Guideline For Design of SFRC
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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 Verificati Verification on 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 verificati verification on
20 20
5 5.6 5.7 5.8 5.9
Structural analysis Plastic analysis Non-linear analysis Analysis of second order effects with axial load Lateral instabilit instability y of slender beams
20 20 20 22 22
5.10
Prestressed ed members and structur structures es Prestress
22
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6 6.1 6.2 6.3 6.4 6.5
Ultimate limit states (ULS) Bending with or without axial force Shear Torsion Punching Design with strut and tie models
22 22 23 25 25 26
6.7 6.8
Partially loaded areas Fatigue
27 27
7 7.3 7.4
Serviceabilit y limit states (SLS) Serviceability 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 Lightweig ht aggregate aggregate concrete structures
37
Annex E (Informative)
2
38
Annex K (Normative) – Detailed determination of the factor
39
Annex L (Normative) – Determination and verification of fibre orientation factors
40
Part 2 - Supplements and modifications modification s to DS EN 206-1
42
1
Scope
42
2
Normative references
42
3 3.2
Definitions, symbols and abbreviations abbreviations abbreviations ns Symbols and abbreviatio
42 42
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4 4.3
Classification Hardened concrete
43 43
5 5.4
Requirements for concrete and methods of Requirements verification Requirement Requirements s for fresh concrete
43 43
6 6.2
Specification of concrete Specification Specifica Specification tion 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 composition on and initial testing Concrete compositi 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 - 14651 Supplements and modifications to DS EN
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 tion of concrete Specifica Delivery, reception and site transport of fresh concrete Placing and compactio compaction n
62 62
8.4
Part 5 - Supplements and modifications to BIPS C213 Tegningsstandarder Tegningssta ndarder 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, a spects, 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 Stahlfaser beton" from March 2010, but contains a number of modifications 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 Limit State SLS and Ul Ultimate timate 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
Reinforced Reinforc ed concrete
F
F
F
Dl = n.wRC
Dl = wSFRC
wPC
Dl
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 in case of self-compacting steel fibre reinforced concrete the t he fibre orientation factors. 1 The supplier of the steel fibre reinforced concrete is responsible for fulfilling the required performance class and delivering a concrete c oncrete 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) re bar) 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 anchored fibres are usually undulated, hook hooked ed 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 ex posure classes XS2, XD2, XS3 and XD3, XD3, if the steel fibres are considered in the structural verifications
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Note to last bullet: Steel fibres can be considered 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 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 c ross section for bending.
1.5.2.8 Performance class. Classification of steel fibre reinforced concrete
based on the characteristic values of post-crack 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 sym bols 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 t ests according to Part 3 for evaluation of the residual tensile strength in performance class 1
Crack mouth opening displacement in the tests according 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
1 2 , , ,
Performance class
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 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 com plete stress-strain curve according to Figure G.1 or Figure G G.2 .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 G.2 .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 com plete stress-strain curve according to Figure G.1 or Figure G G.2 .2
Design value of the axial residual tensile strength of steel fibre reinforced concrete in performance class 2 when applying the com plete stress-strain curve according to Figure G.1 or Figure G G.2 .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
γ ε ε
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
Partial factor for the residual tensile strength of steel fibre reinforced concrete
Calculation value of compressive strain of steel fibre reinforced concrete
Calculation value of tensile strain of steel fibre reinforced concrete
ε,
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 int o 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 re inforced 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
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An additional column is added in Ta ble 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 contri bution of fibres should be taken taken into account in the design of dyn dynamically amically loaded structures. Additional investigations are required to verify the t he design assumptions, if this guideline is applied to prestressed or post-tensioned steel fibre reinforced structures.
