JANUARY 2014 SFRC CONSORTIUM
DESIGN GUIDELINE FOR STRUCTURAL APPLICATIONS OF STEEL FIBRE REINFORCED CONCRETE
Published by: SFRC Consortium Thomas Kasper, Bo Tvede-Jensen - COWI A/S Henrik Stang - Danish Technical University Peter Mjoernell, Henrik Slot, Gerhard Vitt - Bekaert Lars Nyholm Thrane - Danish Technological Institute Lars Reimer – CRH Concrete A/S Copyright © 2014 SFRC Consortium
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CONTENTS Foreword
7
Part 1 - Supplements and modifications to DS EN 19921-1
8
1 1.1 1.2 1.5 1.6
General Scope Normative references Definitions Symbols
8 8 9 9 10
2 2.2 2.4 2.5
Basis of design Principles of limit state design Verification by the partial factor method Design assisted by testing
13 13 13 14
3 3.5 3.6
Materials Steel fibres Steel fibre reinforced concrete
14 14 14
4 4.4
Durability and cover to reinforcement Methods of verification
20 20
5 5.6 5.7 5.8 5.9 5.10
Structural analysis Plastic analysis Non-linear analysis Analysis of second order effects with axial load Lateral instability of slender beams Prestressed members and structures
20 20 20 22 22 22
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6 6.1 6.2 6.3 6.4 6.5 6.7 6.8
Ultimate limit states (ULS) Bending with or without axial force Shear Torsion Punching Design with strut and tie models Partially loaded areas Fatigue
22 22 23 25 25 26 27 27
7 7.3 7.4
Serviceability limit states (SLS) Crack control Deflection control
27 27 32
8 8.2 8.10
Detailing of reinforcement and prestressing tendons – General Spacing of bars Prestressing tendons
33 33 33
9 9.1 9.2 9.3 9.5 9.6 9.8
Detailing of members and particular rules General Beams Solid slabs Columns Walls Foundations
33 33 33 35 36 36 37
11
Lightweight aggregate concrete structures
37
Annex E (Informative)
38
Annex K (Normative) – Detailed determination of the factor 2
39
Annex L (Normative) – Determination and verification of fibre orientation factors
40
Part 2 - Supplements and modifications to DS EN 206-1
42
1
Scope
42
2
Normative references
42
3 3.2
Definitions, symbols and abbreviations Symbols and abbreviations
42 42
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4 4.3
Classification Hardened concrete
43 43
5 5.4
Requirements for concrete and methods of verification Requirements for fresh concrete
43 43
6 6.2
Specification of concrete Specification for designed concrete
43 43
8 8.2
Conformity control and conformity criteria Conformity control for designed concrete
43 43
9 9.2 9.5 9.9
Production control Production control systems Concrete composition and initial testing Production control procedures
44 44 44 45
Annex A (normative) – Initial test
47
Annex H (informative) – Additional provisions for high strength concrete
48
Annex L (normative) – Determination of the steel fibre content
49
Annex M (normative) – Initial test of steel fibre reinforced concrete
53
Part 3 - Supplements and modifications to DS EN 14651
56
1
Scope
56
7 7.1 7.2 7.3
Test specimens Shape and size of test specimens Manufacture and curing of test specimens Notching of test specimens
56 56 56 57
9 9.3
Expression of results Residual flexural tensile strength
58 58
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Test report
6
60
Part 4 - Supplements and modifications to DS EN 13670 / DS 2427
62
1
Scope
62
4 4.3
Execution management Quality management
62 62
8 8.1 8.3
Concreting Specification of concrete Delivery, reception and site transport of fresh concrete Placing and compaction
62 62
8.4
Part 5 - Supplements and modifications to BIPS C213 Tegningsstandarder Del 3 - Betonkonstruktioner og Pæle
62 64
65
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Foreword This guideline for the design of steel fibre reinforced concrete structures is to be applied in conjunction with DS EN 1992-1-1 incl. Danish National Annex. While this guideline covers the design aspects, execution aspects for casting of steel fibre reinforced concrete, in particular steel fibre reinforced self-compacting concrete, are given in the "Guideline for execution of SFRC". This guideline is based on the German guideline "DAfStb-Richtlinie Stahlfaserbeton" from March 2010, but contains a number of modifications as discussed in the background document to this guideline. Steel fibres transfer tensile forces across cracks similar to rebar reinforcement. This property can be utilized both in Serviceability Limit State SLS and Ultimate Limit State ULS. However, it needs to be considered that the residual tensile strength due to the effect of the steel fibres typically decreases with increasing deformation (crack opening). Figure F.1 illustrates the tensile behaviour of steel fibre reinforced concrete in comparison with plain concrete and conventionally reinforced concrete. F
