Round-robin analysis of the RILEM TC 162-TDF -.pdf

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Mater ia l s a nd S t ruc tures /

M at r r i aux e t Cons t ruc t i ons , Vo l . 36 , No vem ber 2003 , pp 609-620

~ RILEM TC 162-TDF: Test and design methods for steel fibre reinforced concrete

R o u n d r o b i n a n a l y s i s o f t h e R I L E M T C 1 6 2 T D F b e a m

b e n d i n g te st : P a r t 1 T e s t m e t h o d e v a l u a t io n

P r e p a r e d b y B . I .G . B a r r ~ a n d M . K . L e e ~ w i th c o n t ri b u ti o n s f r o m E . J. d e P l a c e H a n s e n 3

D . D u p o n t 4 E . E r d e m s S . S c h a e r l a e k e n s 2 B . S c h n t i t g e n 5 H S t a n g 3 a n d L . V a n d e w a l l e 4

( 1 ) C a r d i f f U n i v e r s i t y , W a l e s

(2 ) Bel g i an Research Ins t i t u t e , Bel g i um

( 3 ) T e c h n i c a l U n i v e r si t y o f D e m n a r k , D e n m a r k

( 4 ) K a t h o l i e k e U n i v e r s i te i t L e u v e n , B e l g i u m

( 5 ) R u h r - U n i v er s i ty o f B o c h u m , G e r m a n y

A B S T R A C T

A r o u n d r o b i n t e s t p r o g r a m m e w a s c a r r i e d o u t o n t h e

b e a m - b e n d i n g t e s t r e c o m m e n d e d b y t h e R I L E M T C 1 6 2 -

TD F [1 ] . P l a i n concre t e a nd s t ee l f i b re r e i n fb rced conc re t e

( S F R C ) b e a m s w e r e i n c l u d e d i n t h e t e s t p r o g r a m m e . T h e

mat er i a l var i ab l es fo r t he SFR C bea ms c ons i s t ed o f two

concre t e s t r eng t hs , t h r ee f i b re dosages and t h ree t ypes o f

f i b res . A com prehens i ve s t a t i s t ica l ana l ys i s was car r i ed ou t

t o de t e rmi ne t he app l i cab i l i t y and robus t ness o f t he t es t

met hod . I t was t bund t ha t a l t hough i n t e r - l ab var i a t i ons do

occur , t h i s was r e l a t i ve l y smal l compared t o t he i nheren t

mat er i a l var i a t ion . I t i s a l so poss i b l e t ha t t he h i gh v ar i a t ions

observed cou l d be due t o t he r e l a t ive l y smal l c ross sec t ions

used fo r t he t es t beams . Add i t i ona l l y , an i nves t i ga t i on was

car r i ed ou t t o eva l ua t e t he ob j ec t i veness o f the c a l cu l a t i on

p rocedure p roposed

b y

R I L E M T C 1 6 2 -T D F t o o b t a in t h e

necessary des i gn paramet er s . I t was found t ha t t he

p rescr i bed ca l cu l a t i on p rocedure was sa t i s f ac t o ry , as t he

var i a t i on be t ween t he des i gn paramet er s ca l cu l a t ed a t

d i f f e r en t l abo ra t o r i es was genera l l y wi t h i n t he r ange o f

• A n a l te r n a ti v e m e t h o d o f o b t a i n in g t h e d e s i g n

param et er s , by c ons i der i ng r es idua l s t r eng t hs , i s sugges t ed

as i t s i mp l i f i es t he ca l cu l a t i on p rocedure and t he t es t

m e t h o d . I n g e n e r a l, t h e b e a m t e s t w a s f o u n d t o b e a g o o d

robus t t es t and r e l a t i ve l y easy t o car ry ou t . .

R SUMs

Un program rne d 'e.~ais comp aratifi entre laboratoires a dtO

rdalisd po ur le tes t de poutre soumise h la lexion, comm epreser#

pa r TC 1 62-TD F de la RILEM. D es poutres en b~ton normal e t en

b~ton de fibres m~tall iqu~s (BFM ) sont inclue s dans le

program me d 'es~i~ . Pcatr les poutres en BFM, on a con~Mdrd

com rne variables de ma t&'ia ux: deux rdsi~tanc~es gl la

compression, tro~ dosages ate ibres et trois (vpes de fibres. Une

anaO,se stat~tique exkxtustive a Ot~ erAcmOe ~m r determ iner la

pertinence c4 Ia solMitd de la m ~thode d'essai. On a constatO que,

bien qu e des variation s de r~,~ltats entre les laboratoires existent,

celles~'i sont relativement petites; surtout lorsque l',on compare

avec lea' :mriat ions in tr im ~ es des mat&iawc eux-m~mes. Ces

dern i~es variations peuv ent ~ re ~galement &4es cnec sections

trans~ersales relativemen t petites q ui so nt utilis.~es po ur les essais

de poutre. Ensu ite, une analyse a ~td rdalisOe en vu d'&,a.hter

l'objectbeit~ de la m Othode de calcut q~d est proposd par TC 162-

TD F de la R1LE]ff pou r obtenir les paramfitres n~cessaires lots

du dim emionnement. On a cons, aM que la m~thode de calcul

prescrite dtait satisftisante, parce que la variation des

param~tres; calcut~e par les dij]~rents k~oratoires pour le

dimensionnement; Otait d'u n ordre de grandeur de +_5%. Une

mdthode alternatfi~ est ndanmoins proposOe pou t obtenir les

pa ra, 'n ~es de dimem'ionnement en prena nt en comid~ration la

r~sistance rds'iduelle. Cette m~tho de sinwlifie la mdttuM e de c ak ~l

et la m~thode d'essai. En gOndral, l ' ssai de pou tre soumise h la

f lexion s imple , comm e pre~cri t pa r le TC 162-TD F de la RILE?r

est un essai rob uste e t relativement simp le ?t exdcuter.

1359 5997/03

9 R I L E M

6 9



T C 1 6 2 - T D F

1 . I N T R O D U C T I O N

In the b eginning of 1999, a research eonsort i tml cortsist ing

o f e leven academ ic and industria l partners was created

tb l lowing an award o f a Cont rac t unde r the Indus tr ia l and

Mate r ia l s Technolog ies P rogram m e (Br i t e -EuRam HI) to ca r ry

out a

proje t

ent i t led Tes t and D esign metho ds ; for S teel F ibre

Re in tbrced Concre te (Des ign of S F RC ) . One o f the ob jec tives

of the p ro jec t was to inves tiga te appropr ia te te s t m e thods to

characterise the bas ic materia l propert ies of SFRC materia ls .

As pa r t o f the e f fo r t to fu l fi l tha t ob jec t ive , a round rob in t e s t

p rogram m e was ca r r i ed ou t on two te s t conf igura t ions i e

notched beam s un der th ree -po in t bend ing and un i -ax ia l t ensi l e

tes t on cyl inders . This pape r presents the resul ts for the round

rob in p rogram m e ca r r i ed ou t on the th ree -po in t beam -bending

tes t . The s e t -up chosen fo r eva lua t ion was based upon the

r e c o m m e n d a ti o n s o f t h e R I L E M T C 1 6 2 -T D F [ 1 ] w i t h s o m e

minor modificat ions as deta i led la ter . The main a im was to

inves t igate the s trengths , l imita tions and appropria teness o f the

proposals .

Tw o conc rete st rengths wer e considere d in the tes t

p rogram m e. The conc re te g rades cons ide red were C25/30 ,

t e rm ed as norm a l s t reng th conc re te (NS C) and C70/85 , t e rm ed

as high s trength cono~ete ( t lSC ). The le t ter C indicates a

characteris t ic compress ive s t rength and the numerals indicate

the com pres s ive s t reng ths in N/m m 2 measu red f i 'om cyl inde rs

and cubes re spec t ive ly . Three d i f fe ren t f ib re dosages were

em ployed in the t e s t p rogram m e

i e

25 kg /m3, 50 k g/m 3 and

75 kg /m3. In addi t ion, pla in concrete beams w ere a lso included

in the tes t progranmqe. The pla in concrete beanas essent ia l ly

p lay the ro le o f con t ro l spec im ens and were a m ean s o f

inves t igat ing the s t rengths, l imita t ions and

sens i t ivi ty o f the pro posed tes t :method, as

they do no t con ta in va r ia t ions in t roduced

by fibre dis tr ibut ion and orienta t ion.

F i v e t e s t i n g l a b o r a t o r i e s w e r e

i n v o l v e d i n t h i s p a r t o f t h e r o u n d r o b i n T e s t i n g

p r o g r a m m e , w i t h C a r d i f f U n i v e r s i t y l a b

( U W C ) a s t h e t a s k c o - o r d i n a t o r . T h e

labora to r ie s a re ( in a lphabe t i ca l o rde r ) :

CST C - Belgian Building Research CSTC

Institute DTU

D T U - Technical Univers i ty of Derunark KUL

K U L - Katholieke Univers i te i t Leuve n RUB

RU B - Ruhr-Universi ty of Boc hum UWC

UW C - Cardiff' University (task co- Total

ordinator)

Th e abov e acron3qns for each Note:

part ic ipat ing laboratory wil l be used

hence forth. During the s tat is t ical analys is ,

each individual laboratory was ass igned a

nm n ber (kno wn on ly to the t a sk co-ord ina tor ) to m a in ta in the

object iveness o f the s ta t is tical s tudy.

2 . T E S T P R O G R A M M E

I t was dec ided a t an ea r ly s t age tha t i t would be wise to

d iv ide the fo reseen round rob in t e s t p rogranune in to two

phases . The f i rs t phase was considered a pi lot phase to

inves tiga te the s t reng tks and weakn es ses o f the p roposed b eam

test . Subseq uently, this valuable experie nce wo uld be fed into

the s econd phase where a wide r range o f m a te r ia ls would be

tes ted. F or the f i rs t phase, UvWC cas t a l l o f the specimens

involved. For the second phase, three other labs

i e

C S T C ,

DTU and RUB prepa red the spec im ens . Tab le 1 g ives the

overa l l round rob in t e s t p rogram m e.