3 Materials New Section 3.5 is added
New Section 3.6 is added
3.5 Steel fibres (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 Steel fibre reinforced concrete 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 a s 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 t ests with steel fibre reinforced slump concrete according to Part 3. For steel fibre reinforced self-compacting concrete, the test t est 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 rei nforced concrete are identified with the prefix L. The performance classes shall be specified in accordance with the crack openings associated with the limit li mit state and failure mode. Table G.1 contains recommended performance class definitions. The first value specifies the performance class L1 for a crack c rack mouth opening displacement = 0.5 mm and the second value the performance class L2 for = 3.5 mm.
values and performance classes for steel fibre reinforced concrete
Table G.1:
Performance class
Verification in
L1
SLS
L2
ULS
values determined according to Part 3 of this guideline = 0.5 mm = 3.5 mm
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 f ollowing examples: C30/37 L1.2/0.9 - XC1 XC1 for a steel fibre reinforced r einforced 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 cf. guideline
XC1
Exposure class of the concrete
NOTE: The performance performance class L1 is typically larger than or equal to perform performance ance 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)
For the rectangular stress block
For SLS
= 0.4307
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= 0.40 = 0.25
(3) If the ratio of the performance class values L2/L1 is larger than 0.7, and 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 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
coefficient of variation = 1.0 +
∙
0.5 ≤ 1.70 0.5
= 0.5 shall be used Fibre orientation factor. For slump concrete, 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 t o 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 members subject to pure bending without 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 corre sponding basic values of the axial residual tensile strength in MPa
L1
1) 2)
,
L2
, ,
,
2)
0
< 0.16
0
–
–
–
0.4 )
0.16
0.4 )
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 2.7
0.96 1.08
2.4 2.7
0.60 0.68
0.89 1.00
0.89 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
or
, only
are allowed to be used in the design.
3.6.4 Stress-strain relation for non-linear structural analysis and for deformation analysis (1) The stresses and strains model notionally the behaviour of steel fibre reinforced concrete. Depending on the ratio L2/L1 (cf. Annex K), either the trilinear stressstrain relation or the rectangular stress block shall be used. Symbols in Figure G.1 and Figure G.2 are as follows:
, , ,
Tensile stress 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 entire stress-strain curve given in Figure G.1 and Figure G.2
Design value of the axial residual tensile strength of steel fibre reinforced concrete in performance class 2 when applying the entire stress-strain curve given in Figure G.1 and Figure G.2 Design value of the axial residual tensile strength when applying
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the rectangular stress block
, ε γ
Design value of the axial residual tensile strength in SLS
Strain of steel fibre reinforced concrete
Partial factor according to Table 2.1N
= 0.85; reduction factor tailored to the design concept to take account of long-term effects on the residual tensile strength of steel fibre reinforced concrete
(2)P For non-linear analysis, the linear progression of the stress-strain curve up to should be considered. This also holds for detailed deformation analysis. For the determination of cross sectional forces and for approximate deformation analysis the linear progression up to may be disregarded.
f e ct ( )
25
3.5
0.3 f ctm Ecm
f
1.04 f ctR,L2 f
1.04 f ctR,u
f
1.04 f ctR,L1
f ctm
f
s ct (MPa)
Figure G.1: Stress-strain relation of steel fibre reinforced concrete in the tension zone for the determination of sectional forces by non-linear structural analysis and for deformation analysis
3.6.5 Stress-strain relation for cross section verification Depending on the ratio L2/L1 (cf. Annex K), either the complete stress-strain relation (solid lines) or the rectangular stress block (dashed lines) in Figure G.2 shall be used in the tension zone for the cross section design in UL ULS. S. f
e ct ( )
25
3.5 f
f
0.1
f ctd,L2 = a c . f ctR,L2 g ct
f
f
f
f
f ctd,u = a c . f ctR,u g ct f
f
f
f
f ctd,L1 = a c . f ctR,L1 f
g f ct f
s ct (MPa) Figure G.2: Stress-strain relation of steel fibre reinforced concrete in the tension zone for cross sectional design in ULS except for non-linear structural analysis
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4 Durability and cover to reinforcement 4.4 Methods of verification 4.4.1 Concrete cover 4.4.1.2 Minimum cover, cmin
Paragraph (1)P is supplemented
For the verification of fire resistance of structural members with combined reinforcement, DS EN 1992-1-2 incl. Danish National Annex applies.