F
SFRC
Plane concrete F
Reinforced concrete
F
F Dl = wSFRC
wPC
Dl
Dl = n.wRC
Dl
Figure F.1: Tensile load-displacement behaviour of plain, steel fibre reinforced and conventionally reinforced concrete
This guideline classifies steel fibre reinforced concrete based on performance classes. It distinguishes between •
Performance class L1 for small crack openings
•
Performance class L2 for larger crack openings
The designer is responsible for specifying the required performance classes, and in case of self-compacting steel fibre reinforced concrete the fibre orientation factors. The supplier of the steel fibre reinforced concrete1 is responsible for fulfilling the required performance class and delivering a concrete with a uniform fibre distribution. The contractor is responsible for achieving a uniform fibre distribution and the required fibre orientation in the structure. 1
The supplier of the steel fibre reinforced concrete is the party mixing the fibres into the concrete.
Dl
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Part 1 - Supplements and modifications to DS EN 1992-1-1 1 General 1.1 Scope 1.1.2 Scope of Part 1-1 of Eurocode 2 Paragraph (1)P is replaced
(1)P This guideline applies in conjunction with DS EN 1992-1-1 to the design of civil engineering structures with steel fibre reinforced concrete and concrete with combined (steel fibre and steel rebar) reinforcement. The guideline applies up to and including strength class C50/60. The guideline applies only when using steel fibres with mechanical anchorage. NOTE: Mechanically anchored fibres are usually undulated, hooked end or flat end fibres. For members loaded in bending or in tension designed according to this guideline, it must be verified that the ultimate load of the system is larger than the crack initiation load. This verification is only possible, if at least one of the following conditions is fulfilled: •
Redistribution of sectional forces within statically indeterminate structures
•
Application of combined (steel fibre and steel rebar) reinforcement
•
Axial compression forces due to external actions
Statically determinate structures that obtain their bending capacity only by steel fibres in a single cross section are not allowed. For these cases the cross section equilibrium must be ensured by additional steel rebar reinforcement. Paragraph (4)P is supplemented
Furthermore, this guideline does not apply to: •
Lightweight aggregate concrete
•
High strength concrete of compressive strength class C55/67 or higher
•
Steel fibre reinforced sprayed concrete
•
Steel fibre reinforced concrete without steel rebar reinforcement in the exposure classes XS2, XD2, XS3 and XD3, if the steel fibres are considered in the structural verifications
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Note to last bullet: Steel fibres can be considered in the structural verifications in all exposure classes in case of combined steel fibre and steel rebar reinforcement. If this guideline is applied to prestressed or post-tensioned steel fibre reinforced structures, additional investigations shall be carried out to verify the design assumptions. New paragraph (G.5) is added
(G.5) In principle, the application of this guideline for design of non-load bearing members is possible. The application of the guideline for that purpose should be agreed upon for the individual case.
1.2 Normative references 1.2.2 Other reference standards The following reference standards are added
DS EN 14889-1:
Fibres for concrete - Part 1: Steel fibres - Definitions, specifications and conformity
DS EN 14651:
Test method for metallic fibre concrete - Measuring the flexural tensile strength (limit of proportionality (LOP), residual)
1.5 Definitions 1.5.2 Additional terms and definitions used in this Standard The following terms are added
1.5.2.5 Steel fibre reinforced concrete. Steel fibre reinforced concrete is a concrete according to DS EN 206-1, to which steel fibres are added to achieve certain properties. This guideline takes account of the effect of the fibres. 1.5.2.6 Residual tensile strength. Notional residual tensile strength of the steel fibre reinforced concrete in the tension zone. It relates the true tensile forces in the steel fibres to the area of the tension zone and to the direction perpendicular to the crack plane. 1.5.2.7 Residual flexural tensile strength. It represents the post-crack flexural tensile strength of the cross section for bending. 1.5.2.8 Performance class. Classification of steel fibre reinforced concrete based on the characteristic values of post-crack flexural tensile strength for crack mouth opening displacements = 0.5 and 3.5 mm in DS EN 14651 beam tests according to Part 3 of this guideline.
