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BEHAVIOR OF HIGH-STRENGTH CONCRETE
PLATES UNDER IMPACT LOADING
O Suryawan Munradi
A thesis submitted lo the School of Graduate
Studies in panial fulfillment of the
requirements for the degree of
Master of Engineering
Faculty of Engineering and Applied Science
Memorial University of Newfoundland
March 1999

ABSTRACT
High-smnsh concrete plater are frequently used !n vmous slrucrurnl cngmeenng
systems and vaneuer of elvd cngsnecnnp apphcanonr. A research pmgmm was cdrned
out at Memonal Unlver~~ty of Newfoundland to lnvcrtsgvle the behsvlor of h~gh-ilrengh
concrete two-way plecr subjected to Impact lon&n& The research program included bath
expnmental lnverrlgarlon and numerical tnverugnlon.
The c umt rercawh nncludes an expenmental lnverllgruon on rlrteen concrete
plater wtth dtmenston of 950x950 mm md 1Wmm rhtcknesr. The plales were rupponcd
by r specla1 fame dengncd far thlr tnvemgunon. The suppan fnme 1s made from
~oncrele and steel wllh free opennng of 7Wx700 mm. Normal-strength md htgh-strength
concrete placer were tested undsr two end eondtsonr. x.e. fixed and slmply supponed. All
of ,he rpzctmms were two-way rennforccd plater *ah relnfomsmcnt rmo that vaned
from I%-? 5% I" tmslon face and 0.7%-0.8% ~n eomprerslon face. A ng~d project~lc was
used lo apply the Impact lard to the tesled re~nforced concrete specamens. The ng~d
projecttle was a mlmd steel cylmda wrth ??O-kg mass md 3011.5 mm diameter contact
area. The projeellle was dropped fmm a vanable helght of up to 4 m. An sccelemmeter
~9th +2W-g cnpvelly was attached to the eylnnder steel lo record the actual lest
aecclersuon. A data acqutslrlon system b ad on a penonal computer acquired the drtil at
I rampllng rate of IWO Hr. The structural behavtor wlIh respect lo d~splacement.
eoncrele and steel stmns. fatlure mode, and energy rbmrpt~an were exammed. The effect
of d pme loading. concrete strength, reinforcement atdtlo, and suppan patterns were the
test parameters.

A numcncnl mvertigatnon ww conducted lo cvvluore the rest rerultr wlth respect
to the Nonh Amenean code and some European d erp codes A lhnerr elwllc fmcture
mechanics Impact load expressam was used to evnluate Le effect of nle of loading on
the dynamtc behavnor of high-arength concrete plates. Based on the cxpcnmental rerl
results 11 hw been found that the punch~ng fanlures of the lmpacl loodnng were about
lwlce the Slauc punchmng shear capnclly The cnltcal velocltte$ of ~rfnnuon cm he
csrfmated ;~ccurately for all hlgh-rrrengh concrele rpcctmenr accordtng lo CEB dynamic
cde expresson. The ratlo of tmpaa versus rlalnc fracture mergy far high-sirenph
concrete plate war found lo be much hngher than that for normal-strength concrea.
Therefore. hngh-strength concrelc plates are eonrndered to be more efficient lhan normal-
strength concrete plates under tmpacr loading.

ACKNOWLEDGEMENTS
Thlr lherlr was completed at Memonal Unlvcnmty of Newfoundlmd as pan of Master of
Eng~neenng degree program. The expenmental work has been caned out n the concrete
and itruclure labonlory of Memonal Untveraoly of Newfoundland. Cim~da. Fundzng !n
the form of graduate fcllowsh!p from the Govcmmnt of Republic lndonesla md ~se;vch
supplement from Mcmonal Unxvcrstty are gracfully acknowledged.
Grateful acknowledgement s alro due lo Dr H. Marzouk. Pmfer~oi of Clvnl
Engmeenng. under whose gumdance and supervls>on thc lhertr was carned out.
Acknowledeement Ir alro addressed to Dr. M.R. Haddam. Associate Dem 01
Englnsenng Graduate Srudnes and Research. far has encouragement and the frctllner
provtdcd.
AcLnowledpmer~lr me alro made to the Technical Staff for their nrnnmcc ~n the
expenmental prognm. espemdly Mr. C. Ward. Mr. A. Bur~ey. and Mr. R. O'Dnwall for
then prepdntlon of [he test speelmenr and lest equnpment Spectvl thank to Dr. A.
Husseln and Dr. M.A. Fard for their ruppon and dnxurrlon dunng expenmental work.
Last. but nor lesl, the author takes thls chance to express his profound gruntuds
to all htr famsly members. espccnally hnr parents for thew prayer and blersng. nlsa he
wffe and son for their patence. continuing encouragement. and afkuan.

Table of Contents
ACKNOWLEDGMENTS
Table of Contents
Lstof Symbols ..................................................................................................

2.1.2.2 2. Fine Aggregates I2
2.1.2.3 Admtxtures .............................................. 13
2 1.2.3 1. Mtneral Admlxrurcs .............................. 11
2.1.2.3.2. Chemtcrl Admixtures ............................. 15
2.1.3. Bmhrng and Mnrlng Squcncer
2.2 Punching Shear Strength
2.3 Impact Performance of C
2.3.1 Ovcrvtew of Mamal Modeilng
......................................
2.32. Smmn Rarer for Vanou3Typrr of Load>% ...................... 31
2.3.3. Prapemesof Concrete Under Dynamnc Laadtng ................. 36
2.3.3 I Compress~ve Strength
2.3 3 2. Modulr. of Elasue~ty ............................................. 27
2.3.3.3. Ult~malc Strrln
2.3 3.4 Comprerrlve Fm
2.3.3.5.Tenrale Laad~ng
2.3.3.6. Tenston Modulus of Elarttcnty
2.3.3.7. Tensile Fracture Energy
.............................. 29
2.3.4. lmpacl Reslrl~ncc of Relnforced Hlgh-Smnglh Concrete Siabr 32
2.3.4.1. Desg hncttcc 32
2.3 4.2. Eumpan Dertgn Codes for Punching Shear Capaclly
and Cnlical Pefiorft~on Velocnlv ........................... 34

Chqlei 3
EXPERIMENTAL INVESTIGATION
Chapter 4
3.2.1. Re~nfoxomcnt
3.3. Test Spctmens
3.4. Fabncatlon of Speclmenr
3 6. lnrtrurnsntation System
3.6. I. Tertmg Load
3.7. Test Pmcedurc
3.6.3.1 Steel Strams
TEST RESULTS AND DISCUSSION
4.1 Craclung Charaaenrtter 66
4.2. Laad-Deflection Chaactensucr 67

Chapter 5
4.3. Dynam~c Fracture Energy
4.4 Steel and Concrete Strmnr
4.5. Mder ofFvilure
4 6. Effect of Concrete Strength
4.7. Effect of Sucl Ranforcement Rauo
IS. Effem of Ssppan Patem
4.9 Effect of Dynamlc Load, ......................................
NUMERICAL EVALUATION
Chaplet 6
5 1. lntmducr$on I I3
5.2. Impact Load I I4
5.3. Punching Shear (StascCrpac~ty) 115
5.4 Code Recommendauonr 118
5 5 Cnttcnl Veloctly of Pcrfantton I20
5.6. Fnccure Mcchrnlcs Analys~r of Impact Laad .................................... 122
5 7. Dynam~c Fmcrure Energy 119
SUMMARY AND CONCLUSIONS
6.1. Expnmental Invesugaean 132
6.2. Numerical lnvest~gvt~an 135
REFERENCES ....................................................................................................... 137

List of Figures
Figure 3.1. Cross scuon A-A of lyplcal spclmen under fired suppon ............... A7
Rgure 3.1. Typ~cal steel re~nfarcement of rpc~men
Fngure 3.3. Arrangement of steel relnfarccmcnr reba
F~gure 3 4 Casting of fresh concrete fmm Ihe mser to the formwork ............ TO
Fkgure 3.5. Compresswe nrength lest of a concrete eyllnder ................................. 5 1
F~gre 3.6. Concrete beams of thetest frame 51
Fngure 3 7.Concretc and steel beams for fired-suppon 53
Figure 3.8 Speetmen under Axed ruppon ............................................................. 54
Figure 3.9 Bottom rennforcement of the concrete base of the tcrttng frame ........... 55
Flgure 3.10. Top relnforccmenl of the concrete base of the lertlng frame ................. 56
Ftgure 3.11. Complclc tcsl fnme wvh guide steel cylinder .................................. 57
Ftgure 3 12 Test set-up for fixed rpctmen
Rpre 3.14 A rpeclmcn dunng ompact te~nng
Figure 3.15. LPDT fixed ar !he center of rpnmen
Flgum 3.16. Lacat~ons of steel rtraln gageson tenrlon and camprelrlon facer .......... 62
F~gure 3.17. Concrete strain-gage locsuon
Figure 3.18. Dataacquirntian systcm
Figure 3.19. lnsmmentataon blockdiagram
Rgure 4.1. Failure panems of lest specimens HSSI. HSS2. HSS3, and HSS4 ......... 75
F~gure 4.2. Failure parlems of test rpeelmcnr HSFI. HSF2. HSF3, and HSF4 ........ 76

F1gure4.3. Filllure paltrmr of lest specimens NSSI . NSS? . NSS3 . ;md NSS4 .......... 77
Fbgure 4 4 Failure parems of test spcctrnenr NSFI . NS F2. NSF3 . and NSF4 ......... 78
Flgurt4.5 Fatlure pallem of a rrpmcal tcrtrpeenmcn at Ihecornprerrron face .......... 79
F~gure 4.6. Load-deflecllon curves for rpectrncn no 1 . 2 . 3 . and 4 ....................... 80
Ftgurc 4.7 bad-defleeuon curves far specmen no . 6 . 7 .and 8 ............................ 81
Flpurp J 8 Loaddeflect$on curves fmorpamen no 9. 10. and I I RZ
hgure 4 9 Lad-deflecuon curves for specmen no . 14 . 15 . md 16 .................... 83
Rgure 4.10. Lord-deflecrron curves for spamen no I and 9 ............................ 84
Figure 4.1 I . Load-defletlon curves for specmen no . 2.6. 10 .and I4 ................... 85
Ftgure 4.12. Load-deflectson curves for specmen no 3.7. I1 . md 15 ................. 86
Figure 4.13. Load-dcflecuon curves far specmen no . 4 . 8 .and 16 ........................... 87
Ftgure 4 14 . bad-erne curves for spectrnen no . 1 . 2 . 3 . and 4 ................................. 88
Figure 4.15. bad-tlm curves far rpcclmcn no . 6 . 7 .and 8 .............................. 89
F~gure 4.16. bad-rtms curves for spec~rnen no 9 . LO. and 11 ............................... 90
Ftgure 4 I7 Load-hmcurvel for rpeclmen no . I4 . IS . and 16 .............................. 91
Flgure4.18 Deflectton-arnecurver for specmen no . I . 2 . 3 . and4 ....................... 92
Fsgure 4.19. Deflecl8on-nme curves for rpcnmen no . 5 . 6 . 7 . and 8 ....................... 93
Figum4.20. Deflectton-tlmecurver for rpectmen no . 9 . LO . I I . and 12 ............... 94
Flgure4.21. Deflectton-nmc curves for specmen no . I3 . 14 . IS . and 16 .................. 95
Figure 4.22. Slccl and concrete rmmr of specmen HSSl ......................................... 96
Figm 4.23. Steel and concrete srrans of specmen HSS2 97
Figure 4.24. Steel and concrete rtmns of spscirnen HSS3 98
Flgurt 4.25. SPel and concrete strains of specmen HSS4 99

Ftpure 4.26. Steel and concrete stnlns of rpeclmen HSFl ...................................... 100
Figure 4.27 Steel and concrete srralnr of specmen HSF2 ................................ 101
Ftgure 4 28 Sreel and concrete srranr of rpec!mcn HSF3 .................................... 102
Fmpure 4.29. Steel and concrete rtnlnr of rpse~men HSF4 .................................. 103
F~UR 4.30. Steel and concrete ~ tn~ns of specmen NSSI ................................ IM
Rpore 4.31. Steel mdconcrete rams of rpeclmen RSSl ....................... I05
Ftgure 4.32. Sleel and concrete Etnlnl of rpeelmen NSS3 .................................... 106
Rere 4.33 Sleel and concrete strains of specmen NSS4 ............................... 107
Ftgvre 4.34. St-! and concrete stramsof specmen NSFl ................................. 108
F~gure 4.35. Steel and concrete rrrdlns of rpeclmen NSF2 .............................. 109
Ftgure 4.36. Steel and mncrele nraknr of specmen NSF3 ................................... 110
Fipure 4.37. Steel and concrete rtntnr of rpectmm NSW ............................. 111
Figure 4.38. Htph-strength vmus normal-strength concrete plrte behawor
under lmpvct loodnng 112
F~pure 5 1 Method of crlculattng N rom rlrerr!ng n data ................................ I26
Rpure 5.1. Typical load-denealon curve 130

List of Tables
Table 2.1 Typ~cal rtnm rarer far various rwr of lodtnp . ...... . .. . ...... . .. . . 25
Table 3.1. MIX propanlo" for I I' of nonnalirrengrh concrete ...... .... ........ . .... 37
Table 3.2. MIX propomon for l m'of h~gh-smngth concrctc .......... ..... ...... . . 38
Table 3.3 Prnpen!cr of steel retnforcement
Table 3.4 Delallr of specmen
Table 4.1. Test results
Table 5.1. Cntlcal velac~ty of perfanuon .. ........... ... . . .. .... ............................ 120
Tnble 5.3. C~lculaled cnllcal velocnty campmd wtlh test velac,ty 121
Tlblc 5 4 Values of ZV fmm ~mpact tests 128
Tnblc 5.5. Companm of dynamsc fracture energy wtth rtatte fraeturccnegy ...... 131

List of Symbols
area of rsel remfa~ement
enck length
final crack on fncture
lnlcial enck kfore lertlng
accelcratton of pm,ecule
total aeceleml~an
ride dnmenrlan of square ioaded area
pnmelsr of mueal recrlon for shear ~n plater
pnphsry around rhc column excludtng apenlngr
effecuve depth of the slab
- do slress rate or vanallon of rmss wtlh frmc
I
E modulus delnn~aty
E, modulus aieiast!e!ty of concrete
E, modulus elarl!cnty of aeel
EeV
dynamic (impact) modulus of elastlenty
E,,, nauc modulus of slvsticnty
Fir1 Impact loadng
1, mean cencme mmgth

I

lmpact test load
mlrrlle penmeter
penmeter of the govern!"% rectlon at a dlrtance 1.0 d fmm the loaded wen
deflect~an at the load paml
ilccclerslron at the load pala
velm~y of crack errenslan
ult!rnnlc shear force
ullnmste load for flexural fatlure
nomlnsl shear stress
ult~mac shear stress
EOnCrelc denslly
crack wdth
wtdlh of the fracture pmccsr zone
crack uldth when f, rexhes rem
crack opentng velwlty
dynamtc matenal pmpeny
Pacar whtch adlusts r,for ruppon dlmennons
mtloaf long ride to rhan ride of thc concentrated load
fracture surface energy
malenal eaffielent for relnforc~d
tC"S11~ SVdl"
y~cld slmn of steel remfmrnca

maxxmurn lenrtle rtnln
impact ullxrnare stram
stme ultlmare rtmin
111~1" nre
rtnln rate n quasi s tali^ condltmn
rcnsllc mnforccrncnt ratio
comprerrlve retniare~mcnt nuo
penmeter of the column
frxture sucngh of concmre
final rucrr of 3 Ipecnmtn measured ~n a fracture test
lnltlal arerr of n rpcclmcn
stress rare or vanallon of nerr wtth tune
stress nle a qwlsl rletc condtuon.