Paragraph (5) is supplemented
The minimum cover c min,dur only applies to rebar reinforcement and not to steel fi bres. Fibres close to the surface surface may corrode, which m may ay cause rust stains. HowevHowever, the durability is not affected by corrosion of fibres.
5 Structural analysis 5.6 Plastic analysis 5.6.1 General New paragraph (G.5)P is added
(G.5)P Methods based on plastic analysis are generally applicable for steel fibre reinforced concrete structures, if the major part of the tensile and bending resistance is provided by rebar reinforcement. Otherwise, the application of plastic analysis is limited to ground supported slabs, anchored underwater concrete slabs, pile supported floor slabs, shell shell structures and monolithically cast, pre prefabricated fabricated containing structures.
5.7 Non-linear analysis Paragraph (1) is supplemented
Non-linear methods of analysis analysis are generally applicable for steel fibre reinfor reinforced ced concrete structures, if the major part of the tensile and bending resistance is provided by rebar reinforcement. Otherwise, the application of non-linear analysis is limited to ground supported slabs, anchored underwater concrete slabs, pile supported floor slabs, shell structures and monolithically cast, prefabricated containing structures.
Paragraph (G.6) to (G.11) are added
(G.6) A suitable non-linear method of analysis including i ncluding cross section verification is described in paragraph (G.6) to (G.11). For steel fibre reinforced concrete structures, the design resistance is defined as
= ;1. 0 4∙,, ; ; /
(G.5.12.1)
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where:
1.04∙,
the mean value of the residual tensile strength of steel fibre reinforced concrete in performance class 1 and 2 according to Section 3.6.3 the respective mean value of the strength of concrete and rebar reinforcement steel:
, == 0.01.1,..815∙ ∙ ∙ = 1.1.05 ∙ = 1.1.08 ∙
(G.5.12.2)
(G.5.12.3)
for Class A
(G.5.12.4)
for Class B
(G.5.12.5)
the partial factor for the resistance of the structural system
(G.7)P For deformation analysis and determination of internal forces of steel fibre reinforced concrete, the stress-strain relation in Figure G.2 shall be used for the tension zone. For the compression zone, Section 3.1.5 applies without modification. For rebar reinforcement steel, Section 3.2 applies.
1.3 ≤ 1.3 + 0 0..1 +∙ ≤ 1.4
(G.8) For steel fibre reinforced concrete, = 1.4 shall be applied. a pplied. For combined reinforcement, generally = 1.35 may be applied, or
and
(G.5.12.2)
are explained in i n Figure G.3.
Fcd
x
Compression zf
h d
zs Tension
Ffd Fsd
b
Figure G.3:
Contribution of steel fibres F fd and contribution of rebar reinforcement F sd
to the bearing capacity
(G.9)P The design resistance must not be smaller than the design value of the effect of actions. (G.10)P The ultimate limit state is reached, if the ultimate strain of the concrete,
ε
the ultimate strain of the rebar reinforcement steel or the ultimate strain of steel = 25 ‰ according to Section 3.6.4 is reached in any fibre reinforced concrete cross section of the structural system. The ultimate limit state is further reac reached, hed, if
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= 0.025
a state of indifferent i ndifferent equilibrium is reached in (part of) tthe he structural system. The ultimate strain of the rebar reinforcement steel shall be taken as or
= () + 0.025 ≤ 00..9
.
(G.11) For steel fibre reinforced concrete, tension t ension stiffening should be considered according to the standard rules for reinforced concrete. When calculating the stress in the rebar reinforcement, the effect of the steel fibres f ibres should be considered.