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1.6 Symbols
The following symbols are added
Latin upper case letters Tension zone area of cracked cross sections or plastic hinges associated with the respective equilibrium state ,
Minimum rebar reinforcement area of steel fibre reinforced concrete Crack mouth opening displacement Crack mouth opening displacement in the tests according to Part 3 for evaluation of the residual tensile strength in performance class 1 Crack mouth opening displacement in the tests according to Part 3 for evaluation of the residual tensile strength in performance class 2 Flexural tensile force resulting from the residual tensile strength of the steel fibre reinforced concrete Performance class
1 2
Performance class 1 Performance class 2 , , ,
Design value of the shear resistance of steel fibre reinforced concrete without shear reinforcement Design value of the shear resistance due to the contribution of the steel fibres Design value of the shear resistance of steel fibre reinforced concrete with shear reinforcement including the contribution of the steel fibres
Latin lower case letters Basic value of the axial residual tensile strength of steel fibre reinforced concrete ,
Basic value of the axial residual tensile strength of steel fibre reinforced concrete in performance class 1 when applying the complete stress-strain curve according to Figure G.1 or Figure G.2
,
Basic value of the axial residual tensile strength of steel fibre reinforced concrete in performance class 2 when applying the com-
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plete stress-strain curve according to Figure G.1 or Figure G.2 ,
Basic value of the axial residual tensile strength of steel fibre reinforced concrete when applying the rectangular stress block
,
Basic value of the axial residual tensile strength of steel fibre reinforced concrete in SLS Characteristic value of the flexural residual tensile strength of steel fibre reinforced concrete
,
Design value of the axial residual tensile strength of steel fibre reinforced concrete in performance class 1 when applying the complete stress-strain curve according to Figure G.1 or Figure G.2
,
Design value of the axial residual tensile strength of steel fibre reinforced concrete in performance class 2 when applying the complete stress-strain curve according to Figure G.1 or Figure G.2
,
Design value of the axial residual tensile strength of steel fibre reinforced concrete when applying the rectangular stress block
,
Design value of the axial residual tensile strength of steel fibre reinforced concrete in SLS
,
Calculation value of the axial residual tensile strength of steel fibre reinforced concrete
,
Calculation value of the axial residual tensile strength of steel fibre reinforced concrete in performance class 1 when applying the complete stress-strain curve according to Figure G.1 or Figure G.2
,
Calculation value of the axial residual tensile strength of steel fibre reinforced concrete in performance class 2 when applying the complete stress-strain curve according to Figure G.1 or Figure G.2
,
Calculation value of the axial residual tensile strength of steel fibre reinforced concrete when applying the rectangular stress block
,
Calculation value of the axial residual tensile strength of steel fibre reinforced concrete in SLS Length, over which a crack in the steel fibre reinforced concrete is considered as smeared in order to calculate the tensile strain of steel fibre reinforced concrete
!
,
Design value of the shear resistance along the control perimeter due to the contribution of the steel fibres
!