1.1. General
Chapter 1
INTRODUCTION
ll 1s appropnatc to dlxurr and clmfy a number of fundamental poma ~n the subject or
dealing wnth rpec!Rc derlgn munpmcnt. Thm SIX three polnts that rhould be cian8ed
before examsnlng the behavior of concrete plates under lmpilcl loading. Frrrlly. thc high-
strength concistc plate should be defined. Secondly. the dcfin~tton of Impact loadtng
rhould beoutlmed. Fmally. the ohjcct#ves of the research should he dewnbed cledrly.
Hngh-strength concrete IS defined as any concrete wtth eomprernve-strength over
41 MPa. Hlgh-sucnglh 8s reallred thmugh the use of silica fume as a pantal replacement
for cement to pmduec extrsmely srmng, hlghly abrvnlon remnant. impmneil. ble. very
durable conmle agalnrt freeze-thaw damage and salt water aanck. Thlr marenal has
already been successfully used far offshore platforms. marine ruuctures. tall buildangs.
and long span bridges.
Impact loading ~r a result d a mllinon between two bodes thar aceur m a very
small interval of 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
structural element that has to be dengncd to rerlri lmpacl Ioadsng Thlr loadmg IS mostly
eimme lwildang ~8th mnfrequsnt probbbltty of extrtenee dunng the Ihfeume of !he
structure. However. falure due to Bmpxt loadtng often results ~n a senous rtruclunl
&mag. Marenal propcn!es like hlgh-cnergy absorprlon have lo be llken lnta
conadcnoon I" the dcrlgn of sttic concrcte structure.
Many rmcturer experience Impact loadcng. Some of the structures La murl have
the porrtbml~ry of Impact loudtng consldered m them desngn are offshore fnc#l~ner. ptles.
deknw shelters. and rlructures ~n retrmlc areas. The tmpacl loading can be ~gnored tn the
derlgn pmcerr when the Iodlng lntcnstry has small Ilumualonr. However. when the
rnsgn!tude of the fluclualng component af londlng 3s large. lhc Impact lwdd~ng can be
very rtgnllicmt. Engineers should be able to decsde whelher the mpxt lord~ng must be
accounted for ~n des~gn or neglect a. The resvns!bnltty of the data engnncer IS to solve
problems m a safe. effimmt. and economic manner. Therefore. the dcslgn cng~ner
should consdm how the overall ntruclure behaves under lmpact loadmg.
The use of h$&-strength concrew IS ~ncrr~nng faster than the development of
apprapnale dertgn code recommcndaltan In spite of the wtde use of high-rtrmgth
concrete. l~ttle research has been canduel~d on the structural behavtor of high-strength
concrele beams. slab and columns under dynamic loadmg. The rtruclunl behavlor of
concrete plater, especially under lmpxt loadnng, needs funher Invenlgaoon. The
concrete plare in a nmple. sonarnica!, and popular nruclunl rysrem. Therefore. hlgh-
strength coneme flat plate was chosen ~n this research, rlnce it bar wvenl clvll
engrnecnng applicat!ons.

1.2. Research Scope
The %ope of lhls study IS ro nnvenlgnte the dpamlc behav~or of two-way remforced
concrete plates under tmpacl loadtng. The 6nvesugatlon tncludcr an expenmental
anuertlganan and a numerical evaluaton The two phwr of the mnversgattons are
dexnbed as fallowr:
The expenmental rerung pmgmm will be conducted on wvenl speclmenr
rub~eeted to fmpafr loading. The lmpuc: load sped target rmge between 4 to 9 mls as
~!ccelcrat.tlon ir nnge between 70 to 120 g The rpectmenr will be tested under Axed md
rrmply supponed end-cond8nanr. The behavior of high-rmnglh concrete plaer ulll be
evaluated wnth rerpeet lo deflection. concrete md stel smtns, energy rbsorpr~on
capsclry. and fracture encqy.
The numneal evaluilllon will be cmed ou~ lo venfy the valndnty of the current
codc prcd!cttonr. The lmpaEl lo~d ccapacllles wlll be compared wlrh Xauc capvcltlcr of
the coder A fmacture mechanxcr Impact load analytnr based on lhnear elilrt#cr fracture
mechanics ILEFM) wnll be conducted. The purpare of the numerical evaluutton 1s to
prov~de a more detall anvlyrns on the effect of the rate of loading on the dynamtc
behawor of h~gh-nrength concrete plates The dynamtc fracture energjes of the tested
plates wdl be compared lo sratlc fmcture snsrglsr calculated fmm prevnous Invcst>galon.
The nudy wlll provide adcslgn gut& forengnneem on the effect of nte of loading an the
behvvtor of high-strength concrete plate.

1.3. Research 0b.iectives
Thrr ==arch wmll nnvesrngale the rest results of 16 different rpectmens Based on the
e\penmenlal lnveslrgatlon a better undentand~ng of [he khavlar of htgh-smnph
ranforced concrete plates under Impact loading will be reahzed. The mqor objeclwcr are
nor lhmtrcd ro hut wdl conram the followrng objecnver:
(I1 lnverugrtc the rtrvctvnl behrvlor of high-strength concrete plate under dynamic
tmpact loadtng.
(21 S~udy the effect of the md condttgons on the rttuctunl khavtor of hhgh-strength
concrete plate under ampact loadnng.
(3) Examme the effect of re#nforcemmt nu0 an the behi~vtor of high-strength concrete
plates.
(4) Record actual concrete strdxns. see1 strams. and deflectlan of htgh-strength concrete
plater under Impact loadnng.
(5) lnvcrtlgate the tnfluence of the rate of lodtng on the Impact bchavlor of rpeclmens
usmg fraclure mechanics equatlanr and ten results.
I61 Pmv~de new lnfomallon on the farce-dlrplacement relunonrh~pr of h~gh-strength
concrete plater.
(7) Compare the result of the invenlgatton with rhcoretrcai erpresaonr and code
equilttanr.
(8) Evaluate the fnnure energy of the concrete plate undm Impact loading.

1.4. Format
Thnr therls can be dlvlded Inla three pans. Pan I sppem under Chaprers I and 2 Chapter
I covers the tntmductlon and rhc ablecclver of lhir ~nvsmignt~on. Chapter 2 presents !he
lttenrure revtew of prevfour xnvestlgatonr.
Pan 11 appears under Chapter 3 thal cover all the cxpcnmental tnvessgauon
camed out to study the effect of concrete strength and relnfonement nllo an the
behawor of relnfoned concrete plaler subjected to Impact loddnng. Thlr chapter coven
the sa-up of labaratory and crpcnmcnral pmgram
Pan Ill appcarr under Chapters 4 and 5. cover the enrlre research Andlngr. rest
results and anrlyllcal tnverugauon ~ncludlng evnluatlan of severdl models lo predlcl rhc
iheilr-mrenglh of hlgh-stmgth concrete plate. Thlr chirplei also presents I numerical
evaluat~on bared on a fracture mechanics vnalys8r to evvluare thc effect of rate of loudtng
on the behavior of conc~te plater. Rnully. r conclus8on summanrer the cxpenmcnval
and analyttcrl lnvatkgatnonr are grven 8" Chapter 6.

Chapter 2
REVIEW OF LITERATURE
2.1. High-Strength Concrete
2.1.1. General
Qurlnty of concrete IS generally derenbed by as eomprr!ve nrength. Accordtng to the
Amencan Concrete Innlture. ACI 363 (1992). ordsnav strucrural cancrele has been used
wrlh r cornpreslve rlrength in b e nnge of 20 to 40 MPa. Whtle. hjgh-strength concrete
1s defined as any concrew wtth over 41 MPa compresswe strength. But. in the 1st two
decadcr. concrete ~8th hlgher compresswe strength has been used tn rhe cansrructlon of
high-nw buildrngr. long-span bndger. and offshore structures. The new hlgh-strength
concrete has n compresswe strength of 70 MPa and IW MPa.
The uoe of high-strength concrete a sprendlng rapadly all aver the world and
lncrearing faster than the development of appmpnate derlgn code recommendat8ons.
Several recent invertlgatlons have been conducted on hlgh-strength concrete behvv~m to
find the charancnstic behavlm of high-nrmgth concrete and to up@ the cumt

derugn recommendar~ons so thac the polsnt!rl of hngh-strength concrete can be fully
expoad.
Recent tnveniguuonr on high-rtrengrh concrete can be clnrrlficd ~nto three masn
cnrcgoncs. 1.c. khavlor of matenal pmpentes. behav~or of rlmclunl memberr. and
develapmcnr of teslsng equtpment. There three man cacgona can be dercnbed bnelly
~n the followlnp:
(I) W~th altenr~an to the mvtcnal pmpenler. rcvenl ~tudler have been camcd out to
tnvcstlgvle Ihc bchavln of h~gh-strength concrete rubjcctcd lo dtfferent stress
condlllms.
(2) Wtrh respect to the behavior of rrmcrural members. several rrudler hive been
conducted to lnvestlgate the behavior of structuml elements conslmcted wtlh hlgh-
slrmgh concne.
(31 Rnally. with eonsrderatson to the development of tesung equlpmenl. xvenl
resenrchcr have been gwen to tmpmvc the lestlng equnpment tn order to ~nvesttgate
ilccurntely the behrv~ar of hmgh-strength concrete.
Dunng the pan decade. rcvenl concrete matcnnl and stmctunl mvenlgarnonr
were conducted at Mcmonal Unlvers~ty of Newfoundland. Mmouk and Hurrcin (19913)
conducted the development of hlgh-nrenph mnr den@ fmm lacal mrtenalr It h& been
concluded that Iacal matmalr can be used wtth s~llca fume and fly ash to provtde
strength of 70 MPn at 28 days. Manouk and Chcn (1995) recommended a const~lut~ve
relatronshlp br the behavior d high-rurngth concrete under unlarsrl tension load
~ncludtng the pat-pak sabnmg rerponx and fncture energy.

Mmouk and Husretn (1991) reported that the use of the cuble mot of the
compresave strength to predlet rhc punehtng shear reststance of hcgh-smngth concrete
slabs Ir much better erprerrnon compared to the square mot expresseon used m all Nonh
Amencan coder. Mvnouk and Jtang (1994) ~nvcsrtgatcd rlr different methods la
enhancement of the punchang shear capacity. The strucrural behawor of hnoh-nrengh
concrete plater rvns cvalunrcd ~n terms of ovcrrll load-defleetmn response. ulilmotc
loadrng capaerty. ducultly and energy absarpoon. Fanlure patterns and nlnm dtstnhut~an
we= also dlscurrcd.
2.13. Mix Design of High-Strength Concrete
Hlgh-strength concrete IS made wlrh the rumc baste ~ngredlentr as normal-strength
concrete. Famy and Pana~ (1993) reported that the praducuon of hlgh-xrcnglh
concrete is achncvcd by opt!mizar~on of the follaw~ng facton.
(1) ehaactenrt~cr of the eemenung medium.
(2) chnnctcnrtxe~ of the aggregates.
(3) pmportlonr of the pasts.
(4) paste-agpgates ~ntsraclian.
(5) mixmg, consolidating, and cunng. md
(6) testing pmecdum.
Some relatan of mmalr and mlxrng methods are being explored thmugh research.
However, atlendon to the &ve nx basic arras Ir of exveme impanance whether wlng
exirttng or new materials and techniques. In the United Stater and Canada, the ACI

Commltlee 363 (1992) report 8s used 3s r gutde for the dcngn and construcrlon of hngh-
slrengh ConCrete EtWClURE
LI.LI. Cement
Cemcn~ pule 4s an imponant faeror ~n malang htgh-strength concrete. Selection of r
panlmd cement for htgh~strcngth eancretc should bc bxcd on compmti\.c stxnglh lcrlr
of cemea at 28 and 90 dayr. A cement that ytelds the hlghesr compresswe arengh al (he
later age. 90 dayr. Ir obvlourly pefcnblc.
Zrn el nl. (1993) dernbcd tha the cholce of nppropnate cementltlour matenills
war governed by consaderat~onr d:
Ill can.
121 av~ilabnhly.
(31 cvtdence of rartrfncrary performance.
(4) the cngtneeis confidence in rpec~fylng the mutenal. and
(51 the contrxtor's absllty to produce, handle. and place concrete contalnnng Le pmduct.
In the Unlted Swres and Canada. ACI-363 (19921 recommendatlonr rqulre n
mtnlmum cement content of 360 kg/ml. In order to make hngh-strength concrete: the
mlxrure rhould have r cemenooaur mvtenals content of between 360 ta 603 k#m3
However. the use of htgh cement content ~n masslvc rtmctures frequently leads la
thermal erxlung. Thermal mbng increases the permeabll8ly and Rduccs the dunbnlity.
Therefore, developnng hxgh-rmngth cement wnth modeate hear of hydmt~on 1s
recommended ~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 of cements to pmduce hngh-
strength COnClelE.
Watersemen1 muo a typtcnlly expressed as the total weight of water to the total
wctgh! of cement. In addanon. warerscmenrlllous matenvl ratlo ,r expressed as !he rota1
werght of wscr to the total combnncd wash1 of all ccmentttlous marenalr. In both carer.
:hc total uelgh! of uateiexcludes that absorbed by The aggregales. but lncludei my uatlr
intrduich !ntn ?he mlrture as pan of an adm#xIure. Some of the more finely ground
ponland cements such as ASTM type I11 (h~gh-early-~trcngth) will have hlghcr mnxnng
water requrement for equal workab~bty. pantcularly at law wnlereemenr ratnos. nnd mny
pmmoa npvd st!ffcn~ng m hot weather. Unfonunatcly. thm type of cement !r not
recommended for high-strength concrete
2.12.2. Aggrewta
Aggregates are lhorc pans of the concrele that constttule the bulk of the Sntshed product
Aggregates constatute the major pan of the mlr and compnre 60% lo 80% of the volume
of the concrete, They have to be so graded that the whole mass of concrete scs ;Is I
relntlvely rohd. homogcncou~. dense camb~natlon. wxrh the rmtller rlus acung ar an
filler of the votdn.
Usually, the man components of aggregates can bs dtvlded ~nto two typr (I)
coarse aggregate: gravel, emshcd rcnc. or blast furnace dag: and (1) Snc aggregate:
nauml or manufacturd sand. The coarse and fine aggregates are de~cnbed bneny m the
followmg drwusnm.

2.1.22.1. Cmmc Aggregates
The charactenrr#cr of the aggregate rngaficandy influence the pmpenler of concrete.
lnclud~ng rrrength. The strength of aggregates 3s always greater than the strength of
cement pate. However, for htgh-nrengrh concrrrc pmducnon, the strength of the cement
pane Ir hlgh enough to nvnl the rcrength md other vital pmpcntes of the aggregate. The
slrength ofthe ugregae. the bond or ldhenlon between cemen! paste 2nd qgreglte. md
the abrarptnon chancrensuc of the aggregate all become more imponant for high-
strength concrete than for normal-strength concrete. For thns reason. any one of there
propcnles could be n lmlt factor far ultimare nrengh.
There Ir a pnnqcal value ~n determlnlng the oplnmum rlze of come aggresJte for
dtfferenr concrete ltrrngth levels. The optlmum nu depends on the followtng factors
(I1 relelve strength of the cement paste.
(2) cement-aggregate bond. and
(3) rlrenglh of the aggregate pan~cler.
The chemncvl conant of the aggregates. that Is the mlnnol present, does lend some
~nrnght snto predicting the mnreract~on bctwen cement paste and aggregate pantcler Stall.
rnvl batches provide the most prxncrl lnformar~on for chaorlng the best aggregae for il
concrete mtxture.
For normal-strength concrete. Walker and Bloem (19M1) explanned that mlrlng
water qulrement IS reduced a coarse aggregate nze Is ~ncreased. The net effect s u
lower watersemcnt rauo and htgher rmngth. Water qulrernent tr a funcrxon of the
averall fineness of lhc oolid mgredteas.

