a[mm]/l - Memorial University of Newfoundland DAI
a[mm]/l - Memorial University of Newfoundland DAI
a[mm]/l - Memorial University of Newfoundland DAI
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BEHAVIOR OF HIGH-STRENGTH CONCRETE<br />
PLATES UNDER IMPACT LOADING<br />
O Suryawan Munradi<br />
A thesis submitted lo the School <strong>of</strong> Graduate<br />
Studies in panial fulfillment <strong>of</strong> the<br />
requirements for the degree <strong>of</strong><br />
Master <strong>of</strong> Engineering<br />
Faculty <strong>of</strong> Engineering and Applied Science<br />
<strong>Memorial</strong> <strong>University</strong> <strong>of</strong> <strong>Newfoundland</strong><br />
March 1999
ABSTRACT<br />
High-smnsh concrete plater are frequently used !n vmous slrucrurnl cngmeenng<br />
systems and vaneuer <strong>of</strong> elvd cngsnecnnp apphcanonr. A research pmg<strong>mm</strong> was cdrned<br />
out at Memonal Unlver~~ty <strong>of</strong> <strong>Newfoundland</strong> to lnvcrtsgvle the behsvlor <strong>of</strong> h~gh-ilrengh<br />
concrete two-way plecr subjected to Impact lon&n& The research program included bath<br />
expnmental lnverrlgarlon and numerical tnverugnlon.<br />
The c umt rercawh nncludes an expenmental lnverllgruon on rlrteen concrete<br />
plater wtth dtmenston <strong>of</strong> 950x950 <strong>mm</strong> md 1W<strong>mm</strong> rhtcknesr. The plales were rupponcd<br />
by r specla1 fame dengncd far thlr tnvemgunon. The suppan fnme 1s made from<br />
~oncrele and steel wllh free opennng <strong>of</strong> 7Wx700 <strong>mm</strong>. Normal-strength md htgh-strength<br />
concrete placer were tested undsr two end eondtsonr. x.e. fixed and slmply supponed. All<br />
<strong>of</strong> ,he rpzct<strong>mm</strong>s were two-way rennforccd plater *ah relnfomsmcnt rmo that vaned<br />
from I%-? 5% I" tmslon face and 0.7%-0.8% ~n eomprerslon face. A ng~d project~lc was<br />
used lo apply the Impact lard to the tesled re~nforced concrete specamens. The ng~d<br />
projecttle was a mlmd steel cylmda wrth ??O-kg mass md 3011.5 <strong>mm</strong> diameter contact<br />
area. The projeellle was dropped f<strong>mm</strong> a vanable helght <strong>of</strong> up to 4 m. An sccele<strong>mm</strong>eter<br />
~9th +2W-g cnpvelly was attached to the eylnnder steel lo record the actual lest<br />
aecclersuon. A data acqutslrlon system b ad on a penonal computer acquired the drtil at<br />
I rampllng rate <strong>of</strong> IWO Hr. The structural behavtor wlIh respect lo d~splacement.<br />
eoncrele and steel stmns. fatlure mode, and energy rbmrpt~an were exa<strong>mm</strong>ed. The effect<br />
<strong>of</strong> d pme loading. concrete strength, reinforcement atdtlo, and suppan patterns were the<br />
test parameters.
A numcncnl mvertigatnon ww conducted lo cvvluore the rest rerultr wlth respect<br />
to the Nonh Amenean code and some European d erp codes A lhnerr elwllc fmcture<br />
mechanics Impact load expressam was used to evnluate Le effect <strong>of</strong> nle <strong>of</strong> loading on<br />
the dynamtc behavnor <strong>of</strong> high-arength concrete plates. Based on the cxpcnmental rerl<br />
results 11 hw been found that the punch~ng fanlures <strong>of</strong> the lmpacl loodnng were about<br />
lwlce the Slauc punchmng shear capnclly The cnltcal velocltte$ <strong>of</strong> ~rfnnuon cm he<br />
csrfmated ;~ccurately for all hlgh-rrrengh concrele rpcctmenr accordtng lo CEB dynamic<br />
cde expresson. The ratlo <strong>of</strong> tmpaa versus rlalnc fracture mergy far high-sirenph<br />
concrete plate war found lo be much hngher than that for normal-strength concrea.<br />
Therefore. hngh-strength concrelc plates are eonrndered to be more efficient lhan normal-<br />
strength concrete plates under tmpacr loading.
ACKNOWLEDGEMENTS<br />
Thlr lherlr was completed at Memonal Unlvcnmty <strong>of</strong> Newfoundlmd as pan <strong>of</strong> Master <strong>of</strong><br />
Eng~neenng degree program. The expenmental work has been caned out n the concrete<br />
and itruclure labonlory <strong>of</strong> Memonal Untveraoly <strong>of</strong> <strong>Newfoundland</strong>. Cim~da. Fundzng !n<br />
the form <strong>of</strong> graduate fcllowsh!p from the Govc<strong>mm</strong>nt <strong>of</strong> Republic lndonesla md ~se;vch<br />
supplement from Mcmonal Unxvcrstty are gracfully acknowledged.<br />
Grateful acknowledgement s alro due lo Dr H. Marzouk. Pmfer~oi <strong>of</strong> Clvnl<br />
Engmeenng. under whose gumdance and supervls>on thc lhertr was carned out.<br />
Acknowledeement Ir alro addressed to Dr. M.R. Haddam. Associate Dem 01<br />
Englnsenng Graduate Srudnes and Research. far has encouragement and the frctllner<br />
provtdcd.<br />
AcLnowledpmer~lr me alro made to the Technical Staff for their nrnnmcc ~n the<br />
expenmental prognm. espemdly Mr. C. Ward. Mr. A. Bur~ey. and Mr. R. O'Dnwall for<br />
then prepdntlon <strong>of</strong> [he test speelmenr and lest equnpment Spectvl thank to Dr. A.<br />
Husseln and Dr. M.A. Fard for their ruppon and dnxurrlon dunng expenmental work.<br />
Last. but nor lesl, the author takes thls chance to express his pr<strong>of</strong>ound gruntuds<br />
to all htr famsly members. espccnally hnr parents for thew prayer and blersng. nlsa he<br />
wffe and son for their patence. continuing encouragement. and afkuan.
Table <strong>of</strong> Contents<br />
ACKNOWLEDGMENTS<br />
Table <strong>of</strong> Contents<br />
Lst<strong>of</strong> Symbols ..................................................................................................
2.1.2.2 2. Fine Aggregates I2<br />
2.1.2.3 Admtxtures .............................................. 13<br />
2 1.2.3 1. Mtneral Admlxrurcs .............................. 11<br />
2.1.2.3.2. Chemtcrl Admixtures ............................. 15<br />
2.1.3. Bmhrng and Mnrlng Squcncer<br />
2.2 Punching Shear Strength<br />
2.3 Impact Performance <strong>of</strong> C<br />
2.3.1 Ovcrvtew <strong>of</strong> Mamal Modeilng<br />
......................................<br />
2.32. S<strong>mm</strong>n Rarer for Vanou3Typrr <strong>of</strong> Load>% ...................... 31<br />
2.3.3. Prapemes<strong>of</strong> Concrete Under Dynamnc Laadtng ................. 36<br />
2.3.3 I Compress~ve Strength<br />
2.3 3 2. Modulr. <strong>of</strong> Elasue~ty ............................................. 27<br />
2.3.3.3. Ult~malc Strrln<br />
2.3 3.4 Comprerrlve Fm<br />
2.3.3.5.Tenrale Laad~ng<br />
2.3.3.6. Tenston Modulus <strong>of</strong> Elarttcnty<br />
2.3.3.7. Tensile Fracture Energy<br />
.............................. 29<br />
2.3.4. lmpacl Reslrl~ncc <strong>of</strong> Relnforced Hlgh-Smnglh Concrete Siabr 32<br />
2.3.4.1. Desg hncttcc 32<br />
2.3 4.2. Eumpan Dertgn Codes for Punching Shear Capaclly<br />
and Cnlical Pefiorft~on Velocnlv ........................... 34
Chqlei 3<br />
EXPERIMENTAL INVESTIGATION<br />
Chapter 4<br />
3.2.1. Re~nfoxomcnt<br />
3.3. Test Spctmens<br />
3.4. Fabncatlon <strong>of</strong> Speclmenr<br />
3 6. lnrtrurnsntation System<br />
3.6. I. Tertmg Load<br />
3.7. Test Pmcedurc<br />
3.6.3.1 Steel Strams<br />
TEST RESULTS AND DISCUSSION<br />
4.1 Craclung Charaaenrtter 66<br />
4.2. Laad-Deflection Chaactensucr 67
Chapter 5<br />
4.3. Dynam~c Fracture Energy<br />
4.4 Steel and Concrete Strmnr<br />
4.5. Mder <strong>of</strong>Fvilure<br />
4 6. Effect <strong>of</strong> Concrete Strength<br />
4.7. Effect <strong>of</strong> Sucl Ranforcement Rauo<br />
IS. Effem <strong>of</strong> Ssppan Patem<br />
4.9 Effect <strong>of</strong> Dynamlc Load, ......................................<br />
NUMERICAL EVALUATION<br />
Chaplet 6<br />
5 1. lntmducr$on I I3<br />
5.2. Impact Load I I4<br />
5.3. Punching Shear (StascCrpac~ty) 115<br />
5.4 Code Reco<strong>mm</strong>endauonr 118<br />
5 5 Cnttcnl Veloctly <strong>of</strong> Pcrfantton I20<br />
5.6. Fnccure Mcchrnlcs Analys~r <strong>of</strong> Impact Laad .................................... 122<br />
5 7. Dynam~c Fmcrure Energy 119<br />
SUMMARY AND CONCLUSIONS<br />
6.1. Expnmental Invesugaean 132<br />
6.2. Numerical lnvest~gvt~an 135<br />
REFERENCES ....................................................................................................... 137
List <strong>of</strong> Figures<br />
Figure 3.1. Cross scuon A-A <strong>of</strong> lyplcal spclmen under fired suppon ............... A7<br />
Rgure 3.1. Typ~cal steel re~nfarcement <strong>of</strong> rpc~men<br />
Fngure 3.3. Arrangement <strong>of</strong> steel relnfarccmcnr reba<br />
F~gure 3 4 Casting <strong>of</strong> fresh concrete f<strong>mm</strong> Ihe mser to the formwork ............ TO<br />
Fkgure 3.5. Compresswe nrength lest <strong>of</strong> a concrete eyllnder ................................. 5 1<br />
F~gre 3.6. Concrete beams <strong>of</strong> thetest frame 51<br />
Fngure 3 7.Concretc and steel beams for fired-suppon 53<br />
Figure 3.8 Speetmen under Axed ruppon ............................................................. 54<br />
Figure 3.9 Bottom rennforcement <strong>of</strong> the concrete base <strong>of</strong> the tcrttng frame ........... 55<br />
Flgure 3.10. Top relnforccmenl <strong>of</strong> the concrete base <strong>of</strong> the lertlng frame ................. 56<br />
Ftgure 3.11. Complclc tcsl fnme wvh guide steel cylinder .................................. 57<br />
Ftgure 3 12 Test set-up for fixed rpctmen<br />
Rpre 3.14 A rpeclmcn dunng ompact te~nng<br />
Figure 3.15. LPDT fixed ar !he center <strong>of</strong> rpnmen<br />
Flgum 3.16. Lacat~ons <strong>of</strong> steel rtraln gageson tenrlon and camprelrlon facer .......... 62<br />
F~gure 3.17. Concrete strain-gage locsuon<br />
Figure 3.18. Dataacquirntian systcm<br />
Figure 3.19. lns<strong>mm</strong>entataon blockdiagram<br />
Rgure 4.1. Failure panems <strong>of</strong> lest specimens HSSI. HSS2. HSS3, and HSS4 ......... 75<br />
F~gure 4.2. Failure parlems <strong>of</strong> test rpeelmcnr HSFI. HSF2. HSF3, and HSF4 ........ 76
F1gure4.3. Filllure paltrmr <strong>of</strong> lest specimens NSSI . NSS? . NSS3 . ;md NSS4 .......... 77<br />
Fbgure 4 4 Failure parems <strong>of</strong> test spcctrnenr NSFI . NS F2. NSF3 . and NSF4 ......... 78<br />
Flgurt4.5 Fatlure pallem <strong>of</strong> a rrpmcal tcrtrpeenmcn at Ihecornprerrron face .......... 79<br />
F~gure 4.6. Load-deflecllon curves for rpectrncn no 1 . 2 . 3 . and 4 ....................... 80<br />
Ftgurc 4.7 bad-defleeuon curves far specmen no . 6 . 7 .and 8 ............................ 81<br />
Flpurp J 8 Loaddeflect$on curves fmorpamen no 9. 10. and I I RZ<br />
hgure 4 9 Lad-deflecuon curves for specmen no . 14 . 15 . md 16 .................... 83<br />
Rgure 4.10. Lord-deflecrron curves for spamen no I and 9 ............................ 84<br />
Figure 4.1 I . Load-defletlon curves for specmen no . 2.6. 10 .and I4 ................... 85<br />
Ftgure 4.12. Load-deflectson curves for specmen no 3.7. I1 . md 15 ................. 86<br />
Figure 4.13. Load-dcflecuon curves far specmen no . 4 . 8 .and 16 ........................... 87<br />
Ftgure 4 14 . bad-erne curves for spectrnen no . 1 . 2 . 3 . and 4 ................................. 88<br />
Figure 4.15. bad-tlm curves far rpcclmcn no . 6 . 7 .and 8 .............................. 89<br />
F~gure 4.16. bad-rtms curves for spec~rnen no 9 . LO. and 11 ............................... 90<br />
Ftgure 4 I7 Load-hmcurvel for rpeclmen no . I4 . IS . and 16 .............................. 91<br />
Flgure4.18 Deflectton-arnecurver for specmen no . I . 2 . 3 . and4 ....................... 92<br />
Fsgure 4.19. Deflecl8on-nme curves for rpcnmen no . 5 . 6 . 7 . and 8 ....................... 93<br />
Figum4.20. Deflectton-tlmecurver for rpectmen no . 9 . LO . I I . and 12 ............... 94<br />
Flgure4.21. Deflectton-nmc curves for specmen no . I3 . 14 . IS . and 16 .................. 95<br />
Figure 4.22. Slccl and concrete r<strong>mm</strong>r <strong>of</strong> specmen HSSl ......................................... 96<br />
Figm 4.23. Steel and concrete srrans <strong>of</strong> specmen HSS2 97<br />
Figure 4.24. Steel and concrete rtmns <strong>of</strong> spscirnen HSS3 98<br />
Flgurt 4.25. SPel and concrete strains <strong>of</strong> specmen HSS4 99
Ftpure 4.26. Steel and concrete stnlns <strong>of</strong> rpeclmen HSFl ...................................... 100<br />
Figure 4.27 Steel and concrete srralnr <strong>of</strong> specmen HSF2 ................................ 101<br />
Ftgure 4 28 Sreel and concrete srranr <strong>of</strong> rpec!mcn HSF3 .................................... 102<br />
Fmpure 4.29. Steel and concrete rtnlnr <strong>of</strong> rpse~men HSF4 .................................. 103<br />
F~UR 4.30. Steel and concrete ~ tn~ns <strong>of</strong> specmen NSSI ................................ IM<br />
Rpore 4.31. Steel mdconcrete rams <strong>of</strong> rpeclmen RSSl ....................... I05<br />
Ftgure 4.32. Sleel and concrete Etnlnl <strong>of</strong> rpeelmen NSS3 .................................... 106<br />
Rere 4.33 Sleel and concrete strains <strong>of</strong> specmen NSS4 ............................... 107<br />
Ftgvre 4.34. St-! and concrete strams<strong>of</strong> specmen NSFl ................................. 108<br />
F~gure 4.35. Steel and concrete rrrdlns <strong>of</strong> rpeclmen NSF2 .............................. 109<br />
Ftgure 4.36. Steel and mncrele nraknr <strong>of</strong> specmen NSF3 ................................... 110<br />
Fipure 4.37. Steel and concrete rtntnr <strong>of</strong> rpect<strong>mm</strong> NSW ............................. 111<br />
Figure 4.38. Htph-strength vmus normal-strength concrete plrte behawor<br />
under lmpvct loodnng 112<br />
F~pure 5 1 Method <strong>of</strong> crlculattng N rom rlrerr!ng n data ................................ I26<br />
Rpure 5.1. Typical load-denealon curve 130
List <strong>of</strong> Tables<br />
Table 2.1 Typ~cal rtnm rarer far various rwr <strong>of</strong> lodtnp . ...... . .. . ...... . .. . . 25<br />
Table 3.1. MIX propanlo" for I I' <strong>of</strong> nonnalirrengrh concrete ...... .... ........ . .... 37<br />
Table 3.2. MIX propomon for l m'<strong>of</strong> h~gh-smngth concrctc .......... ..... ...... . . 38<br />
Table 3.3 Prnpen!cr <strong>of</strong> steel retnforcement<br />
Table 3.4 Delallr <strong>of</strong> specmen<br />
Table 4.1. Test results<br />
Table 5.1. Cntlcal velac~ty <strong>of</strong> perfanuon .. ........... ... . . .. .... ............................ 120<br />
Tnble 5.3. C~lculaled cnllcal velocnty campmd wtlh test velac,ty 121<br />
Tlblc 5 4 Values <strong>of</strong> ZV f<strong>mm</strong> ~mpact tests 128<br />
Tnblc 5.5. Companm <strong>of</strong> dynamsc fracture energy wtth rtatte fraeturccnegy ...... 131
List <strong>of</strong> Symbols<br />
area <strong>of</strong> rsel remfa~ement<br />
enck length<br />
final crack on fncture<br />
lnlcial enck kfore lertlng<br />
accelcratton <strong>of</strong> pm,ecule<br />
total aeceleml~an<br />
ride dnmenrlan <strong>of</strong> square ioaded area<br />
pnmelsr <strong>of</strong> mueal recrlon for shear ~n plater<br />
pnphsry around rhc column excludtng apenlngr<br />
effecuve depth <strong>of</strong> the slab<br />
- do slress rate or vanallon <strong>of</strong> rmss wtlh frmc<br />
I<br />
E modulus delnn~aty<br />
E, modulus aieiast!e!ty <strong>of</strong> concrete<br />
E, modulus elarl!cnty <strong>of</strong> aeel<br />
EeV<br />
dynamic (impact) modulus <strong>of</strong> elastlenty<br />
E,,, nauc modulus <strong>of</strong> slvsticnty<br />
Fir1 Impact loadng<br />
1, mean cencme <strong>mm</strong>gth
I
lmpact test load<br />
mlrrlle penmeter<br />
penmeter <strong>of</strong> the govern!"% rectlon at a dlrtance 1.0 d f<strong>mm</strong> the loaded wen<br />
deflect~an at the load paml<br />
ilccclerslron at the load pala<br />
velm~y <strong>of</strong> crack errenslan<br />
ult!rnnlc shear force<br />
ullnmste load for flexural fatlure<br />
nomlnsl shear stress<br />
ult~mac shear stress<br />
EOnCrelc denslly<br />
crack wdth<br />
wtdlh <strong>of</strong> the fracture pmccsr zone<br />
crack uldth when f, rexhes rem<br />
crack opentng velwlty<br />
dynamtc matenal pmpeny<br />
Pacar whtch adlusts r,for ruppon dlmennons<br />
mtloaf long ride to rhan ride <strong>of</strong> thc concentrated load<br />
fracture surface energy<br />
malenal eaffielent for relnforc~d<br />
tC"S11~ SVdl"<br />
y~cld slmn <strong>of</strong> steel remfmrnca
maxxmurn lenrtle rtnln<br />
impact ullxrnare stram<br />
stme ultlmare rtmin<br />
111~1" nre<br />
rtnln rate n quasi s tali^ condltmn<br />
rcnsllc mnforccrncnt ratio<br />
comprerrlve retniare~mcnt nuo<br />
penmeter <strong>of</strong> the column<br />
frxture sucngh <strong>of</strong> concmre<br />
final rucrr <strong>of</strong> 3 Ipecnmtn measured ~n a fracture test<br />
lnltlal arerr <strong>of</strong> n rpcclmcn<br />
stress rare or vanallon <strong>of</strong> nerr wtth tune<br />
stress nle a qwlsl rletc condtuon.
