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APPLICATIO OF ELASTO PLASTIC CONCRETE BARCHIP MACRO STRUCTURAL SYNTHETICFIBRE REINFORCEMENT FOR THE DESIGN OF CONCRETE GROUND SLABS ON GRADE

1.0 INTRODUCTION

The use of fibres, classically straw and horse hair, to reinforce brittle materials such as bricks and

plaster has a long history - thousand of years. However, it was not until the 1970's that the use of steel

fibre reinforced concrete (SFRC) gained commercial momentum. In the 1988 edition of ConcreteSociety Technical Report No 34 - Concrete Industrial Ground Floors - a guide to design and

construction, minimal reference was made to the use of fibres but in the second edition (1994)comprehensive data was included together with a design example for steel fibre reinforced concrete

(SFRC).

The third addition ofTR34 published in 2003, was written in a limit state format with emphasis on the

ultimate and serviceability limit state (ULS and SLS). For the ultimate limit state the Meyerhofequations were adopted for slab analysis with partial safety factors based on those in the draft Eurcode

2. The Meyerhof equations are based on yield line theory and thus it is necessary to establish positive

(sagging) and negative (hogging) moment capacities, Up and Ma. It is assumed that plain concretedoes not have any significant ability to redistribute bending moments, but the presence or fibres (macrosynthetic or steel) will enhance ductility and the ability to redistribute bending moments.

The ductility of fiber reinforced concrete is characterised by its equivalent flexural strength ratio Re3

(see section 2.0). This provides a residual (i.e. post cracking) positive bending moment capacity Up asfollows:

where:

= partial safety factor for concrete, taken as 1.5 for the ULS.

= equivalent to actual strength ratio in TR34 (2003) it is recommended that sufficientfibers be provided to give the minimum Re3 value of 0.3.

h = slab depth (mm)

/ct, fl = characteristic flexural strength of the plain concrete obtained from TR34 (2003) orEurocode 2 (2004). The use of Eurcode 2 results in a reduced value of /ct, jl

The information has been provided as a guide to performance only, for specific and supervised conditions. The user is advisedto undertake their own evaluation and use the services of professionals to determine product suitability for any particularproject or application prior to commercial use.

1. Method of Measuring Young's Modulus

1) Young's Modulus is extrapolated from tensile test data on the fibres.

2) Perspectives of Young's Modulus

Linear materials (for example. Steel, carbon fibres)Stress-Strain curve draws a straight line and the Young's Modulus is equal to the slope of the line.

2 Non-linear materials (for example like Rubber, plastic)When slightly strained, as it is said to obey Hooke's Law, obtain the slope of S-S curve in the range of slight strain.

Define E- t.nsil. stress 11 Thereforet.nsill strain t

E= a- tore. per unit F/A= =e cNrwed __ per ..... 1engIh ..:\1..141

Where F: Force applied to the object A: cross-sectional areailL : the amount by which the length of the object changesLO : the original length of the object

elongationlload elongation/load

4

123changed length [mm]

oo

40

50

'g20o~

,..,30zL....J

6 12 18 24 30changed length [mm]

o

G~I=+==t===r--~10

300

~oo'0tllo~

100

o

400

3) Conducting tensile tests on fibre

1 Measure decitex (dt) and obtain cross-section area (A) by calculation using density as d=0.91

2 Plot the load points by 0.25mm spacing in between zero point and ruptured point of strain

3 By obtaining tangent line (slope) on Strain: Load, the slope is the elastic modulusLoad at Strain 1mm point on above graph is 20.25N. Obtain the tangent line using 4 strain pointsbefore and after the point at 0.50mm, O.75mm, 1.25mm and 1.50mm. (5 point complex differentiation)

4 As above, supposing there are 100 plot points on Strain-Load, there exist 96 pointsexcluding the 4 points before and after the point from which we can obtain each tangent lineand Young's Modulus.

5 After obtaining 96 Young's Modulus, we select the largest slope (Young's Modulus) as elastic modulus.

(LASlO PLAS'fIC COHC8U(

While fibres increase the ductility of concrete, they do not increase (at the fibre doses generally adoptedfor slabs on grade ofbetween 3 and 7 kgs/m3 macro synthetic fibres) the negative (hogging) momentcapacity Up which is obtained as follows:

(h:JIt should be noted that that the equations above relate to a unit width (b=lmm), refer to workedexamples.

2.0 EQUIVALENT FLEXURAL STRENGTH AND Re J VALUES

Broadly, the properties of fibre reinforced concrete are influenced by:

Cross section (normal, flat, crescent etc) Deformations (straight, undulating, hook ended) Aspect ratio Dosage (generally expressed as kg/m3) Tensile strength Ductility (Toughness)

The aspect ratio (Lid) is defmed as the fibre length (L) divided by its diameter or its equivalent diameter(d) and is generally in the range ono to 100.