For high-ruenah mlrlures. rhc use of small agpgmer with marlmum nomtnrl
rlze d 190. 12.5. and 9.5 mm. usually Ir ~uffie!ent to offset rhe effect of Ihc hlgher
mtrmg water demand. Cmquillo (19851 reponcd that the use of crushed aggregates tr
recommended for the praducrton of htgh-strength concrete. rather than mund aggre~ater
Thts was aunbured lo the reduced nggregae-manar lnrerfvce band nrenglh of natural
pvel aggreertes
However. the mle of aggregates m hngh-arenph concrele Is mmor compared wtth
the role of cernentit~aur malenals. Manouk. Osmun. and Helmy (19981 reponcd that 11
ha been produced a bgh-strength Ihghtwe#ghr concrete up to 80 MPa a the concrete
laboratory of Memonal Unlvennty.
2.I.LZ.L Fine Aggmgates
Saucier. Smllh. md Tynes (1964) ~ndmaed that fine aggregates eontam a much hlghsr
surface area than come aggregates for u gwen we~ghL Because 11 has I much larger
surface area. the fine aggregare isandl can ~nflusnee the amount of mlsnng wafer requred
md affect thc pmpemes of fresh and hardened paste more than the cornc aggregate. In
sands of the wmc gndtng. 1% ~ncresse ~n fine aggregate votdr may tnducs r 5 llm'
~ncwue tn water demand to maaam an equal slump.
Slnce all aggregate m concrete must be coated with paste. the shape and gndnng
of fine aggregate as well as Its pmponnan to coarse aggregate will have a direct Impact on
pasts requlrerncnt. More cement paste tr required when more fine aggregate IS used. The
less sand used. however. the harsher mixture and workability maybe senourly ~mpnred.
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
pasrc.
The band of pwte to line aggregate IS less ngnrlicant lhsn bond lo eorrse
aggregate bccaure of the large ruxface area nvalablc I" the fine aggwgare for bond~ng.
Maxlrn~n~ng the come to 6nc aggregate nuo (CAIFAI can result ~n the mon eihctent.
and ~hcrrforc ecooom~cnl. use of cemenntlaur mxenals The opurnum nlln nf CW4 wlll probably be apprrea fmmtnal batches basedon warkvblltty of the msrture.
Rounded and smooth line aggregate pantcles (natural rand1 are better from the
newpomt of workab,l~ry than sharp and rough panicles imanufsctured rand). Conerere
mnrlures of he same slump and cement factor coaam8ng nau:al sand produce hlgher
rrrengthr than consrctc contmntsg manufactured rand w reponed by Fmy and Pnnmre
119941. The palullcle shlpe and gndlng of !here mntennls are probably rerponrlble for the
strength d~fferencer.
Washlng the sand may be necessary. When natural rmdr contslnlng Irrge
qurnttl!cr of mlcu. clay, and other delelenour macnalr. Thew harmful macn~lr should
be avo~ded as !hey may tncrcare water demand and affect hydrartan md bond of cement
pvrle lo aggregate. Untformrly of grading from bach to batch 1s also Imponant for both
the f~ne and come aggregates because of Itr effect on workability.
2.1.2.3. Admixtures
Adm~rturer am malcnals other than water, agpgares, and cement that arc used as
~ngredtents of concrete. ACI Commltlee 212 (1983) ~poncd that he iunctlan of
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
added lo the batch nmmed~ately before or dunng the mlrtng. There pmpentcr help the
concrete to achlcve high strength and water reductton w~thout loss of worhblllr)
Tnal mlxlums rhould be Mde with the ndmlxlure and job matennlr at the same
temperaturer and humidity anrrlpnted on the job Thtr permrrr an evaluatnon of the
compvtlb~l~ty of an vdm-rture w~th other adm!sturer ad concrete materials. It also server
an evaluarton of Ihc ~dmtxlure effects on the propcnrer of fresh and hardened concne. A
recommendatton by the manufacturer or the apttmum amount &lerm#ncd by lnborvrory
lnnl batches should be used. The major type of adm~xturer can be rummanzed ar mlncral
dm~xlurer and chemlcal adm~xturer. whleh wall be described bnefly an the followmg
dtrcurslon
2.1.23.1. Mineral Admixtures
The most lmponant mnnml admnxturer lo the pmduetlon of hlgh-rtrengh concrete are
pouolmr The two porzolans most commonly used m h~gh-nrength concrete are fly ash
and rlltca fume. However. espei-#ally I" Canada. gmund grunulared blast-furnace slag has
been used more recently instead of ~rllc~ fume. Ground slag far use ~n concrrtc should
confan lo reeuon C989 of the ASTM (1997). rpecllicat!on for ground granulaled blrsl-
furnace slag for uw m concrete and mortar.
Fly ash 1s produced as n by-product of the comburuon of pulverized coal ~n
electnc power generating plant. Th~s marenal 8s used to amend msuffie~ene~es in a
concrete mix by providing mjrsrng fines from the fine aggrrgntc. Usrng fly ash type F to
the mlr can impmvc qual~ties of concrete such as reducing permeability, expansan. and

the cost of concrete-mahng matennls. Unfonunaely. the pmpntes af fly ash can vary
greatly becau~e of the wtde range of comporctton of coals. Conrndenng the acceptance
and un~fomty, rcsrr should made aceardzng to recrlon C618 of the ASTM 0997).
rpeenfiealan for fly ash and nw or calr~ned naural puolsn for us rr a mtnenl
ndmtrture I" panland cement concrete.
S,lrd fume IS a new porrolan~c malenvl (ha! has received constderahle allenllon
~n both research and applleatlon. This malenrl a a byproduct rerult~ng from hngh-punly
qwar wcth coal 10 the clcctnc arc furnace tn the production of snliean md ferrorcl%con
dlloys Unltke fly ash. rillca fume IS extremely fine. Mon of panleler are less than Ipm.
and the average panicle dmmeter 1% about 0 I pm ~8th surface area of nbour Z0.W
m'ikg. For comparison. fly ash surface ma typncally ranges from 300 to 5W m'lkg.
ground slrp fmm about 400 to 600 m'lkg, and lype I cement fmm 300 to 4CnI m'lkg
Attcln and Neville (1993) repned that the addman of slltca fume to the mlx
Increaser the coheaveness. viseonty. and water demand of fresh concrete. In hardened
concrete. the addillon of rtllca fume cm produce slgnlficsnt Increase ~n rtrenpL. modulus
of elrn~mly. md flexural ntrengrh. The use of rnltca fume rhould canbrm ro wcllan
C1240 of the ASTM (1997). rpeclfieauon for sflicr fume for use ~n hydnullc-cement
concrete and monar.
2.1.23.2. Chemical Admirmm
The benefits to be reallzed fmm uw of admlxturu m htgh-strength concrete have
plaeucally mandated tktr use. Thcx ndm>rrures increaw the workab~lity and enable
reducing the cement content in propnlon lo the reduetion in water content. A common

pracuce a to use s water-ieducmg admixture (ruperplantctzer) m comb~nal#an wtth a
water-reducing retarder.
The type of rulphonsed naphthalene formaldehyde ruperplwl!clur nonrlly
used reducer the amount of water requnred by 154%. However. usmg thns
ruprplmle~zer aften results !n hxgh rate of slump loss. malung ~r difficult lo place the
concrete properly The hlgh nle of $lump Imt will he overcome hy the add~laon of the
water-reduc8ngretardcr whch exlends the lnme of set and -81s the placement af a very
low waterxemenf ratlo concrete.
The compar~b~ltty of the vdmlnture~ wlrh the chorce of ccrnea 8s u very lmponanl
cans~deratton lo order to reduce any underlrahle effeas 8n concrete. all chemtcal
admlxlures rhould meet the requlrcmsntr of $maon C494 of the ASTM 0997).
rpecrficanonr for chemtcal adm~xtures for concrele. The use of retarder rhould be
confomcd la ~ccuon C494 lyp B and D of the ASTM (1997). whllc the use of
ruperpl=stlc!ur should be conformed lo recnon C494 typ F of !he ASTM i 1997).
2.15. Batehing and Mixing Squcnra
The vncarpoalton of rllica fume and hrgh-nnge water ~duesn makes It porstble to artan
htgh-nrengtk concrete at early ages. The followang batchlng and mixmg procedure has
heen developed by carlia rerearchen an the concrete Isbomoq of the Memonal
Untvcnlry of Newfoundland far Ihe product~on of workable high-strength mar.
(I) Charge 1W% of coarse aggregates.
(2) Batch 103% of cement.
(3) Balch lW%of fly ash.

(41 Barch 100% of rand.
15) Mlx for 3-5 minuter afkr uddnng 50% the erum~led water wllh water reduclng rsea.
(61 Prepm a slurry of rlltca fume. togelher wtlh 25% of gross ruperplarr~c~zcr dare and
20% of water.
(71 Mlx for 5 mlnuler.
18) Add 30% of mlx!ns water roeerher with utr entnanmnc admtxlure5.
(9) Retemper with the m t of ruperplasoenerdore to target slump
Flowtng concrete was pncnlly achleved unng those mlrturer ~ncludlng
rupcrplart!clur and retarder The a!r content ~n the majonly of [he mlxrurer Ires v~thln
3% lo 5%. Slump values were lmrely at the 100-mm target. while an average value of
the unll welghlof fxsh concrete was 240 kglm'.
2.2. Punching Shear Strength
Renpc!wc ruggrted approaches can be represented u ellher the result of an empmncal
study or a ntnonal srudy to e~labllrh r relartanshnp between Ihc load and stress at i~~lurc
of concrete plates The emplncsl study used I rlal~tlcsi arnslyas of the svallilble lest
results. whsle Le noonal audy descnbcd and ldcvllred rn~thematlcnlly the mechrnnrm of
failure.
In the cue of emp~rieal studies. Forsell and Halcmberg (1946) described that the
cnllcal sectton loeated at a dlstvnce ILQ fmm the lded area. Lt has also been reponed
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
of arqum column. and h Is the effectwe dcpth of the slab.
Mae (1961) conduced an crpenmcntvl mvea#g.atlon to analysts of shear rrrcngth
where rhear and flexure were con~ldered as r comblncd laddtng problem Mae rraxcd that
the cnucal scct!on of a slab subjected to a coneenwaled load was located at the column
pcnmerer md rhrt the shear urengrh tr to some extent dc~ndcnt upon the flexural
strength Bared on $he expenmental program. a "em,-emptncal type of equauon wa
developed to calculate the ult,matc shear rtrenph.
where. u. = ulumnte rhcar nren
V. = ulttmate shear force
V,i.
= ultlmee load for flexunl fatlure
h = rlde dlmenrlon of rqum loaded area
r =periphery amund the column excludtng opnlngr
d = sffcctlvs depth of the slab
= compresswe strength of concrele
It was suggested that Equatxan (2.2) war the be* equalon lo date for predlctlon d
the failure load ~n the repon of ACI-ASCE committee 316 (1962) The Comm~ltec
recommended that the followmg dertgn equauon for calculating ulumale rhem load.

where b lake us the penmeter at a d!rtance of dl2 from the periphery of loaded area. and
v 5 4 .06. f; IS the concrete comprerrlve strength. and d tr the effectwe depth of the
slab.
The shear derlgn methods of ACI-318 Bu!ldlng Code (1995) and CSA A23 3-94
(1994) ore based on the developed I" the most pan an the work Moe 11961). The wto of
the ulrmmste rhcanngeapaelly of the slab to the ulumale flexurrl capac~ry of the rhb IS
defined as Q, = x. the followtng cmpnneal expresrlon w;lr developed fmm
Vn,,
Equauan 12.2) forthe predfctnan of the ult~mace shear stress:
v, = [(1(1 - 0.075 Q) - 5 250, ) 12.41
The devclopmenl of destgn appmachcs of !he Bnurh Codes. BS 81 10 (19851. and
Is based pnmanly on the work of Regan (1981). An cqurtnon WAS developed Lo calculsre
punchtng rherr crprc!ly as:
V,, = K. K,.=@.69d)~C + 7.851) 12.51
where. V, = ult?mrte rhenr force
K,
K ,
= 0.13 for normal concrete andO.105 for Ihghrwe~ghl concrete
= 1 .I5 I4 n leolumn area) 1 (column penmeter)' I"'
IWA. = steel ratlo
bd
f,.
= cube strength of concrete
d = effectwe depth of the slab

ZC = penmeterof the column
The rhear penmeter for a rcczangle column a located at distance 1 25 d out from rhe
column. for a ctxular column tr located ! 25 d out from the column.
Manouk and Hursan (1991) tnvert~gaed the rtruelurxl behavnor of narmrl-
strength and hlgh-nrength concrete slabs wnrh respect la punching reraaance The result
,huwed that h~gh-strength cuncrra erh~btcs r more bnrtie fanlure than normal-nrengrn
concrete The rerearchen have also lndicvted that the Mae's Equnuon (2.41 cmnot he
mommended to predict the punchtng shew capilctty of hsgh-strength concrete sldhs The
punchlng renrtance 13 proponlonal ro rhc cuhlc mot of concrelc camprerrlve strength
Therefore. the assumpeon of the Bnr~rh coder e better than the use of rqusre mat of the
concrele strength as even an the present Nonh Amencan coder such as ACI-318 (1995)
md CSA A33.3-94 (1994).
Gardner and Shva (19961 eonnned the use of cuble mat of compresswe strength
uslng rhetr expenmental resulls regarding the punehlng rhear of a two-way flat relnfarced
concrele slab. An emplncal method urmg u shear penmeter amund rhe lodded area war
prerenrcd. The cmpnncal recommended equatlan was expressed as follows:
where. v. = ult!mate shear rtreor
v, = nommal rhear stress
V. = ulumate rhexfome
tr = penmelcr of loaded m a
d = effectwe depth of the slab

p
s flexural steel mnforcement rauo. calculated over w~dth c + 6d
f, = yield strength olnexuralrreel
f,, = mean concrete strength
2.3. Impact Performance of Concrete Plates
2.3.1. Overview of Material Modeling
CEB (19881 repon No. 187. recommended hat generally the mechanmcdl behrvlor olthe
concrete malenal s deocnbed by n stress-stram relat!onshlp.
taklnz stram rate tnto account lends ro-
where the rtnm rnte a defined ar:
;md ~texprerser the vaneuon of stram wtth nme.
0 = fk) (2.71
b = f(s.f) (2.81
dr
E = - (2 9)
d,
More mesly. several Invesugmronr hrvc revealed that ills (he landing hnrtory should
be tnken lnto account.
b = f (E.Z. fwd bisrop) (2.101
It a obvlaur that material modclr covrnng the relation in Equalton (2.10) are much more
complteaed thvn those for Equalton (Z.7) In this wnx, a bmad vanetter of dtlferent
malenal models erlrt which may be grouped nnro the man categoncs of clartlcay theory.
plarueity. viwoplarucity, ctc.

The different theones appllcabls lo the modeling of eoncrele and steel
re#nfomcmcnr will be dlrcussed bnctly accoidsng to CEB (1988) repon No. 187 rr
follawr.
(I1 Llnearund non-lmear elvstlc models
Llnenr clasttc models m best known due to rhelr nmpltc~ly. buc rr Impact load~ng in
gcneinl cause non-llncwdcfonnation s is not sumd for any aypllcatnon in thtr field
The same may be rtaed for non-Itnear elasl#c models.
(21 Vlvoclvrtlc modelr
Modelr bed on vrruelartlc~ty hrve becn ured for the dercnpllan of creep md
relaxallon phenomena. A few authors have used thlr lheory w~th the ~dev thnr
stm~lvlty between creep md rrraln-rate-effects should erst.
(31 Vtscoplwuc models
Modelr brrcd on !he theory of v~scoplartic~ry have been ured for many years dlro for
the dercnptlon of tmpw problem. The theory of v~scaplvsl~e~ty 13 very conventen1
erpeclally for lhc madclmng of the remforc~ng steel. md may be r~mplrfied to a varl
extent at lea1 for the one-dtmennonal caw.
(41 MDdCls based on planuaty
Madelr k d on the theory of plart~ctly can be arnnged nnlo twocareganes such nr'
(a1 Elaruc-perfectly plarrre matenal behavtor
The material shows elartle behavtor up to a ccnan level, for example
comprerrlve strength where stran IS mcresed at constant stress. The tnfluence of
stress rate can be taken into account by tnereastng the yteld level aecordnng to this
SIRIS mte

fb) Elastlc plastic behavior wath hwdcn~ng
lnltead of under~osng unllmlred deformatlan at ;r conslant rrress level. rhe rrrerser
lncrearc with lncrearlng stram Rate effects upon the yzcld surface are ~ntmduced.
for cramplc tn the form of rate hardenmg paramcrcrr.
(5) Endachmntc models
Modclr hared on cndachmn~c theory havr been devclopd for concrete and
re~nforctng steel. Onginally Ihe cndochronlc theory was bared on the vnscoplnruc
Leoq. supplemenled by a new lntemal vanable. the lnlnnrlc tlme. Although the
endoehmn~c theory war the subject of cantroverrul dnrcurnonr, a Eecms that some
phenomena. likc the influence of the loadnng hlrtory upon the stress-stram
relalonrhjp and the rmtn-rule depndancy. are very well represcntd. For relntorcing
rtel this model a adequate. but for concrete. the problem of dnlntancy a1 high nrun
IS not salved yet.
(6) Fneture mcchiln~cs models
Fmcare mechanics has to be ruM#v~ded tnto r lhnear and r nan-Itnear lhwry The
Itnear theory provlder a pod barns to predlet unstable or eatanmph~c propagatton.
Relauonr exla between frrctunng stress. crack length, md ~ lra~n ras. Lanew fmclure
mechanics doer not take any planlc dcformalon or mrm-cracklng ~n the regIan of
the cmck ep ~nro account. However. as concrete and ductile steel are concerned. thls
mu* be lncludcd because of the fact that the energy consumed m the plart~c or mtero-
cracked p mes zone IS more relevam than the elasttc pan.