1.1. General<br />
Chapter 1<br />
INTRODUCTION<br />
ll 1s appropnatc to dlxurr and clmfy a number <strong>of</strong> fundamental poma ~n the subject or<br />
dealing wnth rpec!Rc derlgn munpmcnt. Thm SIX three polnts that rhould be cian8ed<br />
before examsnlng the behavior <strong>of</strong> concrete plates under lmpilcl loading. Frrrlly. thc high-<br />
strength concistc plate should be defined. Secondly. the dcfin~tton <strong>of</strong> Impact loadtng<br />
rhould beoutlmed. Fmally. the ohjcct#ves <strong>of</strong> the research should he dewnbed cledrly.<br />
Hngh-strength concrete IS defined as any concrete wtth eomprernve-strength over<br />
41 MPa. Hlgh-sucnglh 8s reallred thmugh the use <strong>of</strong> silica fume as a pantal replacement<br />
for cement to pmduec extrsmely srmng, hlghly abrvnlon remnant. impmneil. ble. very<br />
durable conmle agalnrt freeze-thaw damage and salt water aanck. Thlr marenal has<br />
already been successfully used far <strong>of</strong>fshore platforms. marine ruuctures. tall buildangs.<br />
and long span bridges.<br />
Impact loading ~r a result d a mllinon between two bodes thar aceur m a very<br />
small interval <strong>of</strong> time, one wtth a h~gh tntt~al speed strilung another at a stelonmy
porltlon by gneraung large forcer. The rlruck oblect. #n clvll engmeenng. Is urually a<br />
structural element that has to be dengncd to rerlri lmpacl Ioadsng Thlr loadmg IS mostly<br />
ei<strong>mm</strong>e lwildang ~8th mnfrequsnt probbbltty <strong>of</strong> extrtenee dunng the Ihfeume <strong>of</strong> !he<br />
structure. However. falure due to Bmpxt loadtng <strong>of</strong>ten results ~n a senous rtruclunl<br />
&mag. Marenal propcn!es like hlgh-cnergy absorprlon have lo be llken lnta<br />
conadcnoon I" the dcrlgn <strong>of</strong> sttic concrcte structure.<br />
Many rmcturer experience Impact loadcng. Some <strong>of</strong> the structures La murl have<br />
the porrtbml~ry <strong>of</strong> Impact loudtng consldered m them desngn are <strong>of</strong>fshore fnc#l~ner. ptles.<br />
deknw shelters. and rlructures ~n retrmlc areas. The tmpacl loading can be ~gnored tn the<br />
derlgn pmcerr when the Iodlng lntcnstry has small Ilumualonr. However. when the<br />
rnsgn!tude <strong>of</strong> the fluclualng component af londlng 3s large. lhc Impact lwdd~ng can be<br />
very rtgnllicmt. Engineers should be able to decsde whelher the mpxt lord~ng must be<br />
accounted for ~n des~gn or neglect a. The resvns!bnltty <strong>of</strong> the data engnncer IS to solve<br />
problems m a safe. effi<strong>mm</strong>t. and economic manner. Therefore. the dcslgn cng~ner<br />
should consdm how the overall ntruclure behaves under lmpact loadmg.<br />
The use <strong>of</strong> h$&-strength concrew IS ~ncrr~nng faster than the development <strong>of</strong><br />
apprapnale dertgn code reco<strong>mm</strong>cndaltan In spite <strong>of</strong> the wtde use <strong>of</strong> high-rtrmgth<br />
concrete. l~ttle research has been canduel~d on the structural behavtor <strong>of</strong> high-strength<br />
concrele beams. slab and columns under dynamic loadmg. The rtruclunl behavlor <strong>of</strong><br />
concrete plater, especially under lmpxt loadnng, needs funher Invenlgaoon. The<br />
concrete plare in a nmple. sonarnica!, and popular nruclunl rysrem. Therefore. hlgh-<br />
strength coneme flat plate was chosen ~n this research, rlnce it bar wvenl clvll<br />
engrnecnng applicat!ons.
1.2. Research Scope<br />
The %ope <strong>of</strong> lhls study IS ro nnvenlgnte the dpamlc behav~or <strong>of</strong> two-way remforced<br />
concrete plates under tmpacl loadtng. The 6nvesugatlon tncludcr an expenmental<br />
anuertlganan and a numerical evaluaton The two phwr <strong>of</strong> the mnversgattons are<br />
dexnbed as fallowr:<br />
The expenmental rerung pmg<strong>mm</strong> will be conducted on wvenl speclmenr<br />
rub~eeted to fmpafr loading. The lmpuc: load sped target rmge between 4 to 9 mls as<br />
~!ccelcrat.tlon ir nnge between 70 to 120 g The rpectmenr will be tested under Axed md<br />
rrmply supponed end-cond8nanr. The behavior <strong>of</strong> high-rmnglh concrete plaer ulll be<br />
evaluated wnth rerpeet lo deflection. concrete md stel smtns, energy rbsorpr~on<br />
capsclry. and fracture encqy.<br />
The numneal evaluilllon will be cmed ou~ lo venfy the valndnty <strong>of</strong> the current<br />
codc prcd!cttonr. The lmpaEl lo~d ccapacllles wlll be compared wlrh Xauc capvcltlcr <strong>of</strong><br />
the coder A fmacture mechanxcr Impact load analytnr based on lhnear elilrt#cr fracture<br />
mechanics ILEFM) wnll be conducted. The purpare <strong>of</strong> the numerical evaluutton 1s to<br />
prov~de a more detall anvlyrns on the effect <strong>of</strong> the rate <strong>of</strong> loading on the dynamtc<br />
behawor <strong>of</strong> h~gh-nrength concrete plates The dynamtc fracture energjes <strong>of</strong> the tested<br />
plates wdl be compared lo sratlc fmcture snsrglsr calculated f<strong>mm</strong> prevnous Invcst>galon.<br />
The nudy wlll provide adcslgn gut& forengnneem on the effect <strong>of</strong> nte <strong>of</strong> loading an the<br />
behvvtor <strong>of</strong> high-strength concrete plate.
1.3. Research 0b.iectives<br />
Thrr ==arch wmll nnvesrngale the rest results <strong>of</strong> 16 different rpectmens Based on the<br />
e\penmenlal lnveslrgatlon a better undentand~ng <strong>of</strong> [he khavlar <strong>of</strong> htgh-smnph<br />
ranforced concrete plates under Impact loading will be reahzed. The mqor objeclwcr are<br />
nor lhmtrcd ro hut wdl conram the followrng objecnver:<br />
(I1 lnverugrtc the rtrvctvnl behrvlor <strong>of</strong> high-strength concrete plate under dynamic<br />
tmpact loadtng.<br />
(21 S~udy the effect <strong>of</strong> the md condttgons on the rttuctunl khavtor <strong>of</strong> hhgh-strength<br />
concrete plate under ampact loadnng.<br />
(3) Exa<strong>mm</strong>e the effect <strong>of</strong> re#nforce<strong>mm</strong>t nu0 an the behi~vtor <strong>of</strong> high-strength concrete<br />
plates.<br />
(4) Record actual concrete strdxns. see1 strams. and deflectlan <strong>of</strong> htgh-strength concrete<br />
plater under Impact loadnng.<br />
(5) lnvcrtlgate the tnfluence <strong>of</strong> the rate <strong>of</strong> lodtng on the Impact bchavlor <strong>of</strong> rpeclmens<br />
usmg fraclure mechanics equatlanr and ten results.<br />
I61 Pmv~de new lnfomallon on the farce-dlrplacement relunonrh~pr <strong>of</strong> h~gh-strength<br />
concrete plater.<br />
(7) Compare the result <strong>of</strong> the invenlgatton with rhcoretrcai erpresaonr and code<br />
equilttanr.<br />
(8) Evaluate the fnnure energy <strong>of</strong> the concrete plate undm Impact loading.
1.4. Format<br />
Thnr therls can be dlvlded Inla three pans. Pan I sppem under Chaprers I and 2 Chapter<br />
I covers the tntmductlon and rhc ablecclver <strong>of</strong> lhir ~nvsmignt~on. Chapter 2 presents !he<br />
lttenrure revtew <strong>of</strong> prevfour xnvestlgatonr.<br />
Pan 11 appears under Chapter 3 thal cover all the cxpcnmental tnvessgauon<br />
camed out to study the effect <strong>of</strong> concrete strength and relnfonement nllo an the<br />
behawor <strong>of</strong> relnfoned concrete plaler subjected to Impact loddnng. Thlr chapter coven<br />
the sa-up <strong>of</strong> labaratory and crpcnmcnral pmgram<br />
Pan Ill appcarr under Chapters 4 and 5. cover the enrlre research Andlngr. rest<br />
results and anrlyllcal tnverugauon ~ncludlng evnluatlan <strong>of</strong> severdl models lo predlcl rhc<br />
iheilr-mrenglh <strong>of</strong> hlgh-stmgth concrete plate. Thlr chirplei also presents I numerical<br />
evaluat~on bared on a fracture mechanics vnalys8r to evvluare thc effect <strong>of</strong> rate <strong>of</strong> loudtng<br />
on the behavior <strong>of</strong> conc~te plater. Rnully. r conclus8on su<strong>mm</strong>anrer the cxpenmcnval<br />
and analyttcrl lnvatkgatnonr are grven 8" Chapter 6.
Chapter 2<br />
REVIEW OF LITERATURE<br />
2.1. High-Strength Concrete<br />
2.1.1. General<br />
Qurlnty <strong>of</strong> concrete IS generally derenbed by as eomprr!ve nrength. Accordtng to the<br />
Amencan Concrete Innlture. ACI 363 (1992). ordsnav strucrural cancrele has been used<br />
wrlh r cornpreslve rlrength in b e nnge <strong>of</strong> 20 to 40 MPa. Whtle. hjgh-strength concrete<br />
1s defined as any concrew wtth over 41 MPa compresswe strength. But. in the 1st two<br />
decadcr. concrete ~8th hlgher compresswe strength has been used tn rhe cansrructlon <strong>of</strong><br />
high-nw buildrngr. long-span bndger. and <strong>of</strong>fshore structures. The new hlgh-strength<br />
concrete has n compresswe strength <strong>of</strong> 70 MPa and IW MPa.<br />
The uoe <strong>of</strong> high-strength concrete a sprendlng rapadly all aver the world and<br />
lncrearing faster than the development <strong>of</strong> appmpnate derlgn code reco<strong>mm</strong>endat8ons.<br />
Several recent invertlgatlons have been conducted on hlgh-strength concrete behvv~m to<br />
find the charancnstic behavlm <strong>of</strong> high-nrmgth concrete and to up@ the cumt
derugn reco<strong>mm</strong>endar~ons so thac the polsnt!rl <strong>of</strong> hngh-strength concrete can be fully<br />
expoad.<br />
Recent tnveniguuonr on high-rtrengrh concrete can be clnrrlficd ~nto three masn<br />
cnrcgoncs. 1.c. khavlor <strong>of</strong> matenal pmpentes. behav~or <strong>of</strong> rlmclunl memberr. and<br />
develapmcnr <strong>of</strong> teslsng equtpment. There three man cacgona can be dercnbed bnelly<br />
~n the followlnp:<br />
(I) W~th altenr~an to the mvtcnal pmpenler. rcvenl ~tudler have been camcd out to<br />
tnvcstlgvle Ihc bchavln <strong>of</strong> h~gh-strength concrete rubjcctcd lo dtfferent stress<br />
condlllms.<br />
(2) Wtrh respect to the behavior <strong>of</strong> rrmcrural members. several rrudler hive been<br />
conducted to lnvestlgate the behavior <strong>of</strong> structuml elements conslmcted wtlh hlgh-<br />
slrmgh concne.<br />
(31 Rnally. with eonsrderatson to the development <strong>of</strong> tesung equlpmenl. xvenl<br />
resenrchcr have been gwen to tmpmvc the lestlng equnpment tn order to ~nvesttgate<br />
ilccurntely the behrv~ar <strong>of</strong> hmgh-strength concrete.<br />
Dunng the pan decade. rcvenl concrete matcnnl and stmctunl mvenlgarnonr<br />
were conducted at Mcmonal Unlvers~ty <strong>of</strong> <strong>Newfoundland</strong>. Mmouk and Hurrcin (19913)<br />
conducted the development <strong>of</strong> hlgh-nrenph mnr den@ f<strong>mm</strong> lacal mrtenalr It h& been<br />
concluded that Iacal matmalr can be used wtth s~llca fume and fly ash to provtde<br />
strength <strong>of</strong> 70 MPn at 28 days. Manouk and Chcn (1995) reco<strong>mm</strong>ended a const~lut~ve<br />
relatronshlp br the behavior d high-rurngth concrete under unlarsrl tension load<br />
~ncludtng the pat-pak sabnmg rerponx and fncture energy.
Mmouk and Husretn (1991) reported that the use <strong>of</strong> the cuble mot <strong>of</strong> the<br />
compresave strength to predlet rhc punehtng shear reststance <strong>of</strong> hcgh-smngth concrete<br />
slabs Ir much better erprerrnon compared to the square mot expresseon used m all Nonh<br />
Amencan coder. Mvnouk and Jtang (1994) ~nvcsrtgatcd rlr different methods la<br />
enhancement <strong>of</strong> the punchang shear capacity. The strucrural behawor <strong>of</strong> hnoh-nrengh<br />
concrete plater rvns cvalunrcd ~n terms <strong>of</strong> ovcrrll load-defleetmn response. ulilmotc<br />
loadrng capaerty. ducultly and energy absarpoon. Fanlure patterns and nlnm dtstnhut~an<br />
we= also dlscurrcd.<br />
2.13. Mix Design <strong>of</strong> High-Strength Concrete<br />
Hlgh-strength concrete IS made wlrh the rumc baste ~ngredlentr as normal-strength<br />
concrete. Famy and Pana~ (1993) reported that the praducuon <strong>of</strong> hlgh-xrcnglh<br />
concrete is achncvcd by opt!mizar~on <strong>of</strong> the follaw~ng facton.<br />
(1) ehaactenrt~cr <strong>of</strong> the eemenung medium.<br />
(2) chnnctcnrtxe~ <strong>of</strong> the aggregates.<br />
(3) pmportlonr <strong>of</strong> the pasts.<br />
(4) paste-agpgates ~ntsraclian.<br />
(5) mixmg, consolidating, and cunng. md<br />
(6) testing pmecdum.<br />
Some relatan <strong>of</strong> <strong>mm</strong>alr and mlxrng methods are being explored thmugh research.<br />
However, atlendon to the &ve nx basic arras Ir <strong>of</strong> exveme impanance whether wlng<br />
exirttng or new materials and techniques. In the United Stater and Canada, the ACI
Co<strong>mm</strong>ltlee 363 (1992) report 8s used 3s r gutde for the dcngn and construcrlon <strong>of</strong> hngh-<br />
slrengh ConCrete EtWClURE<br />
LI.LI. Cement<br />
Cemcn~ pule 4s an imponant faeror ~n malang htgh-strength concrete. Selection <strong>of</strong> r<br />
panlmd cement for htgh~strcngth eancretc should bc bxcd on compmti\.c stxnglh lcrlr<br />
<strong>of</strong> cemea at 28 and 90 dayr. A cement that ytelds the hlghesr compresswe arengh al (he<br />
later age. 90 dayr. Ir obvlourly pefcnblc.<br />
Zrn el nl. (1993) dernbcd tha the cholce <strong>of</strong> nppropnate cementltlour matenills<br />
war governed by consaderat~onr d:<br />
Ill can.<br />
121 av~ilabnhly.<br />
(31 cvtdence <strong>of</strong> rartrfncrary performance.<br />
(4) the cngtneeis confidence in rpec~fylng the mutenal. and<br />
(51 the contrxtor's absllty to produce, handle. and place concrete contalnnng Le pmduct.<br />
In the Unlted Swres and Canada. ACI-363 (19921 reco<strong>mm</strong>endatlonr rqulre n<br />
mtnlmum cement content <strong>of</strong> 360 kg/ml. In order to make hngh-strength concrete: the<br />
mlxrure rhould have r cemenooaur mvtenals content <strong>of</strong> between 360 ta 603 k#m3<br />
However. the use <strong>of</strong> htgh cement content ~n masslvc rtmctures frequently leads la<br />
thermal erxlung. Thermal mbng increases the permeabll8ly and Rduccs the dunbnlity.<br />
Therefore, developnng hxgh-rmngth cement wnth modeate hear <strong>of</strong> hydmt~on 1s<br />
reco<strong>mm</strong>ended ~n order to avoid thlr problem. In the Untted Slates ASTM type I cement
and m Canada CSA type LO cement are the most used type <strong>of</strong> cements to pmduce hngh-<br />
strength COnClelE.<br />
Watersemen1 muo a typtcnlly expressed as the total weight <strong>of</strong> water to the total<br />
wctgh! <strong>of</strong> cement. In addanon. warerscmenrlllous matenvl ratlo ,r expressed as !he rota1<br />
werght <strong>of</strong> wscr to the total combnncd wash1 <strong>of</strong> all ccmentttlous marenalr. In both carer.<br />
:hc total uelgh! <strong>of</strong> uateiexcludes that absorbed by The aggregales. but lncludei my uatlr<br />
intrduich !ntn ?he mlrture as pan <strong>of</strong> an adm#xIure. Some <strong>of</strong> the more finely ground<br />
ponland cements such as ASTM type I11 (h~gh-early-~trcngth) will have hlghcr mnxnng<br />
water requrement for equal workab~bty. pantcularly at law wnlereemenr ratnos. nnd mny<br />
p<strong>mm</strong>oa npvd st!ffcn~ng m hot weather. Unfonunatcly. thm type <strong>of</strong> cement !r not<br />
reco<strong>mm</strong>ended for high-strength concrete<br />
2.12.2. Aggrewta<br />
Aggregates are lhorc pans <strong>of</strong> the concrele that constttule the bulk <strong>of</strong> the Sntshed product<br />
Aggregates constatute the major pan <strong>of</strong> the mlr and compnre 60% lo 80% <strong>of</strong> the volume<br />
<strong>of</strong> the concrete, They have to be so graded that the whole mass <strong>of</strong> concrete scs ;Is I<br />
relntlvely rohd. homogcncou~. dense camb~natlon. wxrh the rmtller rlus acung ar an<br />
filler <strong>of</strong> the votdn.<br />
Usually, the man components <strong>of</strong> aggregates can bs dtvlded ~nto two typr (I)<br />
coarse aggregate: gravel, emshcd rcnc. or blast furnace dag: and (1) Snc aggregate:<br />
nauml or manufacturd sand. The coarse and fine aggregates are de~cnbed bneny m the<br />
followmg drwusnm.
2.1.22.1. C<strong>mm</strong>c Aggregates<br />
The charactenrr#cr <strong>of</strong> the aggregate rngaficandy influence the pmpenler <strong>of</strong> concrete.<br />
lnclud~ng rrrength. The strength <strong>of</strong> aggregates 3s always greater than the strength <strong>of</strong><br />
cement pate. However, for htgh-nrengrh concrrrc pmducnon, the strength <strong>of</strong> the cement<br />
pane Ir hlgh enough to nvnl the rcrength md other vital pmpcntes <strong>of</strong> the aggregate. The<br />
slrength <strong>of</strong>the ugregae. the bond or ldhenlon between cemen! paste 2nd qgreglte. md<br />
the abrarptnon chancrensuc <strong>of</strong> the aggregate all become more imponant for high-<br />
strength concrete than for normal-strength concrete. For thns reason. any one <strong>of</strong> there<br />
propcnles could be n lmlt factor far ultimare nrengh.<br />
There Ir a pnnqcal value ~n determlnlng the oplnmum rlze <strong>of</strong> come aggresJte for<br />
dtfferenr concrete ltrrngth levels. The optlmum nu depends on the followtng factors<br />
(I1 relelve strength <strong>of</strong> the cement paste.<br />
(2) cement-aggregate bond. and<br />
(3) rlrenglh <strong>of</strong> the aggregate pan~cler.<br />
The chemncvl conant <strong>of</strong> the aggregates. that Is the mlnnol present, does lend some<br />
~nrnght snto predicting the mnreract~on bctwen cement paste and aggregate pantcler Stall.<br />
rnvl batches provide the most prxncrl lnformar~on for chaorlng the best aggregae for il<br />
concrete mtxture.<br />
For normal-strength concrete. Walker and Bloem (19M1) explanned that mlrlng<br />
water qulrement IS reduced a coarse aggregate nze Is ~ncreased. The net effect s u<br />
lower watersemcnt rauo and htgher rmngth. Water qulrernent tr a funcrxon <strong>of</strong> the<br />
averall fineness <strong>of</strong> lhc oolid mgredteas.