The quantity of macro synthetic fibres in a mix can be expressed in three ways:

Wi = lOOT! = lOOF = 7850Vr eqn (i)Te We We

where

Wi percent of fibres by weight of concreteTf weight of fibres in a batch (kg)Te weight of plain concrete in a batch (kg)F = weight of fibres per unit volume of plain concrete (kg/m3)We unit weight of plain concrete (kg/m3)VI volume fraction of fibres, percentage

It is common practice in the UK and Europe to specify the fibre dosage as a weight per unit volume ofplain concrete (F). For slabs on ground, typical values of F are in the range 3 to 7 kg/m3 whichcorrespond to volume :fractions (Vr ) of0.25% and 0.75% respectively. It should be noted that test data

The information has been provided as a guide to performance only, for specific and supervised conditions. The user is advisedto undertake their own evaluation and use the services ofprofessionals to determine product suitability for any particularproject or application prior to commercial use.

t:LASTO PLASTIC CONCRETE

for SynFRC can be misleading as the volume percentage of fibres is not always quoted and may be

between 1% and 2%. An important characteristic of macro synthetic fibres is their toughness orductility. A measure of this toughness can be obtained from the American Standard ASlM C1069 or

the Japanese Society of Civil Engineers - JSCE-SF4. The Japanese Standard is easier to use and the

starting point is to use a flexural test apparatus to detennine the modulus ofrupture (fit) ofbeams usinga third point loading test, see Fig, (1).

With the range of fibre doses used in ground supported slabs, that is, 3 to 7 kglm3, it is generally

accepted that the value of fit for plain concrete will not differ significantly from the stress at :first crackfor steel fibre reinforced beams. However, the deformation characteristics after cracking of macro

synthetic fibre concrete beams will differ considerably from those for plain concrete beams. Depending

on the fibre type and dosage, macro synthetic steel fibre concrete beams can be shown to have

considerable toughness (ductility). From the third point loading beam test, the area below the loaddeflection curve (Tb) up to a deflection of 1/150 of the span (3 mm for L = 450 mm) can be measured,see Fig. (2).

so

40~~ 30! 20

Fig2 Load defonnation chart

1.0 2.0 3.0 (UISU)

The equivalent flexmal strength Fe.3 can be expressed as:Tb LFe,3 = - X --3 bh2

The equivalent flexural ratio Re3, expressed IS a percentage, is given by:

Re,3 = /e,3 X 100 eqn (ii)/el

The infonnation has been provided as a guide to perfonnance only, for specific and supervised conditions. The user is advisedto undertake their own evaluation and use the services of professionals to detennine product suitability for any particularproject or application prior to commercial use.

[LASlO Pt.t..HIC (OHCA[I(

Slab tests Wldertaken at the University ofWestem Sydney Australia (7) and the Technical University of Brunswick,

Gennany (8) have shown that a significant increase of load bearing capacity can be achieved by the addition of

macro synthetic fibres in the dosage range 3 kglm3 to 7 kglm3 The greater the value of Re, 3, the greater the increase

in load capacity and ductility.

Tb LFig. (2): Detennination ofEquivalent Flexural S1rength Fe, 3 :="3 X bh2

Further developments in assessing Re3 values include the large round determinate panel test, the

ASTM. C- 1609 beam test and the centrally loaded beam test as given in Technologies in Structural and

Engineering (TSE) report of October 2006, report No 169.

This report's test work at the University of Greenwich at Chatham Maritime has validated the ability of

Barchip macro synthetic fibres to enhance the ductility of plain concrete when subjected to concentratedloads. The University of Greenwich tests complied with the Japanese Society of Civil Engineers

publication - Methods of Tests for Flexural Strength and Flexural Toughness of Fibre Reinforced

Concrete JSCE-SF4, 1984.

3.0 PUNCHING SHEAR

In TR34 (2003) and TR63 (2007) a design procedure is given for punching shear with slabs reinforcedwith steel fibres (SFRC). TR34 also includes a worked example (appendix B) which demonstrates thatthe shear capacity of plain concrete can be enhanced by the presence of steel fibres. Thus the total shear

capacity is Vr =Ve +Vr where Ve is the capacity of the plain concrete Vr that of the steel fibres.

Vr is a function of the equivalent flexural strength ratio (Re 3) and the characteristic flexural strength ofthe concrete (/ct, jT) .

The situation for macro synthetic fibres is still to be determined. Both TR34 (2003) and TR65 (2007)state that for synthetic fibre reinforced concrete the design should be based on the assumption that the

shear capacity is the same as unreinforced concrete. A desk study is currently being undertaken at

the University ofGreenwich and some draft proposals have been issued for comment.

The information has been provided as a guide to performance only, for specific and supervised conditions. The user is advisedto undertake their own evaluation and use the services ofprofessionals to determine product suitability for any particularproject or application prior to commercial use.