(71 Damage meehanncr models
Models based on damaxe theory are relrtzvelv recent. erpec~ally on concrete The
method 8s based on the ldsa (ha damage occurs u an ~mvcn~ble dcgmdelon uf thc
mnlenal under deformanon. A damage pameter as rnuoduccd as ;l scalar or vcctonsl
funcr~on of thus degndatlon process. The degadauon pmesr IS a contlnuaur and
:lobs1 pracenr and doer not constdcr only degmdatrcn wlthln n dehult l~kr the
fmaurc mechanics concept
(81 Staehastlc models
The frdcture pmcrs withon the malnr of concrete IS formulated urmg rrochast!~
farmul~ulon Concrete 8s modelled u a group of cauplsd elements wllh two or three
different phases. A lopnthm~c relalan between rhe reststance of concrete and rtrerr
or rtraln nle can be formulated.
23.2. Strain Rate For Various T yp alLoading
In men1 years. mspccmble atlentlon has been glven to the influence of rtmln rate or
stress nte an the msshvn~cal pmpnlcr of concrete. relnforclng $reel. and pre-nrernng
steel. Steel and concrctc wdl be tw~tcd 8" two rubwquent recuonr. The prerentsrlon or
the data will be such [ha a deslgn engtneer ern use such panmeters m sample hand
cnlculrnons and m n llmttcd manner also 8" advanced computer codcs. The propcnlcs
will be gwen ~n graphs and or m fununnlonal farm with rerpea to stnm or stress nte.
Table 2.1 gwes some global est~mares of rrraln nter whlch acur dunng vanaur
types of loalng. As reponed ~n CEB (1988) repon No. 187, lhev values are not expen
entlmater and have lo be delermmned more exactly for rplfic structures and load~ng

configunoanr On the other hmd. 11 wnll be Shawn that most relattons between nrcnglh
and strain rare. or ulomrle rm!n and rmm rate. are Ihneavloganthmr or double
loganthm~e whlch means tha crrct accuncy IS nor necessary Wtth regard to the second
remarl. there or no mcchrn~crl pmpeny whtch decreases as value at h~gher ream rates
Table 1 I Typlevl strun rarea for vanour type3 of Ioadln:
Traffic
23.3. Properties of Concrete under Dynamic Loading
A procsedlng of the mlemniond rympaslum released I" Germany, BAM (1982).
reported that the most of the dynnmtc loadtng research were confined to plam concrete
wtth normal-weight natunl aggregates. The mechnnlcnl pmpenncs whlch were
~nvestigated include the campresswe and tenstie rrrenglh. ulumate rtnln at comprersive
and tenrrle strength. Young's madulus. blaxlal strmgth, rod fracture energy ar tenrtle

loild#n$ Some of there pmpenles are well e~rabltrhcd rr a funel!an of rrrenr or Erram
vale, deflned as stress or rrwn lmreare tn nme. others are much less ~nvenlgeed.
Unlortunatcly, nor all of research papcrr an thtr rubjh-I conrsn the lnformal~on
requ~red to relate hzgh stress rate tests to standard rtatlc lest Thlr ~nfonnauan Is very
important lopwe enough detatlr m order lolud%e the vnl~dlty of the results and the rang
of apphcattan. However. an altcmpt was made lo crvmlne the rcponcd tesull 10 dcnvr
mOR relatlonr.
Since most mvcnlgauons n htgh rsaln rater were tntended to determfnr the
strength of rnaenal. data on ultlmae nrarn are nlher Ihmtted. Furthermore. data are
romet!mr not complete ~n the wnss that starlc refsrenccs are not pwen Thrr maker
compilnron depndenl on assumptions lhat me bared on general knowleds. Although
there relnlonr. for rlrann, we weaker than the strength relat~ons they may rl~ll be useful.
233.1. Campmsivr Strength
A bullcl~n synthenr repan on concrete structure under tmprct and #mpul~lve lardnng war
publlrhed by Camlte Eum-lnlematlonal du Betan. CEB (19881. steed that the sraI.llc
lerung rate war taken ar a, = I MPulr. Srrerr nte 8s convened !"to rtrm rats by
arsumlng elastnc maenal behawor wtth a modulur of elarllctty of E, = 330M) MPa
The strength rela~onnhxp staned a1 unlty for *talc lerung and reached a value of about 2
far law grade concrete. and about 1.4 for hlgh gnde concrete. when lovded more rapndly
at a rate of a, = 10~MPalr. Beyond this ares nces rhe increase higher reachlnq values
of four and greater. 11 should be noted. however. that thrs steep tnneare has been
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
not fully confirmed lhls prsdlcrlon
Ammaon and Nusrbvumsr (1995) dcsenbed that the compressrve nrcnglh of
concrete can be wntlen m lcrmr of stram mle as
where. E = %ran raa
6, = rrraan rate at qunrl stauc condtuon
f, = rtatlc cube rtrenah of concrete
Thlr relalonrhnp reveals that the lnfluenee of loadmg raw decreases as the grade of
concrete tncreasss. If ,he influence of the load~ng ma on !he modulus were no,
considered, the power of the equauan above would be I0 o where a IS the dynnmlc
mrrenal pmpny as defined m Eqvatron (2.1 11.
253.2. Modulus of ElasliEity
The modulus of elasrrc8ty IYoung'r modulus1 of the concrete tn eomprerslon lncresrer
wnth stress and srran me. The relatlon between rrauc and dynamlc (Impact) modulus of
slvrl~c~ry Ir given by Ammnnn and Nusrbaumer r 19951 ~n the follawlng equason.
0.025
with E. = 30.10-~ r-I
-- :I - (

where. a = stress rare or vanallon of EtrCPr with tmc. 01
a,,= stress rate a qua$, swtlc condltnan.
2.3.3.3. Ultimate Strain
The ulumnle %ram ID compresston tr the raam tha occurs dl mnxlrnurn nresr. The
ulttmate rrrdln sr a funcllon of stram rate gwen by Ammann mdNussbuumer (19951 tr.
233.4. Compmsive Fmelure Energy
The fracare energy 3s usually defined as the area unk the complete stress-nratn curve
mult~pl!ed by the appmpnale volume element. Whereas numemun rerulls were avaclable
far struc loudrng. there was no complete nms-stmm curve nvalable for high stram rater
of compresston loadlng. However, fmm the occumncc of htgher strength and ulumate
stram tagetha with evldencc of enhanced cracking, 11 may be concluded tho1 the fracture
energy tnneascs with tnneaslng smsr rate and rtm~n rae.

23.3.5. Te~ile Loading
Ammmn and Nursbaumer (1995) have also descnkd the propenler of i'oncres under
lens~le lordtng In conuart to compressive failure. rcnrllc fxslure Is always n dlscrclc
phenomenon. Usually one cnck occurs which dlvldes a rpcrmcn lnto two pans. These
two pans would unload ar the enck width mcwrrer. Energy consumption occurs ~n the
cnck$n$ zone The wluuonrh~pr ktwecn a mechsn$crl pmpeny and the slresr or rtriltn
rate are snmxlar to chore obnmcd. The fomulat~on or also r~mslar to compresswe nrengch
except for the value of the cocffiacnt.
Tilklng account vgan of the lnfluencc of aram ntc on modulus of elnrttclty. n
relrtton can be defined ktwcsn rtnm rate and renrlls strength 8n (he fallow~ng.
where f, a rwt!ecuk strength ofconcrete.
Tenrde nrength $3 more rsnrlttve lo rtnm or nrerr nle !f the concrete ha n low
gnde and Lr more wnnttve lo rtnln mte than eomprerrlve arensh. UEually compresrlve
strength Is the reference value for the concrete gnde and Ir therefore known. The tensile
rt~ngh can be ertlmeed fmm:
f, = 0.?0(f;)"~ MPa (1.17)
There values of concrete strength have also ken recommcndcd by CEB-RP (1990).
2.336. Tension Modulus of Elasticity
The influence of svess rate on madulus of elastxcity far lension Ir smaller than for
comprur!on. The formvlat~on prcsmted by Ammmn and Nurlaumer (1995) such ar:

arc irltd for all iricii and srmm mlcs. andall caneiclc gndc.
The definlrran of rtrvsn m a tcnrnle experiment only mrbr Eenrc up to the
moment where a dlrmre aack rtanr la open. t e.. unnl the maximum rtrerr cr re~ched.
Beyond ,has poln~ the cracks open and !he rrmnlnsng undamaged pan of the concrele
unloads. Ult~m~lc rtnln tr ,us !he smtn ar marlmum srresr Few expenmeno are
ava#lahle whnch allow anc ro eslabl~rh a relatoon between EltXln and the stress or nrxn
rate Thnr relatton 8s also oven by Amman" md Nursbnumcr (1995) such u:
Thcrc relaeanshnpr are valid for all stress rates. rrnln rarer. and concrete grade
2.3.3.7. Tenslle QrPrtvm Energy
The fraclm energy is defined as are0 under the nrerr-crack opening curve multsplled by
rhc cmsr-sectanal area of !he rFsnmsn. The parlsmcked behavior war treated ~8th a
bnltle fracture concept pmpod by Hillerborg (1985). The value can be calculated fmm

mregnnng the complete tensfle stress.cnck openxng d~rplacement or crack wtdth such us
follow:
G, = 1;. f, dw
where. Gf = fracturemergy requored to form an unit areaof crack surface
1, = ten~lle nress. rr r Rnctton of r,
b,. = crack wtdth
u, = enck width when f, wilehcs zem.
(2.12)
More common an the descnptton of englnccnng maanal. the cxpmrion for GI
cun be arnnged and expressed a% ;l funaton of a stress-$tram Inw. Thus. Wf Is defaned ar
the fracture energy dennty. or work per unit volume. d~ssopated by cnck~ng. cdn be
expressed rr
where. f, = rcnsllc rrressexprerred on lcrms of tcnrlle slnln
~r, = wtdlh of the fracture praccrs zone
E, = tenslb stram
(2 23)
emax= martmum tensnle stmm when f,reaeher zero at the end of the tenslo"
roftenlng bnnch.
As repaned by Marrouk and Chen (IW5). the fracture energy of high-nrength
concrete 13 sbout five ttmcr he area under ascendtng ponton of its complete stress-rtnnn
curve. Fraaum energy 8s ertmawd about tm times the ;ma under ascending ponion of 11%
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
lenr~on than normal-strength concrete.
CEB (1988) stated that thc relsllon between fnclure energy under rtalc and
dynamic Impact) londlng rr expressed by the following equarlon:
where, x =the cnck opnlng velmtry
I

lensen. Holwrh. m d Hansen (19931 concluded Iha the ersenual element ~n Lc
lint method IS the duclillry m d the punchtnp rhsvr capacity of high-rrrengrh cancres
under Impact and ~mpulr~ve laadln~ The val~dlly of the two other methods are lhmttcd to
ccnaln mtrnle velmt>er and concrete lfles. therefore L e methods have lo be vcnfied
An expnmenL.1 Invenlplton on !he cnpactly of nnfoned high-niength concrete dabs
under ~mpact load~n~ 19 recommended The results may prnv~de venficnttnn ol rnalyr~crl
methods as well rsderngn recammendal~onr.
Banthlz. Minderr. and Tmttter 11996) conducled an expnmoltal Impact
reststance of steel fiber reznfarced conciete urtng u simple lnarumcnl Impzlct m;ach~ne
dealgnsd ro rest concrete m un~arial tenson. B has been reponed that fiber re~nforcement
Ir renr#ttve mrtcnal to stress nte and Is effecllvc 8" lmpmvnng fracture energy absorption
under Impact. Whnle. Banthla. Yun. nnd Sakrl (1998) studled [he lmpael rertrtvnce of
concrete plnles relnforeed wtth n fiber relnbrced plrrt~c gnd. The plates reanforced wlrh
fiber relnforccd plarltc were found to fail ln a bnlile manner and absorb only a th~d of
the energy abrarbcd by those remfarccd wtth a trrd#!tonal steel pd. It hrr also been
repaned that the most lmpmvemcntr ~n ihe lmpacl performance occur with (he use of
fiber reinforced concrete. lmpmvemenlr occur tn bolh the ullrmrte laud camytng cnpauty
and the energy abrorptnon eapnbtltly
B~rr el al. (1982) studled Ihc rpphcrb!hty of repltcn scalmg ra the dynnmtc
behav~or of rexnforccd concrete slabs ~mpacted by ngld m~rnles. Erpenmental results
were presented for models wllh rehtlve linear scaler of 1. 0.37. and 0.12. It has hem
found [hat the rear faces of all 3 wales of target showed very rlmilar damage and
cracking. A sllght tendency of more rear face damage and more concrete nnppmg

occumd tn the bigger target care than ~n the smaller turgrr. The pnenl shapes of
perforation crates were also stmtlvr on ail 3 r~rcr of targel. h har ken concluded that the
use of wale models. over the Elre range terted. to prow& dar~ an the perforallon
performance of retnforced concrete are jun#ficd.
2.3.42. Eumpan Dsign Codes for Punching Shear Capscity and Critical
Perforation Velocity
The rtatlc punchtng shsarcapactty as rpeclfied ~n the Norwcgvan Code Ir expressed as
follows
where. f,,, = derngo lenrllc strength ot concrete
y, = matenal coefficncnt for retnforced
k,, = IW ~lmm'
1.0 < k,.(= l.Sdldl)c 1.4 . dl = I0 m
d = mean slab deph tn the two reinforcement dlrectlonr
a = lmgrh of penmeter of the gavcmlng xellan at a dnnance 1.0 d
fmm the l&d area
p = geametneal mean of the onhogonal tenrlon remforrcmenl noa.
(2.25)
Thc upper value of the deslgo punching ~hevcapx~ty is ismlted by comprerslve fanlure.
However. thls llmltatlon a not rrlevnnt m the case di~used here.
The enucal vcloclly of perforat~on for the dynvm~e loading of a two-way plate ar
recommended by Cammtnee Euro-lntcmauonal du Beton. CEB (1988) will be cxammed.

The cnrlcrl vcloc8ly of pcrfaivl~on can beexpressed s'
where. W = concrete denr~ty
In = cylmdcr comprerrrve strength
p = mtsstlc penmcler
Ir = concrete rlabthmcknsar
M = m!rr~le mars
p = rclnfomementqurntlty.
Bm. el al. (1982) ~ndcrad that the cnck pattern m Ihe eoncrele vilrget. ar well as
the trmnmr dtsplacement measurements. ~nd~carer Iha bending and shew bllure
mechrnlrm were anvalved ~n concrete bch;lvlor. The rexarcherr provided funher
pruf~catlon for the ruggeruon that Equauon (2.26) rhacld be rnodtfied An altemiltc
bendins nnforcemenl qurnllly dependent war included ~n the follownng.
where d a dmmcter of dmpped obleel. h 1s concrete slab thickness. and m Is mass of
cylindrical dropped oblecl.

Chapter 3
EXPERIMENTAL INVESTIGATION
3.1. Introduction
As r result of vvcnl advancer ~n the mmufacanng of chem!cal sdd~nves nnd mrtcnal
releel~on. $1 has been porrxhle to pmduce hlgh-strength concrete of 80 MPa and hqher
Thc man oh~ecsve of thlr expenmental work. u discussed tn the prerev!our chapter. 8s to
Inverngrs she structunl behavior of hlgh-rlrenzth concrete two-way plater ruhjccted to
tmpacl loddlng.
The prpsnmental program cons~sted of terllng and evnlus#on of the swcrunl
performance of sixteen plates. The dctrtlr of lest rpcclmsnr md laboratory aerup
arrungemencr are dercnbed !n rhe fallow8ng wctlon The erpcnmcntal rest results wtll be
compared wnth Nanh Amencan coder. ACI-318 (1995) md CSA-A23.3 (19941.
Nowegrim Standard NS-3473 (1992). Bntssh Code 88-81 10 (1985). and European code
CEB-FIP (1990) for predicting the shear strength. The crpnmental tat mulls are
prenled ~n the fallowing ehapsn.