For high-ruenah mlrlures. rhc use <strong>of</strong> small agpgmer with marlmum nomtnrl<br />
rlze d 190. 12.5. and 9.5 <strong>mm</strong>. usually Ir ~uffie!ent to <strong>of</strong>fset rhe effect <strong>of</strong> Ihc hlgher<br />
mtrmg water demand. Cmquillo (19851 reponcd that the use <strong>of</strong> crushed aggregates tr<br />
reco<strong>mm</strong>ended for the praducrton <strong>of</strong> htgh-strength concrete. rather than mund aggre~ater<br />
Thts was aunbured lo the reduced nggregae-manar lnrerfvce band nrenglh <strong>of</strong> natural<br />
pvel aggreertes<br />
However. the mle <strong>of</strong> aggregates m hngh-arenph concrele Is <strong>mm</strong>or compared wtth<br />
the role <strong>of</strong> cernentit~aur malenals. Manouk. Osmun. and Helmy (19981 reponcd that 11<br />
ha been produced a bgh-strength Ihghtwe#ghr concrete up to 80 MPa a the concrete<br />
laboratory <strong>of</strong> Memonal Unlvennty.<br />
2.I.LZ.L Fine Aggmgates<br />
Saucier. Smllh. md Tynes (1964) ~ndmaed that fine aggregates eontam a much hlghsr<br />
surface area than come aggregates for u gwen we~ghL Because 11 has I much larger<br />
surface area. the fine aggregare isandl can ~nflusnee the amount <strong>of</strong> mlsnng wafer requred<br />
md affect thc pmpemes <strong>of</strong> fresh and hardened paste more than the cornc aggregate. In<br />
sands <strong>of</strong> the wmc gndtng. 1% ~ncresse ~n fine aggregate votdr may tnducs r 5 llm'<br />
~ncwue tn water demand to maaam an equal slump.<br />
Slnce all aggregate m concrete must be coated with paste. the shape and gndnng<br />
<strong>of</strong> fine aggregate as well as Its pmponnan to coarse aggregate will have a direct Impact on<br />
pasts requlrerncnt. More cement paste tr required when more fine aggregate IS used. The<br />
less sand used. however. the harsher mixture and workability maybe senourly ~mpnred.<br />
A balance must be struck !n pmpontonlng h~gh-nmgth mlrtumr In general. using at
least rand conrnrtent wtth necersq workabnltty has gwen the best rfrengrh for a even<br />
pasrc.<br />
The band <strong>of</strong> pwte to line aggregate IS less ngnrlicant lhsn bond lo eorrse<br />
aggregate bccaure <strong>of</strong> the large ruxface area nvalablc I" the fine aggwgare for bond~ng.<br />
Maxlrn~n~ng the come to 6nc aggregate nuo (CAIFAI can result ~n the mon eihctent.<br />
and ~hcrrforc ecooom~cnl. use <strong>of</strong> cemenntlaur mxenals The opurnum nlln nf CW4 wlll probably be apprrea f<strong>mm</strong>tnal batches basedon warkvblltty <strong>of</strong> the msrture.<br />
Rounded and smooth line aggregate pantcles (natural rand1 are better from the<br />
newpomt <strong>of</strong> workab,l~ry than sharp and rough panicles imanufsctured rand). Conerere<br />
mnrlures <strong>of</strong> he same slump and cement factor coaam8ng nau:al sand produce hlgher<br />
rrrengthr than consrctc contmntsg manufactured rand w reponed by Fmy and Pnnmre<br />
119941. The palullcle shlpe and gndlng <strong>of</strong> !here mntennls are probably rerponrlble for the<br />
strength d~fferencer.<br />
Washlng the sand may be necessary. When natural rmdr contslnlng Irrge<br />
qurnttl!cr <strong>of</strong> mlcu. clay, and other delelenour macnalr. Thew harmful macn~lr should<br />
be avo~ded as !hey may tncrcare water demand and affect hydrartan md bond <strong>of</strong> cement<br />
pvrle lo aggregate. Untformrly <strong>of</strong> grading from bach to batch 1s also Imponant for both<br />
the f~ne and come aggregates because <strong>of</strong> Itr effect on workability.<br />
2.1.2.3. Admixtures<br />
Adm~rturer am malcnals other than water, agpgares, and cement that arc used as<br />
~ngredtents <strong>of</strong> concrete. ACI Co<strong>mm</strong>ltlee 212 (1983) ~poncd that he iunctlan <strong>of</strong><br />
admixtun is to modify the pmpnter d concrete to impmve warkahllity, or for
economy. or for other purposes such as Impiovmg conerele strength. These malenrls uc<br />
added lo the batch n<strong>mm</strong>ed~ately before or dunng the mlrtng. There pmpentcr help the<br />
concrete to achlcve high strength and water reductton w~thout loss <strong>of</strong> worhblllr)<br />
Tnal mlxlums rhould be Mde with the ndmlxlure and job matennlr at the same<br />
temperaturer and humidity anrrlpnted on the job Thtr permrrr an evaluatnon <strong>of</strong> the<br />
compvtlb~l~ty <strong>of</strong> an vdm-rture w~th other adm!sturer ad concrete materials. It also server<br />
an evaluarton <strong>of</strong> Ihc ~dmtxlure effects on the propcnrer <strong>of</strong> fresh and hardened concne. A<br />
reco<strong>mm</strong>endatton by the manufacturer or the apttmum amount &lerm#ncd by lnborvrory<br />
lnnl batches should be used. The major type <strong>of</strong> adm~xturer can be ru<strong>mm</strong>anzed ar mlncral<br />
dm~xlurer and chemlcal adm~xturer. whleh wall be described bnefly an the followmg<br />
dtrcurslon<br />
2.1.23.1. Mineral Admixtures<br />
The most lmponant mnnml admnxturer lo the pmduetlon <strong>of</strong> hlgh-rtrengh concrete are<br />
pouolmr The two porzolans most co<strong>mm</strong>only used m h~gh-nrength concrete are fly ash<br />
and rlltca fume. However. espei-#ally I" Canada. gmund grunulared blast-furnace slag has<br />
been used more recently instead <strong>of</strong> ~rllc~ fume. Ground slag far use ~n concrrtc should<br />
confan lo reeuon C989 <strong>of</strong> the ASTM (1997). rpecllicat!on for ground granulaled blrsl-<br />
furnace slag for uw m concrete and mortar.<br />
Fly ash 1s produced as n by-product <strong>of</strong> the comburuon <strong>of</strong> pulverized coal ~n<br />
electnc power generating plant. Th~s marenal 8s used to amend msuffie~ene~es in a<br />
concrete mix by providing mjrsrng fines from the fine aggrrgntc. Usrng fly ash type F to<br />
the mlr can impmvc qual~ties <strong>of</strong> concrete such as reducing permeability, expansan. and
the cost <strong>of</strong> concrete-mahng matennls. Unfonunaely. the pmpntes af fly ash can vary<br />
greatly becau~e <strong>of</strong> the wtde range <strong>of</strong> comporctton <strong>of</strong> coals. Conrndenng the acceptance<br />
and un~fomty, rcsrr should made aceardzng to recrlon C618 <strong>of</strong> the ASTM 0997).<br />
rpeenfiealan for fly ash and nw or calr~ned naural puolsn for us rr a mtnenl<br />
ndmtrture I" panland cement concrete.<br />
S,lrd fume IS a new porrolan~c malenvl (ha! has received constderahle allenllon<br />
~n both research and applleatlon. This malenrl a a byproduct rerult~ng from hngh-punly<br />
qwar wcth coal 10 the clcctnc arc furnace tn the production <strong>of</strong> snliean md ferrorcl%con<br />
dlloys Unltke fly ash. rillca fume IS extremely fine. Mon <strong>of</strong> panleler are less than Ipm.<br />
and the average panicle d<strong>mm</strong>eter 1% about 0 I pm ~8th surface area <strong>of</strong> nbour Z0.W<br />
m'ikg. For comparison. fly ash surface ma typncally ranges from 300 to 5W m'lkg.<br />
ground slrp f<strong>mm</strong> about 400 to 600 m'lkg, and lype I cement f<strong>mm</strong> 300 to 4CnI m'lkg<br />
Attcln and Neville (1993) repned that the addman <strong>of</strong> slltca fume to the mlx<br />
Increaser the coheaveness. viseonty. and water demand <strong>of</strong> fresh concrete. In hardened<br />
concrete. the addillon <strong>of</strong> rtllca fume cm produce slgnlficsnt Increase ~n rtrenpL. modulus<br />
<strong>of</strong> elrn~mly. md flexural ntrengrh. The use <strong>of</strong> rnltca fume rhould canbrm ro wcllan<br />
C1240 <strong>of</strong> the ASTM (1997). rpeclfieauon for sflicr fume for use ~n hydnullc-cement<br />
concrete and monar.<br />
2.1.23.2. Chemical Admir<strong>mm</strong><br />
The benefits to be reallzed f<strong>mm</strong> uw <strong>of</strong> admlxturu m htgh-strength concrete have<br />
plaeucally mandated tktr use. Thcx ndm>rrures increaw the workab~lity and enable<br />
reducing the cement content in propnlon lo the reduetion in water content. A co<strong>mm</strong>on
pracuce a to use s water-ieducmg admixture (ruperplantctzer) m comb~nal#an wtth a<br />
water-reducing retarder.<br />
The type <strong>of</strong> rulphonsed naphthalene formaldehyde ruperplwl!clur nonrlly<br />
used reducer the amount <strong>of</strong> water requnred by 154%. However. usmg thns<br />
ruprplmle~zer aften results !n hxgh rate <strong>of</strong> slump loss. malung ~r difficult lo place the<br />
concrete properly The hlgh nle <strong>of</strong> $lump Imt will he overcome hy the add~laon <strong>of</strong> the<br />
water-reduc8ngretardcr whch exlends the lnme <strong>of</strong> set and -81s the placement af a very<br />
low waterxemenf ratlo concrete.<br />
The compar~b~ltty <strong>of</strong> the vdmlnture~ wlrh the chorce <strong>of</strong> ccrnea 8s u very lmponanl<br />
cans~deratton lo order to reduce any underlrahle effeas 8n concrete. all chemtcal<br />
admlxlures rhould meet the requlrcmsntr <strong>of</strong> $maon C494 <strong>of</strong> the ASTM 0997).<br />
rpecrficanonr for chemtcal adm~xtures for concrele. The use <strong>of</strong> retarder rhould be<br />
confomcd la ~ccuon C494 lyp B and D <strong>of</strong> the ASTM (1997). whllc the use <strong>of</strong><br />
ruperpl=stlc!ur should be conformed lo recnon C494 typ F <strong>of</strong> !he ASTM i 1997).<br />
2.15. Batehing and Mixing Squcnra<br />
The vncarpoalton <strong>of</strong> rllica fume and hrgh-nnge water ~duesn makes It porstble to artan<br />
htgh-nrengtk concrete at early ages. The followang batchlng and mixmg procedure has<br />
heen developed by carlia rerearchen an the concrete Isbomoq <strong>of</strong> the Memonal<br />
Untvcnlry <strong>of</strong> <strong>Newfoundland</strong> far Ihe product~on <strong>of</strong> workable high-strength mar.<br />
(I) Charge 1W% <strong>of</strong> coarse aggregates.<br />
(2) Batch 103% <strong>of</strong> cement.<br />
(3) Balch lW%<strong>of</strong> fly ash.
(41 Barch 100% <strong>of</strong> rand.<br />
15) Mlx for 3-5 minuter afkr uddnng 50% the erum~led water wllh water reduclng rsea.<br />
(61 Prepm a slurry <strong>of</strong> rlltca fume. togelher wtlh 25% <strong>of</strong> gross ruperplarr~c~zcr dare and<br />
20% <strong>of</strong> water.<br />
(71 Mlx for 5 mlnuler.<br />
18) Add 30% <strong>of</strong> mlx!ns water roeerher with utr entnanmnc admtxlure5.<br />
(9) Retemper with the m t <strong>of</strong> ruperplasoenerdore to target slump<br />
Flowtng concrete was pncnlly achleved unng those mlrturer ~ncludlng<br />
rupcrplart!clur and retarder The a!r content ~n the majonly <strong>of</strong> [he mlxrurer Ires v~thln<br />
3% lo 5%. Slump values were lmrely at the 100-<strong>mm</strong> target. while an average value <strong>of</strong><br />
the unll welghl<strong>of</strong> fxsh concrete was 240 kglm'.<br />
2.2. Punching Shear Strength<br />
Renpc!wc ruggrted approaches can be represented u ellher the result <strong>of</strong> an empmncal<br />
study or a ntnonal srudy to e~labllrh r relartanshnp between Ihc load and stress at i~~lurc<br />
<strong>of</strong> concrete plates The emplncsl study used I rlal~tlcsi arnslyas <strong>of</strong> the svallilble lest<br />
results. whsle Le noonal audy descnbcd and ldcvllred rn~thematlcnlly the mechrnnrm <strong>of</strong><br />
failure.<br />
In the cue <strong>of</strong> emp~rieal studies. Forsell and Halcmberg (1946) described that the<br />
cnllcal sectton loeated at a dlstvnce ILQ f<strong>mm</strong> the lded area. Lt has also been reponed<br />
that [he shear stress d~rmbuson over the slab thickness rr assumed parabolrc.
where r 2s the ull#mate shear stress. V Ir the ulumate rhear force. c Is the ride dtmcnrson<br />
<strong>of</strong> arqum column. and h Is the effectwe dcpth <strong>of</strong> the slab.<br />
Mae (1961) conduced an crpenmcntvl mvea#g.atlon to analysts <strong>of</strong> shear rrrcngth<br />
where rhear and flexure were con~ldered as r comblncd laddtng problem Mae rraxcd that<br />
the cnucal scct!on <strong>of</strong> a slab subjected to a coneenwaled load was located at the column<br />
pcnmerer md rhrt the shear urengrh tr to some extent dc~ndcnt upon the flexural<br />
strength Bared on $he expenmental program. a "em,-emptncal type <strong>of</strong> equauon wa<br />
developed to calculate the ult,matc shear rtrenph.<br />
where. u. = ulumnte rhcar nren<br />
V. = ulttmate shear force<br />
V,i.<br />
= ultlmee load for flexunl fatlure<br />
h = rlde dlmenrlon <strong>of</strong> rqum loaded area<br />
r =periphery amund the column excludtng opnlngr<br />
d = sffcctlvs depth <strong>of</strong> the slab<br />
= compresswe strength <strong>of</strong> concrele<br />
It was suggested that Equatxan (2.2) war the be* equalon lo date for predlctlon d<br />
the failure load ~n the repon <strong>of</strong> ACI-ASCE co<strong>mm</strong>ittee 316 (1962) The Co<strong>mm</strong>~ltec<br />
reco<strong>mm</strong>ended that the followmg dertgn equauon for calculating ulumale rhem load.
where b lake us the penmeter at a d!rtance <strong>of</strong> dl2 from the periphery <strong>of</strong> loaded area. and<br />
v 5 4 .06. f; IS the concrete comprerrlve strength. and d tr the effectwe depth <strong>of</strong> the<br />
slab.<br />
The shear derlgn methods <strong>of</strong> ACI-318 Bu!ldlng Code (1995) and CSA A23 3-94<br />
(1994) ore based on the developed I" the most pan an the work Moe 11961). The wto <strong>of</strong><br />
the ulr<strong>mm</strong>ste rhcanngeapaelly <strong>of</strong> the slab to the ulumale flexurrl capac~ry <strong>of</strong> the rhb IS<br />
defined as Q, = x. the followtng cmpnneal expresrlon w;lr developed f<strong>mm</strong><br />
Vn,,<br />
Equauan 12.2) forthe predfctnan <strong>of</strong> the ult~mace shear stress:<br />
v, = [(1(1 - 0.075 Q) - 5 250, ) 12.41<br />
The devclopmenl <strong>of</strong> destgn appmachcs <strong>of</strong> !he Bnurh Codes. BS 81 10 (19851. and<br />
Is based pnmanly on the work <strong>of</strong> Regan (1981). An cqurtnon WAS developed Lo calculsre<br />
punchtng rherr crprc!ly as:<br />
V,, = K. K,.=@.69d)~C + 7.851) 12.51<br />
where. V, = ult?mrte rhenr force<br />
K,<br />
K ,<br />
= 0.13 for normal concrete andO.105 for Ihghrwe~ghl concrete<br />
= 1 .I5 I4 n leolumn area) 1 (column penmeter)' I"'<br />
IWA. = steel ratlo<br />
bd<br />
f,.<br />
= cube strength <strong>of</strong> concrete<br />
d = effectwe depth <strong>of</strong> the slab
ZC = penmeter<strong>of</strong> the column<br />
The rhear penmeter for a rcczangle column a located at distance 1 25 d out from rhe<br />
column. for a ctxular column tr located ! 25 d out from the column.<br />
Manouk and Hursan (1991) tnvert~gaed the rtruelurxl behavnor <strong>of</strong> narmrl-<br />
strength and hlgh-nrength concrete slabs wnrh respect la punching reraaance The result<br />
,huwed that h~gh-strength cuncrra erh~btcs r more bnrtie fanlure than normal-nrengrn<br />
concrete The rerearchen have also lndicvted that the Mae's Equnuon (2.41 cmnot he<br />
mo<strong>mm</strong>ended to predict the punchtng shew capilctty <strong>of</strong> hsgh-strength concrete sldhs The<br />
punchlng renrtance 13 proponlonal ro rhc cuhlc mot <strong>of</strong> concrelc camprerrlve strength<br />
Therefore. the assumpeon <strong>of</strong> the Bnr~rh coder e better than the use <strong>of</strong> rqusre mat <strong>of</strong> the<br />
concrele strength as even an the present Nonh Amencan coder such as ACI-318 (1995)<br />
md CSA A33.3-94 (1994).<br />
Gardner and Shva (19961 eonnned the use <strong>of</strong> cuble mat <strong>of</strong> compresswe strength<br />
uslng rhetr expenmental resulls regarding the punehlng rhear <strong>of</strong> a two-way flat relnfarced<br />
concrele slab. An emplncal method urmg u shear penmeter amund rhe lodded area war<br />
prerenrcd. The cmpnncal reco<strong>mm</strong>ended equatlan was expressed as follows:<br />
where. v. = ult!mate shear rtreor<br />
v, = no<strong>mm</strong>al rhear stress<br />
V. = ulumate rhexfome<br />
tr = penmelcr <strong>of</strong> loaded m a<br />
d = effectwe depth <strong>of</strong> the slab
p<br />
s flexural steel mnforcement rauo. calculated over w~dth c + 6d<br />
f, = yield strength olnexuralrreel<br />
f,, = mean concrete strength<br />
2.3. Impact Performance <strong>of</strong> Concrete Plates<br />
2.3.1. Overview <strong>of</strong> Material Modeling<br />
CEB (19881 repon No. 187. reco<strong>mm</strong>ended hat generally the mechanmcdl behrvlor olthe<br />
concrete malenal s deocnbed by n stress-stram relat!onshlp.<br />
taklnz stram rate tnto account lends ro-<br />
where the rtnm rnte a defined ar:<br />
;md ~texprerser the vaneuon <strong>of</strong> stram wtth nme.<br />
0 = fk) (2.71<br />
b = f(s.f) (2.81<br />
dr<br />
E = - (2 9)<br />
d,<br />
More mesly. several Invesugmronr hrvc revealed that ills (he landing hnrtory should<br />
be tnken lnto account.<br />
b = f (E.Z. fwd bisrop) (2.101<br />
It a obvlaur that material modclr covrnng the relation in Equalton (2.10) are much more<br />
complteaed thvn those for Equalton (Z.7) In this wnx, a bmad vanetter <strong>of</strong> dtlferent<br />
malenal models erlrt which may be grouped nnro the man categoncs <strong>of</strong> clartlcay theory.<br />
plarueity. viwoplarucity, ctc.
The different theones appllcabls lo the modeling <strong>of</strong> eoncrele and steel<br />
re#nfomcmcnr will be dlrcussed bnctly accoidsng to CEB (1988) repon No. 187 rr<br />
follawr.<br />
(I1 Llnearund non-lmear elvstlc models<br />
Llnenr clasttc models m best known due to rhelr nmpltc~ly. buc rr Impact load~ng in<br />
gcneinl cause non-llncwdcfonnation s is not sumd for any aypllcatnon in thtr field<br />
The same may be rtaed for non-Itnear elasl#c models.<br />
(21 Vlvoclvrtlc modelr<br />
Modelr bed on vrruelartlc~ty hrve becn ured for the dercnpllan <strong>of</strong> creep md<br />
relaxallon phenomena. A few authors have used thlr lheory w~th the ~dev thnr<br />
stm~lvlty between creep md rrraln-rate-effects should erst.<br />
(31 Vtscoplwuc models<br />
Modelr brrcd on !he theory <strong>of</strong> v~scoplartic~ry have been ured for many years dlro for<br />
the dercnptlon <strong>of</strong> tmpw problem. The theory <strong>of</strong> v~scaplvsl~e~ty 13 very conventen1<br />
erpeclally for lhc madclmng <strong>of</strong> the remforc~ng steel. md may be r~mplrfied to a varl<br />
extent at lea1 for the one-dtmennonal caw.<br />
(41 MDdCls based on planuaty<br />
Madelr k d on the theory <strong>of</strong> plart~ctly can be arnnged nnlo twocareganes such nr'<br />
(a1 Elaruc-perfectly plarrre matenal behavtor<br />
The material shows elartle behavtor up to a ccnan level, for example<br />
comprerrlve strength where stran IS mcresed at constant stress. The tnfluence <strong>of</strong><br />
stress rate can be taken into account by tnereastng the yteld level aecordnng to this<br />
SIRIS mte
fb) Elastlc plastic behavior wath hwdcn~ng<br />
lnltead <strong>of</strong> under~osng unllmlred deformatlan at ;r conslant rrress level. rhe rrrerser<br />
lncrearc with lncrearlng stram Rate effects upon the yzcld surface are ~ntmduced.<br />
for cramplc tn the form <strong>of</strong> rate hardenmg paramcrcrr.<br />
(5) Endachmntc models<br />
Modclr hared on cndachmn~c theory havr been devclopd for concrete and<br />
re~nforctng steel. Onginally Ihe cndochronlc theory was bared on the vnscoplnruc<br />
Leoq. supplemenled by a new lntemal vanable. the lnlnnrlc tlme. Although the<br />
endoehmn~c theory war the subject <strong>of</strong> cantroverrul dnrcurnonr, a Eecms that some<br />
phenomena. likc the influence <strong>of</strong> the loadnng hlrtory upon the stress-stram<br />
relalonrhjp and the rmtn-rule depndancy. are very well represcntd. For relntorcing<br />
rtel this model a adequate. but for concrete. the problem <strong>of</strong> dnlntancy a1 high nrun<br />
IS not salved yet.<br />
(6) Fneture mcchiln~cs models<br />
Fmcare mechanics has to be ruM#v~ded tnto r lhnear and r nan-Itnear lhwry The<br />
Itnear theory provlder a pod barns to predlet unstable or eatanmph~c propagatton.<br />
Relauonr exla between frrctunng stress. crack length, md ~ lra~n ras. Lanew fmclure<br />
mechanics doer not take any planlc dcformalon or mrm-cracklng ~n the regIan <strong>of</strong><br />
the cmck ep ~nro account. However. as concrete and ductile steel are concerned. thls<br />
mu* be lncludcd because <strong>of</strong> the fact that the energy consumed m the plart~c or mtero-<br />
cracked p mes zone IS more relevam than the elasttc pan.