3 . M A T E R I A L S A N D S P E C I M E N

P R E P A R A T I O N

3 . 1 T y p e o f f i b r e s

T h r e e t y p e s o f f i b r e s , s u p p l i e d b y N . V . B e k a e r t S . A . ,

w e r e u s e d f o r t h e r o u n d r o b i n t e s t p r o g r a m m e . A l l t h e

f i b r e s w e r e h o o k e d a n d c o l la t e d . D e t ai l s o f t h e i r u s a g e c a n

b e s e e n f r o m T a b l e 1 ( f r o m t h e s u p e r sc r i p ts ) . D e t a il s o f t h e

f ib res a re g iven in Tab le 2 .

3 . 2 F i r s t p h a s e

U W C c a s t a ll o f t h e s p e c i m e n s , w h i c h w e r e N S C , { br t h e

f i rs t p h a se . T h e m i x c o m p o s i t i o n , b a s e d u p o n e a r l i e r w o r k

a t UW C [2] , o f cem ent : f ine aggrega te : coa rse aggrega te :

wa te r i s equa l to 1 : 2 : 2 . 5 :0 . 5 6 b y we igh t .

For the f i rs t phase, control specimens in the form o f three

150rmn cubes and three cyl inders (~bl00x200 mm long) were

cas t a long with the actual beam specimen s (150x 150x600 ram)

( N . B . ~ q e r e c o m m e n d e d P d L E M b e a m h a s d i m e n si o ns o f

150x 150x 550m m as s_hown in F ig . 1 ), Two of the con t ro l

spec im ens were re ta ined a t UWC, whereas the th i rd was

transported with the beams to the other tes t ing labs . All

spec im ens were cured under w a te r a t a t em pera tu re o f 20-t2~

T a b l e 1 - O v e r a l l r o u n d r o b i n t e st p r o g r a m m e

N u m b e r o f s p e ci m e n s

F i r st p h a s e S e c o n d p h a s e

C 2 5 / 3 0 C 2 5 / 3 0 C 7 0 / 8 0

252 kg/m3 752 kg/m3 0 kg/m3 253 kg/m 3

6 6 6 6

6 6 6 6

6 6 6 6

6 6 6 6

6 6 6 6

30 30 30

0 kg/m 3 501 kg/m 3

8 8

8 8

8 8

8 8

8 8

40 40

Superscript

indicates Dramix 80/60 BN w as used

Superscript 2 indicates Dramix 65/60 BN was used

Superscript 3 indicates Dram ix 80/60 BP w as used

30

Table 2 - C haract er i s t ic s o f t he f ibres used

D r a m i x D r a m i x D r a m i x

P r o p e r t y 6 5 6 0 B N 8 0 / 6 0 B N 8 0 / 6 0 B P

Carbon

Low Low High

content

Tensile

strength 1000 1000 2500

(MPa)

60 60 60ength (mm)

Aspect ratio

(Length /

Diameter)

65

80

80

6 1 0



M a t e r i a l s a n d S t r u c t u r e s /M a t O r i a u x

e t C o n s t r u c t i o n s

V o l . 3 6 , N o v e m b e r 2 0 0 3

A t 2 1 d a y s , h a l f o f th e b e a m s p e c i m e n s f r o m e a c h m i x

w e r e t a k e n o u t o f t h e w a t e r a n d n o t c h e d . T h e o t h e r h a l f

w e r e l e f t i n t h e w a t e r a s t h e y w e r e t o b e n o t c h e d a t t h e i r

r e s p e c t i v e t e s t i n g l a b s a t a p p r o x i m a t e l y 7 w e e k s . A f t e r

n o t c h i n g , t h e s p e c i m e n s w e r e i m m e d i a t e l y p l a c e d b a c k

und er wa te r fb r fu r the r c tu ing . S ub sequen t ly , a t 28 days , a l l

t h e s p e c i m e n s ( w h e t h e r n o t c h e d o r u n - n o t c h e d ) w e r e

r e m o v e d f r o m t h e w a t e r a n d w r a p p e d i n g o o d q u a l i ty c l i n g

f i lm . T h e y w e r e t h e n s t o r e d i n a c u r i n g r o o m ( R H 6 5 J: 5 % ,

T = 20 ~ :2 ~ A p p r o x i m a t e l y o n e w e e k b e f o r e t e st i ng , t h e

s p e c i m e n s w e r e t a k e n o u t o f th e c u r i n g r o o m a n d s e n t to

the i r re spec t ive t e s t ing l abs .

3.3 Second phase

F o r t h e s e c o n d p h a s e , t h r e e o t h e r l a b o r a t o r i e s w e r e

r e s p o n s i b l e f o r s p e c i m e n p r e p a r a t i o n . R U B p r e p a r e d t h e

s p e c i m e n s w i t h 7 5 k g / m 3 o f f i b re s , w h e r e a s D T U a n d C S T C

p r e p a r e d t h e s p e c i m e n s w i t h 2 5 k g / m 3 o f f i b re s . C S T C a l so

f a b r i c a t e d th e p l a i n H S C t e s t s p e c i m e n s .

D T U p r e p a r e d t h e N S C w i t h 2 5 k g / m 3 o f f i b r e s u s in g a

m i x c o m p o s i t i o n o f 1 : 2. 0 7 : 2 .5 2 : 0 . 5 1 . R U B p r e p a r e d t h e

N S C w i t h 7 5 k g / m 3 o f f i b r e s u s i n g a m i x c o m p o s i t i o n o f 1 :

3 . 89 : 3 . 0 5 : 0 . 6 5 ( N S C m i x c o m p o s i t i o n g i v e n i n t h e f b r m o f

c e m e n t : f i n e a g g re g a t e : c o a r s e a g g r e g a t e: w a t e r ) . C S T C , o n

t h e o t h e r h an d , c a s t th e p l a in H S C a n d t h e H S C s p e c i m e n s

w i t h 2 5 k g / m 3 o f s t e e l f i b r e s u s in g a m i x c o m p o s i t i o n o f 1 :

1 . 9 3 : 2 . 6 6 : 0 . 0 0 7 5 : 0 . 3 5 ( c e m e n t : t i n e a g g r e g a t e : c o a r s e

aggrega te : s i l i ca fum e: wa te r ) . In add i t ion , 7 . 75 l i t re /m3 o f

supe r -p la s t i c ize r was added .

F or the s ec ond phase , a s im i la r p roced ure to the f i r st phase

was im plem ented . However , a s l igh t ly d i f fe ren t approach

was us ed rega rd ing no tch ing o f the spec im ens . Al l the

spec im ens were no tched a t the i r re spec t ive t e s t ing l abs jus t

be fore t e s t ing took p lace

i.e.

7 weeks a ider cas t ing. The

prepa r ing l abs a l so p repa red con t ro l spec im ens , bu t these

were no t t ranspor ted bu t t e s ted a t the p repa r ing l ab i t s el f .

3.4 Notching procedu re

F o r b o t h t h e f i r st a n d s e c o n d p h a s e s , a l l b e a m s w e r e c u t

v i a r o t a t in g d i a m o n d b l a d e s t o m a i n t a i n a l i g am e n t h e i g h t

o f 1 2 5 m m . W h i l s t t h e n o t c h e s w e r e c u t , a j e t o f w a t e r w a s

u s e d t o c o o l t h e s u r f a c e s d u r in g t h e n o t c h i n g p r o c e d u r e . A l l

no tch es were cu t pe rpend icu la r to the top sur thce a t cas t ing .

4 . T E S T SE T U P

4.1 Descrip tion of test set up

Th e tes t se t-up used is i llustrated in F ig. 1 with so me s l ight

m odi f i ca t ions f rom the P dLEM recom m enda t ions . Al l t e s t s

were conduc ted under c losed looped condi t ions . The

m easurem ents wh ich were t aken dur ing t e s ting were the load

applied, mid-span displacements on both s ides of the be am (~St

and 82) and the c rack m ou th open ing d i sp lacem ent (CMO D).

In the RILEM recommendations , i t is s ta ted that the tes ts

should be conduc ted in a m anner s u c h that the average mid-span

deflec tion increases at a constant rate o f 0.2 m rrgmin. A slight

modificat ion was made with re spect to this requirement . Instead

of carrying out the tes ts under average mid-span deflect ion

control , the tes ts were carried out und er CM OD control . I t was

ant ic ipated that the beams wou ld b e s t i ff due to their s ize and the

F

DEVICE

~ ~

PPORT

O n e c o n t o c t h o s t o b e f ~ x e d

t w o d e g r e e s o f f r e e d o m )

A

6 j ~ ~ 1 m

I

I T ~

1 1

L 5 I

F tc - a 1 cr..o.~

- \ gscas om~

Fig. 1 - Schematic diagram showing the b eam bending test set-

up (after [1]).

re la t ively shal low notch. Furthermore, HSC beams were

involved in the tes t program me w hich co uld resul t in unstable

cracking for plain concrete specimens. By conU'olling the tests

via C M OD control a mo re s table tes t could be a , ta ined.

