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Structural Design of LoadBearing Fibre Concrete
Structures
Johan Silfwerbrand
KTH Royal Institute of Technology, Stockholm
Finnish Concrete Day, Helsinki, Oct. 23, 2014
Oct. 23, 2014
J Silfwerbrand, KTH
1
Fibre Concrete
Outline
 Historical background
 Swedish committee work
 Presentation of the new Swedish standard for
designing fibre concrete structures
 Concluding remarks
Oct. 23, 2014
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Historical Background
 Fibre concrete (FC) origins from the 19th century,
there is an American patent from 1874.
 The modern development of FC started in USA in
the mid 1950s.
 Swedish handbook on rock strengthening using
shotcrete (Holmgren, 1992).
 Swedish report on steel fibre reinforced concrete
(Svenska Betongföreningen, 1995).
 Swedish report on industrial concrete floors
(including FC) (Svenska Betongföreningen, 2008).
 Swedish standard on design of FC structures (SIS,
SS 812310:214, 2014).
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Shotcrete for Rock Strengthening
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Industrial
Concrete Floors
Fraktarna, Stockholm, 2001. Foto J Hedebratt.
FC in Elevated Slabs
J Hedebratt, 2012
Swedish Committee Work
 Aim: Guidelines for designing load-carrying fibre
concrete structures.
 Start: 2007.
 Original aim: Addition to the Swedish strucutral
concrete handbook BBK 04.
 But Eurocode 2 was introduced in Sweden in
2009.
 New aim: Addition to Eurocode 2.
 Draft version: Summer 2013.
 Release of printed version: Spring 2014.
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Introduction
1 (2)
 The aim of the standard is to provide Swedish
national guidelines for designing load-carrying FC
structures according to Eurocode 2.
 The standard uses the same headings and
numbering as Eurocode 2.
 Repetitions have been avoided, why the standard
has to be read parallel to Eurocode 2.
 The language of the standard is English.
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Introduction
2 (2)
 On purpose, the committee selected the word
fibre concrete instead of steel fibre concrete or
steel fibre reinforced concrete.
 The idea is that the standard should be materialindependent regarding fibre material.
 The standard authors are know that current
synthetic fibres do provide rather modest
performance if the fibre content is not enhanced
substantially (which in turn may cause mixing & casting
problems).
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Aim
 The Standard applies to the design of buildings
and other civil engineering works with steel or
polymer fibres according to EN 14889-1 & EN
14889-2.
 The Standard does not cover glass, carbon, basalt
or any other type of fibres.
 The Standard is intended to be used in
conjunction with EN 1992-1-1 Eurocode 2 Design of
concrete structures – Part 1-1 General rules & rules for buildings
 -1: Fibres for concrete - Part 1: Steel fibres – Definitions,
specifications and conformity
 -2: Fibres for concrete - Part 2: Polymer fibres – Definitions,
specifications and conformity
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The Content is Connected to
Eurocode 2
1 General
2 Bases of design
3 Materials
5 Structural analysis
6 Ultimate Limit State (ULS)
7 Serviceability Limit State (SLS)
8 Detailing of reinforcement and prestressing
tendons – General
11 Lightweight aggregate concrete structures
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Annexes
O.
P.
Q.
R.
Calculations of strains & stresses in bending
Production & conformity control of fibre concrete
Execution control of fibre concrete
Expected coefficient of variation for beam tests
according to SS-EN 14651
S. Fibre concrete, statically indeterminate
structures, and magnification factors
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Definitions
English
Svenska
Kommentar
Fibre concrete
Fiberbetong
… the concrete matrix
provides compressive
strength & protection of the
fibres whereas the fibres
provide tensile strength …
Steel fibre
Stålfiber
SS-EN 14889-1
Polymer fibre
Polymerfiber
SS-EN 14889-2
Designed concrete
Betong med
föreskrivna
egenskaper
SS-EN 206
Prescribed concrete Betong med
föreskriven
sammansättning
SS-EN 206
1.5.2
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Basis of Design
 Structural components shall have structural
system stability in ULS after a fully developed
crack system though
1. Stress redistribution in statically indeterminate
systems,
2. Combination of steel bar reinforcement or pretensioned steel reinforcement with fibre concrete.
3. External normal forces maintain equilibrium.
2.3.2.1
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Shrinkage & Creep
1 (2)
 Shrinkage & creep shall be considered in ULS
through
1. Stresses caused by restrained shrinkage & creep
are superposed to mechanical stresses (theory of
elasticity) or
2. Effects of shrinkage & creep are considered by
increased ductility demand – in practice: design
for fR,3 instead of fR,1 or for fR,4 instead of fR,2.
(theory of plasticity).
2.3.2.2
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Shrinkage & Creep
2 (2)
 In case of bending, distinguish between
compressive creep & flexural creep.
 In case of polymer fibre concrete, long-term tests
should be conducted (at elevated temperature if
such temperature occurs in reality).
2.3.2.2
