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APPLICATIO OF ELASTO PLASTIC CONCRETE BARCHIP MACRO STRUCTURAL SYNTHETIC FIBRE 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 Concrete Society 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 Meyerhof equations 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 concrete
does not have any significant ability to redistribute bending moments, but the presence or fibres (macro synthetic 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 as follows:
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 sufficient fibers 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) or Eurocode 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 advised to undertake their own evaluation and use the services of professionals to determine product suitability for any particular project 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-
ae
=
E=
t.nsil. stress 11 t.nsill strain t
Therefore
tore. per unit •••
=
cNrwed __ per ..... 1engIh
F/A
..:\1..141
Where F: Force applied to the object A: cross-sectional area ilL : the amount by which the length of the object changes LO : the original length of the object
elongation/load
elongationlload 50
400
•
40
300
,..,30
~oo
z
L....J
'g20 o
'0 tll
o
~
~
100
G~I=+==t===r--~10
o
o o
6
12 18 24 changed length [mm]
30
o
123 changed length [mm]
4
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 modulus Load at Strain 1mm point on above graph is 20.25N. Obtain the tangent line using 4 strain points before 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 points excluding the 4 points before and after the point from which we can obtain each tangent line and 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 adopted for slabs on grade of between 3 and 7 kgs/m 3 macro synthetic fibres) the negative (hogging) moment capacity Up which is obtained as follows:
(h:J It should be noted that that the equations above relate to a unit width (b=lmm), refer to worked examples.
2.0 EQUIVALENT FLEXURAL STRENGTH AND Re VALUES J
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/m 3) 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 Te
We
eqn (i)
We
where
Wi
percent of fibres by weight of concrete
Tf
weight of fibres in a batch (kg)
Te F We
weight of plain concrete in a batch (kg)
VI
=
weight of fibres per unit volume of plain concrete (kg/m3) unit weight of plain concrete (kg/m3) 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 of
plain concrete (F). For slabs on ground, typical values of F are in the range 3 to 7 kg/m3 which correspond 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 advised to undertake their own evaluation and use the services of professionals to determine product suitability for any particular project 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 or ductility. 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 of rupture (fit) ofbeams using a 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 crack for 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 load deflection 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
2.0
1.0
3.0 (UISU)
Fig 2 Load defonnation chart
The equivalent flexmal strength Fe.3 can be expressed as:
Tb
Fe,3 = -
L X -3 bh 2
The equivalent flexural ratio Re 3, expressed IS a percentage, is given by:
Re,3
=
/e,3 /el
X
100 eqn (ii)
The infonnation has been provided as a guide to perfonnance only, for specific and supervised conditions. The user is advised to undertake their own evaluation and use the services of professionals to detennine product suitability for any particular project 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.
Fig. (2): Detennination ofEquivalent Flexural S1rength
Tb L Fe, 3 :="3 X bh 2
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 concentrated loads. 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 reinforced with steel fibres (SFRC). TR34 also includes a worked example (appendix B) which demonstrates that the shear capacity of plain concrete can be enhanced by the presence of steel fibres. Thus the total shear capacity is
Vr
Vr = Ve + Vr
where Ve is the capacity of the plain concrete Vr that of the steel fibres.
is a function of the equivalent flexural strength ratio (Re 3) and the characteristic flexural strength of
the 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 of Greenwich 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 advised to undertake their own evaluation and use the services of professionals to determine product suitability for any particular project or application prior to commercial use.
(LASlO ,,,"'SIIC; CONCIUll
WORKED EXAMPLE - COMPARISON OF BARCHIP AND
SFRC REINFORCED SOG
1. MATERIAL PRoPERTIES Concrete Grade
25/30 EC2
/ct, fl (8.05)
1.8 Imm IV 3
Eern
=
31 fN/mm3
Barchip 5 kgs/m 3 Re3
55% (to be conftrmed)
SFRC (25 kg/m 3) Typical Re3
= =
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
fin 1mm
3
= 150mm = 0.06 say
For slab layout see on last page. Racking Legs 250
Figl Base Plate lOOxl00 (Typical)
1002 = Ila 2 a = (1002 1Il)o.3
= 54.funm = 2x54.fun 250 + 10000 = 38200mm 2 = (382001 Il)O.5
Combined Area Acquis
=110mm Racking leg loads = 50kw 1leg If f =1.2 PU(Rjed) = 2x50m 1.2 =120kw
r
The infonnation has been provided as a guide to perfonnance only, for specific and supervised conditions. The user is advised to undertake their own evaluation and use the services of professionals to determine product suitability for any particular project or application prior to commercial use.
2. PUNCHING -INTERNAL
0 0 =J J 350
VI =700 + 200 =900mm
~
100 Fil2
At face of loaded area
3. BENDING BACK TO BACK PALLET RACKING
/etA,
fl
= [1+(200Ih)0.5] /etA(O.OS) ::; 2/efA / O.a = [1+ (200/150)°.5 ] 1.8 2
= 3.880 Xmm > 2x1.9 x m = 3.6
Adopt.fcIA,Jf = 3.6
0
1mm 2
M 1] = 3.6x1502 16x1.5x1 03 =9.0KNmlm M1]
= Re,3M1]
Re,3 = 0.55anyMp = 0.55x9.0 =4.95 kNmlm M1]+Mp=13.9kNmlm
f
2 ]0.26 = [ Ecmxh 3 112(----)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 advised to undertake their own evaluation and use the services ofprofessionals to detennine product suitability for any particular project or application prior to commercial use.
