

::"r:

-15

200

= o L ^-^

'-^ •• Simply supported at 4 comersA'

Long span directionjr A-A' section

Fig. 1 Dimensions of the specimen ( STD^, STD )

Stress . o (MPaj600 : 1

500 -

400 % x^

300 r

200 t4_

100 B

T '"T

00 2x10^ 4x10^ 6x10^ 8x10^ 1x10" 1.2x10" 1.4x10"

Strain . £ (ji)

Fig. 2 An example of rebar stress-strain curve



RC panel spec,ohfa^v-^i

Apparatus for high speed loading tests Set up of a specimen

Fig. 3 Loading apparatus and set up of a specimen

A:] «::l '^_ - , - .

:oo

# ! DellectionA • Acceleration

Fig. 4 Measurement items and locations

(b) 0.017 s, after initial cracks (c) 0.041 s, maximum load

(d) 0.045 s, failure of cover (e) 0.066 s, Propagation of (f) 0.09 s, End of loadingconcrete cracks

Fig. 5 Process of the high speed loading



(a) Top (a) Top

(b) Bottom (b) Bottom

(c) Side

(l)STDn, Dynamic

(c) Side

(2) STDg, Static

Fig. 6 Failure mode of RC panels



Load,P(kN)600 I

500

400 -

300

200

100

00

- STD^ (Dynamic)- STD, (Static)

* Initial concrete cracko Initial rehar yieldA Cover concrete failurea Max. load• Unloading

Unloading due tostroke limit

50 100 150Central deflection . 5 (mm)

200

Fig. 7 Comparison of load deflection curve

Strain , e (\JL)

-2000

-4000

-6000

Strain . £ (

- Cl- C2

-8000 -80000 50 100 150 200 0 50 100 150 200

Central deflection , § (mm) Central deflection , 8 (mm)

(1) (2) STDs

Fig. 8 Concrete strain



Strain , e (j-i)40000 r— •--

300(X)r

-20000'

-30000-'0

Strain40000

30000

20000

10000

0

-10000

-20000

7f \f\f\f\

, e 0-0

01 0 CM bj- - - S2 - S6: S3- S7

S4

50 100 150Central deflection . 5 (mm)

(a) STD

( 1 ) Rebars in top layers.

200 0 50 100 150 200Central deflection . 5 (mm)

(b)

Strain . e (jj.)KXXXX)

Load mtroduct on plate

4CXXX)

2(X)00

-S10SllS12S13

0. i;_ _j :

0 50 100 150 200Central deflection , 5 (mm)

(a) STD

o50 mO 150 200Central deflection . 5 (mm)

(b)

(2) Rebars in bottom layers.

Load introduction plate

Fig. 9 Variation of rebar strain with central deflection



Table 4 Dynamic increase factor

ConcretecompressiveConcrete \tensile

Rebar

D

1.

1

1

.I.F

25

0

1rebarlayer

Fig. 10 FEM Model

MPa)

load(kN)

concrete rebar(1) Dynamic analysis

Fig. 11 Material Properties

684 2500ancrete

(2) Static analysis

Input load-time functionfor the dynamic analysisMeasured load-time

0.0035 0.0135 0.046 time(s)Fig. 12 Input load time function

for dynamic analysisload(kN)

500L J400t,. . '" ' ...... ..---•' -j300 ^ 4200:100-0

analysisexperiment

Fig. 13 Comparison of deflectiontime history

load(kN)600 —r—^500 r400 r-300 L2001.100 S/0

0 10 20 30 40 50 60 70 80 0 10 20 30 40 50 60 70 80Load-deflection (mm) Load-deflection (mm)

Fig. 14 Comparison of load deflection% STDH ^ STDs

Fig. 15 Maximum rebar strain of analysis (bottom)



Appendix

In the measurement, the dynamic effects due to the inertial force of the

specimen at the initial high acceleration stage in the high-speed loading areincluded in the load-time curve of the dynamic test of STDn. In thepresent study, the compensating method expressed by the followingequation was used to remove these dynamic effects to extract the bearingcapacities of the specimen and to compare dynamic and static load

deflection curves.

Fc(t) = F(t) - ot(t) x Mewhere; Fc(t) '. compensated load.

F(t) : measured load record.a(t) ! measured acceleration record.Me ! equivalent mass. Me = (3 x M(3 I coefficient determined by the shape function of the panel

estimated by the dynamic nonlinear FEM simulation

analysis. P = 0.3.M I the mass of specimen.

t I time.

The compensated load time history was then smoothed by using aHamming's lag time window to remove high frequency noises and spikes.The smoothing method using the Hamming's lag time window is expressed

by;

W(t) = 0.54 + 0.46 cos(7it / tjwhere; W(t) '• Hamming's lag time window.

tm • width of the Hamming window, tm= 0.005(s).t I time.

Figure Al shows the time histories of STDn, (load, displacement andacceleration) and the compensated load deflection curve. Finally, the loaddeflection curves of the dynamic case STDn and the static case STDs arecompared as shown in Fig. 7.



0 0.02 0.04 0.06 0.08 0.1 fs)(a) Measured load-time history (b) Measured acceleration

Time

Fc (kN)600 r

500h

400 i-

300h

200 h

lOOf-

;'iY4,iA

Fc(t) = F(t) - cc(t) x Me

Smoothing,(c) Compensated load-time history '™

P fkN)600-500

400

300200

1000

0 0.02 0.04 0.06 0.08 0.1 (s)(d) Smoothed load-time history

8 (mm)200

^_o_j"0 0.02 0.04 0.06 0.08 O.I fs)(e) Measured deflection-time history

Load , P fkN)600,

3oor /

^

MX) |;

Unloading due tostroke limit

........ 50 100" " 150 "Central deflection . 6 (mm)

(f) Smoothed load-deflection curve

Fig. Al Compensation of dynamic effects and load deflection curve


Documents

1 Introduction - WIT Press · 2014-05-20 · 3.3 Simulation analysis Tests results were simulated analytically by using a nonlinear finite element method (FEM). The analytical code