5.8 Analysis of second order effects with axial load 5.8.2 General New paragraph (7) is added
(G.7) For steel fibre reinforced members subject to buckling, the effect of the fibres must not be considered in the design.
5.9 Lateral instability of slender beams New paragraph (5) is added
(G.5) For the verification of lateral instability of slender steel fibre reinforced beams, the effect of the fibres must must not be considered.
5.10 Prestressed members and structures If the provisions in this section are applied to steel fibre reinforced concrete structures, additional investigations shall be carried out to verify the design assumptions.
6 Ultimate limit states (ULS) 6.1 Bending with or without axial force Paragraph (2)P is supplemented
When determining the ultimate resistance of steel fibre reinforced concrete cross sections, the following additional assumptions are made:
The compressive and tensile stresses in the steel fibre reinforced concrete
•
are determined by means of the stress-strain curve in Figure G.4.
For a cross section without rebar reinforcement, the effective depth is
ℎ
•
taken equal to the overall depth of the cross section . For a steel fibre reinforced concrete cross section with rebar reinforcement the rules in DS EN 1992-1-1 apply.
•
The strain in the tension zone is limited to
, = ε, = 25
‰.
SFRC DESIGN GUIDELINE
23
b
h
d
Fs
e s and e Figure G.4:
f ct
(
)
e f ct,u = 25 e f ct= 3.5 0 e c2 e cu2
e
f c(
)
s ctf
Determination of stresses and strains for steel fibre reinforced concrete
New paragraph (G.9)P is added
(G.9)P For bending with or without normal force of steel fibre reinforced concrete
New paragraph (G.10)P is added
(G.10)P The contribution of the steel fibres must not be considered in construction joints.
cross sections, the fibre orientation factor the cross section.
shall represent the strength normal to
6.2 Shear 6.2.1 General verification procedure
Paragraph (1)P is supplemented
Paragraph (4) is supplemented
, ,
is the design value of the shear resistance of steel fibre reinforced concrete without shear rebar reinforcement
is the design value of the shear resistance of steel fibre reinforced concrete with shear rebar reinforcement including the contribution of the steel fibres
For steel fibre reinforced concrete, the t he minimum shear reinforcement according to DS 1992-1-1 9.2.2 (5) may reduced to zero for according beam-like to structures ≤ 5 EN h) by taking into account thebecontribution of thealso fibres Equation(b (G.9.5.a).
6.2.2 Members not requiring design shear reinforcement Paragraph (1) is supplemented
The design value of the shear resistance
,
of steel fibre reinforced concrete
members should generally be determined according to:
, = , + ,
where:
,
according to DS EN 1992-1-1, Equation (6.2)
(G.6.2.c)
SFRC DESIGN GUIDELINE
∙ , ∙ ∙ ℎ , = , ,
(G.6.2.d)
For the determination of
,
24
= ∙ ≤ ∙ 1.5500
shall be taken as
shall be based on a fibre orientation factor
.
which represents the strength
in the direction normal to the 45 degrees shear crack.
k a c r c r a h e S
45 deg.
Figure G.5:
f f ctR,u
Shear resistance due to the contribution of the steel fibres
For cross sections subject to a tensile normal force, the effect of the fibres must not be considered for shear:
, = 0.
NOTE: For beams, beams, a minimum reinforcement is always required, unless the fibre contribution according to 9.2.2 is sufficient.
6.2.3 Members requiring design shear reinforcement re inforcement Paragraph (3) is supplemented
The design value of the shear resistance
,
of steel fibre reinforced concrete
members with vertical shear reinforcement shall be determined according to: t o:
, = , + , ≤ ,
(G.6.8.1)
where:
,
, ,
according to DS EN 1992-1-1, Equation (6.8), and according to Equation (G.6.8.1). The maximum shear resistance shall be determined according to DS EN 1992-1-1, Equation (6.9). Paragraph (4) is supplemented
The design value of the shear resistance
,
of steel fibre reinforced concrete
members with inclined shear reinforcement shall be determined according to Equation (G.6.8.1) where:
,
,
according to DS EN 1992-1-1, Equation (6.13), and according to Equation (G.6.2d). The maximum shear resistance shall be determined according to DS EN 1992-1-1, Equation (6.14).