3.2. Materials
3.2.1. Concrete
Ordlnay Ponland cemml 15s 10. produced ~n Newfoundland. quanznte ~nndrtone. and a
crushed granite of 19 mm mvrlmum nommal nze were used for all lest rpeclmens. In
order to produce hlgh-strength concrete with low water cemenutlaus ratm (wlcl oi ahour
0.27. the follawtng millenllr were added:
(11 Stllcl fume I" n powder farm ~n [he mtlo 88 of cement welght.
(2) Class Fhgnan fly rrh fmm Nova Scotla ~n the nt~o 12% ofccrncnt we~ght.
(31 Suprplmnclzer of sulfonared nnphlhallne formaldehyde bare (Eucon 37).
(41 Rerarder of polyhydrorycnrboxyllc base (TCDA type DXI rupplled by Eucltd
Adrnlxture Cvnda Inc.
The recommendatton of thc earl~sr mvcrtrgatlon by Msaouk md Husreln 11M)
was used for the mlx proponton of wlectcd matmalr. The mix propon~anr for 1 m' ;rre
gwcn tn Table 3.1 for nonrl-nrenglh concrele and Trblc 3.2 for high-strength concrete
The mln wnr dertgned for il comprerslve-nrength targets of 35 MPJ for normal-nrenglh
and 80 MPa for htgh-strength concrete
Tnblc 3.1 MLX propMtton for 1 m'ot normal-strength concrete
IPonland Cement 350 kg
Cmm Ag~eg=ate.tc~ (gnnae 19-mm) 1160 kg
fine Aggregates (graded mnd) 690 kg
Warcr 175 lit"

Table 3 2. MIX propomon for I m' of hngh-strength concrcle
Ponland Cement
StInca Fume
1 Fly Ash
Come 4:gcegater (gmnlle 19-mm)
Ftne Aggregates (graded undl
water
Wiccment~tlou~ marenrls ratlo
Superplarlre~zer
Rcwrder
3.2.2. Relnforrcmenl
Gmde 4W steel relnfarcrng wlth deformed rebm were used conform~ng ro CSA
nwdardr. The steel nnforcemena were abtrlned from one supplner. Two typlcrl No 10
M and No. 15 M bum were uxd as specmen rernforcement. The diameters of No 10 M
md No. IS M b m an: 11.3 mm md 16.0 mm. respectively. as deraled by the Canadian
code. A 3W bps (1335 W) Ttnus Oslen hydraulic tcrtmg mrchnne war used to test the
tenale strength of the twosampler of the relnforctng rebnn. Whnle. elecmcal rtmn gages
were applied to determlne the rtmn of the retnforcmg rebam and WDTs (L~mnr
Potentid Diffsxnual Tmrducsm) were utiltwd ro measure the specmen deformation up
to the failure. The pmpnler of the steel reinforcements are summanzed m Table 3 3.

Table 3 3 Pmpenles of steel retnforcement
number fmm) fmm'l yield rtrerr ult8mae Elasl!c~ly
(MPa) (MPa) ICPJ)
No.lOM 11.3 LOO 0.03235 150 660 191
No 15 M 16.0 200 0.00?25 435 670 193
3.3. Test Specimens
Thlr study has been eonduered on over 16 rpeamenr. Two spcclmcnr were used at the
begtnnlng ns a reference to ertahl!rh the tertnng pmcsdure. ro check the lnrtlumenrrrton
accuracy. lo wl the rate of loading and the rate of rcvnnlng data. The dimcnrnan for all
tell speclmenr were 950 mm rquarr and 100 mm th~ck and wvenl vmables were
conrlderrd ~n the ~nvcrt~ga~on The variables xncluded the effeel of concrete arcnph.
ruppan patern. and mnforcemea mlo Detallr of the ~ndw~dual rpeclmens and #a
vanabler arc given ~n Table 3 4
As even #n the table. each specmen tr ldentlfied ~n column two by three Icrlers
and one numeral. The flrrt and raond letters lndlcate the nmnglh of concne: HS
!ndicares hlgh-strenph and NS !nd#cater normal-srmglh. The thtrd letter ~ndlcater the
type of rupvpon pattcm, where F cndtcatcr fixed and S indicates simply rupponed. The
last numeral tndtcates the vmable of the tenston retnfonement ntto, where number I
lndlcates mnforcemcnt mllo of about 1%. 2 mdteates 1.5%. 3 tndlcaer 2% and 4
indlcrter 2.5%. A rypjcal au of the rested specmen s gwcn in Figure 3.1. and Figure
3.2 presents a ryplcd reinfommens pattern on lenstan and compresston faces.

Trble 3.4. Detalr of [err rpclmens
Senes
I HSSl Stmply supponed 81 7 068 7.00
2 1 ,
Notation
HSS: I ,
Suppon fc' Retnforremenr Pm~ccnle'r
No.
Candtlton
p p' Velacltler
(MPa) (51 1%) lmlr)
I I I
Stmply supponed I :: : 1 1 1 7 67
3 HSS3 S~mply~uppmd R 79
4 HSS4 Elmply suppaned 1 81.7 1 I.5 1 0 82 1 8.86
5
6
7
8
9
10
I I
12
13
14
I5
16
HSFl
HSR
HSF3
HSF4
NSSl
NSS?
NSS3
NSS4
NSFl
NSF?
NSF3
NSF4
3.4. Fabrication of Specimens
3A.1. Formwork
Fired
Fixed
Faxed
Fixed
Slmplysupponcd
Slmply supported
Simply rupporled
S~mplyrupponed
Fixed
Ftxed
Ftxed
F~red
79 1
79.1
79.1
79.1
33.1
33.1
33.1
33.1
36 6
36.6
36.6
36.6
10
1.5
2.0
1.5
1.0
1.5
2.0
2.5
10
1.5
1.0
2.5
0.68 1 700
0.68 7 67
0.74 8.29
0.82 8.86
0.68
0.68
0.74
0.82
4.43
4.95
5.42
5.86
The formwork for the test rpeenmcns was fnbnsatcd 8" the conmete laborarory The
formwork consisted of four 960 r 964 mm decks made wlth 20 mm th~eknesr plywood

wlrh IW mm height. The bottom of Ihc form was made of rleel plates. The form war
constructed such that 11 can be d!rilrrembled and re-used Before each cnstlng. all of the
steel plater and plywood surface were cleaned and coated w~lh ihght mould o ~l Dunng
casang. grear care was also gpen to ensure that the four rpeclmenr pmv~ded were
unlfom
3.42. Steel Reinforcement
The lenrlon rleel nnforccrncnl at bottom face and the eomprcrslon rleel remforccmnt dl
lop face were manged bared on the derlgn rpxlng. The tenrlon nee1 relnforcemenc were
rupponcd on the eomprersnon steel retnforcemenr by LO-mm dv~meler rpreers. The
rpzcerr airo pmv~ded the concrete clear cover. The spacers were welded lo the ncel
re~nforcernenr at selected loeatlon to el~rnlnxe the effect of weldmg. The relnfarcemen!
cap war placed I" the form. both the lenston and cornpreranan rleel reinforcement were
rled togelher wlrh steel wtres. As shown rn Rgure 3.3. thc steel retnfarcemnt were
placed I" the form before eusung
3.43. Mixing, Casting, and Curing
The capaclty of concrete mlrer was 0.1 m'. The quvntlty war required lo c~n one
spcelmen using one batch. Befm concrete was placed. the formwork and Ihe relnforclng
reban were thoroughly cleaned.
Figure 3.4 shows the pounng of fresh concrete from the batch lo the fomwah
Dch concrete batch was poured tnro the formwork and lhcn was vibrated urmg an
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
of the specmen was then leveled and finlrhcd wlrh wooden and steel rmwcl. Four hours
liter edrang. the surface of thc spectmenr wcre cured under polyethylene shcctr ~n the
forms. Thtr cunng eonttnued far a week by pounng waer lo Its surface eve? 24 hours
The formwork forthe Epclmen war rtnpped at an average nge of one week after carnng.
In order lo dercrmme the comprelrtve arenghi af the rpecmenr, three li0~30n
mm concrete eyllnden wcre raken from each batch accordnng to the procedure of wctlon
C192 of rhe ASTM (1997). Thc ten cylznders were rublectcd to rhc rnmc cunng
condlt~onr as the rcsl rpecunens. The compresswe strengths for the rest cyllnderr wcre
crrned out oiLe 28 days of casnng. A roll lest 2670 W machine was used to dctsrmme
the concrete eomprerrtve strength. Fggure 3.5. shows u rpeclrnen dunng compresnve
strength lest.
3.5. Test Set-up
The rpeclmenr were nmply-supponed along the edge on n retniorced concrete irrme
with r ireeapenmg of 650x650-mm border to s8mulvte r iired-ruppon. four steel plater
wcre bolted to fir the upper face of the rpeelmens. A rpclll lcsttng frame war derlped
!ncludnng four eonerere beams for rupponlng the rpsclmcn and steel beams to fix the
edge of speelmen as detvlled m Figurer 3 6 and 3.7. Flgure 1.8 shows a specmen under
fixed suppon.
The rpc~al terung frame was placed on a 2MX)x?WOx2W mm concrete bare. The
concrete base was made in o&r to protect the basement laboratory flwr. Ftgures 3.9 and

3.10 show the detvllr of rreel re!nforcemenr of concrete base tn bottom face md top face.
respecuuely
In order to ensure tha the pmjecllle strikes Ihe rpec8mm cxilctly at center md
keep 11 ~n that place after hatmq the rpeclmenr. n hollow steel cylmder war used to guldc
the fly~ng pralect#le. The hollow rleel cylnnder war 6 mm thlcknerr rreel wolh 50 mm
d~ameter md 1WO mm height The steel cylxndcr wm welded to the supponed steel as
pan of the tessng frame to provlde r clwr dnrwnce from the rpecsmen rurfnce A
photograph oithc rpeclal lest frameandthe gade steel cylinder Is shown ln Rgre 3.1 1.
3.6. Instrumentation System
3.6.1. Testing Load
Impact lest$ an the rpeclmns were crrncd 0s after n msntmum of 18 drys from catlng.
The impact load was nppllcd ven!crlly lo Ls lest spectmens ustng admp ngbd project~lc.
A solid rrsel cylmder was used a r projsel8lc. The cyllndcr has a 220-kg msrs nnd 304 5
mm dnvmctcr flat coarsl ma. whtch can be dmpped fmm vanable hctghtr of up to 1 m.
The photographs m Ftgures 3.12 and 3.13 show the ngtd pmjecrtle to be ready to k
droppd for Rred and sbmply suppaned rpeclmen. rerpectwely. While. Ftgure 3.14
shows the ngrdpmj~t~le was movlngto hu ;lgsmrt the rcrtedrpemmen.
The rtntlonilry specimen 8s ruddmly rubjeeted lo very hlqh accelerrt~on ~n she
dimllan of the projectile when the ngd pmjecttle dmpplng at a hngh sped rlnkes rhe
specimen. An accelemmeter war attached to the projcalle. The accelsrometer can read
up to i?00 g, where g 8s Eanh'r gravitauonal aecelemtlon. Before each Irrt. rhe
aceelcmmstcr was calibrated. The cal~bratlan chan for the accslsromctcr war rupplted by

the manufncrurer. Th~r nccelemmerer recorded the venmcal acceleratton of Le pm~cettle
together wllh rhe plate. The Impact velocnly was !hen calculared.
3.62. Deflections
Deflecuan of the rest rpeetmen war mevrund dunng sspenmsntrl by m e*.lcmnl LPDT
pga Dcflcction was iecordcd at thc center of th* plate. The mastzr pancl iccarded the
defleclton d~ta. and the elcctncal straln gages reading were stored a the data vcqulslllon
system
The voltage readmgr were convened to defleeuanr ustng the LPDT crllbnuon
fiactor. The awnlog clecrncnl slgnalr cams fmm the tnrtnrmeno were convened lhmugh
the data ilcqulrnlton board lo dmgllrl ngnalr and recorded tn n d>g,wl computer filer a!
svmplnng rate of IWO M as well. The LPDT at the center of the terced yxamen wa
plrccd m !tr posltaan Marc rccunng the rpeclmen ~n pos8tlon as shown ~n Figure 3 15
3.63. Strains
3.6.3.1. S-1 Stmim
In order to oblrrn the srntn dssrnbul~on at the cracking prwesr zone. four eleetnsal
reanance sleel rtnm gages wnth gage length of 10 rnm were rttrchcd at dlfferent
lwat8ons. Theelectncal rerlrlancc rtratn gages had a resistance of 120t0.39. ohms nnd a
gage factor of Z.M+0.5% was used forcalrbratlon.
For pmectlon agarnst any passlble waer damage dunng concrete casung, the
steel swam gages wett coated wnh a pmtective swlmt and then covered with a rhnnk

tube waxed at beth cndr. A ryplcal lwarnons of the rteel stram gages on renraon md
compresston laces are shown #n Figure 3.16
3.63.2. Concrete Strains
The concrete strams were mezsured on the compresstan lace of the concrete plnlcr by
meam of rpc~al concrete rtnx zager wrlh gtge length of 50 mm The

face Concrele rtraln war recorded on [he comprcrslon surface only. Before conducun:
the test. the concrece specmen and the cqutpmcnl were carefully ~nrpecred. Careful
awnnon had rlra been :men to the scrul~ny of psges. wxres and data ilcquirnt~on synem
dunnp tcnmg.
A dnla acqutrxtlon system based an 3 personal computer at I rampl~ng rate of
IW HI war used ln thlr clipenmen1 Labteeh Nnebwk software wu% used inr dvla
acqu~s~t!on and pmess fonlml software was uultud. The data acqulrnton ryrrcm her n
bu~ld-ttmc rhs enabler to configure the set-up. and a run-tlms (ha eontmlr 3e dau
ncqu~nson and other functton Thns bra acqulrtrton system cm be used to conunuourly
manftar ilnd record all types oc pracers vannbler tneludlng volmge. arannr. d~rplacement.
md ncceleranonr at the wannmg ttme of 1 mtcm-second.
There are two barlc types of pmecsr contml. open loop and closed loop In m
open loop controlling pmcers. as used I" thlr research, analog output blacks mnsmlr
wavefamr Lo the contml hardware dunng mn-ttmc operatton. In closed loop control. the
controlled system rends response data through Ihc tnsrfacc device to rhc m-rime The
dau ourput functmn uses lhlr tnfomat~on to convert raw data from an tnterface devtce
into rppropnntc rc~enulic or engnneenng unit such ar stnsn. dlrpk~cemcnt and
accelerallan The data acqulslrton rptem used 8" lhns study 13 shown tn Rpure 3.18 and
mrtrumentn8on black-dnagrdm a gwen ~n Rgure 3.18.