4.2 Strain rates

In the f i r s t phase o f the ro tm d rob in t e s t p rogram m e, the

C M O D s t r a i n ra t e w a s n o t s t a t e d e x p l i c it l y . I n s t e a d , th e

RIL EM recom m end a t ions were used a s a rough gu ide f ior the

SFRC specimens . Therefbre , i t was fotmd that the variou~s

tes t ing labs used differen t s t ra in rates. S om e of the labs used

varying s tra in ra tes whereas the others used a constant s t ra in

rate . Table s 3 and 4 give the s t ra in ra tes adopted fo r the pla in

I T a b l e 3 - S t r a i n r a t e r e g i m e s u s e d i n t h e f i r st

Te s t ing

lab

CSTC

DTU

C o n s t a n t / " C M O D a t w h i c h S t r a in

V a r y i n g s t r a i n r a t e w a s r a t e

strai n rate ap plie d (Era) ...... (#m /m in)

9 0 to 100 9 20

9 100 to 250 9 50

Varying 9 250 to 500 9 250

9 500 to end of test 9 500

Constant Who le of test 120

Constant Whole of test 50

* 0to 200' . . .. . *3 0

Varying 9 200 to end of est 9 60

K U L

UWC

611



T C 1 6 2 - T D F

T a b l e 4 - S t r a i n r a t e r e g i m e s u s e d i n t h e f i r st

Te s t ing

lab

C S T C

D T U

K U L

R U B

U W C

C o n s t a n t /

V a r y i n g

strain ra te

p h a s e ( .f or t h e S F R C b e a m s )

C M O D a t w h i ch

strain rate wa s

applied (~tm)

* 0 to 100

e 100 to 250

Va r y i ng 9 250 t o 500

e 500 to 4000

, 4 0 0 0 to end oftest

Cons t a n t

Cons t a n t

Constant

Va r y i ng

W ho l e o f t e s t

W ho l e o f t e s t

Who l e o f t e s t

9 0 to 200

9 200 t o e nd o f te s t

Strain rate

(~tm/min)

9 20

,,, 50

9 250

9 500

9 2000

250

200

250

* 30

* 240

T a b l e 5

-

S t r a i n r a t e r e g i m e s u s e d i n t h e s e c o n d

p h a s e

Typ e o f c oncr e te

Plain

Steel f ibre

re inforced

CM O D s train r ate s

50 ~tm/min until rupture

9 200 gm/m in until CM OD reaches 3.5 mm.

9 Af t e r CMO D o f 3 .5 mm , s pe e d c a n

opt ional ly be increased to 2000 ~tm/min

25

c o n c r e t e a n d S F R C b e a m s d u r i n g t h e f ir s t p h a s e o f th e r o u n d

r o b i n p r o g r a m m e r e s p e c t i v e ly .

I n t h e s e c o n d p h a s e , i t w a s a g r e e d t h a t a m o r e s t ri n g e n t

t e s t c h a r a c t e r i s a t i o n i n t e r m s o f t h e s t r a i n r a t e s h o u l d b e

e m p l o y e d f o r b o t h t h e p l a i n a n d S F R C b e a m s p e ci m c m s .

T h e s e r a t e s a r e g i v e n i n T a b l e 5 .

5 R E S U L T S A N D D I S C U S S I O N

5 1 C o n t r o l s p e c i m e n s

T a b l e 6 s h o w s t h e s t r e n g t h a n d d e n s i t y t e s t r e s u l t s t b r t h e

c o n t r o l s p e c i m e n s . I n g e n e r a l , t h e v a r i a b i l i t y f o r th e c o n t r o l

s p e c i m e n s i s l o w t h u s i n d i c a ti n g t h a t th e s p e c i m e n

p r e p a r a t i o n p r o c e d u r e w a s s a t is f a c to r y .

5 2 Typica l resu l ts

F r o m t h e r a w d a t a o b t a i n e d f r o m t h e r o u n d r o b i n t e s t

p r o g r a m m e , t h e l o a d - a v e r a g e m i d - s p a n d e f l e c t i o n (P - 6 ) c u r v e s

a n d t h e l o a d - C M O D ( P - C M O D ) c u r v e s c a n b e o b ta in e d .

T y p i c a l P - 5 a n d P - C M O D c u r v e s fo r t h e p la i n N S C a n d H S C

c onc r e t e a r e g i ve n i n F i g s . 2 a nd 3 r e s pe c t i ve l y . On t he o t he r

h a n d , F i g s . 4 a n d 5 s h o w t y p i c a l p l o t s o f P - 5 a n d P - C M O D I b r

25

20

15

Z

13

t@

~*NSC

-4-HSC

0

0 0,1 0,2 0,3 0,4 0,5 0,6

Average mid-span deflection ;5 (ram)

Fig. 2 - Typica l P-6 curves for the p la in concre te beams.

25

20

Z

-,,~NSC

,m-HSC

O 0.1 0,2 0,3 0.4 0,5 0.6

Crack mo u t h o p en i n g d i spl acemen t , CM O D ram)

Fig, 3 - Typica l P-C M OD curves for the p la in concre te beams,

20-

t5-

Z

,a 10,

0

o

--~- C25/30(25)

-.~- C25J3f~50)

-a- C25130(75)

-,i~ C70/85(25)

0,5 1 1,5 2 2.5

Average mid-span deflection ;5 (ram )

Fig. 4 - T ypica l P-6 curves for the SFRC b eams.

20

-~.- C25t30(25>

,.~-C25t30(50)

,.~-C25/30(75)

-~*C70185(25)

o o.5 1 ~5 2 Z5 3

C r ac k m o u th ~ n l n g d t s p l a c e ~ , C M O D m m )

Fig, 5 - Typica l P-CM OD curves for the SFR C beams.

612



Ma te r ia l s and S t r uc tur es / M a t d r i a u x e t Co n s t ru c t i o n s V o l . 3 6 , N o v e m b e r 2 0 0 3

C o n c r e t e

g r a d e

C25/30

T a b l e 6 - R e s u l t s f o r t h e c o n t r o l s p e c i m e n s

C25/30

C25/30

C25/30

C70/85

C70/85

Note:

F i b r e

d o s a g e

(kg/m~

0

25 ~

50 ~

75 ~

0

253

D e n s i t y

P

( k ~ / m 3 )

2367

(0.45)

2400

(0.45)

2370

(0.88)

2407

0.55)

2395

(0,66) ......

2401

Cube

s tr e ng th

( N / r a m2)

44.5

(8.58)

N/A

42.6

(10:28)

45.0

(2.50)

91.8

(4.69)

89.6

I n d i r e c t

te ns i l e

strength

f,

( N / m m2)

3.89

(8.77)

N/A

N/A

C y l i n d e r

s tr e ng th

N / a m 5

35.3

(8.68)

39.5

(3.56)

N/A

N/A N/A

N / A N / A

N / A N / A

0 . 3 2 ) 2 . 4 5 )

Superscript l indicates Dramix 80/60 BN was used

Superscript 2 indicates D ramix 65/60 BN was used

Superscript 3 indicates Dramix 80/60 B P was u sed

Coefficients of variation, V, given in brackets ( )

N/A - not available

5O

g

>

4

m

30 Variation for

peak loads

6

20

t ~

x

o

o

o

tn

D

Qr

A

/

O / ~ X

x x

Lab 1

O Lab 2

Lab 3

~ o

X Lab 5

A -O -Overall

x

0.1 0,2 0.3 0,4 0,5

A v e r a g e m i d - s p a n d e f l e c t i o n , <5 m m )

F i g , 6 - I n t r a - l a b v a r i a t i o n f o r p l a i n N S C b e a m s .

5o

0,6

g

>

4

m

30

E

20

6

o

8

0

0

&

Var ia tion fo r /O

3eak oads /

/

I I /

Z u

|

_.0. / * *

/ o &

i ]

0,1 0,2 0.3 0,4 0,5

A v e r a g e m i d - s p a n d e f l e c t i o n , 8 ( m m l

Lab1

[] Lab 2

Lab 3

-O- Overall

0.6

Fig. 7 - Intra-lab variation for plain HS C beams.

the S F RC beam spec im ens . I t can be obse r ved tha t the

P - 5 and P - CM OD cur ves have shna ilar shapes. Th e

r e la t ionsh ip be tween 6 and CMOD has been

invest igated in deta i l dur ing the cou rse of the round

robin tes t ing programme [3, 4] . However , this

re la t ionship wil l not be p resented here , as i t is repor ted

in deta i l in a com panio n paper .

5 . 3 I n t r a - l a b v a r i a t i o n

In the investigation of intra-lab variation, the

coef f ic ient o f varia tion, V , o f the load measured a t

several m id-spa n deflections for eac h testing lamb is

calculated. This has been done for a l l types of concrete

beam s tested for all the testing labs.

F i g s, 6 a n d 7 s h o w a p l o t o f V o f t h e l o a d a t

i n c r e as i n g v a l u e s o f m i d - s p a n d e f l e c t io n f o r t h e

N S C a n d H S C b e a m s r e s p e c t i v e l y . F o r p l a i n

c o n c r e t e , t h e m o s t i m p o r t a n t v a l u e i s t h e m a x i m u m

l o a d a n d t h e c o e f f i c ie n t o f v a r i a ti o n f o r t h i s v a l u e i s

wi th in 10 ind ica t ing tha t the t e s t s e t - ups a r e

r obus t w her e in t r a - lab t e s t ing i s conce r ned .

I t may be observed that the var ia t ion increases w ith

increasing mid-span deflection. For the NSC, the overall V

increases from 7.87 to 33.2 tbr the rang e considcq~xl.

Similarly, tb r the H SC , V inc~.ases ti,om 9.81 to 32.8 . This

increas ing value o f V can be exp lained by the thct that, once

well into the post-w-~_k region tbr plain conc rele beams, the

applied load is very, small . Cor tsequ~tly, a small change in

applied load wil l resul t in a re la t ively large value for V. The

range o f varia tion in the N SC beam_s seems to be muc h larger

than Oa t observ 'ed tbr the H SC beams. This is because for the

NS C beam s , the beam s r ece ived by each lab com e f r om two

mixes , each contr ibut ing four beams. On the othe r hand, for the

HSC beams, each tes t ing lab received 6 beam, , a l l coming f rom

different mLxes. Thu s, the probability o f a lab oratory receiving a

set of beams of a par t icular nature (be i t higher or lower in

s trength) is increased in the case o f he pla in NSC beams.