,
SFRC DESIGN GUIDELINE
25
6.2.4 Shear between web and flanges of T-sections Paragraph (4) is re placed
= ℎ = ∆ ∆ 1.0 cot = 1.2
(4) The shear resistance may be verified according to Equation (G.6.2.c) and Equation (G.6.2.d), with and . may be taken as the average longitu-
cotcot =
dinal normal stress in the flange over the length . As a simplification, and may be assumed for tension and compression flanges, respectively.
6.2.5 Shear at the interface between concrete cast at different times Paragraph (1) is supplemented
The contribution of the steel fibres must not be considered in construction jjoints. oints.
6.3 Torsion 6.3.1 General Paragraph (G.6)P is added
(G.6)P The contribution of the steel fibres f ibres must not be considered in the verification of torsion resistance.
6.4 Punching 6.4.3 Punching shear calculation
Paragraph (1)P is supplemented
,
Paragraph (2) is
The shear forces for the punching verification shall be determined based on the
supplemented
theory of elasticity.
Paragraph (2) point b) is replaced
Punching shear reinforcement is not necessary if:
is the design value of the punching shear resistance of a steel fibre reinforced slab without punching shear rebar reinforcement along the control section considered, taking into account the contribution of the steel fibres.
≤ ,
(G.6.37.1)
6.4.4 Punching shear resistance of slabs and column bases without shear reinforcement Paragraph (1) is supplemented
For steel fibre reinforced slabs and a nd foundations without punching shear reinforcement, the design punching shear resistance [MPa] may be calculated as follows:
, = 2 , + , ≤ ,
(G.6.47.1)
SFRC DESIGN GUIDELINE
26
where:
,
according to DS EN 1992-1-1, Equation (6.47)
∙ , , , = =0.1.18.54 ∙ , ,
(G.6.47.2)
shall be based on a fibre orientation factor
(G.6.53.1) which represents the strength
in the direction normal to the 45 degrees punching shear crack.
, = 0.
For cross sections subject to a tensile normal force, the effect of the fibres must not be considered for punching: punching: For slabs,
= = 2
.
NOTE: In ground ground supported slabs without without rebar reinforcement for bending, bending, no tension chord can be established due to the softening material behaviour of steel fibre reinforced concrete. Therefore, bending failure is always governing.
6.4.5 Punching shear resistance of slabs and column bases with shear reinforcement Paragraph (1) is supplemented
The combined action of steel fibres and punching shear reinforcement must not be applied in the design without detailed verifications.
Paragraph (4) is supplemented
For steel fibre reinforced concrete,
0.,15/
,
in Equation (6.54) may be replaced re placed by
according to Equation (G.6.47.1), if .
,
is determined with
, =
6.5 Design with strut and tie models 6.5.1 General New paragraph (G.2)P is added
(G.2)P If one of the following conditions is fulfilled, tie forces may be taken by steel fibres only:
The tensile stresses before cracking are smaller than
•
,
based on a fibre orientation factor
in the direction of the tie force).
,
(with
which represents the strength
Crack widths in ULS are verified to be limited to
•
= 0.5
mm.
Otherwise, rebar reinforcement is required and only up to 30 % of the tie force are allowed to be taken by the steel fibres (based on
,
).
SFRC DESIGN GUIDELINE
27
6.7 Partially loaded areas Paragraph (4) is supplemented
The tie force in Figure G.6 may be taken by steel fibres only or by combined rein-
,
forcement according to Section 6.5. The verification shall be based on
, , , (with
and
based on a fibre orientation factor
the strength in the direction of the tie force).
and
which represents
Idealized stress distribution in ULS
Tie force
h1
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