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Partial Factors for Materials
Design
situations
c for
concrete
s for
s for pre-
reinforcing stressing
steel
steel
f for fibre
concrete
Persistent &
transient
1,5
1,15
1,15
1,5
Exceptional
1,2
1,0
1,0
1,2
SLS
1,0
1,0
1,0
1,0
2.4.2.4
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Testing Fibre Concrete
 3 point bending tests on notched FC beams
according to SS-EN 14651
 fR,i = (3/2)(FR,il)/(bwhsp); i = 1, 2, 3, 4
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Testing FC According to Svenska
Betongföreningen
F/2
F/2
h
l/3
l/3
l/3
b
l = 450 mm, b = 125 mm, h = 75 mm
Flexural Tensile Strength According
to Svenska Betongföreningen
(1) Cracking strength (3) Residual strength
(2) Ultimate strength
Max flexural stress
fflu
fflcr
fflres
2
3
1
cr
5.5cr
10.5cr
15.5cr
Midspan deflection 
Residual Flexural Tensile
Strength
 Characteristic residual flexural tensile strength of
fibre concrete = characteristic value of the flexural
tensile strength after cracking
 ffl,res = R10,Xffl,cr/100; X = 20, 30, 40, …
 Comparison between the international EN 14651 &
the Swedish SBF test method:
 fR,1 ≈ R10,20ffl,cr/100
 fR,2 ≈ R10,30ffl,cr/100
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Classifying Residual Flexural
Tensile Strength 1 (3)
 Classes defined for all four levels of the residual
flexural tensile strength fR,1, fR,2, fR,3 & fR,4
 For everyone, six steps with the interval = 1,0
MPa.
 In total: 4×6 = 24 classes.
 Residual flexural tensile strength are determined
thrugh beam testing according to SS-EN 14651
after 28 days.
 The classes are based on the characteristic value
(lower 5 % fractile).
3.5.1
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Classifying Residual Flexural
Tensile Strength 2 (3)
Class
R1
fR,1
Class
R2
MPa
fR,2
Class
R3
MPa
fR,3
Class
R4
MPa
fR,4
MPa
R11
1.0
R21
1.0
R31
1.0
R41
1.0
R12
2.0
R22
2.0
R32
2.0
R42
2.0
R13
3.0
R23
3.0
R33
3.0
R43
3.0
R14
4.0
R24
4.0
R34
4.0
R44
4.0
R15
5.0
R25
5.0
R35
5.0
R45
5.0
R16
6.0
R26
6.0
R36
6.0
R46
6.0
3.5.1
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Classifying Residual Flexural
Tensile Strength 3 (3)
Example of classifying:
 C30/37 – R13/R32 
 Compressive strength = 30 MPa (cylinder)
 37 MPa (cube)
 Residual flexural tensile strength = 3 MPa in class
R1
 Residual flexural tensile strength = 2 MPa in class
R3
 All values = characteristic values
3.5.1
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Prerequisite on Fibre
Concrete
 C1 = 100×fR,1/fctk,0,05 ≥ 50 %
 100×fR,3/fR,1 ≥ 50 %
 The intention is to ensure a certain ductility of the
fibre concrete.
3.5.1
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Bending Hardening or
Bending Softening?
3.5.1
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Characteristic Residual Tensile
Strength
f ft,R1  0,45  f R,1
f ft,R3  0,37  f R,3
3.5.1
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Design Residual Tensile
Strength
 Ultimate Limit State (ULS):
f ftd,R1   f  det 
f ft,R1
f
f ftd,R3   f  det 
f ft,R3
f
 Serviceability Limit State (SLS):
f ftd,R1   f 
Oct. 23, 2014
f ft,R1
f
3.5.2
J Silfwerbrand, KTH
Fibre Orientation Factor f
 Factor considering the fibre orientation in the
concrete.
 f ≥ 0,5
 For horizontally cast concrete members, set f =
1,0 (width > 5×thickness).
 For other members, select 0,5 < f ≤ 1,0
dependent on member dimensions, fibre length, &
casting procedure.
 For SLS, f = 1,0.
3.5.2
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Factor Considering Degree of
Statically Determination det
 Statically indeterminate structures provides
possible stress redistribution. There are several
cross sections to consider.
 The probability that several cross section have low
strength is less than the probability for just one
single low strength cross section (= the case for
statically determinate structures).
 Slabs have considerably larger possibilities to
stress redistribution than beams.
 Annex S is a background document for the tabled
values.
3.5.2
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Values of the Factor det
1 (3)
Case Type of structural member
No
det
1
2
1
1,4
3
4a
Statically determinate beams
Statically indeterminate
beams
Rectangular slabs with 2
opposite edges simply
supported (others free)
Simply supported circular
slabs
1
1,4
3.5.2
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Values of the Factor det
Case Type of structural member
No
4b
Rectangular slabs with ≥ 3
edges simply supported
5a
Circular slabs with clamped
edges
5b
5c
Rectangular slabs with ≥ 1
edge clamped (others simply
supported)
Slabs-on-grade
2 (3)
det
1,4
2
2
2
3.5.1
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Values of the Factor det
Case Type of structural member
No
5d
Interior spans of pile-supported
slabs
5e
Interior spans of columnsupported slabs
5f
Interior spans of simply
supported continuous slabs
3 (3)
det
2
2
2
3.5.1
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ULS – Bending Moment
c  fcd
c =  fcd
c =  fcd
c
x
fctd
fftd,R1
st
ft  ftu
x
x
fftd,R1
fftd,R3
Fst = st  Ast
Fst = st  Ast
ft  fftd,R3
ft  fftd,R3
a)
a) General stress distribution
b) 1st simplified distribution
c) 2nd simplified distribution
Fst = st  Ast
fftd,R3
b)
 ft  f ftd,R 1 
c)
 ft
 f ftd,R 1  f ftd,R 3 
 ftud
6.1
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ULS – Shear
 In cases without shear reinforcement:
VRd,cf
1/ 3
 0.18