F igs . 8 to 11 show s im i la r p lo t s o f V f or the load

m e a s u r e m e n t s a t i n c r e a s i n g m i d - s p a n d e f l e c t i o n s f o r t h e

S F R C b eam s . I n gene r a l , i t i s c lea r tha t V f or the S F R C

beam s i s r e la t ive ly h ighe r in com par i son wi th the p la in

c o n c r e t e b e a m s . U n l i k e t h e p l a i n c o n c r e t e b e a m s , t h e

over a l l V does no t inc r ease s ign i f i can t ly a s the m id-

de f lec t ion inc r eases . Th is i s because , in con t r a s t wi th the

p l a in c o n c r e t e b e a m s , t h e l o a d re s i s te d b y t h e S F R C b e a m s

ar e gene r a l ly m uch h ighe r than those r e s i s ted by the p la in

c o n c r e t e b e a m s a n d t h u s t h e e r r o r i n t r o d u c e d w i l l b e

c o r r e s p o n d i n g l y lo w e r . T h e o v e r a l l V i s t h e h i g h e st t b r t h e

b e a m s w i t h a f i b r e c o n t e n t o f 2 5 k g / m 3 re g a r d le s s o f

concr e te s t r eng th . The lowes t ove r a l l V i s r ecor ded f o r the

beam s w i th a f ib r e con ten t o f 75 kg /m 3 .

F ig . 12 show s the va r ia t ion of loads m easur ed a t spec i f i c

m id- sp an d e f lec t ions f o r a l l the S F 'RC types in vo lve d in the

r ound r ob in t e s t p r ogr am m e. I t i s appa r en t tha t the

va r iab i l i ty o f the lo w f ib r e con ten t beam s i s s ign i f i can t ly

h i g h e r c o m p a r e d t o t h e b e a m s w i t h 7 5 k g / m 3. T h e v a r i a ti o n

o f t h e b e a m s w i t h 5 0 k g / m 3 fi b r e c o n t e n t i s i n b e t w e e n

these two ex t r em es . I t i s in te r e s t ing to no te tha t bo th the

N S C a n d H S C b e a m s w i t h l o w f i b r e c o n t e n t o f 2 5 k g / m 3

exhib i t va r ia t ion of a s im i la r o r de r . Th is would ind ica te tha t

the f ib r e con ten t i s the dom inan t f ac to r in de te r m in ing the

va r ia t ion in the beam te s t r e su l t s . As the f ib r e con ten t

6 1 3



T C 1 6 2 - T D F

O

C

"6

o

O

4 0

X X

X •

3 0

2 0

1 0

X

......... A A

.....

O

.............

O

............... .. ...... .... O

A A A

D

O L a b 1

O

O L a b 2

A Lab 3

x L a b 4

x L a b 5

....o

Overall

0 . 5 ~ ~ . 5 2 2 . 5 3

3 5

A v e r a g e m i d - s p a n d e f l e c ti o n , 5 ( m m )

Fig. 8 - lntra-lab variation fbr the C25/3 0 wit h 2 5 k g / m 3

o f D r a m i x

6 5 / 6 0 B N f i b re s ) S F R C

beams.

4 0 .

3 0 .

~ 20.

~

@ L a b 1

El L a b 2

L a b 3

X Lab 4

L a b 5

- -@-

Overall

- I - - I t - - t l

z

@ 0 0 I~, II , I>

0 . 5 ~ ~ 5 2 2 . 5 a

A v e r a g e m i d - s p a n d e f l e c t i o n , 6 ( r a m )

Fig . 9 - In tra-lab var ia t ion for the C25/30 with 5 0 k g / m 3

o f D r a m ix 6 5 / 6 0 B N f i b r e s) S F R C beams.

o r O O

x

x X

....... ....... [] 0 ........ .... ...... ..

0 '

A A ~

13

B A

X

A •

O Lab 1

D L a b 2

A Lab 3

x Lab 4

, o Overall

0 .5 1 1 .5 2 2 .5 3

A v e r a g e m i d - s p a n d e f l e c t io n , ~ ( m m )

3.5

3 0

>

_o

o

2 0

s

j

0

3 , 5

Fig. 10 -

Intra-lab variation for the C25/3 0 with

7 5 k g / m 3

o f D r a m i x 6 5 / 6 0 B N f i b r e s ) S F R C b e a m s .

i n c r e a s e s , t h e v a r i a b i l i t y i s r e d u c e d . T h i s i s b e c a u s e a s t h e

l i m i t o f t h e a m o u n t o f f i b r e t h a t t h e c o n c r e t e m i x c a n

>

E

>

O

40

30

2 0

1 0

o o

<> s o

0

0

• •

O ~ ZX

O Q 1~ A

A

A

O Lab 1 I

n L a b 2 I

A Lab 3 I

• L a b 4

0 0 , 5 1 t . 5 2 2 . 5 3 3 5

A v e r a g e m i d - s p a n d e f l e c ti o n , S ( m m )

Fig. 11 - lntra~lab variation fo r t h e C 7 0 / 8 5 w i t h 2 5 k g fm 3

o f D r a m i x 8 0 / 6 0 B P f i b re s ) S F R C beams.

4 0

~ x x

o

E o [3 o D o o

~ 20

0

A A

' ~ A A A A

10 o C25/30{25)

9 o C 2 5 / 3 o ( 5 o )

A C 25/30(75)

O X C70/85(25)

0 . 5 1 1 . 5 2 2 , 5 3 3 . 5

A v e r a g e m i d - s p a n d e f l ec t i o n , ~5 ( r a m )

Fig . t2 - Com pila t ion o f ov era l l varia tion for a l l the S F R C

b e a m s p e c i m e n s .

a c c o m m o d a t e i s a p p r o a c h ed , t h e p r o b a b il i ty o f a c h i e v i n g a

m o r e u n i f o r m m i x i s i n c r e a s e d . T h i s w o u l d r e d u c e t h e

v a r i a b i l i t y i n t h e f i b r e d i s ~ b u t i o n a n d t h u s t e s t r e s u l t s w i t h

l o w e r v a r ia b i li ty c a n b e e x p e c t e d .

I n g e n e r a l , fo r t h e N S C a n d H S C b e a m s w i t h t h e l o w e s t

f i b r e c o n t e n t o f 2 5 k g / m 3 , th e o v e r a l l v a r i a t i o n i s i n t h e

r e g i o n o f 2 4 % t o 3 8 % . T h e v a r i a t io n w i t h i n e a c h l a b o n t h e

o t h e r h a n d c a n v a r y f r o m a p p r o x i m a t e l y 1 2 % t o 3 5 % .

A s t h e f i b r e c o n t e n t i s i n c r e a s e d , t h e v a r i a t i o n i s

g e n e r a l ly d e c r e a s e d . F o r t h e N S C b e a m s w i t h 5 0 k g / m 3 o f

f i b r e s , t h e o v e r a l l v a r i a t i o n i s a p p r o x i m a t e l y 2 3 % f o r t h e

d i s p l a c e m e n t s c o n s i d e r e d . T h e v a r i a t i o n w i t h i n e a c h l a b

r a n g e s a p p r o x i m a t e ly i n t h e o r d er o f 1 3 % t o 2 5 % .

F o r t h e N S C b e a m s w i t h t h e h i g h e s t f i b r e c o n t e n t o f

7 5 k g / m 3 , t h e o v e r a l l a v e r a g e v a r i a t i o n i s v e r y m u c h

i m p r o v e d . G e n e r a l l y , t h e o v e r a l l v a r i a t io n i s i n t h e r e g i o n

o f 1 5 % t o 1 7% f o r t h e l o a d s c o n s i d e r e d . T h e v a r i a t io n s

w i t h i n l a b s v a r y f r o m 1 0 % t o 2 3 % . T h i s i s a s i g n i f i c a n t

i m p r o v e m e n t i n r e l a ti o n t o t h e b e a m s w i t h t h e l o w e s t f i br e

c o n t e n t o f 2 5 k g / m 3 .

In summ axy, i f a 10% variation leve l i s cons idered, the

variations obse rved are qu i te h igh for a l l th e concrete types

6 1 4



M at e r i a l s and S t r uc t u r es /

M a t O r i a u x e t C o n s t r u c t i o n s

V o l . 3 6, N o v e m b e r 2 0 0 3

cons i de r ed w i t h i n t he r ound r ob i n l i ' ~ unewor k . T he nex t t wo

sect ions wi l l t ry to identi t~r the sourc e or so urces o f var ia t ion

observed wi thin the tes t resul t s . In par t icular , a t tent ion wi l l be

g i ven t o t he i n t e r -l ab and w i t h i n - mi x va r i a t i ons.

5 . 4 I n t e r - l a b v a r i a t i o n

I n a n y t e s t p r o g r a m m e c o n d u c t e d a t d i f f e r e n t p l a c e s ,

t h e r e a r e b o u n d t o b e d i f f e r e n c e s i n t r o d u c e d b y t h e t e s t se t -

u p s u s e d . H o w e v e r , m o r e i m p o r t a n t l y , o n e w o u l d b e

i n t e r e st e d t o k n o w t h e e x t e n t a n d s e v e r i t y o f t h is v a r i a b i l it y .