Figure 3.1. Cmsr sccrlan A-A of a typtcal rpclmen under fired-ruppon

Figure 3.2. Typical sLHl retnforremcnl of a test spcexmen
48

Figure 3.3. Anwgemcnt of steel reinf-mnt rebars in the fnmwnk bcfon cdng

Figure 3.4. Cmg of fxe& coacnte fmm tk rmxa a tk fmmmk

a[mm]/l
it----*l
Figure 3 6. Concme beams of the 1st frame
11158 150mrn
< I y f 1 [ H
I5Omrn L
Note: - L has two valuer: 650 mm and 950 mm

x
Y
urnm

H
:Cm mm
Rgu~ 3.9. Bottom re~nforeemenl of rhc concrete base of the wrung frame

h 4
2WO mm
Ftgure 3.10 Top relnforcemenl of the concrete bore of the lerlnng frame
-
A
*
ZWO mm

y. 'i'

t
F1pt-e 3.13. Test 8st-u~ fordmply-e Bpsimn

1 Campresslon face (lop)
Rgure 3.16. Loeaions of sled slmn gages an tenennon and comprsrsion faces

f
one conaete atrain-gage
located al Ihe lop of
mnaac Ppsimen

Figun 3.18. Dam acquisition sptm

Chapter 4
TEST RESULTS AND DISCUSSION
Thlr chapter dtrcurser the test results of the present research inverupt~an ~ncludlng the
cnck paucrns. ult~mate 104s. dsflcsuanr. ducl~l~ry and energy ilbsopson. modes of
fatlure. nratns both in concrete and steel remforcemen[. A compvnvln was made btwccn
high-strength and normal-strength concrete slabs (erred under rwllc loading !n the same
iabomtory by prev,aur research warken. Marrout and Husoc~n (1990).
Mcasuremntr obmned fmm laboratory Invcrugalon are prewnted ~n the
followtng remlon. Due lo rhe large rmounl of recorded data. only a few reprexntnt~vc of
the (err resulls are selected ~n thlr prermtauon In addtaon. the crack patterns at failure
are represented graphteally by means of photograph.
4.1. Cracking Characteristics
The crack paltemr, aflcr failures. are depncled ~n Figures 4.1 thmugh 4 4 for tenson face
damages. While the srripprng of the concrete cover fmm the compression face shown in
Ftgure 4.5. Both the renrton face and he compression face of all sptmenr showed very
rimtlarcraclung damage.

It war not parrtble to determnnc a relmahle value far the shear-cmhng load. 1.e.
the load dl whmch the shear cracks rtmcd up The erumntlon of such load from the crack
pattern was uncenan because there was no fundamental d~fferencc between shes crack
and flexural crack erpnnd~ng m tangentgal d#rectsan However. employng the decrease of
!he rlcel stram ~n the nnforcement can be used as a p de for delermlnsng Lhe shear
crarkln: load? As pmpred hy K~nnunen and Nylander (10601. the observed punching
lards of two-way concrete slabs w~rhout shear re~nforcement were wound 70-80 percent
of r k ult!mnte lo&.
For dynamtc loadmg. a rbght trend of mon tenston face damilge and more
concrete stnpplng aceumd at u larger relnforccmenl steel ntlo p than the rmallcr ratlo.
The same obssrviltlan war more evident for the care of hsgh-strength concrete th~n
normal-strength eoncrele Radtal cncb expandtng to the edger of the spclmenr were
evdent on all the test spclmenr. The cnck lnd~eater that bendmg and shew fatlure
mechrnl~mr were detected m all the specnmm Therefore. ~t can be concluded tha all the
rpeclmenr were falied under aduclnle shctr failure
4.2. Load-Deflection Characteristics
The Impact lauds vmur the deflccuon at the center of the plater for the dlfferea rest
wner an pnscntcd in Ftgure 4 6 through 4.11. The load-time curves for the different lest
sene3 have also shown in Figure 4.14 thmugh 4.17. whtle the dcfleet~an -tmc curves
given m Figure4.18 thmugh 4.21.
The deflsctnonr far all tested specimens were obtained using LPDT measurements
at the center of rpmmen. Urlng dynamne tquillbnum m the venrcal dlmdon, the Impact

lard war oblalned fmm the aceelerartonr that war pmv~ded fmm the areelemmeter. The
dynam~c equllsbnum m Le vemcal dmeuon tr dexnbed ~n Be follow!ngequatton
where. FlrJ = Impart loading
,on = mar of pro)cctlle
I. = msr of specmen
o, = arceleranon of project~lc.
FIIJ = f m, + 0.5 m.1 o,
The load versus deflcetnon curve can be used for csttmaung the cncrgy rbrorplton
clpxily by ~alculallng the area under the load-deflecuon curve. In add#l!on. load-
dlrplaccment curve cm be apprornmarcd by ~veral straght lhncs wtth dlffcrent slopes
The awend~ng curve has a slope that represents to the ruffncrr of the qeclmen before
cracked. Wtlhxn a glven curve, the pre-craclung stage represented by the rlape of the
rrcendtng curves a normally steeper than the desccndnng curve of the port-cracktng
nrge. As expected. the ~t~ffncss of concrete plater were decreased after cncktng.
Laud-deflccean curves of the test specimens shown ~n Figurer 1.6 lhmugh 4.9
were made wtth dzffeml Erecl resnforeement ratla. md had the rnmc concrete strengths
as well as the same support condtnonr. Rgumr 4.6 to 4.9 show that for pre-cracking
stages. the slope of arcend!ngfurve of the btgpr nnfareemcnc ratto were al~ghtly htgher
thvn thme fmm plates wlrh smaller re8nfommnt rauo. This lnd~cater chat the plate
rttffness tncreased with the ,"crease of nnforeemea mtto.
Repting the lam menrnoned pmcedure for different spec~mens wlth different
concrete strength and suppon eondlttans are shown m Flgures 4.10 thmugh 4.13. All the
figures lndicated that the plate stiffness lnfreacd with the lncrrorr of concrete-strength.

The rtlffncsses of concrete plates were rl!ghtly lncreared wlrh the change of cnd-
condltions from rlmply rupncd to fired
4.3. Dynamic Fracture Energy
The ener$y ahromt~on eupaty IS defined as the ma under rhe load-d!rplxemenl curve
The lest rerula .?re glven I" Table I The results include the energy abrorplmn Clpnclty of
all tested lpeenmenr at blure
Table 4.1 Test results
1 1
1 1 1 1 " 1
ser~r Slab Svppn 6' Re8niorrsmsnt Sped hrccl D~spl Emey
No No
I
Condlllon
P P'
nt cnlcr Aburpaoo
(MPaI 1%) 1%) Ids1 1x1 lmml IkNnmb
I I , I I I I
HSSI Slmplysuppned 81 7 095 0.68 7W 110 120 l h
eHSS3 S~mply suppned d 8 81 7 1 HSSJ Simply ruppncd 81 7 2.32 0 82 8 86 290 1121
9
I0
I1
12
I3
14
I5
16
NSSI Lmply~upponcd 33 1
NSS2 Simply suppaned 33 1
NSS3 Shmply suppaned 33 1
NSY Stmply suppaned 11 I
NSFI Fmed
NSP. Rxcd
NSF3 Rrrd
NSF4 Rxed
366
3b6
166
366
095
126
1.90
1.32
095
I26
190
232
068
0 68
074
082
068
068
074
082
542
626
7 W
767
443
4.95
542
586
70
76
95
106
It s evident fmm the gtvcn table that the cn~rgy atsqtlon capnclty nncreaad as
he concrete suength inc-cd. Tert results of the spccnmens made with different
72
78
85
98
51
I9
108
11 2
47
6.0
84
100
77
162
181
?55
61
110
186
2M)

concrete strength. and had rhc same re~nfommencmtia and ruppon cond1r8an revealed
that energy absarptmn mereased wnth !he tneredw of concrete nrengh. The use of hlgh-
rtrengrh concrete plate can be employed 10 lmpmvs the energy absarpllon cirpahtl~ry of
the concrete plate by aboul4 ttmcs hlgherthan normal-rtrenah mnereleplare
The effect of supponsond~t~on on the energy abrorptlan capaclty war nor r
e:nlficml fsctor hr Lc cndsondltlon changed fmm Rxcd to rlmply-wpponcd. a 5llohr
change ~n the energy absorprlon eapxaly of the ten plate was recorded. On !he other
hand. the effect of relnforccmsnt ntro on the energy absorption capaclly was rlgnlficml.
For errmple. tncreaslng the retnfarcement nuo imm I% ro 2%. rhe energy abrorptlon
crpclty of the rpetmen sncreascd by about lhme t>msr. both for the care of htgh-
rtrengh and nomal-strength concrete.
4.4. Steel and Concrete Strains
F~gures 4 22 through 4.37 show the dtrtnbut~on of the measured steel nmns snd concrete
itrams of all rpemmenr. The rtwns were mcarured at polar of speclnl lnteresl ~n order lo
obtan ~nformat~on on the aate of r!mra. as menuoned #n recuonr 3.6.3.1 and recrton
3.6.3.2. Unfonunately. not all the mcarursd data are reponed snce Eame stram gages
were lost due to slecmcal problems and dzimages lo tho gags dung castlng.
All the tested spcimens eipnmeed ylcldlng of steel relnforccmnt befare
punehtng fatlure accumd. The tenston reinforcement reached the yteld pomr at straw of
about 0.W25. Comparing the lenston rrel stnln at approximately same locartan from [he
compresslo" face. It has been found that the steel strains m the ease of tmpact loading
were about rwlm htgher than those corded for static load~ng as lrpned prrviourly.

There was aconccnrrarton of stresses at the m a under tmpact load Whde u large
are* of steel had ynelded. the amn at the concrete compresslo" filce lusl reached to n
mrr~mum of 17M) mcm strain at fu~lurc. Thtr Is rppmx~mately half the value tha
obtained expenmentally at the same location under rtvtlc loadfng as repaned prewourly.
Since. I" the case of rmpacr loading. the conciete sudace suddenly perfordled. the
concrew surface have been separated, hence the concrete rtnlnr on the separate face were
no1 recorded.
4.5. Modes of Failure
Moder of fadure of convcnt~onnl two-way plates under rtatle lord cm k clarrllicd lnlo
three casegones
(11 Pure flexural fallure
111 Pure rhear faxlure
(31 Ducuie rhea faxlure.
Pure flexural falure taker place ~n plater where mon of the relnfocemcnt ylclds
before punchlng occurs. Conrequenlly. the plater erhtblt large dcflectlonr pnor the
fanlurr. Usually thlr type of failure happens m the case of lightly remiarced plates. As the
reinforcement ratlo decreases, more steel yxelding approaches la the coral area of the
tsnllan steel relnforcement.
The second category of hlux 1s pure shear fnllure. Pure rhear fanlvrr occurs
when the yl~lding of tk lensson reel Is very lacal~zed at the center of loading. U~ually.
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 of fmlure Ir aeuc
of transttlon between pure punchmg and pure flexure failures.
As mentioned ~n the Sccuan 4 1, all rpeccmens failed under duct~le she= fallure.
Thlr falure can be calegonzed under the thlrd type of failure. The Impact punching lmd
~ncreased nr the concrete-strength mereased and the steel re~nfarcement ratlo tncreued.
The fxlum rurf3ee of nomc of the rested rpclmcnr were csrrful!y removed and
eliamtned. The observed angler of failure surface had some vanallon. Far normal-
sirength concrete plates. the observed angle of falure surface war about 60 de~ee. wh~le
for hlgh-smngth concrete plates. !he angle war found lo about 65 depe. In addmon. Le
punching shear radius on the tenstan face happened a a dtrrance of (1 6-2.0) rlrncr the
plate depth (dl fmm the edge of loaded urrn for most of the tested rpeflmcns compared to
a dtnance d/Z for nasc load~ng.
4.6. Effect of Concrete Strength
The dertpled FompEsSlve strength targea for rhtr Inveseea!on were 35 MPil for narmdl-
strength and 80 MPP for hlgh-strength concrete as described ~n secllon 3.1. Increnang the
concrete compresswe rmngth fmm normal-strength to hlgh-smngth concrete mcre~sed
the energy abrorpl~an capac#ty, cntlcvl velocity of perforelon. and deflecaon al the
centerof speclmenr.
The energy absorption capnclty increaxd by nnge of about 3-5 smn, whdc the
cnrscal velas~ty of perfmuon nncreaxd by a range of about 20-30 percent. The
displacements st the center of spclrnm also increased amund twlu. This obrervntlon
nndicated that high-rmngth conerrre can pmvide higher ducrlltty for concrete plater.

4.7. Effect of Steel Reinforcement Ratio
The tenson remforcement ratios were 1%. 15%. 2%. and 2.5% Ar renrlon steel nu0
was ~ncrevwd fmm about 1% to 1.5%. the cnr~cal veloctly of perfoniton ~ncrcnred by
about ten percenl. The energy sbsorptron cnpnctry has also lncrerred by about fifty
percent for hlgh-strength concrete and hundred percent for normal-strength concrete
lncrerrlng tenrlon reeel ratlo from 1% to 2%. the cntlcal velac~ly of perfonl~on
~ncrsnsed by ahouttwenty percenr. While. thc cnergy ahrorpt~on eapsclty af the specmen
lncreared by about three t lm, both ~n hlgh-strength and tn normal-strength concrsa. In
add~tton. when the tensnon steel ratlo tnsreased fmm I% to 2.5%. the cnrtcal vclocaly of
perforatton 1ncrs3ssd by about chmy percent. In thts ease. the energy rbrarptmon cilpnry
h;ls also lncreilred by about four tunes for hlgh-strength concrete us well as normal-
strength concrete.
4.8. Effect of Support Pattern
As menuoned !n ~etnon 3.3. this study was conducted on I6 rpeczmr under lwo types
of ruppon patterns, fixed and amply rupponed. The effect of ruppon pauem can he
dercnkd bnclly m the follow~ng recnon.
Energy absorption sapnclty of the two types had nearly the same behavtor bath in
the case of Bred and stmply supported. Therefore, hers was no ~lgn~ficanl effecl of
support pattern for specimens regardrng the energy abrorpuon capacity.
However. ("creasing lhe concrete rtrength fmm 35 MF'a to 80 MF'a resulted tnto a
significant effect on the critical veloctty of pelioration. The enrlcal veloctly of

perfomt~an ~ncreascd by about 10-30 percent for rpeelmens under rtrnply supponed end
eondltton. and 50-M) p ent for speclmenr under fixed end condlllon
4.9. Effect of Dynamic Loading on Peak Strain
Carnpanng Le rtatlc loadtng to the dynamic (Impact) loudlng can be rummanzed ~n the
tollaw~ng Eectlan 1" case ot 11311C loildnng, the peak rtmn and the marlmum detlectton
happen an the same tlmc wlth the peak load. However, under dynarnlc laad~ng. the pcsk
slraln accurs rl8ghlly delayed wlth renpfft to !he peak load but ahead lo the rnax~mum
deflectaan. An ~llunrallon of the dnfference behsvtor between normal-strength and hleh-
strength concrete br shown m Ftgurs 4.38.
Under lmpm loadmg. the lenston steel stt-~#tt ts est$matd by about twlce that
under rrattc lordcng. On the other hand. the concrete rtmn on the outer r>& Area of
conraa loading decreased by about half. As dercnbed !n the previous rectlon. the
concrete surface suddenly perfonled under dynmlc lauding. hence the concrete rrranr
on the repanted macould not be recorded.