f ct,R3 

  f ck   0.15   cp   bw  d

 k  100   1  7.5 
f ctk 

  C



Fibre contribution
 Conventional reinforcement is needed.
 Consciously choice of the committee (safe side).
 The equation is based on an Italian proposal that has been found to
represent test data from the literature best (Mondo, 2011).
6.2.2
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ULS – Punching
 In cases without shear reinforcement:
1/ 3


f ct,R3 

0,18
  f ck   0,15   cp
 k  100   1  7,5 
vRd,cf 
C
f ctk 



Fibre contribution
 For FC ground-supported slabs & column bases
without conventional reinforcement:
 vRd,cf = vRd,f = (k/2)CfR,3/f
 k = thickness dependent factor in EC 2, 6.2.2
 C = constant = 0,45
6.4.4
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Recommended Values of Max
Crack Width wmax (mm)
Exposure
class
L50
L100
Note
X0, XC1
-
-
Crack width
does not
influence
durability.
XC2, XC3
0,5
0,4
XC4
0,4
0,3
XS1, XS2, XD1,
XD2
0,3
0,2
XS3, XD3
0,2
0,1
Combination
with reinf.
necessary.
The values deal with the case ”fibres only” considering
durability.
7.3.1
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Minimum Reinforcement
As, min   s  k c  k  1  k f   f ct,eff  Act
f ftd,R1
kf 
 1 .0
f ct m
7.3.2
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Control of Cracking without
Direct Calculation
s,f  s 







 s  As b
4  h  d   f ct,0

1
1  k f 
2
 s
f ct,eff
f ct,0

1
1  k f 2
s,f = modified bar reinforcement size for FC
s = steel stress according to EC 2, Table 7.2N
As = tensile reinforcement area
h = section height
d = internal level arm for the bar reinforcement
b = width of the tensile zone
fct,0 = 2,9 MPa
7.3.3
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Computation of Crack Widths
 The calculation is based on the same principle as
used for RC in EC 2.
 Calculate characteristic crack width wk.
 Calculate strain difference (sm-cm) using one of
two alternatives.
 Calculate max crack spacing sr,max.
 Calculate max crack width at bending wmax.
 Calculate max crack width for restraint stresses
wmax.
7.3.4
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Minimum Reinforcement in
Beams






Minimum reinforcement:
As,min = Ac(kcfctm – fdetfct,R3)/fyk
Condition for ”fibre only” cases:
fdetfct,R3 > kcfctm
Ac = tensile concrete area (in bending), hct = h/2
kc = stress distribution coefficient (in bending)
9.2.1.1
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Concluding Remarks
 Finally, there is a standard for designing loadbearing FC structures!
 The expectation is that this standard shall provide
the structural engineers with an additional
alternative.
 It is essential that the guidelines are solid and
solidly supported by the society. New fibres are
welcome but new fibre concretes have still to fulfil
the requirement and the spirit of the guidelines.
 Do not put fibres against conventional
reinforcement – combination is in many cases the
optimal solution.
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