(71 Damage meehanncr models<br />
Models based on damaxe theory are relrtzvelv recent. erpec~ally on concrete The<br />
method 8s based on the ldsa (ha damage occurs u an ~mvcn~ble dcgmdelon uf thc<br />
mnlenal under deformanon. A damage pameter as rnuoduccd as ;l scalar or vcctonsl<br />
funcr~on <strong>of</strong> thus degndatlon process. The degadauon pmesr IS a contlnuaur and<br />
:lobs1 pracenr and doer not constdcr only degmdatrcn wlthln n dehult l~kr the<br />
fmaurc mechanics concept<br />
(81 Staehastlc models<br />
The frdcture pmcrs withon the malnr <strong>of</strong> concrete IS formulated urmg rrochast!~<br />
farmul~ulon Concrete 8s modelled u a group <strong>of</strong> cauplsd elements wllh two or three<br />
different phases. A lopnthm~c relalan between rhe reststance <strong>of</strong> concrete and rtrerr<br />
or rtraln nle can be formulated.<br />
23.2. Strain Rate For Various T yp alLoading<br />
In men1 years. mspccmble atlentlon has been glven to the influence <strong>of</strong> rtmln rate or<br />
stress nte an the msshvn~cal pmpnlcr <strong>of</strong> concrete. relnforclng $reel. and pre-nrernng<br />
steel. Steel and concrctc wdl be tw~tcd 8" two rubwquent recuonr. The prerentsrlon or<br />
the data will be such [ha a deslgn engtneer ern use such panmeters m sample hand<br />
cnlculrnons and m n llmttcd manner also 8" advanced computer codcs. The propcnlcs<br />
will be gwen ~n graphs and or m fununnlonal farm with rerpea to stnm or stress nte.<br />
Table 2.1 gwes some global est~mares <strong>of</strong> rrraln nter whlch acur dunng vanaur<br />
types <strong>of</strong> loalng. As reponed ~n CEB (1988) repon No. 187, lhev values are not expen<br />
entlmater and have lo be deler<strong>mm</strong>ned more exactly for rplfic structures and load~ng
configunoanr On the other hmd. 11 wnll be Shawn that most relattons between nrcnglh<br />
and strain rare. or ulomrle rm!n and r<strong>mm</strong> rate. are Ihneavloganthmr or double<br />
loganthm~e whlch means tha crrct accuncy IS nor necessary Wtth regard to the second<br />
remarl. there or no mcchrn~crl pmpeny whtch decreases as value at h~gher ream rates<br />
Table 1 I Typlevl strun rarea for vanour type3 <strong>of</strong> Ioadln:<br />
Traffic<br />
23.3. Properties <strong>of</strong> Concrete under Dynamic Loading<br />
A procsedlng <strong>of</strong> the mlemniond rympaslum released I" Germany, BAM (1982).<br />
reported that the most <strong>of</strong> the dynnmtc loadtng research were confined to plam concrete<br />
wtth normal-weight natunl aggregates. The mechnnlcnl pmpenncs whlch were<br />
~nvestigated include the campresswe and tenstie rrrenglh. ulumate rtnln at comprersive<br />
and tenrrle strength. Young's madulus. blaxlal strmgth, rod fracture energy ar tenrtle
loild#n$ Some <strong>of</strong> there pmpenles are well e~rabltrhcd rr a funel!an <strong>of</strong> rrrenr or Erram<br />
vale, deflned as stress or rrwn lmreare tn nme. others are much less ~nvenlgeed.<br />
Unlortunatcly, nor all <strong>of</strong> research papcrr an thtr rubjh-I conrsn the lnformal~on<br />
requ~red to relate hzgh stress rate tests to standard rtatlc lest Thlr ~nfonnauan Is very<br />
important lopwe enough detatlr m order lolud%e the vnl~dlty <strong>of</strong> the results and the rang<br />
<strong>of</strong> apphcattan. However. an altcmpt was made lo crvmlne the rcponcd tesull 10 dcnvr<br />
mOR relatlonr.<br />
Since most mvcnlgauons n htgh rsaln rater were tntended to determfnr the<br />
strength <strong>of</strong> rnaenal. data on ultlmae nrarn are nlher Ihmtted. Furthermore. data are<br />
romet!mr not complete ~n the wnss that starlc refsrenccs are not pwen Thrr maker<br />
compilnron depndenl on assumptions lhat me bared on general knowleds. Although<br />
there relnlonr. for rlrann, we weaker than the strength relat~ons they may rl~ll be useful.<br />
233.1. Campmsivr Strength<br />
A bullcl~n synthenr repan on concrete structure under tmprct and #mpul~lve lardnng war<br />
publlrhed by Camlte Eum-lnlematlonal du Betan. CEB (19881. steed that the sraI.llc<br />
lerung rate war taken ar a, = I MPulr. Srrerr nte 8s convened !"to rtrm rats by<br />
arsumlng elastnc maenal behawor wtth a modulur <strong>of</strong> elarllctty <strong>of</strong> E, = 330M) MPa<br />
The strength rela~onnhxp staned a1 unlty for *talc lerung and reached a value <strong>of</strong> about 2<br />
far law grade concrete. and about 1.4 for hlgh gnde concrete. when lovded more rapndly<br />
at a rate <strong>of</strong> a, = 10~MPalr. Beyond this ares nces rhe increase higher reachlnq values<br />
<strong>of</strong> four and greater. 11 should be noted. however. that thrs steep tnneare has been<br />
delermlned theoretically and lhat expenmental evidence a only atta~nabls for natunl
ocks. Mnlvem. et nl. (1985) reponed lhar recent expnmental results for concrete have<br />
not fully confirmed lhls prsdlcrlon<br />
A<strong>mm</strong>aon and Nusrbvumsr (1995) dcsenbed that the compressrve nrcnglh <strong>of</strong><br />
concrete can be wntlen m lcrmr <strong>of</strong> stram mle as<br />
where. E = %ran raa<br />
6, = rrraan rate at qunrl stauc condtuon<br />
f, = rtatlc cube rtrenah <strong>of</strong> concrete<br />
Thlr relalonrhnp reveals that the lnfluenee <strong>of</strong> loadmg raw decreases as the grade <strong>of</strong><br />
concrete tncreasss. If ,he influence <strong>of</strong> the load~ng ma on !he modulus were no,<br />
considered, the power <strong>of</strong> the equauan above would be I0 o where a IS the dynnmlc<br />
mrrenal pmpny as defined m Eqvatron (2.1 11.<br />
253.2. Modulus <strong>of</strong> ElasliEity<br />
The modulus <strong>of</strong> elasrrc8ty IYoung'r modulus1 <strong>of</strong> the concrete tn eomprerslon lncresrer<br />
wnth stress and srran me. The relatlon between rrauc and dynamlc (Impact) modulus <strong>of</strong><br />
slvrl~c~ry Ir given by A<strong>mm</strong>nnn and Nusrbaumer r 19951 ~n the follawlng equason.<br />
0.025<br />
with E. = 30.10-~ r-I<br />
-- :I - (
where. a = stress rare or vanallon <strong>of</strong> EtrCPr with tmc. 01<br />
a,,= stress rate a qua$, swtlc condltnan.<br />
2.3.3.3. Ultimate Strain<br />
The ulumnle %ram ID compresston tr the raam tha occurs dl mnxlrnurn nresr. The<br />
ulttmate rrrdln sr a funcllon <strong>of</strong> stram rate gwen by A<strong>mm</strong>ann mdNussbuumer (19951 tr.<br />
233.4. Compmsive Fmelure Energy<br />
The fracare energy 3s usually defined as the area unk the complete stress-nratn curve<br />
mult~pl!ed by the appmpnale volume element. Whereas numemun rerulls were avaclable<br />
far struc loudrng. there was no complete nms-st<strong>mm</strong> curve nvalable for high stram rater<br />
<strong>of</strong> compresston loadlng. However, f<strong>mm</strong> the occumncc <strong>of</strong> htgher strength and ulumate<br />
stram tagetha with evldencc <strong>of</strong> enhanced cracking, 11 may be concluded tho1 the fracture<br />
energy tnneascs with tnneaslng smsr rate and rtm~n rae.
23.3.5. Te~ile Loading<br />
A<strong>mm</strong>mn and Nursbaumer (1995) have also descnkd the propenler <strong>of</strong> i'oncres under<br />
lens~le lordtng In conuart to compressive failure. rcnrllc fxslure Is always n dlscrclc<br />
phenomenon. Usually one cnck occurs which dlvldes a rpcrmcn lnto two pans. These<br />
two pans would unload ar the enck width mcwrrer. Energy consumption occurs ~n the<br />
cnck$n$ zone The wluuonrh~pr ktwecn a mechsn$crl pmpeny and the slresr or rtriltn<br />
rate are snmxlar to chore obnmcd. The fomulat~on or also r~mslar to compresswe nrengch<br />
except for the value <strong>of</strong> the cocffiacnt.<br />
Tilklng account vgan <strong>of</strong> the lnfluencc <strong>of</strong> aram ntc on modulus <strong>of</strong> elnrttclty. n<br />
relrtton can be defined ktwcsn rtnm rate and renrlls strength 8n (he fallow~ng.<br />
where f, a rwt!ecuk strength <strong>of</strong>concrete.<br />
Tenrde nrength $3 more rsnrlttve lo rtnm or nrerr nle !f the concrete ha n low<br />
gnde and Lr more wnnttve lo rtnln mte than eomprerrlve arensh. UEually compresrlve<br />
strength Is the reference value for the concrete gnde and Ir therefore known. The tensile<br />
rt~ngh can be ertlmeed f<strong>mm</strong>:<br />
f, = 0.?0(f;)"~ MPa (1.17)<br />
There values <strong>of</strong> concrete strength have also ken reco<strong>mm</strong>cndcd by CEB-RP (1990).<br />
2.336. Tension Modulus <strong>of</strong> Elasticity<br />
The influence <strong>of</strong> svess rate on madulus <strong>of</strong> elastxcity far lension Ir smaller than for<br />
comprur!on. The formvlat~on prcsmted by A<strong>mm</strong>mn and Nurlaumer (1995) such ar:
arc irltd for all iricii and sr<strong>mm</strong> mlcs. andall caneiclc gndc.<br />
The definlrran <strong>of</strong> rtrvsn m a tcnrnle experiment only mrbr Eenrc up to the<br />
moment where a dlrmre aack rtanr la open. t e.. unnl the maximum rtrerr cr re~ched.<br />
Beyond ,has poln~ the cracks open and !he rrmnlnsng undamaged pan <strong>of</strong> the concrele<br />
unloads. Ult~m~lc rtnln tr ,us !he smtn ar marlmum srresr Few expenmeno are<br />
ava#lahle whnch allow anc ro eslabl~rh a relatoon between EltXln and the stress or nrxn<br />
rate Thnr relatton 8s also oven by A<strong>mm</strong>an" md Nursbnumcr (1995) such u:<br />
Thcrc relaeanshnpr are valid for all stress rates. rrnln rarer. and concrete grade<br />
2.3.3.7. Tenslle QrPrtvm Energy<br />
The fraclm energy is defined as are0 under the nrerr-crack opening curve multsplled by<br />
rhc cmsr-sectanal area <strong>of</strong> !he rFsnmsn. The parlsmcked behavior war treated ~8th a<br />
bnltle fracture concept pmpod by Hillerborg (1985). The value can be calculated f<strong>mm</strong>
mregnnng the complete tensfle stress.cnck openxng d~rplacement or crack wtdth such us<br />
follow:<br />
G, = 1;. f, dw<br />
where. Gf = fracturemergy requored to form an unit area<strong>of</strong> crack surface<br />
1, = ten~lle nress. rr r Rnctton <strong>of</strong> r,<br />
b,. = crack wtdth<br />
u, = enck width when f, wilehcs zem.<br />
(2.12)<br />
More co<strong>mm</strong>on an the descnptton <strong>of</strong> englnccnng maanal. the cxpmrion for GI<br />
cun be arnnged and expressed a% ;l funaton <strong>of</strong> a stress-$tram Inw. Thus. Wf Is defaned ar<br />
the fracture energy dennty. or work per unit volume. d~ssopated by cnck~ng. cdn be<br />
expressed rr<br />
where. f, = rcnsllc rrressexprerred on lcrms <strong>of</strong> tcnrlle slnln<br />
~r, = wtdlh <strong>of</strong> the fracture praccrs zone<br />
E, = tenslb stram<br />
(2 23)<br />
emax= martmum tensnle st<strong>mm</strong> when f,reaeher zero at the end <strong>of</strong> the tenslo"<br />
r<strong>of</strong>tenlng bnnch.<br />
As repaned by Marrouk and Chen (IW5). the fracture energy <strong>of</strong> high-nrength<br />
concrete 13 sbout five ttmcr he area under ascendtng ponton <strong>of</strong> its complete stress-rtnnn<br />
curve. Fraaum energy 8s ertmawd about tm times the ;ma under ascending ponion <strong>of</strong> 11%<br />
complete rtress-stmn curve for normal-mgth concrete as repomd by Mass~coue. Elwl.
and Mdregor (1990). Thls lndlcares rhar rhc hlgh-strength concrere a more bntlle tn<br />
lenr~on than normal-strength concrete.<br />
CEB (1988) stated that thc relsllon between fnclure energy under rtalc and<br />
dynamic Impact) londlng rr expressed by the following equarlon:<br />
where, x =the cnck opnlng velmtry<br />
I
lensen. Holwrh. m d Hansen (19931 concluded Iha the ersenual element ~n Lc<br />
lint method IS the duclillry m d the punchtnp rhsvr capacity <strong>of</strong> high-rrrengrh cancres<br />
under Impact and ~mpulr~ve laadln~ The val~dlly <strong>of</strong> the two other methods are lhmttcd to<br />
ccnaln mtrnle velmt>er and concrete lfles. therefore L e methods have lo be vcnfied<br />
An expnmenL.1 Invenlplton on !he cnpactly <strong>of</strong> nnfoned high-niength concrete dabs<br />
under ~mpact load~n~ 19 reco<strong>mm</strong>ended The results may prnv~de venficnttnn ol rnalyr~crl<br />
methods as well rsderngn reca<strong>mm</strong>endal~onr.<br />
Banthlz. Minderr. and Tmttter 11996) conducled an expnmoltal Impact<br />
reststance <strong>of</strong> steel fiber reznfarced conciete urtng u simple lnarumcnl Impzlct m;ach~ne<br />
dealgnsd ro rest concrete m un~arial tenson. B has been reponed that fiber re~nforcement<br />
Ir renr#ttve mrtcnal to stress nte and Is effecllvc 8" lmpmvnng fracture energy absorption<br />
under Impact. Whnle. Banthla. Yun. nnd Sakrl (1998) studled [he lmpael rertrtvnce <strong>of</strong><br />
concrete plnles relnforeed wtth n fiber relnbrced plrrt~c gnd. The plates reanforced wlrh<br />
fiber relnforccd plarltc were found to fail ln a bnlile manner and absorb only a th~d <strong>of</strong><br />
the energy abrarbcd by those remfarccd wtth a trrd#!tonal steel pd. It hrr also been<br />
repaned that the most lmpmvemcntr ~n ihe lmpacl performance occur with (he use <strong>of</strong><br />
fiber reinforced concrete. lmpmvemenlr occur tn bolh the ullrmrte laud camytng cnpauty<br />
and the energy abrorptnon eapnbtltly<br />
B~rr el al. (1982) studled Ihc rpphcrb!hty <strong>of</strong> repltcn scalmg ra the dynnmtc<br />
behav~or <strong>of</strong> rexnforccd concrete slabs ~mpacted by ngld m~rnles. Erpenmental results<br />
were presented for models wllh rehtlve linear scaler <strong>of</strong> 1. 0.37. and 0.12. It has hem<br />
found [hat the rear faces <strong>of</strong> all 3 wales <strong>of</strong> target showed very rlmilar damage and<br />
cracking. A sllght tendency <strong>of</strong> more rear face damage and more concrete nnppmg
occumd tn the bigger target care than ~n the smaller turgrr. The pnenl shapes <strong>of</strong><br />
perforation crates were also stmtlvr on ail 3 r~rcr <strong>of</strong> targel. h har ken concluded that the<br />
use <strong>of</strong> wale models. over the Elre range terted. to prow& dar~ an the perforallon<br />
performance <strong>of</strong> retnforced concrete are jun#ficd.<br />
2.3.42. Eumpan Dsign Codes for Punching Shear Capscity and Critical<br />
Perforation Velocity<br />
The rtatlc punchtng shsarcapactty as rpeclfied ~n the Norwcgvan Code Ir expressed as<br />
follows<br />
where. f,,, = derngo lenrllc strength ot concrete<br />
y, = matenal coefficncnt for retnforced<br />
k,, = IW ~l<strong>mm</strong>'<br />
1.0 < k,.(= l.Sdldl)c 1.4 . dl = I0 m<br />
d = mean slab deph tn the two reinforcement dlrectlonr<br />
a = lmgrh <strong>of</strong> penmeter <strong>of</strong> the gavcmlng xellan at a dnnance 1.0 d<br />
f<strong>mm</strong> the l&d area<br />
p = geametneal mean <strong>of</strong> the onhogonal tenrlon remforrcmenl noa.<br />
(2.25)<br />
Thc upper value <strong>of</strong> the deslgo punching ~hevcapx~ty is ismlted by comprerslve fanlure.<br />
However. thls llmltatlon a not rrlevnnt m the case di~used here.<br />
The enucal vcloclly <strong>of</strong> perforat~on for the dynvm~e loading <strong>of</strong> a two-way plate ar<br />
reco<strong>mm</strong>ended by Ca<strong>mm</strong>tnee Euro-lntcmauonal du Beton. CEB (1988) will be cxa<strong>mm</strong>ed.
The cnrlcrl vcloc8ly <strong>of</strong> pcrfaivl~on can beexpressed s'<br />
where. W = concrete denr~ty<br />
In = cylmdcr comprerrrve strength<br />
p = mtsstlc penmcler<br />
Ir = concrete rlabthmcknsar<br />
M = m!rr~le mars<br />
p = rclnfomementqurntlty.<br />
Bm. el al. (1982) ~ndcrad that the cnck pattern m Ihe eoncrele vilrget. ar well as<br />
the trmnmr dtsplacement measurements. ~nd~carer Iha bending and shew bllure<br />
mechrnlrm were anvalved ~n concrete bch;lvlor. The rexarcherr provided funher<br />
pruf~catlon for the ruggeruon that Equauon (2.26) rhacld be rnodtfied An altemiltc<br />
bendins nnforcemenl qurnllly dependent war included ~n the follownng.<br />
where d a d<strong>mm</strong>cter <strong>of</strong> dmpped obleel. h 1s concrete slab thickness. and m Is mass <strong>of</strong><br />
cylindrical dropped oblecl.
Chapter 3<br />
EXPERIMENTAL INVESTIGATION<br />
3.1. Introduction<br />
As r result <strong>of</strong> vvcnl advancer ~n the <strong>mm</strong>ufacanng <strong>of</strong> chem!cal sdd~nves nnd mrtcnal<br />
releel~on. $1 has been porrxhle to pmduce hlgh-strength concrete <strong>of</strong> 80 MPa and hqher<br />
Thc man oh~ecsve <strong>of</strong> thlr expenmental work. u discussed tn the prerev!our chapter. 8s to<br />
Inverngrs she structunl behavior <strong>of</strong> hlgh-rlrenzth concrete two-way plater ruhjccted to<br />
tmpacl loddlng.<br />
The prpsnmental program cons~sted <strong>of</strong> terllng and evnlus#on <strong>of</strong> the swcrunl<br />
performance <strong>of</strong> sixteen plates. The dctrtlr <strong>of</strong> lest rpcclmsnr md laboratory aerup<br />
arrungemencr are dercnbed !n rhe fallow8ng wctlon The erpcnmcntal rest results wtll be<br />
compared wnth Nanh Amencan coder. ACI-318 (1995) md CSA-A23.3 (19941.<br />
Nowegrim Standard NS-3473 (1992). Bntssh Code 88-81 10 (1985). and European code<br />
CEB-FIP (1990) for predicting the shear strength. The crpnmental tat mulls are<br />
prenled ~n the fallowing ehapsn.