(LASlO ,,,"'SIIC; CONCIUll

WORKED EXAMPLE - COMPARISON OF BARCHIP AND SFRC REINFORCED SOG

1. MATERIAL PRoPERTIES

Concrete Grade

/ct, fl (8.05)Eern = 31 fN/mm3

Barchip 5 kgs/m3Re3

SFRC (25 kg/m3)Typical Re3 =

=

25/30 EC2

1.8 IV 3Imm

55% (to be conftrmed)

50 Undulating (61 d = 50)55 Hook ended (61 d =75)60 Hook ended (61 d =60)

All the above to be conftrmed by suppliers.

Slab Depth h = 150mmfin 1mm3 = 0.06 say

For slab layout see on last page.

Racking Legs250

Figl

Base Plate lOOxl00 (Typical)1002 =Ila2

a =(1002 1Il)o.3=54.funm

Combined Area =2x54.fun 250 +10000=38200mm2

Acquis =(382001 Il)O.5=110mm

Racking leg loads =50kw 1legIf rf =1.2

PU(Rjed) =2x50m 1.2=120kw

The infonnation has been provided as a guide to perfonnance only, for specific and supervised conditions. The user is advisedto undertake their own evaluation and use the services of professionals to determine product suitability for any particularproject or application prior to commercial use.

2. PUNCHING -INTERNAL

0 0 =J 100J 350 ~ Fil2VI =700 +200 =900mm At face of loaded area

3. BENDINGBACK TO BACK PALLET RACKING

/etA, fl = [1+(200Ih)0.5] /etA(O.OS) ::; 2/efA / O.a

=[1+ (200/150).5 ] 1.8

= 3.880 Xmm 2 > 2x1.9 x m = 3.6

Adopt.fcIA,Jf = 3.6 0 1mm2

M 1] =3.6x1502 16x1.5x103

=9.0KNmlm

M1] =Re,3M1]Re,3 = 0.55anyMp =0.55x9.0

=4.95 kNmlm

M1]+Mp=13.9kNmlm

[3 2 ]0.26f = Ecmxh 112(----)k

=623.7mm

For a, see page 2

a equiv =110mm

a If =110/623.7

=0.176

The infonnation has been provided as B guide to perfo~ only, for specific and supervised conditions. The user is advisedto undertake their own evaluation and use the services ofprofessionals to detennine product suitability for any particularproject or application prior to commercial use.

alf=0.2

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4. INTERNAL LoADING

aU =0 Pu =2n(MT'/ =Mp)= 2n x 13.95=B7.61kn

aU = 0.2 Pu =87.61+(184d -B7.61)0.176/0.2= 174.5leh

If the racking leg loads are SOleh & rf = 1.2For static loading, Pa required:

=100x1.2

= 120leh

BASTO HASTIC CONC~(T(

PYNCIDNG.(i)BARCmp

(i) At face of loaded area - mn:.to TR34 or 65Refer to P.4 of Shear Report (Shut11)

h=150mmUf =4 x 100 x 400mm

From TR34V max :::: 0.5k2 fc .eqn P.28

kz = 0.6(lx25 / 350)=0.54

fed = fell/ k=16.67 NI 2

ImmVmgtr = 0.5x0.54xI6.67

=4.5 hi 3Imm

Ppmax =4.5 X 900 x150 X lOx] = 607.5 kN270> 120 OK

PuNcmNG AT JOINTS(i) AT FACE OF WADED AREA

(a) Barchipv max = 4.5 tr/ 2/mm

vf=400h=150

Pp = 4.5x550x150xl00 3= 371.25kN > 120

(b) SFRCPp = 4.5x550xI12.5xlO 3

= 278.44kN > 120

The infonnation has been provided as a guide to performance only, for specific and supervised conditions. The user is advisedto undertake their own evaluation and use the services ofprofessionals to determine product suitability for any particularproject or application prior to commercial use.

UA5fO "LA'SIIC CONCRtl(

il) AT CRITICAL PERIMETER

(a) Barchipvc = 0.495 N/ 3/mmuc =350x200 +1Z'x300

=1492mmPp = 0.495x1492x150xl00 3

= 1l0.78kv,120

(b) SFRCVc=0.735N/ 3/mmUc =350+ 200+ 1Z'x225

= 1256.5mm(

Pp =0.735xI256.5x312.5xlOO 3= 103.9kN < 120

Thus load transfer is required.

SUMMARY (Racking Loads)

2x50=100kvyftlOO = 120kN ULT. LOAD RERD.

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The infonnation has been provided as a guide to perfonnance only, for specific and supervised conditions. The user is advisedto undertake their own evaluation and usc: the services ofprofessionals to detennine product suitability for any particularproject or application prior to commercial use.