Rgre 4 6 Lord-deflecson curves for spslmen no. I. 2.3 nnd 4

LOAD. DEFLECTION
Ilwimnr 6. I. and 8)
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
(SpRim 14.15,and 16)
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 forrpeetmmr 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-
(~mar9.10,ll.ndl?)
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.)
STEEL AND CONCRETE STRAWS OF HSSj

STEEL AND CONCRETE STRAINS OF HSS2
Rgure 4.23. Steel and concrete rtmnr of specimen HSSZ

STEEL AND CONCRETE STRAINS OF HSS3
Fsgure 4.24. Steel and concrete rmnr of specimen HSS3

STEEL AND CONCRETE STRAINS OF HSS4

600
;
: 3.0 ------
B 2.0 -
too
STEEL AND CONCRETE STRAINS OF HSFl
-- .
I0 I, 10 3, 10
Tim..",.
Flgure 4.26 Steel and concrete stralnr of specmen HSFl

Figure 4.27 Steel and concrete smns of rpccnmen HSF2

STEEL AND CONCRETE STRAINS OF HSF3
Figu~ 4.28. Steel and concrete stnlnr of Ipcc>men HSF3

,000
STEEL AND CONCRETE STRAINS OF HSF4
Rgure 4.19. Steel and concfelc smms of specmen HSW

STEEL AND CONCRETE STRAINS OF NSSI
Figure 4.30 Steel and concrete nratnr of rpeclrncn NSSI

STEEL AND CONCRETE STRAINS OF NSS2
Figure 4.31. Slcel and concrete srrans of specimen NSS?

m --
STEEL AND CONCRETE STRAINS OF NSS3
Figure 4.32. Stecl and concrete strains of specmen NSS3

-
STEEL AND CONCRETE STRAINS OF NSS4
Figure 4.33 Steel and concrete smns of speenmcn NSS4

' :I:-
500
:::,
$00
,m -'
70B
STEEL AND CONCRETE STRAINS OF NSFl
*: 7 .. -.__ . . -. . . . .
-- --_i..
TI,".. m.
(Concrete nratnr are not uvaxlabie)
Flgurx 4.34. Steel andconcrete swns d npeelmcn NSFl
--

STEEL AND CONCRETE STRAINS OF NSFP
Figure 4.35. Steel and concrete rnains of spslmen NSR

STEEL AND CONCRETE STRAINS OF NSW
I \
i 'm
. ,.---__ .-. .
dm-- ! "1 ', ,,\,,.
-ST<
... ST,
ST.
--
L -.
dm-
.-....
',~
..___..___._.----- ---...- -
>IXJ , , . ... . -- . .
. . .
10 7 1 111 21
-
1
::=
nm. m.
,400
;
E 600 -
so0
200
,o 1, *a
Ti."., m.
F~gure 4.36. Steel and conerere rlrainr of specmen NSF?
110

STEEL AND CONCRETE STRAINS OF NSF4
Tim, rnr
Figure 4.37. Slsel and concha seains of specimen NSF4

Figure 4.38. High-strength vsnus normal-strength sonnctc plats behavior under impan
loading

5.1. Introduction
Chapter 5
NUMERICAL EVALUATION
Htgh-strength concrete has a dlfferent behavior than normal-strength concrete. B falls by
cnclung through the vggregarer rerultmg tn a smwth facture surface. whlle normal-
nrength conerete fndr by the aggregate pulltng out d the matnx multlng I" r mugh
tracture surface. This phenomenon can s~gtficanlly affect the structural performance of
concrete marenal ~n many appllcationr. For example. the shear transfer rnechrn~rm ~n
rennforeed concrete rlruclures relies pan~rlly an as,-gate ~nterlociong across the shear
cmckr. Thls mchanlrm will be reduced greatly for high-strength concrete as a result of
le failure mode.
Thnr chapter presents a numerical evaluauon of the test results. The performances
of numerical evaluation am evaluated aganrt Nonh Amencan coder and some Eumpean
codes such as BS-8110 (1985). CEB-FIP (1990). and NS-3473 (1992). The analyrnr wnll
lncludc a cornpanson betwem the ratios of dynamic to stattc tmpact load. The rrauc
punchlng shear rvength capactttes according to the current cade pdmians will be

examlned with respect ro the expenmmwl results The values of the cnacal vcla~ty of
perfowlon calcularcd fmm rhc test results are compared lo vrlucr calculared according to
the dynamle code CEB (1988).
A fracture mechanics analysis was used to evaluate the tmpact loads on hhlgh-
strength concrete plate. The fracture rnechanncs appmach 3s consldsred r s od promnrxng
approach bi lnvtsttgarlng the hnltle fa~lun of amcrunl concrete clcmenn accurately
The fracture mechvnlcr appmvch 18 usedto mvcrllgate the effect of the rate of laadlng on
a bnttlc marenal bared a Isnear cla~r~c fracture rnechan~cs (LEFM) Onc of the
ahjecllve~ of the prewnt study IS to pmvlde the deslgn englnssrn with a rate renrltlvlty
numkr for high-strength concrete plates
5.2. Impact Load
In order ro calculae the Impact load of the lest nrulfr. the venncal equation of dynamrc
cqu~l~bnum. tgnonng damping. cm be wntten as.
Ftr) = m, m, (5.11
where F(r)lr rhs total force. a,lr the total xcclerat~ons, and the total mass m, Ir the
rum of the projectile mars and half of the specmen mass. If 0, Is equal to the projesulc
accclera8an rrp. whtlc ntpand rn, are the masses of the pmjeetile and the specnmen.
rerpecnvely. Equation (5.1) ean then bs wnnen as:
F(r) = (mp + 0.5 m , ) ~ ~
Equntlan (5.2) can thm be used for ccalculat~ng the impact lest load P,#,, = Fit1

5.3. Punching Shear (Static Capacity)
The derp shear strength equauon !ncorporaled tn bulldlng codes are a dlrecr result of
empt~ical pmccdurer developed fmm laboratory lerts. Ar mennoned prevtourly. the
Nanh Amencan codes arc based pnnclpally on Mae's (1961) wok. whde the Bntlsh
codes arc based mnmnly on Regan's (1981) work. It becomes necessary lo cx;lmtnc rhc
exsung formula strength of h~gh-strength concrete plater of 80 MPa compresswe
nrength.
Martmum shear stress rertrranee prov~ded by a concrete plate wlthos rhea
relnfoxement. v,. calculated according lo ACL-318 (1995) under S.1 untt. rhrll be the
rmallest of.
where. &= ratno of long side to shon sldc of the comenmlcd load
f,= speetfied compresswe strength of canere*
a,= factor which adjusts v, for ruppon dtmenstans
15.3n)
d = dl~tanee fmm eimmc compresslan fiber to ccntmtd of lenston nnforcemmt
be= perimeter of cnlical section for shear in plates.

The Cornmlrtee recommended that the following deslgn equntlon for calculattng ulrtmae
shear loud.
V,, = v,, b. d
(5.4)
The cnttcnl sectson shall k n rectlan perpendscular lo the plane of the plate and located
ro that tu penmeter. b,. tr u mnnnmum. But. the sccson need not approach closer lhdn
dl2 to Ihs penmeler of the concentnted load. Thereiore. b, = n (c + El. where c Is the
dlametcr of loaded arw.
The Bntlrh Codes. 0s-8110 (19851. and code of pracuce for structural urc of
concrele. CP-I I0 (1972). rrcommendsd the followtng equallon for cnlsulaune. punchmg
V, = Ka K,,=(?.69d)~C + 7.85d) (5 5)
where. V, = ult!mate shear force (N)
K,
K,
f,.
= 0.13 for normal concrete 0.105 fo~ hghrwefghr concrete
= I I5 [4n(column arcall lcolumn pnmeler)' 1"'
= cube smgth of concrele IMPa)
d = effective dcph of the slab (mm)
ZC = penmeter of the column (mm)
The rhear pmmelcr for a rectangle column 1s located a distance 1.25 d out fmm the
column. for a clrfuiar column a located 1.25 d out fmm the column. Aeeordtng lo the

code predrmwmr. the abavs llmll of 40 MPU of the cube strength of Equation (5.5) was
neglccred when calsulat~ng he shear strength.
Norntnd shear strew. vc. according to CEB-FIP (1990) Is'
vc =018 [,+El= (5.6)
Thc hlghcsl conciclc strength conrldcred I" CEB-FlP (1993) 1% SO &%Pa. The control
penmeter Ir !he mnnimum length taken fmm 2d fmm the concentrated load penphery
Equauon (54) can also be used for srlculauon the punch~ng rhear espclty, where. the
penmctcr ho for arcular loaded area IE = x IC + W.
The Nowcgnan code NS-3473 (1992) rpeclfier the punehzng rhcrrcapaclly as
Vd = 0.33(f,d +kAply,)udk,. < 0.66f,udk, 15.7)
where. frd = derngn tenrlle nlrengh of concrete
y, = malenal coefric!enr for reonforced concrete = 1.0
tA = IW Nlmm:
1.0 < k,,l=1.5dldl) < 14. dl = 1.0rn
d = mean platsdspth in the twore~nfommcnt d~rectnons
I = the length of penmeter of the governing reclnon at a dnaancc I 0 dfrom
loaded area
p = lcnrlon re~nforccmcnt ratto.
Compress~ve amngth Is usually given ar. the reference value for a concrete pade.
According to the CEB-FIP (1990) recommendation for mean values. the tcnsllc nmngth
of concrete can be enimavd fmm compresswe strength by:

J,~ = 0 . 2 0 ~ ~ ~ ~ ~ (5.8)
The measured rest tmpact loads P, and the calculation of Ihe shear strength by dtfferent
codes are wbulared ~n Table 5.1.
5.4. Code Recommendations
In order to evaluate the validbty of the current dessgn npecificalonr. the calcuiatlonr of
the formulas f a sratnc punehrng shear capaclrler llrted m Table 5 1 are to be dnrcursed
bncfly !n present recnon. The r!s!c punehlng shear rcru of all rpeclmens can be used ar
a reference for all of the dynumte lmpnct tens.
The naltc punehtng shear capncltler calculated aerordin~ to ACI-318 (19951 and
[he dynvmlc test results we used for the dynvm~c shear capactt8es. The ratno of dyndmlc
to statlc punching shear tr m the range of 1.39-2.31: a the same ratio n npd between
150-1.82. 1.361.65. and 1.87-2.33 accordnng to the BS-8110 (1985). CEB-FIP (19W).
and NS-3473 (1992). respecsuely.
The lmpaer tesl results ~ndlcare that the punch~ng failures were at a much higher
load level than the rtnlc punchtng rhear capaclly. The ntlo of Impact vcnur rtnuc lord
aecadlng to the Nonh Amencan coder 1s normally vaned between u wider range
compared to the European codes. The rario of dyonmlc to rtatlc punehtng shear accordmg
to NS-3473 (19921 is almml con~lrtcnt and hlgher than other coder predictnonr. b
concluaon, the resulU con be used as a destgn guide lor engtnecn to predict the dynrm~c
capaclty of high-mph concrete plates.

5
6
7
8
9
10
11
12
HSF1
HSF2
HSF3
HSF4
NSS1
NSSZ
NSS3
NSS4
79 1
79 1
79.1
791
331
33.1
33.1
33.1
0.95
1.26
1.90
2.32
095
126
1.90
232
NIA
328 50
37681
389.70
225.44
244.77
305 96
341 39
23660
23660
22639
22639
15305
15305
147.74
147.74
194 34
213 52
23428
250.40
14536
15971
175 23
187.29
212 22
233 17
25890
276 72
15873
174.40
193 65
20698
161.90
172 73
196.99
201.05
10521
11604
132 65
14671
NIA
139
165
171
147
180
2.07
2.31
N/A
154
161
156
1.55
153
175
182
N/A
141
146
1.41
1.42
140
156
165
NIA
1.90
2.02
1.94
2.14
2.11
2 31
233

5.5. Critical Velocity of Perforation
'The values of the cntlcal velalry of perforatnon can be cnlculared aceord~ng the formula:
where. W = concreledcns8ly
Thccrlsulnt~onr of cnrtcrl velwlry then am given ~n Table 5.1 as follows:
Table 5.Z. Cnttcal veloclry of prforamn

In order to evaluate the pred!etton of Equalon (5.9). the calculated cnucal
velactty tr then compared to the actual ten velaclly. The eompanson between the
ealculrted cnncal velacnty and rhc actual rent velaclly are g ~en ~n Table 5.3 below:
Table 5.3 Calculated cntical vclactty compared wtth tea velacnty
enes Noiatan Marlmum Maxlmum Cmlsal Test
No P.ccsleration Displacement Velacny Velmny
at Center frm code
(gl lmml (mbl lrmsl
It can be seen fmmTable 5.3 that under lmpact loadmg, both of the menrured and
salculacd accclcrations for h~gh-strength sonoere wcre htghcr lhnn normal-strength
concrete. The acceleration for heavy re8nforccmnt plater were h&er than [ha far
lhghtcr mnforeement. Thlr lndrcatcn that the aeceleratlon rnagnrtude increased when the
concrete strength and EWI nnfaacmenl ratio wcre ~ncrrarrd. lncrear~ng concrete
strenah from nonnal-strenph to high-strength. horn abut 35 MPa to 80 MPa. increased

the acceleml~on by about 40% I" the case of somply-supported and lncrravd about 30%
~n the case of fired support. In addltion. as the rlul remforcemcnr ntlo ~ncre;csd by
about 0 5%. the aeeelenttan lncread by about 10%.
The cntlcal vcloc8ty of pcrfonr~on aceord~ng to CEB (1988) were very close lo
the test re~ults for hlgh-strenpth ConerCle plates. both tn the case of fired and nmply-
supported However. br normal-strength concrete. the cnucal velmlaer were different.
Under fired condlnon, the ten results of normal-strength concrete plam were much
hlgher by about 308 than the code predicttan. On [he other hand. for ~nmply-supported
plses. the test mulls were rl~ghtlv lower by about 4% than the CEB (19881 predict8an.
In concluaon. the predietxon of cntlcal vcloctty bared on the CEB 11988) Equvtlon (5.9)
8s adequate md ern bs used to erttrnate the cnt~cal vclaclty of hlgh-strength concrete
plates rublecred lo tmpact loading accurately.
5.6. Fracture Mechanics Analysis of Impact Load
The strength of mtcnals depends on how rapndly the stress a applncd Thus. the rare of
lodlng effect 13 crtrrmcly Impman,. smec It sets a lhmtr on the allowable slresrcs ~n
structures based on the expled ttme under load. One of the mntn objective Is to use
fncture mcchantcr to pmvlde a more detvtled estamatc of the nte of loading effects on
the behanor of the concrete plats under Impact.
The fmture mshanlcs appmach to the nte of loading effect I" bnttle matmrlr 8s
bawd on he classical Griffith (1925) theory. The fracture 1% governed by equatnon:

where, a, = fracture rlrenglh
E = modulus of elast#c#ty
y = fncturs surface energy
o = cnck length
If G, = Zy IS the cnt~cvl anin energy release rile. then the Equation (5.10) can also k
wntten ~n the form:
An lntnnrnc marcnal propcny called fncars toughness. K, . can then be defined as
K, = a (5.12)
In order to sracs that fracture wtll %cur when the crack length. a. reacher some cnllcal
value. rubrt!tuting Equalon (5.121 lnlo Equaaon (5.1 1) g~ve-
Subcnl8cal cack gmwth a defined as the gmwth of cracks [ha are loo small to
cause frllure under the prevanllng nrrerr. Dunng ruknucal crack gmwth. an emplncal
relat~anshtp IS also ut~l~zed that describes the crack vsloc!ty as
whm. V = 6 = rate ofcrack extenson. w hkA and Nanconaanu. KI 8s the stress
lntenslty factor and equal to K, at the cntncal stress condion.
Assumtng. Y = &. Equalton (5.131 become.

a -K,
( - *,"2
Umg r more genenl form. Equalton (5.151 can be expressed as.
K = YO
Combtnmg Equallan (5.16) wllh Equatlan (5.141 glvcr:
The rare of stress can be define ax
da
- = AylYah',&r?
d,
db - =
dt
Alrernrttvely. 10 other way. Equatlan (5.181 can be wnaen as:
I5 181
dt = dP 15.191
0
Subsntuung Equatlan (5.191 lnro Equarlon (5 17) and leads to the !nregmuan gtver.
J:,,,-N~?~. = (5.201
d
1 L,-,N-~,?, ,;, N-112,]= AyN_O,N*I
iq (N+l)U
(5.21)
where the sukcnpt i and f refer lo he initla1 cond~tnan before terung and the final
condition on fncturs. respscttvely. lnrenlng Equauon (5.15) into Equarlon (5.111. gvcs:
Lert~ng:
a,n+l - ~ aKc~-~(N+l) L,N-2 -0,~-2]
AY2(N-2)
- ZKC'-~ (N+l)
AY?(N-Z)
(5.221
(5.231

And.
otN+l = B., b,'V-? - ofN.? ]
ofN+' + BoatN-l = Boo,N-~
From Equalon (5 251. ~f the final strength of a specmen tr measured m r fracture ten.
the lnlllal strength can be computed by knowing the slrcrring rate a Conversely. tf the
nn!t~nl strength of s rpcclmcn IS known. @he fracture rmngth m any constant loudlng nte
lest can be defined from Equallan 15.251 by numencvl methods.
As reported by Nadeau. Bennet. and Fuller 11982). urlng the pnncnples of Ihnear
elanc fracrure mechan!er. the dependence of strength on the rare of loadmg cnn be
expressed by [he lagmthmlc fm of Equation (5.24). The erpresrlon can be wntlen ar
follows.
Ino, = L l n ~ + o -L ln,!o,'-' -
Ntl N+I af'v-2 )
(5.26)
Analysis of Equrtaon (5.261 tmpllcr that a plot of Ino, Venus In0 would have a
slope of [II(N+I)] ar lower valuer of o . Rnaily, s would reach I eonnant value lrem
rlapcl as high values of 6. Thts tseonsnstent with the suknl#cal cnck growth model that
ar very hlgh loadtng ntcs. the strcngth would be largely andependent of loading me.
Sbnee. there 3s not enough time for rukntlcal crack gmwth to occur. the mltlal md final
strength ue eswnually equal.
In Xcmt yean, there are three nndependent mcthcds for evaluating the constant B
in Equatlon (5.23) by detcrmnnnng the conswt N baed on.