3.2. Materials<br />
3.2.1. Concrete<br />
Ordlnay Ponland ce<strong>mm</strong>l 15s 10. produced ~n <strong>Newfoundland</strong>. quanznte ~nndrtone. and a<br />
crushed granite <strong>of</strong> 19 <strong>mm</strong> mvrlmum no<strong>mm</strong>al nze were used for all lest rpeclmens. In<br />
order to produce hlgh-strength concrete with low water cemenutlaus ratm (wlcl oi ahour<br />
0.27. the follawtng millenllr were added:<br />
(11 Stllcl fume I" n powder farm ~n [he mtlo 88 <strong>of</strong> cement welght.<br />
(2) Class Fhgnan fly rrh f<strong>mm</strong> Nova Scotla ~n the nt~o 12% <strong>of</strong>ccrncnt we~ght.<br />
(31 Suprplmnclzer <strong>of</strong> sulfonared nnphlhallne formaldehyde bare (Eucon 37).<br />
(41 Rerarder <strong>of</strong> polyhydrorycnrboxyllc base (TCDA type DXI rupplled by Eucltd<br />
Adrnlxture Cvnda Inc.<br />
The reco<strong>mm</strong>endatton <strong>of</strong> thc earl~sr mvcrtrgatlon by Msaouk md Husreln 11M)<br />
was used for the mlx proponton <strong>of</strong> wlectcd matmalr. The mix propon~anr for 1 m' ;rre<br />
gwcn tn Table 3.1 for nonrl-nrenglh concrele and Trblc 3.2 for high-strength concrete<br />
The mln wnr dertgned for il comprerslve-nrength targets <strong>of</strong> 35 MPJ for normal-nrenglh<br />
and 80 MPa for htgh-strength concrete<br />
Tnblc 3.1 MLX propMtton for 1 m'ot normal-strength concrete<br />
IPonland Cement 350 kg<br />
C<strong>mm</strong> Ag~eg=ate.tc~ (gnnae 19-<strong>mm</strong>) 1160 kg<br />
fine Aggregates (graded mnd) 690 kg<br />
Warcr 175 lit"
Table 3 2. MIX propomon for I m' <strong>of</strong> hngh-strength concrcle<br />
Ponland Cement<br />
StInca Fume<br />
1 Fly Ash<br />
Come 4:gcegater (gmnlle 19-<strong>mm</strong>)<br />
Ftne Aggregates (graded undl<br />
water<br />
Wiccment~tlou~ marenrls ratlo<br />
Superplarlre~zer<br />
Rcwrder<br />
3.2.2. Relnforrcmenl<br />
Gmde 4W steel relnfarcrng wlth deformed rebm were used conform~ng ro CSA<br />
nwdardr. The steel nnforcemena were abtrlned from one supplner. Two typlcrl No 10<br />
M and No. 15 M bum were uxd as specmen rernforcement. The diameters <strong>of</strong> No 10 M<br />
md No. IS M b m an: 11.3 <strong>mm</strong> md 16.0 <strong>mm</strong>. respectively. as deraled by the Canadian<br />
code. A 3W bps (1335 W) Ttnus Oslen hydraulic tcrtmg mrchnne war used to test the<br />
tenale strength <strong>of</strong> the twosampler <strong>of</strong> the relnforctng rebnn. Whnle. elecmcal rtmn gages<br />
were applied to determlne the rtmn <strong>of</strong> the retnforcmg rebam and WDTs (L~mnr<br />
Potentid Diffsxnual Tmrducsm) were utiltwd ro measure the specmen deformation up<br />
to the failure. The pmpnler <strong>of</strong> the steel reinforcements are su<strong>mm</strong>anzed m Table 3 3.
Table 3 3 Pmpenles <strong>of</strong> steel retnforcement<br />
number f<strong>mm</strong>) f<strong>mm</strong>'l yield rtrerr ult8mae Elasl!c~ly<br />
(MPa) (MPa) ICPJ)<br />
No.lOM 11.3 LOO 0.03235 150 660 191<br />
No 15 M 16.0 200 0.00?25 435 670 193<br />
3.3. Test Specimens<br />
Thlr study has been eonduered on over 16 rpeamenr. Two spcclmcnr were used at the<br />
begtnnlng ns a reference to ertahl!rh the tertnng pmcsdure. ro check the lnrtlumenrrrton<br />
accuracy. lo wl the rate <strong>of</strong> loading and the rate <strong>of</strong> rcvnnlng data. The dimcnrnan for all<br />
tell speclmenr were 950 <strong>mm</strong> rquarr and 100 <strong>mm</strong> th~ck and wvenl vmables were<br />
conrlderrd ~n the ~nvcrt~ga~on The variables xncluded the effeel <strong>of</strong> concrete arcnph.<br />
ruppan patern. and mnforcemea mlo Detallr <strong>of</strong> the ~ndw~dual rpeclmens and #a<br />
vanabler arc given ~n Table 3 4<br />
As even #n the table. each specmen tr ldentlfied ~n column two by three Icrlers<br />
and one numeral. The flrrt and raond letters lndlcate the nmnglh <strong>of</strong> concne: HS<br />
!ndicares hlgh-strenph and NS !nd#cater normal-srmglh. The thtrd letter ~ndlcater the<br />
type <strong>of</strong> rupvpon pattcm, where F cndtcatcr fixed and S indicates simply rupponed. The<br />
last numeral tndtcates the vmable <strong>of</strong> the tenston retnfonement ntto, where number I<br />
lndlcates mnforcemcnt mllo <strong>of</strong> about 1%. 2 mdteates 1.5%. 3 tndlcaer 2% and 4<br />
indlcrter 2.5%. A rypjcal au <strong>of</strong> the rested specmen s gwcn in Figure 3.1. and Figure<br />
3.2 presents a ryplcd reinfo<strong>mm</strong>ens pattern on lenstan and compresston faces.
Trble 3.4. Detalr <strong>of</strong> [err rpclmens<br />
Senes<br />
I HSSl Stmply supponed 81 7 068 7.00<br />
2 1 ,<br />
Notation<br />
HSS: I ,<br />
Suppon fc' Retnforremenr Pm~ccnle'r<br />
No.<br />
Candtlton<br />
p p' Velacltler<br />
(MPa) (51 1%) lmlr)<br />
I I I<br />
Stmply supponed I :: : 1 1 1 7 67<br />
3 HSS3 S~mply~uppmd R 79<br />
4 HSS4 Elmply suppaned 1 81.7 1 I.5 1 0 82 1 8.86<br />
5<br />
6<br />
7<br />
8<br />
9<br />
10<br />
I I<br />
12<br />
13<br />
14<br />
I5<br />
16<br />
HSFl<br />
HSR<br />
HSF3<br />
HSF4<br />
NSSl<br />
NSS?<br />
NSS3<br />
NSS4<br />
NSFl<br />
NSF?<br />
NSF3<br />
NSF4<br />
3.4. Fabrication <strong>of</strong> Specimens<br />
3A.1. Formwork<br />
Fired<br />
Fixed<br />
Faxed<br />
Fixed<br />
Slmplysupponcd<br />
Slmply supported<br />
Simply rupporled<br />
S~mplyrupponed<br />
Fixed<br />
Ftxed<br />
Ftxed<br />
F~red<br />
79 1<br />
79.1<br />
79.1<br />
79.1<br />
33.1<br />
33.1<br />
33.1<br />
33.1<br />
36 6<br />
36.6<br />
36.6<br />
36.6<br />
10<br />
1.5<br />
2.0<br />
1.5<br />
1.0<br />
1.5<br />
2.0<br />
2.5<br />
10<br />
1.5<br />
1.0<br />
2.5<br />
0.68 1 700<br />
0.68 7 67<br />
0.74 8.29<br />
0.82 8.86<br />
0.68<br />
0.68<br />
0.74<br />
0.82<br />
4.43<br />
4.95<br />
5.42<br />
5.86<br />
The formwork for the test rpeenmcns was fnbnsatcd 8" the conmete laborarory The<br />
formwork consisted <strong>of</strong> four 960 r 964 <strong>mm</strong> decks made wlth 20 <strong>mm</strong> th~eknesr plywood
wlrh IW <strong>mm</strong> height. The bottom <strong>of</strong> Ihc form was made <strong>of</strong> rleel plates. The form war<br />
constructed such that 11 can be d!rilrrembled and re-used Before each cnstlng. all <strong>of</strong> the<br />
steel plater and plywood surface were cleaned and coated w~lh ihght mould o ~l Dunng<br />
casang. grear care was also gpen to ensure that the four rpeclmenr pmv~ded were<br />
unlfom<br />
3.42. Steel Reinforcement<br />
The lenrlon rleel nnforccrncnl at bottom face and the eomprcrslon rleel remforccmnt dl<br />
lop face were manged bared on the derlgn rpxlng. The tenrlon nee1 relnforcemenc were<br />
rupponcd on the eomprersnon steel retnforcemenr by LO-<strong>mm</strong> dv~meler rpreers. The<br />
rpzcerr airo pmv~ded the concrete clear cover. The spacers were welded lo the ncel<br />
re~nforcernenr at selected loeatlon to el~rnlnxe the effect <strong>of</strong> weldmg. The relnfarcemen!<br />
cap war placed I" the form. both the lenston and cornpreranan rleel reinforcement were<br />
rled togelher wlrh steel wtres. As shown rn Rgure 3.3. thc steel retnfarcemnt were<br />
placed I" the form before eusung<br />
3.43. Mixing, Casting, and Curing<br />
The capaclty <strong>of</strong> concrete mlrer was 0.1 m'. The quvntlty war required lo c~n one<br />
spcelmen using one batch. Befm concrete was placed. the formwork and Ihe relnforclng<br />
reban were thoroughly cleaned.<br />
Figure 3.4 shows the pounng <strong>of</strong> fresh concrete from the batch lo the fomwah<br />
Dch concrete batch was poured tnro the formwork and lhcn was vibrated urmg an<br />
electrical md nbratm. The vibrator was applied to the whole plate to consolidate the
concrere and to ensure nts connrtency. When a full eompacnon was asalned. the surface<br />
<strong>of</strong> the specmen was then leveled and finlrhcd wlrh wooden and steel rmwcl. Four hours<br />
liter edrang. the surface <strong>of</strong> thc spectmenr wcre cured under polyethylene shcctr ~n the<br />
forms. Thtr cunng eonttnued far a week by pounng waer lo Its surface eve? 24 hours<br />
The formwork forthe Epclmen war rtnpped at an average nge <strong>of</strong> one week after carnng.<br />
In order lo dercr<strong>mm</strong>e the comprelrtve arenghi af the rpecmenr, three li0~30n<br />
<strong>mm</strong> concrete eyllnden wcre raken from each batch accordnng to the procedure <strong>of</strong> wctlon<br />
C192 <strong>of</strong> rhe ASTM (1997). Thc ten cylznders were rublectcd to rhc rnmc cunng<br />
condlt~onr as the rcsl rpecunens. The compresswe strengths for the rest cyllnderr wcre<br />
crrned out oiLe 28 days <strong>of</strong> casnng. A roll lest 2670 W machine was used to dctsr<strong>mm</strong>e<br />
the concrete eomprerrtve strength. Fggure 3.5. shows u rpeclrnen dunng compresnve<br />
strength lest.<br />
3.5. Test Set-up<br />
The rpeclmenr were nmply-supponed along the edge on n retniorced concrete irrme<br />
with r ireeapenmg <strong>of</strong> 650x650-<strong>mm</strong> border to s8mulvte r iired-ruppon. four steel plater<br />
wcre bolted to fir the upper face <strong>of</strong> the rpeelmens. A rpclll lcsttng frame war derlped<br />
!ncludnng four eonerere beams for rupponlng the rpsclmcn and steel beams to fix the<br />
edge <strong>of</strong> speelmen as detvlled m Figurer 3 6 and 3.7. Flgure 1.8 shows a specmen under<br />
fixed suppon.<br />
The rpc~al terung frame was placed on a 2MX)x?WOx2W <strong>mm</strong> concrete bare. The<br />
concrete base was made in o&r to protect the basement laboratory flwr. Ftgures 3.9 and
3.10 show the detvllr <strong>of</strong> rreel re!nforcemenr <strong>of</strong> concrete base tn bottom face md top face.<br />
respecuuely<br />
In order to ensure tha the pmjecllle strikes Ihe rpec8<strong>mm</strong> cxilctly at center md<br />
keep 11 ~n that place after hatmq the rpeclmenr. n hollow steel cylmder war used to guldc<br />
the fly~ng pralect#le. The hollow rleel cylnnder war 6 <strong>mm</strong> thlcknerr rreel wolh 50 <strong>mm</strong><br />
d~ameter md 1WO <strong>mm</strong> height The steel cylxndcr wm welded to the supponed steel as<br />
pan <strong>of</strong> the tessng frame to provlde r clwr dnrwnce from the rpecsmen rurfnce A<br />
photograph oithc rpeclal lest frameandthe gade steel cylinder Is shown ln Rgre 3.1 1.<br />
3.6. Instrumentation System<br />
3.6.1. Testing Load<br />
Impact lest$ an the rpeclmns were crrncd 0s after n msntmum <strong>of</strong> 18 drys from catlng.<br />
The impact load was nppllcd ven!crlly lo Ls lest spectmens ustng admp ngbd project~lc.<br />
A solid rrsel cylmder was used a r projsel8lc. The cyllndcr has a 220-kg msrs nnd 304 5<br />
<strong>mm</strong> dnvmctcr flat coarsl ma. whtch can be dmpped f<strong>mm</strong> vanable hctghtr <strong>of</strong> up to 1 m.<br />
The photographs m Ftgures 3.12 and 3.13 show the ngtd pmjecrtle to be ready to k<br />
droppd for Rred and sbmply suppaned rpeclmen. rerpectwely. While. Ftgure 3.14<br />
shows the ngrdpmj~t~le was movlngto hu ;lgsmrt the rcrtedrpe<strong>mm</strong>en.<br />
The rtntlonilry specimen 8s ruddmly rubjeeted lo very hlqh accelerrt~on ~n she<br />
dimllan <strong>of</strong> the projectile when the ngd pmjecttle dmpplng at a hngh sped rlnkes rhe<br />
specimen. An accele<strong>mm</strong>eter war attached to the projcalle. The accelsrometer can read<br />
up to i?00 g, where g 8s Eanh'r gravitauonal aecelemtlon. Before each Irrt. rhe<br />
aceelc<strong>mm</strong>stcr was calibrated. The cal~bratlan chan for the accslsromctcr war rupplted by
the manufncrurer. Th~r nccele<strong>mm</strong>erer recorded the venmcal acceleratton <strong>of</strong> Le pm~cettle<br />
together wllh rhe plate. The Impact velocnly was !hen calculared.<br />
3.62. Deflections<br />
Deflecuan <strong>of</strong> the rest rpeetmen war mevrund dunng sspenmsntrl by m e*.lcmnl LPDT<br />
pga Dcflcction was iecordcd at thc center <strong>of</strong> th* plate. The mastzr pancl iccarded the<br />
defleclton d~ta. and the elcctncal straln gages reading were stored a the data vcqulslllon<br />
system<br />
The voltage readmgr were convened to defleeuanr ustng the LPDT crllbnuon<br />
fiactor. The awnlog clecrncnl slgnalr cams f<strong>mm</strong> the tnrtnrmeno were convened lhmugh<br />
the data ilcqulrnlton board lo dmgllrl ngnalr and recorded tn n d>g,wl computer filer a!<br />
svmplnng rate <strong>of</strong> IWO M as well. The LPDT at the center <strong>of</strong> the terced yxamen wa<br />
plrccd m !tr posltaan Marc rccunng the rpeclmen ~n pos8tlon as shown ~n Figure 3 15<br />
3.63. Strains<br />
3.6.3.1. S-1 Stmim<br />
In order to oblrrn the srntn dssrnbul~on at the cracking prwesr zone. four eleetnsal<br />
reanance sleel rtnm gages wnth gage length <strong>of</strong> 10 rnm were rttrchcd at dlfferent<br />
lwat8ons. Theelectncal rerlrlancc rtratn gages had a resistance <strong>of</strong> 120t0.39. ohms nnd a<br />
gage factor <strong>of</strong> Z.M+0.5% was used forcalrbratlon.<br />
For pmectlon agarnst any passlble waer damage dunng concrete casung, the<br />
steel swam gages wett coated wnh a pmtective swlmt and then covered with a rhnnk
tube waxed at beth cndr. A ryplcal lwarnons <strong>of</strong> the rteel stram gages on renraon md<br />
compresston laces are shown #n Figure 3.16<br />
3.63.2. Concrete Strains<br />
The concrete strams were mezsured on the compresstan lace <strong>of</strong> the concrete plnlcr by<br />
meam <strong>of</strong> rpc~al concrete rtnx zager wrlh gtge length <strong>of</strong> 50 <strong>mm</strong> The
face Concrele rtraln war recorded on [he comprcrslon surface only. Before conducun:<br />
the test. the concrece specmen and the cqutpmcnl were carefully ~nrpecred. Careful<br />
awnnon had rlra been :men to the scrul~ny <strong>of</strong> psges. wxres and data ilcquirnt~on synem<br />
dunnp tcnmg.<br />
A dnla acqutrxtlon system based an 3 personal computer at I rampl~ng rate <strong>of</strong><br />
IW HI war used ln thlr clipenmen1 Labteeh Nnebwk s<strong>of</strong>tware wu% used inr dvla<br />
acqu~s~t!on and pmess fonlml s<strong>of</strong>tware was uultud. The data acqulrnton ryrrcm her n<br />
bu~ld-ttmc rhs enabler to configure the set-up. and a run-tlms (ha eontmlr 3e dau<br />
ncqu~nson and other functton Thns bra acqulrtrton system cm be used to conunuourly<br />
manftar ilnd record all types oc pracers vannbler tneludlng volmge. arannr. d~rplacement.<br />
md ncceleranonr at the wannmg ttme <strong>of</strong> 1 mtcm-second.<br />
There are two barlc types <strong>of</strong> pmecsr contml. open loop and closed loop In m<br />
open loop controlling pmcers. as used I" thlr research, analog output blacks mnsmlr<br />
wavefamr Lo the contml hardware dunng mn-ttmc operatton. In closed loop control. the<br />
controlled system rends response data through Ihc tnsrfacc device to rhc m-rime The<br />
dau ourput functmn uses lhlr tnfomat~on to convert raw data from an tnterface devtce<br />
into rppropnntc rc~enulic or engnneenng unit such ar stnsn. dlrpk~cemcnt and<br />
accelerallan The data acqulslrton rptem used 8" lhns study 13 shown tn Rpure 3.18 and<br />
mrtrumentn8on black-dnagrdm a gwen ~n Rgure 3.18.
Figure 3.1. Cmsr sccrlan A-A <strong>of</strong> a typtcal rpclmen under fired-ruppon
Figure 3.2. Typical sLHl retnforremcnl <strong>of</strong> a test spcexmen<br />
48
Figure 3.3. Anwgemcnt <strong>of</strong> steel reinf-mnt rebars in the fnmwnk bcfon cdng
Figure 3.4. Cmg <strong>of</strong> fxe& coacnte f<strong>mm</strong> tk rmxa a tk f<strong>mm</strong>mk
a[<strong>mm</strong>]/l<br />
it----*l<br />
Figure 3 6. Concme beams <strong>of</strong> the 1st frame<br />
11158 150mrn<br />
< I y f 1 [ H<br />
I5Omrn L<br />
Note: - L has two valuer: 650 <strong>mm</strong> and 950 <strong>mm</strong>
x<br />
Y<br />
urnm
H<br />
:Cm <strong>mm</strong><br />
Rgu~ 3.9. Bottom re~nforeemenl <strong>of</strong> rhc concrete base <strong>of</strong> the wrung frame
h 4<br />
2WO <strong>mm</strong><br />
Ftgure 3.10 Top relnforcemenl <strong>of</strong> the concrete bore <strong>of</strong> the lerlnng frame<br />
-<br />
A<br />
*<br />
ZWO <strong>mm</strong>
y. 'i'
t<br />
F1pt-e 3.13. Test 8st-u~ fordmply-e Bpsimn
1 Campresslon face (lop)<br />
Rgure 3.16. Loeaions <strong>of</strong> sled slmn gages an tenennon and comprsrsion faces
f<br />
one conaete atrain-gage<br />
located al Ihe lop <strong>of</strong><br />
mnaac Ppsimen
Figun 3.18. Dam acquisition sptm
Chapter 4<br />
TEST RESULTS AND DISCUSSION<br />
Thlr chapter dtrcurser the test results <strong>of</strong> the present research inverupt~an ~ncludlng the<br />
cnck paucrns. ult~mate 104s. dsflcsuanr. ducl~l~ry and energy ilbsopson. modes <strong>of</strong><br />
fatlure. nratns both in concrete and steel remforcemen[. A compvnvln was made btwccn<br />
high-strength and normal-strength concrete slabs (erred under rwllc loading !n the same<br />
iabomtory by prev,aur research warken. Marrout and Husoc~n (1990).<br />
Mcasuremntr obmned f<strong>mm</strong> laboratory Invcrugalon are prewnted ~n the<br />
followtng remlon. Due lo rhe large rmounl <strong>of</strong> recorded data. only a few reprexntnt~vc <strong>of</strong><br />
the (err resulls are selected ~n thlr prermtauon In addtaon. the crack patterns at failure<br />
are represented graphteally by means <strong>of</strong> photograph.<br />
4.1. Cracking Characteristics<br />
The crack paltemr, aflcr failures. are depncled ~n Figures 4.1 thmugh 4 4 for tenson face<br />
damages. While the srripprng <strong>of</strong> the concrete cover f<strong>mm</strong> the compression face shown in<br />
Ftgure 4.5. Both the renrton face and he compression face <strong>of</strong> all sptmenr showed very<br />
rimtlarcraclung damage.