, ,"
Design value of the shear resistance along the control perimeter of a plate without punching shear rebar reinforcement, taking into
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account the contribution of the steel fibres #
Internal lever arm of the flexural tension force resulting from the residual tensile strength of the steel fibre reinforced concrete
Greek lower case letters $
Ratio of the calculation value of the residual tensile strength of steel fibre reinforced concrete to the mean value of the concrete tensile strength; reduction factor to take account of long-term effects on the residual tensile strength
$
Ratio of the calculation value of the residual tensile strength to the mean value of the concrete tensile strength
$
Reduction factor tailored to the design concept to take account of long-term effects on the residual tensile strength of steel fibre reinforced concrete Factor for determining the basic values of the axial residual tensile strength Factor for the determination of the basic value of the axial residual tensile strength of steel fibre reinforced concrete in performance class 1 when applying the complete stress-strain curve according to Figure G.1 or Figure G.2 Factor for the determination of the basic value of the axial residual tensile strength of steel fibre reinforced concrete in performance class 2 when applying the complete stress-strain curve according to Figure G.1 or Figure G.2 Factor for the determination of the basic value of the axial residual tensile strength of steel fibre reinforced concrete when applying the rectangular stress block Factor for the determination of the basic value of the axial residual tensile strength of steel fibre reinforced concrete in SLS
γ
Partial factor for the residual tensile strength of steel fibre reinforced concrete
ε
Calculation value of compressive strain of steel fibre reinforced concrete
ε ε ε
Calculation value of tensile strain of steel fibre reinforced concrete ,
Calculation value of ultimate tensile strain of steel fibre reinforced concrete Mean strain of the rebar reinforcement taking into account the con-
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tribution of the steel fibres '
Factor to take account of the size of the member (size effect); factor to take account of the fibre orientation
'(
Factor to take into account the influence of the member size on the coefficient of variation
')
Factor to take into account the fibre orientation when determining the calculation values of the axial residual tensile strength from the basic values of the axial residual tensile strength
*
Tensile stress of steel fibre reinforced concrete Modified rebar diameter of rebar reinforcement for the crack width verification with consideration of the steel fibre contribution
φ
2 Basis of design 2.2 Principles of limit state design New paragraph (G.2) is added
(G.2) The ultimate limit state is reached, if in the critical sections of the structure •
the critical strain of the steel fibre reinforced concrete or
•
the critical strain of the steel rebar reinforcement or
•
the critical strain of the concrete is reached
or if the critical state of indifferent equilibrium of the structural system is reached. A stabilisation of the system by considering the tensile strength of the concrete or the tensile strength of steel fibre reinforced concrete is not allowed, whereas the residual tensile strength can be considered.
2.4 Verification by the partial factor method 2.4.2 Design values 2.4.2.4 Partial factors for materials
SFRC DESIGN GUIDELINE
An additional column is added in Table 2.1N
Table 2.1N:
14
Partial factors for materials for ultimate limit states
Design situations
γ for steel fibre reinforced concrete with and without steel rebar reinforcement
Persistent & Transient
1.25
Accidental
1.25
2.5 Design assisted by testing Paragraph (1) is supplemented
Design assisted by testing needs to fulfil the same principles, safety concepts and structural integrity as described in DS EN 1992-1-1 and this guideline. For steel fibre reinforced concrete, special investigations are required if the contribution of fibres should be taken into account in the design of dynamically loaded structures. Additional investigations are required to verify the design assumptions, if this guideline is applied to prestressed or post-tensioned steel fibre reinforced structures.
3 Materials New Section 3.5 is added
3.5 Steel fibres
New Section 3.6 is added
3.6 Steel fibre reinforced concrete
(1)P DS EN 1992-2 and DS EN 14889-1 apply. The conformity of the steel fibres is required to be documented by a CE certificate of conformity (system 1).
3.6.1 General (1)P Steel fibres are oriented in different directions and their ability to transfer tensile forces depends on their orientation relative to the crack plane. The information about the relative amount of fibres in the different directions is referred to as the fibre orientation. If the relative amount of fibres in different directions varies, then the ability of fibres to transfer tensile forces also varies depending on the direction. This will result in a variation of the residual tensile strength in different directions. (2)P The effect of the fibre orientation on the residual tensile strength of steel fibre reinforced concrete is accounted for as follows (Annex L):
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The performance classes define the residual tensile strength for the reference fibre orientation as observed in 3-point beam bending tests with steel fibre reinforced slump concrete according to Part 3. For steel fibre reinforced self-compacting concrete, the test beams are cast with a reference casting method as defined in Part 3, Section 7.2, which results in a reproducible fibre orientation. The strength values from the tests are converted to strength values and performance classes for the reference fibre orientation. The fibre orientations in the actual structural applications are considered by a fibre orientation factor ') . (2)P The performance classes of steel fibre reinforced concrete are identified with the prefix L. The performance classes shall be specified in accordance with the crack openings associated with the limit state and failure mode. Table G.1 contains recommended performance class definitions. The first value specifies the perfor= 0.5 mm and mance class L1 for a crack mouth opening displacement the second value the performance class L2 for = 3.5 mm. Table G.1:
values and performance classes for steel fibre reinforced concrete
Performance class
Verification in
L1
SLS
= 0.5 mm
L2
ULS
= 3.5 mm
values determined according to Part 3 of this guideline
3.6.2 Properties Steel fibre reinforced concrete has a residual tensile strength (cf. Figure G.1 and Figure G.2). This notional residual tensile strength is related to the cross section of the concrete. It must not be used for determining the steel stresses in the fibres.