1 I) dmct observations of crack pwth mensurementr where the constant N IS the slope
and the canrwnt A IS the tntereept of the V-K plot. where V!s cnck vclaclty and K Ir
nntnns~c mvtenal propcny.plot an a lopnthm~c scale.
(2) the mtc of loading effect ~n whtch the firs two terms of Equalon 15.26) are plotled
gwmg bath the slope Nand fmm the lnrcrcept 6.
(3) r !o:mthrnle plot of the spplled stress against the erne to fa~lure. the slop of rhts plot
LS [-!IN].
Mlndesr (1984) reported that the values of N obrnr.ed fmm lrnpacl lerts are
~ssent~rlly Ihe same as those oblaned fmm constant mte of loading lcrlr IIhc second
method). Thtr would suggest that even at these very hngh stress mte, the fmcture
pmeerrer an much the same.
Flpre 5.1. Method of calculating Nfmm stress!ng rate data
108" 0

The method of enlculat~ng N from rtrerstng rate data IS shown m Feure 5.1 when
matcnalr can be assumed to behave m a lhnear elasec manner. The strength. a,. can be
expressed as a funct~on of rrress iate.0 Then. the slop= of loga,. venur lo0 ts
defined as[l/(~+~)] When matenalr can be assumed lo behave on a lhnear e1;rrtr. he
nrers nu m r tea cm be related ro the rtnm rate. e . through n rlmple relation: a = Er
The llrlt hump a stmn versus hllure ,$me plot ~ndteater lncntrl stram and thc second
hump ts where the bnttle matnx fractures. Since the matnx cnck created dunng the
second hump. the value of N m present research obtalned fmm a logrnthmnc plot of
applied stwn venur the tlme to fablure ~n nsnng pan of the second hump The slope of
thxs plot 8s [IN].
The valuer of N ~n the present erpenment are prerenled ~n Table 5.4. The rrble
notwes that the value of N vanes between wide limlts. In general. the valuer of N are
h~gher than normally reported for Mher types of concrete The test ~sull nndxeates that
concrete 8s known lo be far more rensltlve to stress nle under lmprct lo~d~ng than tn any
other mode. Thls phenomenon pmbrbly caused by a lackof a llneilr response. Concrete Ir
not 6dmIly bnttle and the o -c response is far fmm llncar The valuer of N therefore
m ~ not y be expected lo capture the mme nature of nmrs nte Ernlltlvlty ~n these malenlls.
Therefore. as pomted by Mindesr (1985). the vrrumptron of n lhnslr elasuc fracture
response assumed m Equauon (5.14) Ir not enurely valid. However. the pmpenler of
high-strength concrrle BE close to more lhnear response than normal-nrength concrete.
Hence. the uw of linear fracture mechanics far structures made wrth hlgh-strength
concme are mare valld than nonnal-rmgh concrete.

For rpctmenr loaded slowly. mom rtme IS available for slow crack pwlh than
rpeclmens lwdded rapidly. Therefore. Ihc nce of loadnnr effect on the tested rpes~mar
must be conndemd. Under very htph rate of landtn~ such as nnpsct londln$. the crack
velae~ty (crack growth) depends an she valuer of Nas defined by Equauon (5.14) As the
value of N ~ncmascr. the crack velalty rncreass. I1 can be seen ~n Table 5.4 lhat the
crrck vslaclry mcmse as well 2s !n thecase cf an lncrevlc of Ihe concmre strengh and m
the care of a deerem tn steel relnforccment ram
Values of N fmm impact tess
NO.
1
2
3
4
5
6
7
6
9
10
11
12
13
14
15
16
Speclmsn
HSSl
HSS2
HSS3
HSS4
HSFl
HSF2
HSF3
HSF4
NSS1
NSS2
NSS3
NSS4
NSFl
NSF2
NSF3
NSF4
fi'
MPa
81 7
81.7
61 7
81 7
79.1
79.1
79.1
79.1
33.1
331
33 1
33.1
36.6
366
36.6
36.6
70 P
0.95
1.26
1.90
2.32
0.95
1.26
1.90
2.32
0.95
126
1.90
2 32
095
1.26
1.90
2.32
However, some msemhm lhke Relnhardl (1985) suggssrcd an allernatwe
sxplunason af the obssrvsd trends gwcn on the bas,% of "on-Innear fracture mechanics. 11
has bem rceognlud Iha ~mmedtately ahead of a movnng crack is a zone of mtsm
N
28
28
24
23
33
24
22
28
24
16
14
28
24
21
17

cmclung. called process zone. The rze of he zone of mncm-craclung dcpndtng on the
velocity of the crack. A faster crack has a larger zone of mzm-cnclung ahead of 11. At a
hlghei nrerr nle that crack propagates faster, and therefore the pmess zone will be
htggcr. Thar ,"creased mem-craelung may crpliun the h~gher fracture energy
Rqulremenrr at hlgher rtress rates.
The prcvlour ursumenr seems to contnd!ct wrth the argument presented above
The rubsnl>cal cnrk gmwB. predmcrs less mmm-crackmg ~n htgh-rrrerr rrlc loading
rltual!onr However, these two phenomena occur on $he oppornrs rldsr of Ihe pnk lxd.
The concept of rubcntlcal crack gmwth ~s applncable pnor to the pak load whtle the
concept of larger pmerr zone appl~es for orhc pan-peak load regnon where the unrtable
crack propagason commencer.
5.7. Dynamic Fracture Energy
When the pmjectnle htls the rpclmen. a sudden transfer of energy fmm the pmject!le to
the specmen occurs. The energy lost by the pmjeculc Ir panly mnsfemd to the
rpeclmen and panly rrayr wrthtn the pmjccrnic tn the form of slasue rlrrlns and
vlbrauons. The energy mewed by the rpcnmen from the pmjecttie 19 the energy even
by the area under bendrng load versus deflectton curve. as dexnbed m the follow~ng
cqurtmn:
GI(') = ~~PIl)du 15.27)
where. GJ It) =bending energy -wed by the spcrmsn
PI!) = punchmg load

ulrl
= &fleetton at the load polnt
The dcflcctlon slt) can be obluncd by double lnlcgratlon of the extrapolated accclerarlon
ar the load pamr. i(r1. by equation:
"(I) = 66 ti(,) d dt
(5.281
Rpre 5.2 ~llusrrares a typ~cvl load venur defleetlon plat. The area under lond-
deflectnan curve reprexne the haeture energy recelvrd by the ~pecimcn subjecled lo
Impact loudlng.
Figure 5.1. Typtcal load-&fleeson curve
The dynamic fra~lure energy values under tmpul laadlng for all tested Jpectmcnn
are then compared to static fmture energy under rtnttc loading. The valves of naric
fracture energy were obmned fmm prevsou mvesligmrr. t.e. Husem (1990). Marrout.
Em. and Hlld (1995). and Osman. Marrauk. and Hclmy (1998).

The eompan%on d fnctue energy berwccn dyamlc to rtaic tests are then
tabulated tn Table 5.5. The results tnd~eate thar concrete undcr Impact loading. erpeclrlly
hl@ rtrenoh concrete. IS more energy ahorbing lhan undcr slartc lording. In gncnl.
concrete 1s a rensltwe matenal lo the chnng tn the nrerr-a. The nlmr of Impact ro
Erattc fncture energy was found to be hlgher for hngh-nrensh concrete than normal-
strength concrete Thnefnre hlgh-arengh concrete plaler are cansadcrrd to have more
tmpacr mtrrance than normal-strength concrete.
Table 5.5. Comprnron of dyvmlc fracture energy wah rtrllc fracture energy
5
6
7
8
9
Cmdltlon FrCIure Fracture DYnamh
(MPa) (50 (kN%k:!Yld C~?k:'lOs Stat'c
HsS1 Slmph/lupporled 81.7 095
HSS2 Slmply supponed 81 7 1.26 4.21 2.74 1.5
HSS3 Slmplyrupponsd 61.7 1.90 876 3.01 2 9
HSS4 Slmply OUppOned 61.7 2.32 12.27 3.18 3 9
HSFl
HSF2
HSF3
HSF4
NSSl
Fixed
Flxed
Flxed
Flied
Slmply rupponed
79 1
79.1
79 1
79.1
33.1
095
1 26
190
2.32
095
NIA
3.64
8.12
1245
0.77
2.32
2.56
2.44
2.61
243
I IS I NSF~ Flxed 1 36.6 1 1.90 / 1.86 1 NSFI I Fixed 36.6 232 2.60 2.43
.
1 4
3.3
4.8
0.3
2.E ( f (

Chapter 6
SUMMARY AND CONCLUSIONS
The dynamnc behavior of the two-way reinforced concrete plates under lmpvcr lodtng
are rummanzed bncfly. The present rcremh lnvesligllon eomb~ncr lnro an
cxpenmenl~l mvestlgnttan and a numeneal mverrigruon. A summary of [he two phases
of the #nverttgrl8on IS desenbcd m the followmg sectran.
The crpenmsnlal lsstlng program was conducted on sixteen retnfomed concrete
plater under umety of concrete srmgth. steel remforeement rruor. and two end-
condit~onr. The plates were lsrtcd under dynamlc lmpvct laud. The Impact load speed
ranged between 4.0 lo 9.0 mlr as aceelemuon ranged between 70 to 120 g Elghr
rpecnmcnr were constructed wlth high-strength concrete, whtle the other elght spclmens
were conrlructed wtth normal strength concrete. The concrete strength ranged berween 35
to 80 MPaand had r vanety of mnfo~cmcnc rataor m the range of aboa 1.0%-2.5%. and
were tested u nk fired and simply suppaned end-condsllon. The behnvnor of htgh-
strength eonmtc plarcs was evaluated in terms of deflection, concrete and steel strams.
ensrgy absorptnon. and frasturc mergy.

The numeneal lnvcstlgatnon war earned our lo verify the vnl~dnly of the coder'
predimlonr. The resonled lmpaCt load eapncases were compmd with rtatc capacstter of
cumnt coder' predlct~m. In uddltlon. a fracture mechanlcs tmpvet load analyslr based on
lhnear elarucr fncture mcchanxcr (LEFM) was performed. The purpose of Ihe numerical
Inverogauon was ro piovlde a more deratled analyrlr on the effect of the rate of land~ng
on the dynamic behamor of high-strength concrete plater. The dynamscr fixture energy
of the leslcd plates were comparcd lo ~wtlc fracture energy calculsted from prevlaur
inverligeorr.
6.1. Experimental Investigation
Expenmental rtvdxa were conducted on stxteen re~nforced eanmtc twrrway plater
rubjcclcd lo impact lading. The followcng emelus~onr were *ached from the present
tnvesugalan ewcsrnlng the effect of concrete strength. steel rr~niarccmcnt mtlo. md
end-condlttan
I. All EpeCimens fallsd under duct~lc shear fatlure. The observed angles of hilurc were
about M) degree for normal-strength concrete and 65 degree for hlgh-rtrenph
concrete. In addillon. the punchlng shear surface on the tension face was laated at a
dnstanee of 1.6-2.0 tnmer the plate deplh (d) fmm the edge of loaded area for the most
of the tested spamenr.
2. As the concrete ruenph incrensed from nmal-rt-ngth to hlgh-strength (35 MPa to
SO MPa). energy absorption capaelty and cnttcal velasty of perforaim mcrrased.
The energy absorption capanty mncreased by a a gc of about 3-5 timer. and the
critreal velsity of perforat~on inerrad by a range d aboul20%-30%.

3. The steel reunfarcemcnt has a major effect on the dynamle behavtar of h~gh-strength
concrete plates, lncreas~ng retnforcemenr nuo fram 1% to 1.5%. the cncrgy
rbsorptlan tncmarcd by 50% for hcgh-nrengh concrete and 100% for normal-
strength concrete. whnle the cntncal veloclty of perfonuon maeased by about 10%
for both high-strength and normal-strength concrete. lncreas~ng rennforccmsnt ratlo
from 1% to 2%. the cncrgy abrarprlon mcrcascd by about 3004 md the cntlcal
velocxty of perfanuon ,"creased by about 20% for both high-strength and normal-
rrrenglh concne. Increasing re~nforeemsnl nua fram 1% to 2.5%. the energy
ahsorpllon sncreued by about 400% md the crit!cal velocity ~ncreised by about 30%
far hngh-rtmgrh concrete u well as normal-ntrengIh concrete.
4 The effect of the end-condieon was las ~xgn8ficvnt on the behvvlor of hvgh-rrrenph
concrete plater under imprcl lord. Ar concrcrc strength mcreased from normal-
strength lo htgh-strength. the cnrtcal velocity of prforatnon inerwwd by about 20%-
30% for the snmply rupponcd speclmcnr. While under fixed-end candtt!on. he
cnrlcal velrrxty of perfowion lncrersed by about 50%-60%.
5 In the case of rtatle loadmg, the peak-load, peak-nwn md mnr~murn-defleeeon
occurred at the same ume. However. I" the case of tmpacc loadmg. the peak-smln
oecur. rllghtly later than lo the peak-load bur ahsad of manmum-dcflem~on. In
addieon. the tension nee1 nnln s esumared by about twice that recorded under rtattc
loading. The ten results illunnte the difference between ampacr failure mechvntrm
compared to rutsc fatlure mechannsm. All of the impact tcn specimens failed under
ductile shear failure.

6.2. Numerical Investigation
An analr~cal ~nvesugation war camed out an the impact loadrng on a concrele plates
The recorded tmpacr load capaclues were compmd to rtat~c capac~lies calculated by the
formula of cumnr codes. A fracture mshantcs analyslr based on linear elasrlcs frilclure
mechanlcr (LEMI was performed to evaluate the effect of "re of laadang an the
dynamic oehvvtor of high-nrength concrete plater. The dynamner fracture energy was
campmd to nruc fracture energy far all of the tested rpemmenr. The rtgnlficvnce and
contnbutton of the present numeneal lnvertlgallon can be concluded ar follows.
I. The punching shear cvpaclly due lo tmpact loadnng were about twlcc rhrr of the rtalc
punchlng shwr capacity. The rarlo of Impact punching shear clpaclly lo strtlc rr
crtrrnated by [he ACI-318 (1995) was ~n the nnge of 1.39-2.31 The same ratto baed
on BS- 8110 (1985). CEB-FIP (19901. and NS-3473 (1992) were 1.50-1.82. 136-
1.65. ilnd 1.81-2.33. respeet~vcly.
2. The cnlmcal veloc~lmes of perfmson can be ertlmated accurately for all high-strrnglh
concrete specimens according to CEB (1988) code expresson. However. for nondl-
strength concrete under fixed-end condmon. the cntlcal velmly of the ten result wrr
30% hlghcr than the cads predictnon. On the contrary, under simply-suppaned
cond~tnon, the test result war nltghtly lower by abut 4% than the code valuer. In
general. he prediction of the CEB (1988) code can be uoed accurately lo esllrnale Ihe
cnueal Impact velocity, erpecnally for high-strength concrete plater.
3. A linear elastlc fracture mechantcr impact load expoian can be used m evaluate the
effect of rate of loadxng on the dynsmtc behav~or of htgh-~lrength connete plats.
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
lo pmvlde a good degree a1 confidence.
4. The concrere fracture rrrength. a,. can be erpnsed ar a funcrsan of the stress rate.
6 The slopes of log a, Venus logdwere determ~ned expnmenwlly. The
suggested valuer far N and rubqumtly the two canrlanrr A and B can be used to
RpreSent the Etrerr nle renrlttvlty numbers lor hlgh-strength and normal-slrength
concrete plater. Therefore. the recommended valuer can be used by derper la
predtct the dynamsc behavln of any plarc under m prt load~ng.
5 The dynnmnc vcnur rlauc fmture energy rauo of h~gh-rtmgth concrete plate under
~mpact load war found to be much hagher than that for normal-strength cancrele.
Therefore, hlgh-rmph concrete plates rre constdered lo be mare effiaent marenal
for conrtruct!on under Impact loodmg. mgh-nrengrh concrele Is u better matmnl than
nonnrl concrete ~n dynrmlc rttvananr kause of !e tncreassd impact rennance.

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