T o d e t e r m i n e w h e t h e r t h e r e w a s a n y s i g n i f i c a n t

d i f f e r e n c e i n t h e t e s t r e s u l t s d u e t o a n y v a r i a t i o n i n t h e

d i f f e r en t l ab s e t - ups , s t a t i s t i ca l ana l yses wer e ca r r i ed ou t

u s i n g t h e p l a i n c o n c r e t e b e a m s p e c i m e n s . I n t h e r o u n d

r o b i n t e s t p r o g r a m m e , t w o d i f f e r e n t ty p e s o f p l a i n c o n c r e t e

b e a m s w e r e t e s te d ; o n e w a s t h e N S C , C 2 5 / 3 0 , a n d t h e o t h e r

w a s t h e H S C , C 7 0 / 8 5 . T h e p l a i n c o n c r e t e b e a m r e s u l ts w e r e

u s e d f o r th i s p a r t o f t h e s t a t is t ic a l s t u d y b e c a u s e t h i s w o u l d

r e m o v e a n y v a r i a t io n d u e t o t h e i n t r o d u c t io n o f f i b r e s in t o

t h e c o n c r e t e m a t r i x . T h e a n a l y s i s o f v a r ia t i o n ( c o m m o n l y

k n o w s a s A N O V A ) a n d p o s t - h o c t e st s (t w o s u c h t e s ts w e r e

u s e d i . e . t h e S c h e f f 6 a n d t h e B o n f e r r o n i t e s t s ) w e r e c a r r i e d

ou t i n t h i s i nves t i ga t i on .

T he ANOVA met hod i s ab l e t o i nd i ca t e whe t he r t he r e a r e

any s igni f icant di f ferences in the tes t resul t s a t a par t icular

conf i dence l eve l . An f - va l ue can be comput ed us i ng t he

di f ferent se t s of resul t s . This t=value i s then co mp ared w i th the

~t -value obtained i i -om s ta t i s t ical t ables . These s ta t i s t ical

t ab l e s a r e g i ven i n t e r ms o f f ~ ,~ v . T he va l ue o f o t he r e

r epr esen t s t he l eve l o f conf i dence , wher eas u and v a r e t he

degr ees o f f i ~ edom as soc i a t ed w i t h t he t e s t r e su l t s . T he

degr ees o f f r eedom can be s a i d t o be f ac t o r s whi ch t ake i n t o

a c c o u n t t h e n u m b e r o f tr e a t m e n ts a n d s a m p l e s. N o r m a l ly , i n

s ta t is t ical inferences , a value of a=0.0 5 i s adopted. Th is valu e

of c t has b een used i n t h i s s tudy . T he va l ue o f ~ i s t he

pr obab i l i t y o f maki n g a T yp e I ( o r a e r r o r ) i e . w h e n w e a c c e p t

t ha t t he r e i s a d i f f e r ence when i n r ea l it y t he r e i s none . A r a t io

o f f / f . r i l arger than un i ty wo uld indicate the nu l l hypo thes is ( i . e .

t ha t t he r e i s no s i gn i fi can t d i f f e rence ) has t o be r e j ec t ed a t t he

par t icular level ofct .

I n a d d i t i o n t o A N O V A , t w o o t h e r s t a t i s t i c a l t e s t s w e r e

c a r r i e d o u t . T h e s e t e s t s w e r e t h e B o n t ~ r r o n i a n d S c h e f f d

t e st s , c o l l e c t iv e l y k n o w n a s p o s t - h o c t e st s. A N O V A c a n

g i v e a n i n d i c a ti o n o f th e e x i s t e n c e o f s i g n if i c a n t d i ff e r e n c e s

b e t w e e n v a r i o u s s e t s o f re s u l t s b u t i t d o e s n o t t el l u s w h e r e

t h e d i f f e r e n c e o r d i f f e r e n c e s o c c u r . P o s t - h o c t e s t s e n a b l e s

u s t o p i n - p o i n t t h e s o u r c e s o f th e d i f f b r e n c e s . S i m i l a r to t h e

A N O V A t es t , t he po s t - hoe t e s t s r e l i e s on t he t ~ ..... s t a t i s t ica l

t a b l e s . T h e S c h e f f 6 te s t d i f f e r s f r o m t h e B o n f e r r o n i t e s t s i n

t h a t i t i s m o r e c o n s e r v a t i v e i n t h e s e n s e t h a t t h e p r o b a b i l i t y

o f a T y p e I e r r o r is l e s s .

I t i s a c k n o w l e d g e d h e r e t h a t t h e r e a r e s e v e r a l l i m i t a ti o n s

t o t he s t a t i s t i ca l t e s t s ca r r i ed ou t . T he s t a t i s t i ca l t e s t s

a s s u m e t h a t t h e s a m p l e s c o m e f r o m a n i d e n t i c a l s o u r c e ( a

p o p u l a t i o n ) a n d t h u s a n y s i g n i f i c a n t d i f f e r e n c e m u s t b e

c a u s e d o n l y b y t h e d i f f e r e n c e i n t r e a t m e n t , t h e t re a t m e n t i n

t h i s c a s e b e i n g t h e t e s t s e t - u p . H o w e v e r , i n t h e c a s e o f t h e

r o u n d r o b i n t e s t p r o g r a m m e , s a m p l e s w e r e m i x e d i n

b a t c h e s . M o r e o v e r , n o c o n s i d e r a t i o n h a s b e e n g i v e n t o

v a r i a t i o n i n t r o d u c e d b y t r a n s p o r t a ti o n o f t ile c o n c r e t e

c y l i n d e r s , n o t c h i n g p r o c e d u r e e t c . A c o m p l e t e

cons i d e r a t i on o f a ll t hese o t he r f ac t o r s i s no t pos s i b l e .

D e t a i l e d m a t h e m a t i c a l b a s i s o f t h e s e m e t h o d s c a n b e

ob t a i n ed f i 'om bo oks on s t a t i s ti c s [ 5 - 7 ] .

T ab l e 7 show s t he r e su l ts o f t he s t a t i st ica l ana l ys i s o f t he

tes t resul t s . A ra t io o f mor e than uni ty fo r tT t~nt s obtained tbr

t wo va l ues o f ma_ximum l oad

i . e .

t b r b o t h t h e N S C a n d H S C

b e a m s . A s t h e m a x i m u m l o a d i s t h e m o s t i m p o r t a n t

character i s ing paxameter for pla in concrete , thi s indicates that

i n t e r - l ab va r i a t i ons do occur . However , when cons i de r i ng t he

pos t - p eak r eg i me , a ll t he f / ~ t va l ues f b r the l oads a t t he

pr esc r i bed 6 po i n t s cons i de r ed a r c be l ow t he c r i t ica l l eve l.

T ab l e 8 shows t he r e su l t s o f t he pos t - hoc t e s t s conduc t ed .

T he t ab l e shows whi ch l abs d i f f e r s i gn i f i can t l y f r om each

o t he r a t a l eve l o f e t = 0 .05 . B o t h t he S ch e f t ? and B onf e r r on i

tes t s indicate that there i s a s igni f icant di f i%rence in the value

o f P m , ~ f o r t h e p l a i n N S C b e a m s m a d t h e p o s t - h o e t e s t s

i nd i ca t e t ha t t he s i gn i f i can t d i f f e r ence i s dom i na t ed b y L ab 5 .

Apar t f r om t hese r e su l t s , no o t he r s i gn i f i can t d i f f e r ence i s

de t ec t ed . I t i s i n t e r e s t ing t o n o t e t ha t t he pos t - hoc t e s t s do no t

i den t i f y any s i gn i f ican t d i f f e r ence f o r t he va l ue o f P m~ x f o r

t he p l a i n HS C beam r esu l t s due t o t he r a t i o f /l ~r it be i ng v e r y

c l o s e t o t h e v a l u e o f u n i ty .

Up on f u r t he r i nves t iga t i on , i t was f o und t ha t L ab s 1 t o 3

had av e r age P ~ va l ues o f 11 .4 ix .) 11 .8 kN w her eas L ab 5 had

a n a v e r a g e v a lu e o f 1 3 .5 k N . T h e s p e c i m e n s t e st e d b y L a b 5

wer e f r om t he f i r s t mi x and t he r e was a t endency f o r t he mi x t o

be a l i t t l e dry thereby causing an increase in s t rength [8] .

Ho wev er , t h i s i nc r ease i n s t r eng th i s no t s i gn i fi can t in abso l u t e

t e r m s i . e . t h e a v e r a g e v alu e o f t he m a x i m u m l o a d tb r L a b 5

w a s f o u n d t o b e a p p r o x i m a t e l y 2 k N ( ~ 1 5 % i n c re a s e ) m o r e

t han t he o t he r te s t i ng l ab ave r ages . T h i s d i f f e r ence shows u p i n

C o n c r e t e

g r a d e

F i b r e

d o s a g e )

r2

e q

t t 3

O

t ~

Note:

T a b l e 7 - C o m p i l a t i o n o f A N O V A a n a ly s is r e s u lt s f or p la i n c o n c r e te b e a m s

Stat i s t ica l

p a r a m e t e r s

u 3

v 17

f-ratio 7.56

f c r i t 3 .20

fffcrit 2.36

u 2

v I I

f-ratio 4.08

f-cri t 3.98

t7 ~t 1.02

Po.1

L oad , P , a t p r e s c r i b e d a v e r a g e ~5 v a l u e s

P0a5 P0.2 Poa5

3 3 3 3

17 17 17 17

3. t 4 2.43 1.95 1.46

3.20 3.20 3.20 3.20

0.981 0.760 0.609 0,455

11

2

11

1 11

3.48 2.05 1.32 129

3.98 3.98 3.98 3.98

0.516 t.873

0.333

0.325

V0.3

3 3

17 17

1.30 1.42

3.20 3.20

0.405 0.443

2 2

ll 11

1.51 2.95

3.98 3.98

0.379 0.74i

, , , Area

u n d e r t h e

P0 .4 P -5 curv e

3

t4

0.851

3.34

0.255

2

9

3.07

4.46

0.690

Figures in bold indicate tTt~it atios greater than unity

P• indicates the load at the prescribed 6 value of x mm

6 1 5



T C 1 6 2 - T D F

T a b l e 8 - C o m p i l a t i o n o f p o s t - h o e t es t re s u l t s o n p l a i n c o n c r e t e b e a m s

Concrete

grade (Fibre

dosage)

t t ~

r

p

L)

Post -hoe Load P at prescr ibed average ~ values Area

under the

test

Pmax

Poa Poas Po .2 Po.2s Po.3 Po.4 P-~5curve

1-5

Scheff6 2-5 * * * * * *

3-5

1-5

Bonfer roni 2-5 * * * * * *

3-5

Scheff~ * * * * * * *

Bonfer roni * * * * * * *

No t e :

1-5 means s igni f icant d i f ference observed for resul ts be tween labs 1 and 5

* mean s no statist ical differenc e identified

t he i n t e r - l a b va r i a t i on s t a t i s t i c a l a na l y s i s be c a us e t he

c o e f f i c ie n t o f v a r i a t io n o f t h e m a x i m u m l o a d i s l o w a n d

s u b s e q u e n t l y m a g n i f i e s t h e i m p a c t . I f L a b 5 i s d is r e g a r d e d f o r

t he p l a i n NSC be a ms , i t i s obv i ous t ha t t he i n t e r - l a b d i f f e r e nc e

i n th e m a x i m u m l o a d i s n o t a s s i g n i fi c a n t a s b e t b r e ( a v e r a g e s

o f 11 . 4 t o 11 .8 kN ) .