It war not parrtble to determnnc a relmahle value far the shear-cmhng load. 1.e.<br />
the load dl whmch the shear cracks rtmcd up The erumntlon <strong>of</strong> such load from the crack<br />
pattern was uncenan because there was no fundamental d~fferencc between shes crack<br />
and flexural crack erpnnd~ng m tangentgal d#rectsan However. employng the decrease <strong>of</strong><br />
!he rlcel stram ~n the nnforcement can be used as a p de for delermlnsng Lhe shear<br />
crarkln: load? As pmpred hy K~nnunen and Nylander (10601. the observed punching<br />
lards <strong>of</strong> two-way concrete slabs w~rhout shear re~nforcement were wound 70-80 percent<br />
<strong>of</strong> r k ult!mnte lo&.<br />
For dynamtc loadmg. a rbght trend <strong>of</strong> mon tenston face damilge and more<br />
concrete stnpplng aceumd at u larger relnforccmenl steel ntlo p than the rmallcr ratlo.<br />
The same obssrviltlan war more evident for the care <strong>of</strong> hsgh-strength concrete th~n<br />
normal-strength eoncrele Radtal cncb expandtng to the edger <strong>of</strong> the spclmenr were<br />
evdent on all the test spclmenr. The cnck lnd~eater that bendmg and shew fatlure<br />
mechrnl~mr were detected m all the specn<strong>mm</strong> Therefore. ~t can be concluded tha all the<br />
rpeclmenr were falied under aduclnle shctr failure<br />
4.2. Load-Deflection Characteristics<br />
The Impact lauds vmur the deflccuon at the center <strong>of</strong> the plater for the dlfferea rest<br />
wner an pnscntcd in Ftgure 4 6 through 4.11. The load-time curves for the different lest<br />
sene3 have also shown in Figure 4.14 thmugh 4.17. whtle the dcfleet~an -tmc curves<br />
given m Figure4.18 thmugh 4.21.<br />
The deflsctnonr far all tested specimens were obtained using LPDT measurements<br />
at the center <strong>of</strong> rp<strong>mm</strong>en. Urlng dynamne tquillbnum m the venrcal dlmdon, the Impact
lard war oblalned f<strong>mm</strong> the aceelerartonr that war pmv~ded f<strong>mm</strong> the areele<strong>mm</strong>eter. The<br />
dynam~c equllsbnum m Le vemcal dmeuon tr dexnbed ~n Be follow!ngequatton<br />
where. FlrJ = Impart loading<br />
,on = mar <strong>of</strong> pro)cctlle<br />
I. = msr <strong>of</strong> specmen<br />
o, = arceleranon <strong>of</strong> project~lc.<br />
FIIJ = f m, + 0.5 m.1 o,<br />
The load versus deflcetnon curve can be used for csttmaung the cncrgy rbrorplton<br />
clpxily by ~alculallng the area under the load-deflecuon curve. In add#l!on. load-<br />
dlrplaccment curve cm be apprornmarcd by ~veral straght lhncs wtth dlffcrent slopes<br />
The awend~ng curve has a slope that represents to the ruffncrr <strong>of</strong> the qeclmen before<br />
cracked. Wtlhxn a glven curve, the pre-craclung stage represented by the rlape <strong>of</strong> the<br />
rrcendtng curves a normally steeper than the desccndnng curve <strong>of</strong> the port-cracktng<br />
nrge. As expected. the ~t~ffncss <strong>of</strong> concrete plater were decreased after cncktng.<br />
Laud-deflccean curves <strong>of</strong> the test specimens shown ~n Figurer 1.6 lhmugh 4.9<br />
were made wtth dzffeml Erecl resnforeement ratla. md had the rnmc concrete strengths<br />
as well as the same support condtnonr. Rgumr 4.6 to 4.9 show that for pre-cracking<br />
stages. the slope <strong>of</strong> arcend!ngfurve <strong>of</strong> the btgpr nnfareemcnc ratto were al~ghtly htgher<br />
thvn thme f<strong>mm</strong> plates wlrh smaller re8nfo<strong>mm</strong>nt rauo. This lnd~cater chat the plate<br />
rttffness tncreased with the ,"crease <strong>of</strong> nnforeemea mtto.<br />
Repting the lam menrnoned pmcedure for different spec~mens wlth different<br />
concrete strength and suppon eondlttans are shown m Flgures 4.10 thmugh 4.13. All the<br />
figures lndicated that the plate stiffness lnfreacd with the lncrrorr <strong>of</strong> concrete-strength.
The rtlffncsses <strong>of</strong> concrete plates were rl!ghtly lncreared wlrh the change <strong>of</strong> cnd-<br />
condltions from rlmply rupncd to fired<br />
4.3. Dynamic Fracture Energy<br />
The ener$y ahromt~on eupaty IS defined as the ma under rhe load-d!rplxemenl curve<br />
The lest rerula .?re glven I" Table I The results include the energy abrorplmn Clpnclty <strong>of</strong><br />
all tested lpeenmenr at blure<br />
Table 4.1 Test results<br />
1 1<br />
1 1 1 1 " 1<br />
ser~r Slab Svppn 6' Re8niorrsmsnt Sped hrccl D~spl Emey<br />
No No<br />
I<br />
Condlllon<br />
P P'<br />
nt cnlcr Aburpaoo<br />
(MPaI 1%) 1%) Ids1 1x1 l<strong>mm</strong>l IkNnmb<br />
I I , I I I I<br />
HSSI Slmplysuppned 81 7 095 0.68 7W 110 120 l h<br />
eHSS3 S~mply suppned d 8 81 7 1 HSSJ Simply ruppncd 81 7 2.32 0 82 8 86 290 1121<br />
9<br />
I0<br />
I1<br />
12<br />
I3<br />
14<br />
I5<br />
16<br />
NSSI Lmply~upponcd 33 1<br />
NSS2 Simply suppaned 33 1<br />
NSS3 Shmply suppaned 33 1<br />
NSY Stmply suppaned 11 I<br />
NSFI Fmed<br />
NSP. Rxcd<br />
NSF3 Rrrd<br />
NSF4 Rxed<br />
366<br />
3b6<br />
166<br />
366<br />
095<br />
126<br />
1.90<br />
1.32<br />
095<br />
I26<br />
190<br />
232<br />
068<br />
0 68<br />
074<br />
082<br />
068<br />
068<br />
074<br />
082<br />
542<br />
626<br />
7 W<br />
767<br />
443<br />
4.95<br />
542<br />
586<br />
70<br />
76<br />
95<br />
106<br />
It s evident f<strong>mm</strong> the gtvcn table that the cn~rgy atsqtlon capnclty nncreaad as<br />
he concrete suength inc-cd. Tert results <strong>of</strong> the spccnmens made with different<br />
72<br />
78<br />
85<br />
98<br />
51<br />
I9<br />
108<br />
11 2<br />
47<br />
6.0<br />
84<br />
100<br />
77<br />
162<br />
181<br />
?55<br />
61<br />
110<br />
186<br />
2M)
concrete strength. and had rhc same re~nfo<strong>mm</strong>encmtia and ruppon cond1r8an revealed<br />
that energy absarptmn mereased wnth !he tneredw <strong>of</strong> concrete nrengh. The use <strong>of</strong> hlgh-<br />
rtrengrh concrete plate can be employed 10 lmpmvs the energy absarpllon cirpahtl~ry <strong>of</strong><br />
the concrete plate by aboul4 ttmcs hlgherthan normal-rtrenah mnereleplare<br />
The effect <strong>of</strong> supponsond~t~on on the energy abrorptlan capaclty war nor r<br />
e:nlficml fsctor hr Lc cndsondltlon changed f<strong>mm</strong> Rxcd to rlmply-wpponcd. a 5llohr<br />
change ~n the energy absorprlon eapxaly <strong>of</strong> the ten plate was recorded. On !he other<br />
hand. the effect <strong>of</strong> relnforccmsnt ntro on the energy absorption capaclly was rlgnlficml.<br />
For errmple. tncreaslng the retnfarcement nuo i<strong>mm</strong> I% ro 2%. rhe energy abrorptlon<br />
crpclty <strong>of</strong> the rpetmen sncreascd by about lhme t>msr. both for the care <strong>of</strong> htgh-<br />
rtrengh and nomal-strength concrete.<br />
4.4. Steel and Concrete Strains<br />
F~gures 4 22 through 4.37 show the dtrtnbut~on <strong>of</strong> the measured steel nmns snd concrete<br />
itrams <strong>of</strong> all rpe<strong>mm</strong>enr. The rtwns were mcarured at polar <strong>of</strong> speclnl lnteresl ~n order lo<br />
obtan ~nformat~on on the aate <strong>of</strong> r!mra. as menuoned #n recuonr 3.6.3.1 and recrton<br />
3.6.3.2. Unfonunately. not all the mcarursd data are reponed snce Eame stram gages<br />
were lost due to slecmcal problems and dzimages lo tho gags dung castlng.<br />
All the tested spcimens eipnmeed ylcldlng <strong>of</strong> steel relnforccmnt befare<br />
punehtng fatlure accumd. The tenston reinforcement reached the yteld pomr at straw <strong>of</strong><br />
about 0.W25. Comparing the lenston rrel stnln at approximately same locartan from [he<br />
compresslo" face. It has been found that the steel strains m the ease <strong>of</strong> tmpact loading<br />
were about rwlm htgher than those corded for static load~ng as lrpned prrviourly.
There was aconccnrrarton <strong>of</strong> stresses at the m a under tmpact load Whde u large<br />
are* <strong>of</strong> steel had ynelded. the amn at the concrete compresslo" filce lusl reached to n<br />
mrr~mum <strong>of</strong> 17M) mcm strain at fu~lurc. Thtr Is rppmx~mately half the value tha<br />
obtained expenmentally at the same location under rtvtlc loadfng as repaned prewourly.<br />
Since. I" the case <strong>of</strong> rmpacr loading. the conciete sudace suddenly perfordled. the<br />
concrew surface have been separated, hence the concrete rtnlnr on the separate face were<br />
no1 recorded.<br />
4.5. Modes <strong>of</strong> Failure<br />
Moder <strong>of</strong> fadure <strong>of</strong> convcnt~onnl two-way plates under rtatle lord cm k clarrllicd lnlo<br />
three casegones<br />
(11 Pure flexural fallure<br />
111 Pure rhear faxlure<br />
(31 Ducuie rhea faxlure.<br />
Pure flexural falure taker place ~n plater where mon <strong>of</strong> the relnfocemcnt ylclds<br />
before punchlng occurs. Conrequenlly. the plater erhtblt large dcflectlonr pnor the<br />
fanlurr. Usually thlr type <strong>of</strong> failure happens m the case <strong>of</strong> lightly remiarced plates. As the<br />
reinforcement ratlo decreases, more steel yxelding approaches la the coral area <strong>of</strong> the<br />
tsnllan steel relnforcement.<br />
The second category <strong>of</strong> hlux 1s pure shear fnllure. Pure rhear fanlvrr occurs<br />
when the yl~lding <strong>of</strong> tk lensson reel Is very lacal~zed at the center <strong>of</strong> loading. U~ually.<br />
spclmenr with heavy retnforcement ratlo faled under punchtng shear. The thtd t w ol
failure IS ductile shear fatlure or shear failure with ducul~ty. Thln type <strong>of</strong> fmlure Ir aeuc<br />
<strong>of</strong> transttlon between pure punchmg and pure flexure failures.<br />
As mentioned ~n the Sccuan 4 1, all rpeccmens failed under duct~le she= fallure.<br />
Thlr falure can be calegonzed under the thlrd type <strong>of</strong> failure. The Impact punching lmd<br />
~ncreased nr the concrete-strength mereased and the steel re~nfarcement ratlo tncreued.<br />
The fxlum rurf3ee <strong>of</strong> nomc <strong>of</strong> the rested rpclmcnr were csrrful!y removed and<br />
eliamtned. The observed angler <strong>of</strong> failure surface had some vanallon. Far normal-<br />
sirength concrete plates. the observed angle <strong>of</strong> falure surface war about 60 de~ee. wh~le<br />
for hlgh-smngth concrete plates. !he angle war found lo about 65 depe. In addmon. Le<br />
punching shear radius on the tenstan face happened a a dtrrance <strong>of</strong> (1 6-2.0) rlrncr the<br />
plate depth (dl f<strong>mm</strong> the edge <strong>of</strong> loaded urrn for most <strong>of</strong> the tested rpeflmcns compared to<br />
a dtnance d/Z for nasc load~ng.<br />
4.6. Effect <strong>of</strong> Concrete Strength<br />
The dertpled FompEsSlve strength targea for rhtr Inveseea!on were 35 MPil for narmdl-<br />
strength and 80 MPP for hlgh-strength concrete as described ~n secllon 3.1. Increnang the<br />
concrete compresswe rmngth f<strong>mm</strong> normal-strength to hlgh-smngth concrete mcre~sed<br />
the energy abrorpl~an capac#ty, cntlcvl velocity <strong>of</strong> perforelon. and deflecaon al the<br />
center<strong>of</strong> speclmenr.<br />
The energy absorption capnclty increaxd by nnge <strong>of</strong> about 3-5 smn, whdc the<br />
cnrscal velas~ty <strong>of</strong> perfmuon nncreaxd by a range <strong>of</strong> about 20-30 percent. The<br />
displacements st the center <strong>of</strong> spclrnm also increased amund twlu. This obrervntlon<br />
nndicated that high-rmngth conerrre can pmvide higher ducrlltty for concrete plater.
4.7. Effect <strong>of</strong> Steel Reinforcement Ratio<br />
The tenson remforcement ratios were 1%. 15%. 2%. and 2.5% Ar renrlon steel nu0<br />
was ~ncrevwd f<strong>mm</strong> about 1% to 1.5%. the cnr~cal veloctly <strong>of</strong> perfoniton ~ncrcnred by<br />
about ten percenl. The energy sbsorptron cnpnctry has also lncrerred by about fifty<br />
percent for hlgh-strength concrete and hundred percent for normal-strength concrete<br />
lncrerrlng tenrlon reeel ratlo from 1% to 2%. the cntlcal velac~ly <strong>of</strong> perfonl~on<br />
~ncrsnsed by ahouttwenty percenr. While. thc cnergy ahrorpt~on eapsclty af the specmen<br />
lncreared by about three t lm, both ~n hlgh-strength and tn normal-strength concrsa. In<br />
add~tton. when the tensnon steel ratlo tnsreased f<strong>mm</strong> I% to 2.5%. the cnrtcal vclocaly <strong>of</strong><br />
perforatton 1ncrs3ssd by about chmy percent. In thts ease. the energy rbrarptmon cilpnry<br />
h;ls also lncreilred by about four tunes for hlgh-strength concrete us well as normal-<br />
strength concrete.<br />
4.8. Effect <strong>of</strong> Support Pattern<br />
As menuoned !n ~etnon 3.3. this study was conducted on I6 rpeczmr under lwo types<br />
<strong>of</strong> ruppon patterns, fixed and amply rupponed. The effect <strong>of</strong> ruppon pauem can he<br />
dercnkd bnclly m the follow~ng recnon.<br />
Energy absorption sapnclty <strong>of</strong> the two types had nearly the same behavtor bath in<br />
the case <strong>of</strong> Bred and stmply supported. Therefore, hers was no ~lgn~ficanl effecl <strong>of</strong><br />
support pattern for specimens regardrng the energy abrorpuon capacity.<br />
However. ("creasing lhe concrete rtrength f<strong>mm</strong> 35 MF'a to 80 MF'a resulted tnto a<br />
significant effect on the critical veloctty <strong>of</strong> pelioration. The enrlcal veloctly <strong>of</strong>
perfomt~an ~ncreascd by about 10-30 percent for rpeelmens under rtrnply supponed end<br />
eondltton. and 50-M) p ent for speclmenr under fixed end condlllon<br />
4.9. Effect <strong>of</strong> Dynamic Loading on Peak Strain<br />
Carnpanng Le rtatlc loadtng to the dynamic (Impact) loudlng can be ru<strong>mm</strong>anzed ~n the<br />
tollaw~ng Eectlan 1" case ot 11311C loildnng, the peak rtmn and the marlmum detlectton<br />
happen an the same tlmc wlth the peak load. However, under dynarnlc laad~ng. the pcsk<br />
slraln accurs rl8ghlly delayed wlth renpfft to !he peak load but ahead lo the rnax~mum<br />
deflectaan. An ~llunrallon <strong>of</strong> the dnfference behsvtor between normal-strength and hleh-<br />
strength concrete br shown m Ftgurs 4.38.<br />
Under lmpm loadmg. the lenston steel stt-~#tt ts est$matd by about twlce that<br />
under rrattc lordcng. On the other hand. the concrete rtmn on the outer r>& Area <strong>of</strong><br />
conraa loading decreased by about half. As dercnbed !n the previous rectlon. the<br />
concrete surface suddenly perfonled under dynmlc lauding. hence the concrete rrranr<br />
on the repanted macould not be recorded.
Rgre 4 6 Lord-deflecson curves for spslmen no. I. 2.3 nnd 4
LOAD. DEFLECTION<br />
Ilwimnr 6. I. and 8)<br />
Rgure 4 7 Load-defleetlon curves for specmen no. 6.7. and 8
Rgum 4.8. Loaddeflectioncurves for rpccnmen no. 9. 10, and I1
LOAD. DEFLECM)N<br />
(SpRim 14.15,and 16)<br />
Fqure 4.9. Load-deflecuon curves for specmen no 14. IS.nnd 16
Rgure 4.10. Load-deflecoon curves for speelmen no 1 und 9
hgux 4.1 I. Load-deflecuon curves for rpectmen no. 2.6. 10. and I4
Rgum 4.12. Load-denecuon curves far spectmen no. 3.7. 1 I. md IS
F~gure 4 13. Load-deflscnon curves far specmen no. 4.8. md 16
Figure4.14. Load-r~mecurvc~ for rpcsnmens no. I. 2.3. and4
Flsure 4.15. Laad-tlmc curves forrpeet<strong>mm</strong>r no. 6. 7. and 8
R~urc 4.16. Load-ome curves for speclrncnr no. 9.10. and I I
Rgm 4.17. Lord-time curves br Epfftmenr no. 14. IS. and 16
Figure 4 I8 Detlccuon-ome curves for specimens no. 1.2.3 and 4
Ftsure 4.19. Dcfl~t~on-oms curves for rpcclmenr no. 5.6.7. and 8
OeLECnCN AT-<br />
(~mar9.10,ll.ndl?)<br />
Rgure 4.20. Dcflect~on-t~mccurver for rpclmcnr no. 9. 10. I I. and I?