3.6.3 Strength (1)P The performance class values correspond to the characteristic values of the residual flexural tensile strength for the reference fibre orientation and the respective crack mouth openings. These characteristic values are to be verified according to Part 3 of this guideline. Performance classes should be specified according to the following examples: C30/37 L1.2/0.9 - XC1 for a steel fibre reinforced slump concrete SCC30/37 L1.2/0.9 - XC1 for a steel fibre reinforced self-compacting concrete where:
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C30/37 SCC30/37
Compressive strength of the concrete according to DS EN 206-1
L1.2/0.9
Steel fibre reinforced concrete of performance class L1-1.2 for and performance class L2-0.9 for cf. Part 3 of this guideline
XC1
Exposure class of the concrete
NOTE: The performance class L1 is typically larger than or equal to performance class L2. For self-compacting concrete, fibre orientation factors ') and the associated directions shall be specified for each structural member / casting section, cf. Part 5 of this guideline. (2)P The basic values of the axial residual tensile strength in Table G.2 are obtained from the characteristic values of the flexural residual tensile strength as =
, , , ,
=
=
=
∙
, , , ,
∙
∙
∙
(G.3.31) (G.3.32) (G.3.33) (G.3.34)
where: ,
Basic value of the axial residual tensile strength according to Table G.2 column 2
,
Basic value of the axial residual tensile strength according to Table G.2 column 4
,
Basic value of the axial residual tensile strength according to Table G.2 column 5
,
Basic value of the axial residual tensile strength according to Table G.2 column 6 Value according to paragraph (3) Value according to paragraph (3)
= 0.37
= 0.40
For the rectangular stress block For SLS
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(3) If the ratio of the performance class values L2/L1 is larger than 0.7, = 0.40 and = 0.25 may be used. Otherwise, the rectangular stress block must be used for the ULS verification. Reference is made to Annex K for more detailed determination of . (4)P If the ratio of the performance class values L2/L1 is larger than 1.0, the rectangular stress block must not be used. (5)P The calculation values of the axial residual tensile strength are determined based on the basic values of the axial residual tensile strength as: = ') ∙ '( ∙
, , , ,
= ') ∙ '( ∙
= ') ∙ '( ∙
= ') ∙ '( ∙
,
(G.3.35)
,
(G.3.36)
,
(G.3.37)
,
(G.3.38)
where: '( ')
Factor to take into account the influence of the member size on the ∙ 0.5 ≤ 1.70 coefficient of variation = 1.0 +
Fibre orientation factor. For slump concrete, ') = 0.5 shall be used in general, however, for plane structures cast in horizontal position (width > 5 height) ') = 1.0 may be used for flexural and tensile loading. For self-compacting concrete, reference is made to Annex L for determination and verification of fibre orientation factors. Recommended values for fibre orientation factors in specific applications and design aspects are contained in Section 9 of this guideline. Cross sectional area of the cracked areas or plastic hinges in m2 associated with the respective equilibrium state
NOTE: For members subject to pure bending without axial force sumed as 0.9 .
may be as-
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Table G.2: Performance classes L1 and L2 for steel fibre reinforced concrete with corresponding basic values of the axial residual tensile strength in MPa ,
L1
1) 2)
,
L2
,
2)
0
< 0.16
0
–
–
–
0.4 1)
0.16
0.4 1)
0.10
0.15
0.15
0.6
0.24
0.6
0.15
0.22
0.22
0.9
0.36
0.9
0.23
0.33
0.33
1.2
0.48
1.2
0.30
0.44
0.44
1.5
0.60
1.5
0.38
0.56
0.56
1.8
0.72
1.8
0.45
0.67
0.67
2.1
0.84
2.1
0.53
0.78
0.78
2.4
0.96
2.4
0.60
0.89
0.89
2.7
1.08
2.7
0.68
1.00
1.00
3.0
1.20
3.0
0.75
1.11
1.11
Only for plane members (b > 5h) Applies if L2/L1 ≤ 1.0. If L2/L1 > 1.0, see paragraph (4)P
NOTE: In case ,
,
=