T h e r e f o r e , i t i s s a f e t o a s s u m e t h a t d i f l 'e r e n c e s i n t h e t e s t

s e t - u p s a r e m i n i m a l i n t h e s e n s e t h a t i t s h o u l d n o t a d v e r s e l y

a f f e c t t h e b e a m t e s t r e s u l t s t o t h e p o i n t w h e r e t h e v a r i a t i o n

d u e t o d i f f e re n t s e t - u p s o v e r s h a d o w t h e v a r i a ti o n d u e t o t h e

m a t e r i a l i t s e l f

W i t h r e s p e c t to t h e S F R C b e a m s , f o u r t y p e s o f c o n c re t e w e r e

t e s t e d : t h e N S C b e a m s w i t h f i b r e d o s a g e s o f 25 , 50 a nd

7 5 k g / m3 , t oge t he r w i t h HSC be a ms wi t h a s i ng l e f i b r e dos a ge

o f 2 5 k g / m 3 . T a b l e s 9 t o 1 2 s h o w a c o m p i l a ti o n o f t h e A N O V A

a nd pos t - hoc a na l y s i s r e su lt s. S i gn i f i c an t d i f f e r e nc e s be t we e n

t he t e s ti ng l a b s a r e de t e c t e d i n ma ny o f t he va l ue s c ons i de r e d f o r

t h e N S C b e a m s w i t h f ib r e d o s a g e s o f 2 5 a n d 5 0 k g / m 3. Tab les

10 a nd 12 s how t he r e s u l t s o f t he pos t - hoe t es t s. L i ke t he

t he va r i a b i l i t y i s i n t he ma t e r i a l

due t o f i b r e va r i a t i on a t t he

f a i l u r e s e c t i on . Ano t he r

pos s i b i l i t y i s t ha t t he t e s t

s p e c i m e n s h a v e r e l at i v e ly s m a l l

c r o s s s e c t i ons . Cons e que n t l y , a

s ma l l va r i a t i on o r d i f f e r e nc e i n

t he nm nbe r o f :f ib r es ha s a d i r e c t

a nd a r e l a t i ve l y l a r ge i n f l ue nc e

o n t h e t o u g h n e s s o f t h e m a t e ri a l

t e s t e d . T h i s w o u l d b e m o r e

p r o n o u n c e d i n s p e c i m e n s w i t h

l o w f i b re d o s a g e s .

5 . 5 W i t h i n - m i x

v a r i a t i o n

A n o t h e r s o u r c e o f v a r i at i o n

i s t h e i n h e r e n t v a r i a t i o n s

e x i s ti n g w i t h in a n y o n e m i x . T h e r e w e r e t o o m a n y

s p e c i m e n s i n v o l v e d w i t h i n t h e r o u n d r o b i n t e s t p r o g r a m m e

t ha t t h e y c o u l d n o t b e p r e p a r e d i n o n e g o . I n s t e a d , t h e y h a d

t o b e f a b r i c a t e d i n b a t c h e s i . e . s e v e r a l c o n c r e t e m i x e s w e r e

p r e p a r e d . T o i n v e s t i g a t e t h e i n h e r e n t m a t e r i a l v a r i a t i o n , t h e

r e s u l t s w e r e f u r t h e r c o n s i d e r e d b y s e p a x a t i n g t h e r e s t d t s

a c c o r d i n g t o t h e m i x f r o m w h i c h t h e y w e r e m a d e . T h i s ,

h o w e v e r , w a s o n l y d o n e f o r th e N S C b e a m s a n d th e N S C

b e a m s w i t h 5 0 k g / m 3 o f f i b re s

i . e .

s p e c i m e n s f r o m t h e f i rs t

p h a s e o f t h e r o u n d r o b i n p r o g r a m m e . T o e f f e c t i v e l y

i n v e s t i g a t e t h e e f f e c t s o f w i t h i n - m i x v a r i a t i o n , i t i s l o g i c a l

t h a t o n l y t h e f i r s t p h a s e r e s u l t s b e u s e d , a s a l l t h e b e a m

s p e c i m e n s f a b r i c a te d f r o m a n y p a r t i c u la r m i x w e r e s e n t t o

o n e t e s t i n g l a b o n l y ( a n d n o t d i s tr i b u te d a m o n g s t t h e t e s t i n g

l a b s ) . D u r i n g t h e f i r s t p h a s e , e a c h t e s t i n g l a b r e c e i v e d e i g h t

b e a m s , w i t h f o u r b e a m s c o m i n g f r o m o n e m i x . A s i m i l a r

a n a l y s i s c o u l d n o t b e c a r r ie d o u t o n t h e s e c o n d p h a s e

s p e c i m e n s b e c a u s e i n t h e s e c o n d p h a s e , e a c h t e s t i n g l a b

A N O V A t ec hn iq ue , T a b l e 9 - C o m p i l a t i o n o f A N O V A a n a l y s i s r e s u l t s f o r S F R C b e a m s

m a n y d i f f e r e n c e s a r e

o b s e r v e d f o r t h e a b o v e

C o n c r e t e

gra de 07ibre Pmax

m ent io ned con cre te dosage) P0.5 PL0

types, u 4 4 4

The r e s e e m s t o be a ~ v 23 22 22

sys te m at ic in t rod uct ion ~ f - ra t io 6 .97 2 .73 4 .13

o f va r i a t i on due t o t he ~ bc r i t ic a l 2 . 80 2 . 82 2 . 82

resul t s f rom La b 4 for ~ f/s 2 .49 0 .969 1 .46

the C2 5/3 0 wi th 25 , .- , u 4 4 4

O

k g / m 3 o f f i b r e s. ~ v 29 29 30

H ow ev er , th is i s no t a ~ f - ra t io 2 .62 1 .96 2 .59

cau se for con cern , as ~ f -cr it ica l 2 .70 2 .70 2 .70

La b 4 doe s no t app ear f /ref it 0 .969 0 .726 0 .957

i n t he pos t - h oc a na l y s i s ~ u 3 3 3

t-- v 15 15 15

f o r t h e o t h e r S F R C

types . Th ere tbre , there r f - ra t io 0 .735 0 .682 0 .457

i s n o

i n t e r l a b

~ f-crit ical 3.29 3.29 3.29

f / t~ 0 .223 0 .207 0 .139

s y s t e m a t i c i n t r o d u c t io n

u 3 3 3

o f v a r i a t i o n h e n c e

cq v 16 16 t6

sug ges t ing tha t the ~ f - ra t io 4 .11 2 .25 2 .06

d i f f e r e n c e s d o n o t

f-crit ical 3.24 3,24 3.24

o c c u r d u e t o t h e t e s t ~

f r e f i t

1.27 0.695 0.636

s e t - ups a l one . A mor e

l i ke l y pos s i b i l i t y i s t ha t No t e :

Statistical

parameters

Ar e a t o

PLS P~.o

P2 5 P3 O

8 = 3mm

4 4 4 4 4

22 22 22 21 22

5,03 5,42 6.12 7.37 3.83

2.82 2.82 2.82 2.84 2.82

1.79 1.92 2.17 2.59 1.36

4 4 4 3 3

29 28 27 24 24

2.91 3.15 3.53 3.78 3.80

2.70 2.71 2.73 3.01 3.01

1.08 1.16 1.29 1.26 1.26

3 3 3 3 3

15 15 14 13 13

0.509 0 .566 i . 04 0 .958 0 .892

3.29 3.29 3.34 3.41 3.41

O. 155 O. 172 0.312 0.281 0.26 2

3 3 3 3 3

16 16 16 15 15

1.81 1.82 1.79 2.12 2.34

3.24 3.24 3.24 3.29 3.29

05 58 0 .561 0 .552 0 .645 0 .712

Load P at prescr ibed average 5 values

Figure s in bo ld indicate f/fr ratios greate r than unity

Px indica tes the load a t the prescr ibed f i va lue o fx m m

6 1 6



Materials and Structures /Mat ~ria ux

e t Cons t ruc t ions

Vol. 36, November 2003

T a b l e 1 0 - C o m p i l a t i o n o f p o s t - h o e r e su l t s o n S F R C b e a m s

C o n c r e t e

g r a d e F i b r e

d o s a g e )

C25/30(25)

C25/30 50)

C25/30(75)

C70/85(25)

P o s t - h o e

t e s t P ~ x

Scheff6 3-4

Bonferroni 3-4

Scheff6 *

Bonf?rroni *

Scheffd *

Bonferroni *

Scheff6 /-2

Bonferroni 1-2

Note:

L o a d , P , a t p r e s c r i b e d a v e r a g e 6 v a l u e s A r e a

to f i =

P o .5 P ; .o P ~ .s P 2 ,0 P 2~ P 3 . 0 3r a m

4-I 4-1

4-1

* * 4-2 4-2 4-5 *

4-2

4-5 4-5

4-1 4-1 4-14-1

* 2-4 4-2 4-2 4-2 2-4

4-2

4-5 4-5 4-5

* * * * * 1 - 5 *

* * * l - 5 1 - 5 1 - 5 1 - 5

,

,

3-4 means significant difference observed between labs 3 and 4

* means no statistical difference identified

T a b l e 1 1 - C o m p i l a t i o n o f A N O V A a n a l y s i s

f o r R I L E M a r a m e t e r s

C o n c r e t e

g r a d e F i b r e S t a t i s t i c s

d o s a g e )

u 4 4 4

v 23 23 23

C25/30(25) f-ratio 6 . 9 7 1.85 3.07

f-critica l 2.80 2.80 2.80

f/f~it 2.49 0.660 1.10

u 4 4 4

v 28 28 28

C25/30(50) f-ratio 1.50 1,92 3.11

f-critical 2.71 2.71 2.71

f/fcrit 0.554 0.708 1.15

u 3 3 3

v 15 15 14

C25/30(75) f-ratio 2.71 0.678 0.956

f-critical 3.29 3.29 3.34

fff~rit 0.824 0.206 0.286

u 3 3 3

v 16 16 16

C70/85(25) f-ra tio 3,78 1.99 1,91

f-critical 3.24 3.24 3.24

f/ f~ 1.17 0.613 0.588

Note: Figures in bold indicate f/~:rit atio greater

than unity

fr~, f~q2 f~3

T a b l e 1 2 - C o m p i l a t i o n o f p o s t - h o c t e s t r e s u l ts o n

R I L E M

C o n c r e t e

gr a d e F i b r e P o s t - h oe t e s t t fc f cq 2 f~q3

d o s a g e )

Scheff~ 3-4 * *

C25/30(25) Bonf~rroni 3-4 * *

Scheff6 * * *

C25/30(50) Bonferroni * * *

Scheft~ * * *

C25/30(75) Bonferroni * * *

Scheff~ * * *

C70/85(25) Bonferroni 2-4 * *

Note: 3-4 means signifi cant difference observed for

restdts between labs 3 and 4

9 means no statistical di fference identified

received only one beam from any one mix. This introduces

50

both lab and mix variations into the

equation for the second phase of the

testing programme thus rendering

within-mix variation studies for the

second phase specimens

meaningless. Loads at several points

of mid-span deflections were taken

into consideration as has been done

previously. These results are shown

in Figs. 13 and 14.

Figs. 13 and 14 indicate that the

variability is still significant even

when the results were separated

according to mixes. For the plain NSC

beams, the variability of the maxi mum

load is below 10%. On the other hand,

the post-peak load variation increases

from 1.20% to 13.2% at a mid-span

deflection o f 0.1 turn to 9.94% to

==

W

3 0 8 4

E

6

P

6

I

0

o

Variation o r

p e a k l o a d s

O O

O

e

o - +

§ X

_ +

0

+ X

@ <> 0

• N-0-1

r~ N-0-3

A N-0-6

- N -0 -15

x N - 0 - 1 4

o N-0-5

+ N - 0 - 0

0 .1 0 .2 0 .3 0 .4 0 ,5

A v e r a g e m i d - s p a n d e f l e c ti o n , 5 m m )

0.6

Fig, 13 -Within-m ix variations for the plain NSC beams.

40

>

v~

E

to

s..

>

3 0

2 0

I 0

A w

A

+

+ + +

Q

" O

0 0

0 X X

r

,0

o N - 5 0 - 7 o N - 5 0 - 9 / x N -5 0 - 1 1 x N - 5 0 - 2 2

o N - 5 0 - 2 3 + N - 5 0 - 8 - N - 5 0 - 1 0 - N - 5 0 - ~ 7 r

0 .5 1 1 .5 2 2 .5 3 3 .5

A v e r a g e m i d - s p a n d e f l e c t io n ,

5 ( m m )

Fig. 14 - With in-mix variat ions for the C25/30 (with 50 kg/m 3

of Dramix 80/60 BN fibres) SFRC beams.

6 1 7



TC 162-TDF

32.0% at a m id-span deflection of 0.4 mm . Clearly, mo st of the

values of V lie above 10% . However, arguably, the m ost

important coefficient of variation for the plain concrete

specimens is that fbr the maximum load. Since this is within

the arbitrary benchmark of 10%, the test method is robust

where intra-lab tests (with styzcimens fi'om a particular mix)

are concerned.

As tbr the resul ts for the NSC beams with 50 kg/m 3 of

fibres, the variations are much higher. The load varies

approximately from 10% to 30% w ithin the range of mid-

span deflections considered.

5 6 Interpretation of calculation procedure

The method used to calculate the design parameters are

shown in Fig, 15. In the analysis of the beam results from

the round robin tes t programme reported above, al l the

RIL EM TC 162-TDF beam design parameters were

calculated by the task co-ordinator. This was done to avoid

any variation in the calculated results being due to differing

interpretation of the procedure pertaining to the calculation

of the design parameters. However, since the beam test

recommendations are to be used by various parties, i t is

important to determine i f di ffering interpretat ions of the

calculation procedure will introduce significant differences

in the design parameters. Therefore a study was carried out

in collaboration with the other testing labs involved in the

round robin programme to invest igate this issue. By

com paring results from all the tabs, difficulties with the

interpretation of the procedure m ay be identified.

Eight beams were selected, from the pool of beam

results , by the task-coordinator. This bl ind set of beam

results was then sent to the other testing labs with a

protbrma to complete. The identi t ies of the tes t beams were

not made known to the testing labs. Several quantities,

which were relevant to the design parameters proposed by

RILEM TC-TDF, were to be calculated. These parameters

were calculated for both the P-8 and P-CMOD curves.

Fig. 16 shows the coefficients of variat ion of the R1LEM

design parameters obtained from the P-8 curves. Fig. 17

shows the corresponding coefficients of variat ion of the

parameters obtained from the P-CMO D curves.

Fig. 16 - Variations in the calculations from P-8 curves.

Fig. 17 - Variations in the calculations from P-CMO D curves.

Fig. 15 - Diagrams showing method of calculating RILEM design

parameters

i e

fa t, f~q2and feq3 after [1]).

In general, the variability o f most o f the design par.meters

calculated a t the different labs is foun d to be wilhin 5%, an d all

are below 10%. Only two be ams had Fararneters with variation

exceeding 5% . These are ~a values fbr beams 2 and 7. Design

p ~ e r s t ~ and t~q had low variability and hence, ~ and

f~a3 are geneea lly quite s~aighfforw-ard o calculate and do no t

pose significant probk~ns. The parmnc§ f~ f or beams 2 and 7

had a coefficient of vaf i~ on of 8.5% and 9.2%, respectively.

In th e case o f f~.~, t is obviou s that the va aab ility is related to

618



Ma t er i a l s and S t ruc t u res /

M a t d r i a u x e t C o n s t r ~ w t i o n s

Vol . 36 , No vem ber 2003

difficulties in determining F~, becaus e o f their direct relationship.

Al t hou gh t he p rocedure t b r ca l cu l a t i ng t he r equ i r ed

des i gn paramet er s does no t seem t o have s i gn i f i can t

p rob l em s i n i n t e rp re t a t ion , i t is never t he l ess qu i t e a l en g t hy

and r e l a t i ve l y d i f f i cu l t p rocedure t o car ry ou t . The

procedure i n ob t a i n i ng the necessa ry des i gn paramet er s can

be s i mp l i f i ed i f r es i dua l s t r eng t hs a t p rede t e rmi ned

def l ec t i ons (o r CM OD s) a r e u sed i n s t ead . Th i s is des i r ab le ,

as i t w i l l r educe t he t i me needed t o ca l cu l a t e t he des i gn

paramet er s . In add i t i on , i t w i l l t he i l i t a t e t he poss i b i l i t y o f

m e a s u r i n g C M O D a l o n e to o b t a i n t h e p a ra m e t e r s a s i t h a s

been fou nd t ha t t here i s a s i mp l e r e l a t ionsh i p be t ween 8 and

CM OD [3 , 4 ] . Thus , i f on l y r es i dua l s t r eng ths a r e needed

( i ns t ead o f spec i f i c a r eas under t he cu rve) , t he ca l cu l a t i on

p r o c e d u r e a n d t h e t e s t m e t h o d c a n b e s i m p l if ie d .

6 . C O N C L U S I O N

T o e v a l u a te t h e r e p r o d u c ib i li t y o f t h e R I L E M T C 1 62 -

TD F p roposed beam t es t, a s t udy on t he var i a t ion o f t he

round rob i n beam t es t r esu l t s was per fo rmed . F rom t he

s t udy o f t he i n t r a - lab var i a t i ons , i t is ev i den t t ha t mos t o f

t he var i a t i ons i n t he pos t -peak r eg i me fo r bo t h t he p l a i n

concre t e and SFR C beam s are s ign i f i can t .

t lowe ver , the in t ra- lab v ar iat ions f i~r he m axim um load tbr

t he p la i n concre te beams w ere w i t h in 1 0% . As t he mos t

important parameter for the p lain concrete beam is the

maximum load, this suggests that the test is robust , at least

where intra-lab variat ion is concerned. In addit ion, from the

intra-lab var iat ions, there does no t seem to be any sy stemat ic

large o r smal l var iat ion com ing f rom any on e par ticular lab

i . e .

one par t icular lab does no t have a large (or smal l ) var iat ion for

al l of the co ncrete types involved. This suggests that there

cot f ld be more than one source of var iat ion. Thus fur ther

investigations w ere carried out to iden tify the source o r sources

o f variations. M ore importantly, th e investigations ai m to

ident i fy the m ajor source of var iat ion.