Figure 4 11. Deflect>an-t~rneeurver for rpeemenr no. 13. 14. 15. and 16
u.)<br />
STEEL AND CONCRETE STRAWS OF HSSj
STEEL AND CONCRETE STRAINS OF HSS2<br />
Rgure 4.23. Steel and concrete rtmnr <strong>of</strong> specimen HSSZ
STEEL AND CONCRETE STRAINS OF HSS3<br />
Fsgure 4.24. Steel and concrete rmnr <strong>of</strong> specimen HSS3
STEEL AND CONCRETE STRAINS OF HSS4
600<br />
;<br />
: 3.0 ------<br />
B 2.0 -<br />
too<br />
STEEL AND CONCRETE STRAINS OF HSFl<br />
-- .<br />
I0 I, 10 3, 10<br />
Tim..",.<br />
Flgure 4.26 Steel and concrete stralnr <strong>of</strong> specmen HSFl
Figure 4.27 Steel and concrete smns <strong>of</strong> rpccnmen HSF2
STEEL AND CONCRETE STRAINS OF HSF3<br />
Figu~ 4.28. Steel and concrete stnlnr <strong>of</strong> Ipcc>men HSF3
,000<br />
STEEL AND CONCRETE STRAINS OF HSF4<br />
Rgure 4.19. Steel and concfelc s<strong>mm</strong>s <strong>of</strong> specmen HSW
STEEL AND CONCRETE STRAINS OF NSSI<br />
Figure 4.30 Steel and concrete nratnr <strong>of</strong> rpeclrncn NSSI
STEEL AND CONCRETE STRAINS OF NSS2<br />
Figure 4.31. Slcel and concrete srrans <strong>of</strong> specimen NSS?
m --<br />
STEEL AND CONCRETE STRAINS OF NSS3<br />
Figure 4.32. Stecl and concrete strains <strong>of</strong> specmen NSS3
-<br />
STEEL AND CONCRETE STRAINS OF NSS4<br />
Figure 4.33 Steel and concrete smns <strong>of</strong> speenmcn NSS4
' :I:-<br />
500<br />
:::,<br />
$00<br />
,m -'<br />
70B<br />
STEEL AND CONCRETE STRAINS OF NSFl<br />
*: 7 .. -.__ . . -. . . . .<br />
-- --_i..<br />
TI,".. m.<br />
(Concrete nratnr are not uvaxlabie)<br />
Flgurx 4.34. Steel andconcrete swns d npeelmcn NSFl<br />
--
STEEL AND CONCRETE STRAINS OF NSFP<br />
Figure 4.35. Steel and concrete rnains <strong>of</strong> spslmen NSR
STEEL AND CONCRETE STRAINS OF NSW<br />
I \<br />
i 'm<br />
. ,.---__ .-. .<br />
dm-- ! "1 ', ,,\,,.<br />
-ST<<br />
... ST,<br />
ST.<br />
--<br />
L -.<br />
dm-<br />
.-....<br />
',~<br />
..___..___._.----- ---...- -<br />
>IXJ , , . ... . -- . .<br />
. . .<br />
10 7 1 111 21<br />
-<br />
1<br />
::=<br />
nm. m.<br />
,400<br />
;<br />
E 600 -<br />
so0<br />
200<br />
,o 1, *a<br />
Ti."., m.<br />
F~gure 4.36. Steel and conerere rlrainr <strong>of</strong> specmen NSF?<br />
110
STEEL AND CONCRETE STRAINS OF NSF4<br />
Tim, rnr<br />
Figure 4.37. Slsel and concha seains <strong>of</strong> specimen NSF4
Figure 4.38. High-strength vsnus normal-strength sonnctc plats behavior under impan<br />
loading
5.1. Introduction<br />
Chapter 5<br />
NUMERICAL EVALUATION<br />
Htgh-strength concrete has a dlfferent behavior than normal-strength concrete. B falls by<br />
cnclung through the vggregarer rerultmg tn a smwth facture surface. whlle normal-<br />
nrength conerete fndr by the aggregate pulltng out d the matnx multlng I" r mugh<br />
tracture surface. This phenomenon can s~gtficanlly affect the structural performance <strong>of</strong><br />
concrete marenal ~n many appllcationr. For example. the shear transfer rnechrn~rm ~n<br />
rennforeed concrete rlruclures relies pan~rlly an as,-gate ~nterlociong across the shear<br />
cmckr. Thls mchanlrm will be reduced greatly for high-strength concrete as a result <strong>of</strong><br />
le failure mode.<br />
Thnr chapter presents a numerical evaluauon <strong>of</strong> the test results. The performances<br />
<strong>of</strong> numerical evaluation am evaluated aganrt Nonh Amencan coder and some Eumpean<br />
codes such as BS-8110 (1985). CEB-FIP (1990). and NS-3473 (1992). The analyrnr wnll<br />
lncludc a cornpanson betwem the ratios <strong>of</strong> dynamic to stattc tmpact load. The rrauc<br />
punchlng shear rvength capactttes according to the current cade pdmians will be
examlned with respect ro the expen<strong>mm</strong>wl results The values <strong>of</strong> the cnacal vcla~ty <strong>of</strong><br />
perfowlon calcularcd f<strong>mm</strong> rhc test results are compared lo vrlucr calculared according to<br />
the dynamle code CEB (1988).<br />
A fracture mechanics analysis was used to evaluate the tmpact loads on hhlgh-<br />
strength concrete plate. The fracture rnechanncs appmach 3s consldsred r s od promnrxng<br />
approach bi lnvtsttgarlng the hnltle fa~lun <strong>of</strong> amcrunl concrete clcmenn accurately<br />
The fracture mechvnlcr appmvch 18 usedto mvcrllgate the effect <strong>of</strong> the rate <strong>of</strong> laadlng on<br />
a bnttlc marenal bared a Isnear cla~r~c fracture rnechan~cs (LEFM) Onc <strong>of</strong> the<br />
ahjecllve~ <strong>of</strong> the prewnt study IS to pmvlde the deslgn englnssrn with a rate renrltlvlty<br />
numkr for high-strength concrete plates<br />
5.2. Impact Load<br />
In order ro calculae the Impact load <strong>of</strong> the lest nrulfr. the venncal equation <strong>of</strong> dynamrc<br />
cqu~l~bnum. tgnonng damping. cm be wntten as.<br />
Ftr) = m, m, (5.11<br />
where F(r)lr rhs total force. a,lr the total xcclerat~ons, and the total mass m, Ir the<br />
rum <strong>of</strong> the projectile mars and half <strong>of</strong> the specmen mass. If 0, Is equal to the projesulc<br />
accclera8an rrp. whtlc ntpand rn, are the masses <strong>of</strong> the pmjeetile and the specnmen.<br />
rerpecnvely. Equation (5.1) ean then bs wnnen as:<br />
F(r) = (mp + 0.5 m , ) ~ ~<br />
Equntlan (5.2) can thm be used for ccalculat~ng the impact lest load P,#,, = Fit1
5.3. Punching Shear (Static Capacity)<br />
The derp shear strength equauon !ncorporaled tn bulldlng codes are a dlrecr result <strong>of</strong><br />
empt~ical pmccdurer developed f<strong>mm</strong> laboratory lerts. Ar mennoned prevtourly. the<br />
Nanh Amencan codes arc based pnnclpally on Mae's (1961) wok. whde the Bntlsh<br />
codes arc based mnmnly on Regan's (1981) work. It becomes necessary lo cx;lmtnc rhc<br />
exsung formula strength <strong>of</strong> h~gh-strength concrete plater <strong>of</strong> 80 MPa compresswe<br />
nrength.<br />
Martmum shear stress rertrranee prov~ded by a concrete plate wlthos rhea<br />
relnfoxement. v,. calculated according lo ACL-318 (1995) under S.1 untt. rhrll be the<br />
rmallest <strong>of</strong>.<br />
where. &= ratno <strong>of</strong> long side to shon sldc <strong>of</strong> the comenmlcd load<br />
f,= speetfied compresswe strength <strong>of</strong> canere*<br />
a,= factor which adjusts v, for ruppon dtmenstans<br />
15.3n)<br />
d = dl~tanee f<strong>mm</strong> ei<strong>mm</strong>c compresslan fiber to ccntmtd <strong>of</strong> lenston nnforce<strong>mm</strong>t<br />
be= perimeter <strong>of</strong> cnlical section for shear in plates.
The Cornmlrtee reco<strong>mm</strong>ended that the following deslgn equntlon for calculattng ulrtmae<br />
shear loud.<br />
V,, = v,, b. d<br />
(5.4)<br />
The cnttcnl sectson shall k n rectlan perpendscular lo the plane <strong>of</strong> the plate and located<br />
ro that tu penmeter. b,. tr u mnnnmum. But. the sccson need not approach closer lhdn<br />
dl2 to Ihs penmeler <strong>of</strong> the concentnted load. Thereiore. b, = n (c + El. where c Is the<br />
dlametcr <strong>of</strong> loaded arw.<br />
The Bntlrh Codes. 0s-8110 (19851. and code <strong>of</strong> pracuce for structural urc <strong>of</strong><br />
concrele. CP-I I0 (1972). rrco<strong>mm</strong>endsd the followtng equallon for cnlsulaune. punchmg<br />
V, = Ka K,,=(?.69d)~C + 7.85d) (5 5)<br />
where. V, = ult!mate shear force (N)<br />
K,<br />
K,<br />
f,.<br />
= 0.13 for normal concrete 0.105 fo~ hghrwefghr concrete<br />
= I I5 [4n(column arcall lcolumn pnmeler)' 1"'<br />
= cube smgth <strong>of</strong> concrele IMPa)<br />
d = effective dcph <strong>of</strong> the slab (<strong>mm</strong>)<br />
ZC = penmeter <strong>of</strong> the column (<strong>mm</strong>)<br />
The rhear p<strong>mm</strong>elcr for a rectangle column 1s located a distance 1.25 d out f<strong>mm</strong> the<br />
column. for a clrfuiar column a located 1.25 d out f<strong>mm</strong> the column. Aeeordtng lo the
code predrmwmr. the abavs llmll <strong>of</strong> 40 MPU <strong>of</strong> the cube strength <strong>of</strong> Equation (5.5) was<br />
neglccred when calsulat~ng he shear strength.<br />
Norntnd shear strew. vc. according to CEB-FIP (1990) Is'<br />
vc =018 [,+El= (5.6)<br />
Thc hlghcsl conciclc strength conrldcred I" CEB-FlP (1993) 1% SO &%Pa. The control<br />
penmeter Ir !he mnnimum length taken f<strong>mm</strong> 2d f<strong>mm</strong> the concentrated load penphery<br />
Equauon (54) can also be used for srlculauon the punch~ng rhear espclty, where. the<br />
penmctcr ho for arcular loaded area IE = x IC + W.<br />
The Nowcgnan code NS-3473 (1992) rpeclfier the punehzng rhcrrcapaclly as<br />
Vd = 0.33(f,d +kAply,)udk,. < 0.66f,udk, 15.7)<br />
where. frd = derngn tenrlle nlrengh <strong>of</strong> concrete<br />
y, = malenal coefric!enr for reonforced concrete = 1.0<br />
tA = IW Nl<strong>mm</strong>:<br />
1.0 < k,,l=1.5dldl) < 14. dl = 1.0rn<br />
d = mean platsdspth in the twore~nfo<strong>mm</strong>cnt d~rectnons<br />
I = the length <strong>of</strong> penmeter <strong>of</strong> the governing reclnon at a dnaancc I 0 dfrom<br />
loaded area<br />
p = lcnrlon re~nforccmcnt ratto.<br />
Compress~ve amngth Is usually given ar. the reference value for a concrete pade.<br />
According to the CEB-FIP (1990) reco<strong>mm</strong>endation for mean values. the tcnsllc nmngth<br />
<strong>of</strong> concrete can be enimavd f<strong>mm</strong> compresswe strength by:
J,~ = 0 . 2 0 ~ ~ ~ ~ ~ (5.8)<br />
The measured rest tmpact loads P, and the calculation <strong>of</strong> Ihe shear strength by dtfferent<br />
codes are wbulared ~n Table 5.1.<br />
5.4. Code Reco<strong>mm</strong>endations<br />
In order to evaluate the validbty <strong>of</strong> the current dessgn npecificalonr. the calcuiatlonr <strong>of</strong><br />
the formulas f a sratnc punehrng shear capaclrler llrted m Table 5 1 are to be dnrcursed<br />
bncfly !n present recnon. The r!s!c punehlng shear rcru <strong>of</strong> all rpeclmens can be used ar<br />
a reference for all <strong>of</strong> the dynumte lmpnct tens.<br />
The naltc punehtng shear capncltler calculated aerordin~ to ACI-318 (19951 and<br />
[he dynvmlc test results we used for the dynvm~c shear capactt8es. The ratno <strong>of</strong> dyndmlc<br />
to statlc punching shear tr m the range <strong>of</strong> 1.39-2.31: a the same ratio n npd between<br />
150-1.82. 1.361.65. and 1.87-2.33 accordnng to the BS-8110 (1985). CEB-FIP (19W).<br />
and NS-3473 (1992). respecsuely.<br />
The lmpaer tesl results ~ndlcare that the punch~ng failures were at a much higher<br />
load level than the rtnlc punchtng rhear capaclly. The ntlo <strong>of</strong> Impact vcnur rtnuc lord<br />
aecadlng to the Nonh Amencan coder 1s normally vaned between u wider range<br />
compared to the European codes. The rario <strong>of</strong> dyonmlc to rtatlc punehtng shear accordmg<br />
to NS-3473 (19921 is al<strong>mm</strong>l con~lrtcnt and hlgher than other coder predictnonr. b<br />
concluaon, the resulU con be used as a destgn guide lor engtnecn to predict the dynrm~c<br />
capaclty <strong>of</strong> high-mph concrete plates.
5<br />
6<br />
7<br />
8<br />
9<br />
10<br />
11<br />
12<br />
HSF1<br />
HSF2<br />
HSF3<br />
HSF4<br />
NSS1<br />
NSSZ<br />
NSS3<br />
NSS4<br />
79 1<br />
79 1<br />
79.1<br />
791<br />
331<br />
33.1<br />
33.1<br />
33.1<br />
0.95<br />
1.26<br />
1.90<br />
2.32<br />
095<br />
126<br />
1.90<br />
232<br />
NIA<br />
328 50<br />
37681<br />
389.70<br />
225.44<br />
244.77<br />
305 96<br />
341 39<br />
23660<br />
23660<br />
22639<br />
22639<br />
15305<br />
15305<br />
147.74<br />
147.74<br />
194 34<br />
213 52<br />
23428<br />
250.40<br />
14536<br />
15971<br />
175 23<br />
187.29<br />
212 22<br />
233 17<br />
25890<br />
276 72<br />
15873<br />
174.40<br />
193 65<br />
20698<br />
161.90<br />
172 73<br />
196.99<br />
201.05<br />
10521<br />
11604<br />
132 65<br />
14671<br />
NIA<br />
139<br />
165<br />
171<br />
147<br />
180<br />
2.07<br />
2.31<br />
N/A<br />
154<br />
161<br />
156<br />
1.55<br />
153<br />
175<br />
182<br />
N/A<br />
141<br />
146<br />
1.41<br />
1.42<br />
140<br />
156<br />
165<br />
NIA<br />
1.90<br />
2.02<br />
1.94<br />
2.14<br />
2.11<br />
2 31<br />
233
5.5. Critical Velocity <strong>of</strong> Perforation<br />
'The values <strong>of</strong> the cntlcal velalry <strong>of</strong> perforatnon can be cnlculared aceord~ng the formula:<br />
where. W = concreledcns8ly<br />
Thccrlsulnt~onr <strong>of</strong> cnrtcrl velwlry then am given ~n Table 5.1 as follows:<br />
Table 5.Z. Cnttcal veloclry <strong>of</strong> prforamn
In order to evaluate the pred!etton <strong>of</strong> Equalon (5.9). the calculated cnucal<br />
velactty tr then compared to the actual ten velaclly. The eompanson between the<br />
ealculrted cnncal velacnty and rhc actual rent velaclly are g ~en ~n Table 5.3 below:<br />
Table 5.3 Calculated cntical vclactty compared wtth tea velacnty<br />
enes Noiatan Marlmum Maxlmum Cmlsal Test<br />
No P.ccsleration Displacement Velacny Velmny<br />
at Center frm code<br />
(gl l<strong>mm</strong>l (mbl lrmsl<br />
It can be seen f<strong>mm</strong>Table 5.3 that under lmpact loadmg, both <strong>of</strong> the menrured and<br />
salculacd accclcrations for h~gh-strength sonoere wcre htghcr lhnn normal-strength<br />
concrete. The acceleration for heavy re8nforccmnt plater were h&er than [ha far<br />
lhghtcr mnforeement. Thlr lndrcatcn that the aeceleratlon rnagnrtude increased when the<br />
concrete strength and EWI nnfaacmenl ratio wcre ~ncrrarrd. lncrear~ng concrete<br />
strenah from nonnal-strenph to high-strength. horn abut 35 MPa to 80 MPa. increased
the acceleml~on by about 40% I" the case <strong>of</strong> somply-supported and lncrravd about 30%<br />
~n the case <strong>of</strong> fired support. In addltion. as the rlul remforcemcnr ntlo ~ncre;csd by<br />
about 0 5%. the aeeelenttan lncread by about 10%.<br />
The cntlcal vcloc8ty <strong>of</strong> pcrfonr~on aceord~ng to CEB (1988) were very close lo<br />
the test re~ults for hlgh-strenpth ConerCle plates. both tn the case <strong>of</strong> fired and nmply-<br />
supported However. br normal-strength concrete. the cnucal velmlaer were different.<br />
Under fired condlnon, the ten results <strong>of</strong> normal-strength concrete plam were much<br />
hlgher by about 308 than the code predicttan. On [he other hand. for ~nmply-supported<br />
plses. the test mulls were rl~ghtlv lower by about 4% than the CEB (19881 predict8an.<br />
In concluaon. the predietxon <strong>of</strong> cntlcal vcloctty bared on the CEB 11988) Equvtlon (5.9)<br />
8s adequate md ern bs used to erttrnate the cnt~cal vclaclty <strong>of</strong> hlgh-strength concrete<br />
plates rublecred lo tmpact loading accurately.<br />
5.6. Fracture Mechanics Analysis <strong>of</strong> Impact Load<br />
The strength <strong>of</strong> mtcnals depends on how rapndly the stress a applncd Thus. the rare <strong>of</strong><br />
lodlng effect 13 crtrrmcly Impman,. smec It sets a lhmtr on the allowable slresrcs ~n<br />
structures based on the expled ttme under load. One <strong>of</strong> the mntn objective Is to use<br />
fncture mcchantcr to pmvlde a more detvtled estamatc <strong>of</strong> the nte <strong>of</strong> loading effects on<br />
the behanor <strong>of</strong> the concrete plats under Impact.<br />
The fmture mshanlcs appmach to the nte <strong>of</strong> loading effect I" bnttle matmrlr 8s<br />
bawd on he classical Griffith (1925) theory. The fracture 1% governed by equatnon:
where, a, = fracture rlrenglh<br />
E = modulus <strong>of</strong> elast#c#ty<br />
y = fncturs surface energy<br />
o = cnck length<br />
If G, = Zy IS the cnt~cvl anin energy release rile. then the Equation (5.10) can also k<br />
wntten ~n the form:<br />
An lntnnrnc marcnal propcny called fncars toughness. K, . can then be defined as<br />
K, = a (5.12)<br />
In order to sracs that fracture wtll %cur when the crack length. a. reacher some cnllcal<br />
value. rubrt!tuting Equalon (5.121 lnlo Equaaon (5.1 1) g~ve-<br />
Subcnl8cal cack gmwth a defined as the gmwth <strong>of</strong> cracks [ha are loo small to<br />
cause frllure under the prevanllng nrrerr. Dunng ruknucal crack gmwth. an emplncal<br />
relat~anshtp IS also ut~l~zed that describes the crack vsloc!ty as<br />
whm. V = 6 = rate <strong>of</strong>crack extenson. w hkA and Nanconaanu. KI 8s the stress<br />
lntenslty factor and equal to K, at the cntncal stress condion.<br />
Assumtng. Y = &. Equalton (5.131 become.
a -K,<br />
( - *,"2<br />
Umg r more genenl form. Equalton (5.151 can be expressed as.<br />
K = YO<br />
Combtnmg Equallan (5.16) wllh Equatlan (5.141 glvcr:<br />
The rare <strong>of</strong> stress can be define ax<br />
da<br />
- = AylYah',&r?<br />
d,<br />
db - =<br />
dt<br />
Alrernrttvely. 10 other way. Equatlan (5.181 can be wnaen as:<br />
I5 181<br />
dt = dP 15.191<br />
0<br />
Subsntuung Equatlan (5.191 lnro Equarlon (5 17) and leads to the !nregmuan gtver.<br />
J:,,,-N~?~. = (5.201<br />
d<br />
1 L,-,N-~,?, ,;, N-112,]= AyN_O,N*I<br />
iq (N+l)U<br />
(5.21)<br />
where the sukcnpt i and f refer lo he initla1 cond~tnan before terung and the final<br />
condition on fncturs. respscttvely. lnrenlng Equauon (5.15) into Equarlon (5.111. gvcs:<br />
Lert~ng:<br />
a,n+l - ~ aKc~-~(N+l) L,N-2 -0,~-2]<br />
AY2(N-2)<br />
- ZKC'-~ (N+l)<br />
AY?(N-Z)<br />
(5.221<br />
(5.231
And.<br />
otN+l = B., b,'V-? - <strong>of</strong>N.? ]<br />
<strong>of</strong>N+' + BoatN-l = Boo,N-~<br />
From Equalon (5 251. ~f the final strength <strong>of</strong> a specmen tr measured m r fracture ten.<br />
the lnlllal strength can be computed by knowing the slrcrring rate a Conversely. tf the<br />
nn!t~nl strength <strong>of</strong> s rpcclmcn IS known. @he fracture rmngth m any constant loudlng nte<br />
lest can be defined from Equallan 15.251 by numencvl methods.<br />
As reported by Nadeau. Bennet. and Fuller 11982). urlng the pnncnples <strong>of</strong> Ihnear<br />
elanc fracrure mechan!er. the dependence <strong>of</strong> strength on the rare <strong>of</strong> loadmg cnn be<br />
expressed by [he lagmthmlc fm <strong>of</strong> Equation (5.24). The erpresrlon can be wntlen ar<br />
follows.<br />
Ino, = L l n ~ + o -L ln,!o,'-' -<br />
Ntl N+I af'v-2 )<br />
(5.26)<br />
Analysis <strong>of</strong> Equrtaon (5.261 tmpllcr that a plot <strong>of</strong> Ino, Venus In0 would have a<br />
slope <strong>of</strong> [II(N+I)] ar lower valuer <strong>of</strong> o . Rnaily, s would reach I eonnant value lrem<br />
rlapcl as high values <strong>of</strong> 6. Thts tseonsnstent with the suknl#cal cnck growth model that<br />
ar very hlgh loadtng ntcs. the strcngth would be largely andependent <strong>of</strong> loading me.<br />
Sbnee. there 3s not enough time for rukntlcal crack gmwth to occur. the mltlal md final<br />
strength ue eswnually equal.<br />
In Xcmt yean, there are three nndependent mcthcds for evaluating the constant B<br />
in Equatlon (5.23) by detcrmnnnng the conswt N baed on.