"'ASIO """S"II( CO"-"Ull
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
= 1.2
For static loading, Pa required:
=100x1.2 = 120leh < 170.Skh
Therefore slab adequate for intemalloading
5. LoADING AT JOINTS (EDGE LoADING)
a If = 0 Pa = [n(Mp+M7})/2]+2M" =40.90kh alf=0.2 Pa *[ n(Mp+M7})+4MA1 ]
0.8t3
I (l-r;x>
=90.4leh a If = 0.175 Pa = 40.9 + [90.4 - 40.9]xO.176 / 0.2 = 84.46kh < 120kh Thus load transfer required, say 30%. Check with designer of load transfer system.
The infonnation has been provided as a auide to perfonnance only, for specific and supervised conditions. The user is advised to undertake their own evaluation and usc the services of professionals to detennine product suitability for any particular project or application prior to commercial use.
BASTO HASTIC
CONC~(T(
PYNCIDNG.
(i)BARCmp (i) At face of loaded area - mn:.to TR34 or 65 Refer to P.4 of Shear Report (Shut11)
h=150mm Uf =4 x 100 x 400mm From TR34 V max ::::
0.5k2 fc
.eqn P.28
kz = 0.6(lx25 / 350) =0.54 fed = fell/ k =16.67 NI 2 Imm Vmgtr = 0.5x0.54xI6.67 =4.5 hi 3 Imm
= 4.5 X 900 x150 X
Ppmax
270> 120
lOx] = 607.5 kN
OK
PuNcmNG AT JOINTS (i) AT FACE OF WADED AREA
(a) Barchip v
max
tr/ 2 = 4.5 /mm
vf=400 h=150 Pp = 4.5x550x150xl00 3 = 371.25kN > 120 (b) SFRC
Pp = 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 advised to undertake their own evaluation and use the services ofprofessionals to determine product suitability for any particular project or application prior to commercial use.
UA5fO "LA'SIIC CONCRtl(
il) AT CRITICAL PERIMETER
(a) Barchip vc = 0.495 N/ /mm 3 uc =350x200 + 1Z'x300 =1492mm Pp = 0.495x1492x150xl00 3 = 1l0.78kv,120 (b) SFRC
Vc=0.735N/ 3 /mm Uc =350+ 200+ 1Z'x225 = 1256.5mm (
Pp =0.735xI256.5x312.5xlOO 3 = 103.9kN < 120 Thus load transfer is required. SUMMARY (Racking Loads)
2x50=100kv yftlOO = 120kN ULT. LOAD RERD.
C25 /30 Re,3 = 55% Barchip & SFRC Thus for both Barchip & SFRC MTJ =9.0kNm/m Mp = 4.95kN m/m SHEAR REpORT Nov. 2007
The infonnation has been provided as a guide to perfonnance only, for specific and supervised conditions. The user is advised to undertake their own evaluation and use the services of professionals to detennine product suitability for any particular project or application prior to commercial use.
lD)
b<1ge Loaamg lJomts) Pu (Barchip) = 84.46kN,120 Pu (SFRC) = 84.46kN < 120
Note: Load transfer is required at joints for Bar Chip&SFRC
ASTO ' l .... snc COtiCIt£U
(li) PUNCHING
Location (a) Internal at face loaded area. (b) Internal at 2d/2hfrom face of loaded area. (c) Edge, at face of loaded area. (d) Edge, at 2d/2hfrom face of loaded area.
l.a
l.b
(2h) Bar Chip 607.5kN
(2h) SFRC 455.6kN
206.7kN
191.26kN
371.25kN
278.44kN
110.78kN
103.9kN
REVISION FOR PuNCHING -
100
M
.------l
I---------i
h =150 Fig. No.1
See Fig 2
uf=700mm Pu = 4.5x900xI50xl0 m3 = 607.5kN Bar Chip Pu = 4.5x900xI12.1xl om3 = 455.6kN SFRC
Above at face ofloaded area at 2d/2h from face of loaded area: Bar Chip Uc = 900 + 27 x300 = 2784mm Pp = O.495x2784x150xl 0° 3 =2047kN SFRC Uc = 900 + 2nx225 = 2313mm Pp = 0.73 5x.2313xI12.5xl 0° 3 = 191.26kN
V
300=2.h
-
WAREHOUSE FLooR LAYOUT The information has been provided as a guide to perfo~ only, for specific and supervised conditions. The user is advised to undertake their own evaluation and use the services ofprofessionals to detennine product suitability for any particular project or application prior to commercial use.
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The infonnation has been provided as a guide to perfonnance only, for specific and supervised conditions. The user is advised to undertake their own evaluation and usc: the services of professionals to detennine product suitability for any particular project or application prior to commercial use.