Therefo re , i t i s sa f e to a ssum e t ha t d i f f e r ences i n the t es t

se t -ups a r e mi n i mal i n t he sense t ha t i t shou l d no t adver se l y

af f ec t t he beam t es t r esu lt s t o t he po i n t where t he var i a t i on

due t o d i f f e r en t se t -ups over shad ow t he var i a t ion due t o t he

ma ter ial i t sel f.

S i mi l a r t es t s on t he SFRC beams , however , i nd i ca t e t ha t

t here seem s t o be s i gn i f i can t d i f f e r ences i n r esu l ts f rom t he

d i f f e r en t t es ti ng l abs . How ever , t he s t a t i s t ica l t es ts assum e

t ha t t he spec i mens a l l o r i g ina t e f rom a s i ng l e popu l a t i on

i . e .

f rom a s i ng l e mi x . Th i s c l ear l y i s no t t he case and hence ,

t he i nheren t mat er i a l var i a t i on was s t ud i ed .

The w i t h i n -mi x var i a ti on s t udy was based up on t he p l a i n

N S C b e a m s a n d t h e N S C b e a m s w i t h 5 0 k g / m 3 o f f i b res.

Th i s i s because fo r t he f i r s t phase , t he beams r ece i ved by

e a c h l a b c o m e f r o m t w o m i x e s , e a c h c o n t r i b u t i n g f o u r

beams . On t he o t her hand , fo r t he second phase , each

t es t i ng l ab r ece i ved 6 beanas , a l l comi ng f rom d i f f e r en t

mi xes . Thus , t he var i a t i ons wi t h i n t he se cond phase r esu l t s

have b o t h t he i n f l uence o f in t e r - lab and w i t h i n -mi x (o r

i nheren t mat er i a l ) var i a t ions w i t h i n t hem.

From t he wi t h i n -mi x s t ud i es , i t i s apparen t t ha t t he

var i a t i on wi t h i n a m i x i t se l f i s r e l a t i ve l y h i gh . Mos t o f t he

V va l ues a t severa l p rescr i bed average mi d - span def l ec t i on

v a l u e s a r e a b o v e 1 0% ( e x c e p t f o r th e m a x i m u m l o a d f o r t h e

p l a i n concre t e beams) . T he var i ab i l i t y o f t he measu red l oad

wi t h i n t he r ange o f mi d - spa n def l ec t i ons cons i dered ( fo r t he

N S C b e a m s w i t h 5 0 k g / m 3 o f f i b re s ) i s f o u n d t o b e 1 0 % t o

3 0 % .

From t he i n t e r - l ab and wi t h i n -mi x s t ud i es , i t can be

concl uded t ha t t he i nheren t mat er i a l var i ab i l i t y i s t he

dom i nat i ng f ac t o r i n t he r e l a ti ve l y h i gh var i a t ions observed

i n t he round rob i n t es t p rog ram me .

A genera l s t udy o f t he var i a t i on due t o t i m t ype o f

ma t er i a l shows t ha t t here i s a decrease i n t he var i ab i li t y as

t he f i b re con t en t i s i ncreased . A change i n t he concre t e

s t r eng t h mat r i x f rom a no rmal s t r eng t h g rade t o a h i gh

s t r eng t h g rade does no t seem t o i mprove mat t e r s . I t i s

t herefo re ev i den t t ha t t he f f t~ re con t en t i s t he over r i d i ng

fac t o r i n i n f l uenc i ng the var i ab i l i t y i n t he bea m t es t r esu lt s .

The r eason und er l y i ng t h i s observa t i on is t ha t as t he l imi t o f

t h e a m o u n t o f f i b r e t h e c o n c r e t e m i x c a n a c c o m m o d a t e i s

app roached , t he p robab i l i t y o f ge t t i ng a more un i fo rm mi x

i s i mproved . Th i s wou l d r educe t he var i ab i l i t y i n t he f i b re

d i s t r ibu t i on and t hus t es t r esu l t s wi t h l ower var i ab i l it y can

be expec t ed .

Af t e r a t ho rough ana l ys i s o f t he var i a t i on i n t he bem-n

r e s u lt s i n t e ~ s o f b o t h i n tm - l a b , in t e r- l a b a n d w i t h in - m i x

var i a t i on , i t can be sa i d t ha t t he poss i b i l i t y o f ach i ev i ng a

10% convergence be t ween r esu l t s i s no t poss i b l e fo r t he

f i b re con t en t s cons i dered . Even w i t h i n a g i ven l ab and mi x ,

a c o n v e r g e n c e o f 1 0% a m o n g s t b e a m r e s u l ts w o u l d b e

ex t r em el y d i f f i cu l t t o ach i eve . Th i s i s due t o t he d i f f i cu l t y

i n a c h i e v i n g a u n i t b r m f i b r e d i s ~ b u t i o n e s p e c i a l l y w i t h

l ow f i b re con t en t s . An o t her poss i b l e r eason fo r t _he h i gh

var i a t i on i s t ha t t he t es t spec i mens have r e l a t i ve l y smal l

c ross sec t i ons . A smal l var i a t i on o r d i f f e r ence i n t he

number o f f i b res has a d i r ec t and a r e l a t i ve l y l a rge

i n f l uence on t he t oughne ss o f t he mat er i a l t es ted . Th i s

p h e n o m e n o n w o u l d b e m o r e p r o n o u n c e d i n s p e c im e n s w i t h

l ow f i b re dosages .

To i nves t i ga t e t he var i a t i on t o r esu l t s due t o

i n te r p r e ta t io n o f t h e R I L E M T C 1 6 2 -T D F c a l c u la t io n

p rocedure , e i gh t b l i nd beam t es t r esu l t s were sen t t o

var i ous t es t i ng l abs . The v ar i a t ions i n t he ca l cu l a t ions were

t hen a na l ysed . I t was found t ha t , i n genera l , t he var i a t i on in

t he c a l cu l a t ed va l ues o f t he RIL EM des i gn param et er s , t]-~t,

s a n d t;~q.~were wi t h i n 5%. The des i gn param et er s f cq2 and

f~q3 had very low var iab i l i ty for al l the bea ms and i t i s no t

an t i c i pa t ed t ha t t here wi l l be any maj o r p rob l ems i n t he

i n t e rp re t a t ion o f t he p rocedure t o ca l cu l a t e t hem.

I t i s p roposed t ha t t he p rocedure i n ob t a i n i ng t he

nece ssary des i gn paramet er s be s i mp l i f i ed by us i ng res i dua l

s t r eng t hs a t p rede t e rmi ned def l ec t i ons (o r CMODs) . Th i s

wi l l r educe t he t i me needed t o ca l cu l a t e t he des i gn

paramet er s . Moreover , i t w i l l f hc i l i t a t e t he poss i b i l i t y o f

m e a s u r i n g C M O D a l o n e t o o b t a i n t h e p a r a m e t e r s u s i n g a

s i mp l e r e l a t i onsh i p be t ween 6 and CMOD [3 , 4 ] . Hence

wi t h t he u se o f r es i dua l s t r eng t hs i n s t ead o f spec i f i c a r eas

under t he cu rve , t he ca l cu l a t i on p rocedure and t he t es t

me t hod can be s i mp l i f i ed .

From t he exper i ence and a na l ys i s carr i ed ou t wi t h r egards

t o t he r ecom mend ed beam-bend i ng t es t, i t was found t ha t the

t es t was a good an d robus t t es t i ng sys t em. I t was found t ha t

al though in ter- lab var iat ions do occur , th i s was relat ively

sma l l com pared to the inherent mater ial var iat ion.

6 9



T C 1 6 2 - T D F

ACKNOWLEDGEMENTS

The work reported in this paper tbrms part of the Brite-

Eurana project Test and Design M ethods for Steel Fibre

Reinforced Conca'ete , contract no. BRPR -CT98-0813. The

partners in the project are: N.V. B ekaert S.A. (Belgium co-

ordinator), Centre Scientifique et Technique de la Construction

(Belgium), Katholieke Universi tei t Leuven (Belgium),

Technical University o f Denm ark (Denmark), B al tbur Beat ty

Rail L td (Great Britain), University o f Wales C ard iff (Great

Britain), Fert ig-Decken-Union GmbH (Germany), Ruhx-

Universi ty-Bochum (Germany), Technical Universi ty of

Braunschweig (Germany), FCC Construccion S,A. (Spain),

Universi tat Polyt6cnica de Cata lunya (Spain).

REFERENCES

[ ]

RILEM T C t62-TDF, 'R1LEM TC 162-TDF: Test and design

methods for stee l fibre reintbrced concrete. Be ndin g test.

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Mater Struct

33 (22 5) (2000) 3-5.

[2] Taylor, M.R. , Lydon, F.D . and Ba n ' , B.LG. , 'Mix

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Cons t ruc t ion and

Bui ld ing Mater ia l s

10 (6) (1996)445-4 50.

[3] B arr , B.I.G. and Lee, M.K., 'Definit ion o f round robin test .

Preparation of specimens. Execution and evaluation of

round robin testing' , R epor t for Test and D esign Methods

for Ste el Fibre Reinforced Concrete, EU Contract-BRPR -

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[4] Ba rr, B.I.G., Le e, M .K, de Place Hansen. E.J. , Dupont, D.,

Erdem , E., Sc haerlaekens, S., S chn[itgen, S., Stan g, H. and

Van dew alle, L., 'Rour_~l-robinanalysis of the R ILEM TC 162-

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CMO D response' ,

Mater Struct

36 (263) (2003) 621-630.

[5] Cramer ,D., 'Fundam ental statistics for social research: step-

by-step calculations and computer techniques using SPSS

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[6] W ads wo rth, H.M., 'Handbook of Statist ical Methods For

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[7] K ee pin g, E.S., ' Introduction to Statis t ical Inference',

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62

Documents

Round-robin analysis of the RILEM TC 162-TDF -.pdf