1 I) dmct observations <strong>of</strong> crack pwth mensurementr where the constant N IS the slope<br />
and the canrwnt A IS the tntereept <strong>of</strong> the V-K plot. where V!s cnck vclaclty and K Ir<br />
nntnns~c mvtenal propcny.plot an a lopnthm~c scale.<br />
(2) the mtc <strong>of</strong> loading effect ~n whtch the firs two terms <strong>of</strong> Equalon 15.26) are plotled<br />
gwmg bath the slope Nand f<strong>mm</strong> the lnrcrcept 6.<br />
(3) r !o:mthrnle plot <strong>of</strong> the spplled stress against the erne to fa~lure. the slop <strong>of</strong> rhts plot<br />
LS [-!IN].<br />
Mlndesr (1984) reported that the values <strong>of</strong> N obrnr.ed f<strong>mm</strong> lrnpacl lerts are<br />
~ssent~rlly Ihe same as those oblaned f<strong>mm</strong> constant mte <strong>of</strong> loading lcrlr IIhc second<br />
method). Thtr would suggest that even at these very hngh stress mte, the fmcture<br />
pmeerrer an much the same.<br />
Flpre 5.1. Method <strong>of</strong> calculating Nf<strong>mm</strong> stress!ng rate data<br />
108" 0
The method <strong>of</strong> enlculat~ng N from rtrerstng rate data IS shown m Feure 5.1 when<br />
matcnalr can be assumed to behave m a lhnear elasec manner. The strength. a,. can be<br />
expressed as a funct~on <strong>of</strong> rrress iate.0 Then. the slop= <strong>of</strong> loga,. venur lo0 ts<br />
defined as[l/(~+~)] When matenalr can be assumed lo behave on a lhnear e1;rrtr. he<br />
nrers nu m r tea cm be related ro the rtnm rate. e . through n rlmple relation: a = Er<br />
The llrlt hump a stmn versus hllure ,$me plot ~ndteater lncntrl stram and thc second<br />
hump ts where the bnttle matnx fractures. Since the matnx cnck created dunng the<br />
second hump. the value <strong>of</strong> N m present research obtalned f<strong>mm</strong> a logrnthmnc plot <strong>of</strong><br />
applied stwn venur the tlme to fablure ~n nsnng pan <strong>of</strong> the second hump The slope <strong>of</strong><br />
thxs plot 8s [IN].<br />
The valuer <strong>of</strong> N ~n the present erpenment are prerenled ~n Table 5.4. The rrble<br />
notwes that the value <strong>of</strong> N vanes between wide limlts. In general. the valuer <strong>of</strong> N are<br />
h~gher than normally reported for Mher types <strong>of</strong> concrete The test ~sull nndxeates that<br />
concrete 8s known lo be far more rensltlve to stress nle under lmprct lo~d~ng than tn any<br />
other mode. Thls phenomenon pmbrbly caused by a lack<strong>of</strong> a llneilr response. Concrete Ir<br />
not 6dmIly bnttle and the o -c response is far f<strong>mm</strong> llncar The valuer <strong>of</strong> N therefore<br />
m ~ not y be expected lo capture the <strong>mm</strong>e nature <strong>of</strong> nmrs nte Ernlltlvlty ~n these malenlls.<br />
Therefore. as pomted by Mindesr (1985). the vrrumptron <strong>of</strong> n lhnslr elasuc fracture<br />
response assumed m Equauon (5.14) Ir not enurely valid. However. the pmpenler <strong>of</strong><br />
high-strength concrrle BE close to more lhnear response than normal-nrength concrete.<br />
Hence. the uw <strong>of</strong> linear fracture mechanics far structures made wrth hlgh-strength<br />
concme are mare valld than nonnal-rmgh concrete.
For rpctmenr loaded slowly. mom rtme IS available for slow crack pwlh than<br />
rpeclmens lwdded rapidly. Therefore. Ihc nce <strong>of</strong> loadnnr effect on the tested rpes~mar<br />
must be conndemd. Under very htph rate <strong>of</strong> landtn~ such as nnpsct londln$. the crack<br />
velae~ty (crack growth) depends an she valuer <strong>of</strong> Nas defined by Equauon (5.14) As the<br />
value <strong>of</strong> N ~ncmascr. the crack velalty rncreass. I1 can be seen ~n Table 5.4 lhat the<br />
crrck vslaclry mcmse as well 2s !n thecase cf an lncrevlc <strong>of</strong> Ihe concmre strengh and m<br />
the care <strong>of</strong> a deerem tn steel relnforccment ram<br />
Values <strong>of</strong> N f<strong>mm</strong> impact tess<br />
NO.<br />
1<br />
2<br />
3<br />
4<br />
5<br />
6<br />
7<br />
6<br />
9<br />
10<br />
11<br />
12<br />
13<br />
14<br />
15<br />
16<br />
Speclmsn<br />
HSSl<br />
HSS2<br />
HSS3<br />
HSS4<br />
HSFl<br />
HSF2<br />
HSF3<br />
HSF4<br />
NSS1<br />
NSS2<br />
NSS3<br />
NSS4<br />
NSFl<br />
NSF2<br />
NSF3<br />
NSF4<br />
fi'<br />
MPa<br />
81 7<br />
81.7<br />
61 7<br />
81 7<br />
79.1<br />
79.1<br />
79.1<br />
79.1<br />
33.1<br />
331<br />
33 1<br />
33.1<br />
36.6<br />
366<br />
36.6<br />
36.6<br />
70 P<br />
0.95<br />
1.26<br />
1.90<br />
2.32<br />
0.95<br />
1.26<br />
1.90<br />
2.32<br />
0.95<br />
126<br />
1.90<br />
2 32<br />
095<br />
1.26<br />
1.90<br />
2.32<br />
However, some msemhm lhke Relnhardl (1985) suggssrcd an allernatwe<br />
sxplunason af the obssrvsd trends gwcn on the bas,% <strong>of</strong> "on-Innear fracture mechanics. 11<br />
has bem rceognlud Iha ~<strong>mm</strong>edtately ahead <strong>of</strong> a movnng crack is a zone <strong>of</strong> mtsm<br />
N<br />
28<br />
28<br />
24<br />
23<br />
33<br />
24<br />
22<br />
28<br />
24<br />
16<br />
14<br />
28<br />
24<br />
21<br />
17
cmclung. called process zone. The rze <strong>of</strong> he zone <strong>of</strong> mncm-craclung dcpndtng on the<br />
velocity <strong>of</strong> the crack. A faster crack has a larger zone <strong>of</strong> mzm-cnclung ahead <strong>of</strong> 11. At a<br />
hlghei nrerr nle that crack propagates faster, and therefore the pmess zone will be<br />
htggcr. Thar ,"creased mem-craelung may crpliun the h~gher fracture energy<br />
Rqulremenrr at hlgher rtress rates.<br />
The prcvlour ursumenr seems to contnd!ct wrth the argument presented above<br />
The rubsnl>cal cnrk gmwB. predmcrs less <strong>mm</strong>m-crackmg ~n htgh-rrrerr rrlc loading<br />
rltual!onr However, these two phenomena occur on $he oppornrs rldsr <strong>of</strong> Ihe pnk lxd.<br />
The concept <strong>of</strong> rubcntlcal crack gmwth ~s applncable pnor to the pak load whtle the<br />
concept <strong>of</strong> larger pmerr zone appl~es for orhc pan-peak load regnon where the unrtable<br />
crack propagason co<strong>mm</strong>encer.<br />
5.7. Dynamic Fracture Energy<br />
When the pmjectnle htls the rpclmen. a sudden transfer <strong>of</strong> energy f<strong>mm</strong> the pmject!le to<br />
the specmen occurs. The energy lost by the pmjeculc Ir panly mnsfemd to the<br />
rpeclmen and panly rrayr wrthtn the pmjccrnic tn the form <strong>of</strong> slasue rlrrlns and<br />
vlbrauons. The energy mewed by the rpcnmen from the pmjecttie 19 the energy even<br />
by the area under bendrng load versus deflectton curve. as dexnbed m the follow~ng<br />
cqurtmn:<br />
GI(') = ~~PIl)du 15.27)<br />
where. GJ It) =bending energy -wed by the spcrmsn<br />
PI!) = punchmg load
ulrl<br />
= &fleetton at the load polnt<br />
The dcflcctlon slt) can be obluncd by double lnlcgratlon <strong>of</strong> the extrapolated accclerarlon<br />
ar the load pamr. i(r1. by equation:<br />
"(I) = 66 ti(,) d dt<br />
(5.281<br />
Rpre 5.2 ~llusrrares a typ~cvl load venur defleetlon plat. The area under lond-<br />
deflectnan curve reprexne the haeture energy recelvrd by the ~pecimcn subjecled lo<br />
Impact loudlng.<br />
Figure 5.1. Typtcal load-&fleeson curve<br />
The dynamic fra~lure energy values under tmpul laadlng for all tested Jpectmcnn<br />
are then compared to static fmture energy under rtnttc loading. The valves <strong>of</strong> naric<br />
fracture energy were obmned f<strong>mm</strong> prevsou mvesligmrr. t.e. Husem (1990). Marrout.<br />
Em. and Hlld (1995). and Osman. Marrauk. and Hclmy (1998).
The eompan%on d fnctue energy berwccn dyamlc to rtaic tests are then<br />
tabulated tn Table 5.5. The results tnd~eate thar concrete undcr Impact loading. erpeclrlly<br />
hl@ rtrenoh concrete. IS more energy ahorbing lhan undcr slartc lording. In gncnl.<br />
concrete 1s a rensltwe matenal lo the chnng tn the nrerr-a. The nlmr <strong>of</strong> Impact ro<br />
Erattc fncture energy was found to be hlgher for hngh-nrensh concrete than normal-<br />
strength concrete Thnefnre hlgh-arengh concrete plaler are cansadcrrd to have more<br />
tmpacr mtrrance than normal-strength concrete.<br />
Table 5.5. Comprnron <strong>of</strong> dyvmlc fracture energy wah rtrllc fracture energy<br />
5<br />
6<br />
7<br />
8<br />
9<br />
Cmdltlon FrCIure Fracture DYnamh<br />
(MPa) (50 (kN%k:!Yld C~?k:'lOs Stat'c<br />
HsS1 Slmph/lupporled 81.7 095<br />
HSS2 Slmply supponed 81 7 1.26 4.21 2.74 1.5<br />
HSS3 Slmplyrupponsd 61.7 1.90 876 3.01 2 9<br />
HSS4 Slmply OUppOned 61.7 2.32 12.27 3.18 3 9<br />
HSFl<br />
HSF2<br />
HSF3<br />
HSF4<br />
NSSl<br />
Fixed<br />
Flxed<br />
Flxed<br />
Flied<br />
Slmply rupponed<br />
79 1<br />
79.1<br />
79 1<br />
79.1<br />
33.1<br />
095<br />
1 26<br />
190<br />
2.32<br />
095<br />
NIA<br />
3.64<br />
8.12<br />
1245<br />
0.77<br />
2.32<br />
2.56<br />
2.44<br />
2.61<br />
243<br />
I IS I NSF~ Flxed 1 36.6 1 1.90 / 1.86 1 NSFI I Fixed 36.6 232 2.60 2.43<br />
.<br />
1 4<br />
3.3<br />
4.8<br />
0.3<br />
2.E ( f (
Chapter 6<br />
SUMMARY AND CONCLUSIONS<br />
The dynamnc behavior <strong>of</strong> the two-way reinforced concrete plates under lmpvcr lodtng<br />
are ru<strong>mm</strong>anzed bncfly. The present rcremh lnvesligllon eomb~ncr lnro an<br />
cxpenmenl~l mvestlgnttan and a numeneal mverrigruon. A su<strong>mm</strong>ary <strong>of</strong> [he two phases<br />
<strong>of</strong> the #nverttgrl8on IS desenbcd m the followmg sectran.<br />
The crpenmsnlal lsstlng program was conducted on sixteen retnfomed concrete<br />
plater under umety <strong>of</strong> concrete srmgth. steel remforeement rruor. and two end-<br />
condit~onr. The plates were lsrtcd under dynamlc lmpvct laud. The Impact load speed<br />
ranged between 4.0 lo 9.0 mlr as aceelemuon ranged between 70 to 120 g Elghr<br />
rpecnmcnr were constructed wlth high-strength concrete, whtle the other elght spclmens<br />
were conrlructed wtth normal strength concrete. The concrete strength ranged berween 35<br />
to 80 MPaand had r vanety <strong>of</strong> mnfo~cmcnc rataor m the range <strong>of</strong> aboa 1.0%-2.5%. and<br />
were tested u nk fired and simply suppaned end-condsllon. The behnvnor <strong>of</strong> htgh-<br />
strength eonmtc plarcs was evaluated in terms <strong>of</strong> deflection, concrete and steel strams.<br />
ensrgy absorptnon. and frasturc mergy.
The numeneal lnvcstlgatnon war earned our lo verify the vnl~dnly <strong>of</strong> the coder'<br />
predimlonr. The resonled lmpaCt load eapncases were compmd with rtatc capacstter <strong>of</strong><br />
cumnt coder' predlct~m. In uddltlon. a fracture mechanlcs tmpvet load analyslr based on<br />
lhnear elarucr fncture mcchanxcr (LEFM) was performed. The purpose <strong>of</strong> Ihe numerical<br />
Inverogauon was ro piovlde a more deratled analyrlr on the effect <strong>of</strong> the rate <strong>of</strong> land~ng<br />
on the dynamic behamor <strong>of</strong> high-strength concrete plater. The dynamscr fixture energy<br />
<strong>of</strong> the leslcd plates were comparcd lo ~wtlc fracture energy calculsted from prevlaur<br />
inverligeorr.<br />
6.1. Experimental Investigation<br />
Expenmental rtvdxa were conducted on stxteen re~nforced eanmtc twrrway plater<br />
rubjcclcd lo impact lading. The followcng emelus~onr were *ached from the present<br />
tnvesugalan ewcsrnlng the effect <strong>of</strong> concrete strength. steel rr~niarccmcnt mtlo. md<br />
end-condlttan<br />
I. All EpeCimens fallsd under duct~lc shear fatlure. The observed angles <strong>of</strong> hilurc were<br />
about M) degree for normal-strength concrete and 65 degree for hlgh-rtrenph<br />
concrete. In addillon. the punchlng shear surface on the tension face was laated at a<br />
dnstanee <strong>of</strong> 1.6-2.0 tnmer the plate deplh (d) f<strong>mm</strong> the edge <strong>of</strong> loaded area for the most<br />
<strong>of</strong> the tested spamenr.<br />
2. As the concrete ruenph incrensed from nmal-rt-ngth to hlgh-strength (35 MPa to<br />
SO MPa). energy absorption capaelty and cnttcal velasty <strong>of</strong> perforaim mcrrased.<br />
The energy absorption capanty mncreased by a a gc <strong>of</strong> about 3-5 timer. and the<br />
critreal velsity <strong>of</strong> perforat~on inerrad by a range d aboul20%-30%.
3. The steel reunfarcemcnt has a major effect on the dynamle behavtar <strong>of</strong> h~gh-strength<br />
concrete plates, lncreas~ng retnforcemenr nuo fram 1% to 1.5%. the cncrgy<br />
rbsorptlan tncmarcd by 50% for hcgh-nrengh concrete and 100% for normal-<br />
strength concrete. whnle the cntncal veloclty <strong>of</strong> perfonuon maeased by about 10%<br />
for both high-strength and normal-strength concrete. lncreas~ng rennforccmsnt ratlo<br />
from 1% to 2%. the cncrgy abrarprlon mcrcascd by about 3004 md the cntlcal<br />
velocxty <strong>of</strong> perfanuon ,"creased by about 20% for both high-strength and normal-<br />
rrrenglh concne. Increasing re~nforeemsnl nua fram 1% to 2.5%. the energy<br />
ahsorpllon sncreued by about 400% md the crit!cal velocity ~ncreised by about 30%<br />
far hngh-rtmgrh concrete u well as normal-ntrengIh concrete.<br />
4 The effect <strong>of</strong> the end-condieon was las ~xgn8ficvnt on the behvvlor <strong>of</strong> hvgh-rrrenph<br />
concrete plater under imprcl lord. Ar concrcrc strength mcreased from normal-<br />
strength lo htgh-strength. the cnrtcal velocity <strong>of</strong> prforatnon inerwwd by about 20%-<br />
30% for the snmply rupponcd speclmcnr. While under fixed-end candtt!on. he<br />
cnrlcal velrrxty <strong>of</strong> perfowion lncrersed by about 50%-60%.<br />
5 In the case <strong>of</strong> rtatle loadmg, the peak-load, peak-nwn md mnr~murn-defleeeon<br />
occurred at the same ume. However. I" the case <strong>of</strong> tmpacc loadmg. the peak-smln<br />
oecur. rllghtly later than lo the peak-load bur ahsad <strong>of</strong> manmum-dcflem~on. In<br />
addieon. the tension nee1 nnln s esumared by about twice that recorded under rtattc<br />
loading. The ten results illunnte the difference between ampacr failure mechvntrm<br />
compared to rutsc fatlure mechannsm. All <strong>of</strong> the impact tcn specimens failed under<br />
ductile shear failure.
6.2. Numerical Investigation<br />
An analr~cal ~nvesugation war camed out an the impact loadrng on a concrele plates<br />
The recorded tmpacr load capaclues were compmd to rtat~c capac~lies calculated by the<br />
formula <strong>of</strong> cumnr codes. A fracture mshantcs analyslr based on linear elasrlcs frilclure<br />
mechanlcr (LEMI was performed to evaluate the effect <strong>of</strong> "re <strong>of</strong> laadang an the<br />
dynamic oehvvtor <strong>of</strong> high-nrength concrete plater. The dynamner fracture energy was<br />
campmd to nruc fracture energy far all <strong>of</strong> the tested rpe<strong>mm</strong>enr. The rtgnlficvnce and<br />
contnbutton <strong>of</strong> the present numeneal lnvertlgallon can be concluded ar follows.<br />
I. The punching shear cvpaclly due lo tmpact loadnng were about twlcc rhrr <strong>of</strong> the rtalc<br />
punchlng shwr capacity. The rarlo <strong>of</strong> Impact punching shear clpaclly lo strtlc rr<br />
crtrrnated by [he ACI-318 (1995) was ~n the nnge <strong>of</strong> 1.39-2.31 The same ratto baed<br />
on BS- 8110 (1985). CEB-FIP (19901. and NS-3473 (1992) were 1.50-1.82. 136-<br />
1.65. ilnd 1.81-2.33. respeet~vcly.<br />
2. The cnlmcal veloc~lmes <strong>of</strong> perfmson can be ertlmated accurately for all high-strrnglh<br />
concrete specimens according to CEB (1988) code expresson. However. for nondl-<br />
strength concrete under fixed-end condmon. the cntlcal velmly <strong>of</strong> the ten result wrr<br />
30% hlghcr than the cads predictnon. On the contrary, under simply-suppaned<br />
cond~tnon, the test result war nltghtly lower by abut 4% than the code valuer. In<br />
general. he prediction <strong>of</strong> the CEB (1988) code can be uoed accurately lo esllrnale Ihe<br />
cnueal Impact velocity, erpecnally for high-strength concrete plater.<br />
3. A linear elastlc fracture mechantcr impact load expoian can be used m evaluate the<br />
effect <strong>of</strong> rate <strong>of</strong> loadxng on the dynsmtc behav~or <strong>of</strong> htgh-~lrength connete plats.<br />
High-smnglh concrete is more brinlc and close to more Itneat rrspanse pnm to peak
load than normal-strength concrete. Therefore, linear frvture mechsn~sr can be used<br />
lo pmvlde a good degree a1 confidence.<br />
4. The concrere fracture rrrength. a,. can be erpnsed ar a funcrsan <strong>of</strong> the stress rate.<br />
6 The slopes <strong>of</strong> log a, Venus logdwere determ~ned expnmenwlly. The<br />
suggested valuer far N and rubqumtly the two canrlanrr A and B can be used to<br />
RpreSent the Etrerr nle renrlttvlty numbers lor hlgh-strength and normal-slrength<br />
concrete plater. Therefore. the reco<strong>mm</strong>ended valuer can be used by derper la<br />
predtct the dynamsc behavln <strong>of</strong> any plarc under m prt load~ng.<br />
5 The dynnmnc vcnur rlauc fmture energy rauo <strong>of</strong> h~gh-rtmgth concrete plate under<br />
~mpact load war found to be much hagher than that for normal-strength cancrele.<br />
Therefore, hlgh-rmph concrete plates rre constdered lo be mare effiaent marenal<br />
for conrtruct!on under Impact loodmg. mgh-nrengrh concrele Is u better matmnl than<br />
nonnrl concrete ~n dynrmlc rttvananr kause <strong>of</strong> !e tncreassd impact rennance.
REFERENCES<br />
ACI-ASCE Ca<strong>mm</strong>lnee 316. 1962. Shear and Dtapnal Tcnnon. Pmceed!ngs. Amencan<br />
Concrete Inrt#lute. Volume 59. pp. I-M.<br />
ACI Co<strong>mm</strong>~ttce 212. 1983. Adm~rturer for Concrete. ACI Manual <strong>of</strong> Concrete Plasucc.<br />
AC1212.I R-81. Detnt. 29p.<br />
ACI Co<strong>mm</strong>~nee 318 1995. Building Code Reqvlremenls for Svuetunl Concrelc IACI<br />
318M-953 and Co<strong>mm</strong>entary (ACT 318RM-95). Amencan Conc~le Inrurute.<br />
Farm!ngton Hills. MI. 371 p.<br />
ACI Ca<strong>mm</strong>tttee 357. 1985, Guide for Derngn and Canstruelion <strong>of</strong> Fwd Offshore<br />
Swmurer. A<strong>mm</strong>can Concntc Inntale. Dermnl.<br />
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