SIST-TS CEN/TS 1992-4-2:2009
(Main)Design of fastenings for use in concrete - Part 4-2: Headed Fasteners
Design of fastenings for use in concrete - Part 4-2: Headed Fasteners
This document relies on characteristic resistances and distances which are stated in a European Technical Specification.
Bemessung von Befestigungen in Beton - Teil 4-2: Kopfbolzen
Dieses Dokument stützt sich auf charakteristische Widerstände und Abstände, die in einer europäischen Technischen Spezifikation festgelegt sind. Als Grundlage für die Bemessung nach dieser CEN/TS sollten in einer europäischen Technischen Spezifikation zumindest die folgenden charakteristischen Werte angegeben sein:
ccr,sp, scr,sp
cmin, smin, hmin
Grenzwerte für die Betonfestigkeitsklasse des Verankerungsgrundes
Teilsicherheitsbeiwert für den Materialwiderstand, siehe auch CEN/TS 1992-4-1:2008, Abschnitt 4
Conception-calcul des éléments de fixation pour béton - Partie 4-2 : Eléments de fixation à tête
1.1 Généralités
1.1.6 Ce document se fonde sur des résistances caractéristiques et distances caractéristiques énoncées dans une Spécification Technique européenne. Au minimum, il convient que les caractéristiques suivantes soient données dans une Spécification Technique européenne comme base des méthodes de conception-calcul du présent CEN/TS :
NRk,p, NRk,s, VRk,s
ccr,N, scr,N
ccr,sp, scr,sp
cmin, smin, hmin
limites des classes de résistance de l'élément en béton
kcr, kucr, k2, k4, k6, k7
dh, dnom, hef, lf
coefficients partiels Mi des matériaux ; voir aussi la CEN/TS 1992-4-1:2009, Article 4.
Projektiranje pritrjevanja za uporabo v betonu - 4-2. del: Glavna pritrjevala
General Information
Relations
Buy Standard
Standards Content (Sample)
SLOVENSKI STANDARD
SIST-TS CEN/TS 1992-4-2:2009
01-oktober-2009
Projektiranje pritrjevanja za uporabo v betonu - 4-2. del: Glavna pritrjevala
Design of fastenings for use in concrete - Part 4-2: Headed Fasteners
Bemessung von Befestigungen in Beton - Teil 4-2: Kopfbolzen
Conception-calcul des éléments de fixation pour béton - Partie 4-2 : Eléments de fixation
à tête
Ta slovenski standard je istoveten z: CEN/TS 1992-4-2:2009
ICS:
21.060.01 Vezni elementi na splošno Fasteners in general
91.080.40 Betonske konstrukcije Concrete structures
SIST-TS CEN/TS 1992-4-2:2009 en,fr,de
2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.
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SIST-TS CEN/TS 1992-4-2:2009
TECHNICAL SPECIFICATION
CEN/TS 1992-4-2
SPÉCIFICATION TECHNIQUE
TECHNISCHE SPEZIFIKATION
May 2009
ICS 21.060.10; 91.080.40
English Version
Design of fastenings for use in concrete - Part 4-2: Headed
Fasteners
Conception-calcul des éléments de fixation pour béton - Bemessung von Befestigungen in Beton - Teil 4-2:
Partie 4-2 : Eléments de fixation à tête Kopfbolzen
This Technical Specification (CEN/TS) was approved by CEN on 20 October 2008 for provisional application.
The period of validity of this CEN/TS is limited initially to three years. After two years the members of CEN will be requested to submit their
comments, particularly on the question whether the CEN/TS can be converted into a European Standard.
CEN members are required to announce the existence of this CEN/TS in the same way as for an EN and to make the CEN/TS available
promptly at national level in an appropriate form. It is permissible to keep conflicting national standards in force (in parallel to the CEN/TS)
until the final decision about the possible conversion of the CEN/TS into an EN is reached.
CEN members are the national standards bodies of Austria, Belgium, Bulgaria, Cyprus, Czech Republic, Denmark, Estonia, Finland,
France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta, Netherlands, Norway, Poland, Portugal,
Romania, Slovakia, Slovenia, Spain, Sweden, Switzerland and United Kingdom.
EUROPEAN COMMITTEE FOR STANDARDIZATION
COMITÉ EUROPÉEN DE NORMALISATION
EUROPÄISCHES KOMITEE FÜR NORMUNG
Management Centre: Avenue Marnix 17, B-1000 Brussels
© 2009 CEN All rights of exploitation in any form and by any means reserved Ref. No. CEN/TS 1992-4-2:2009: E
worldwide for CEN national Members.
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Contents Page
Foreword .3
1 Scope .4
1.1 General .4
2 Normative references .4
3 Definitions and symbols .4
4 Basis of design .4
5 Determination of action effects .5
5.3 Tension forces in a supplementary reinforcement .5
5.3.1 General .5
5.3.2 Fasteners loaded in tension .5
5.3.3 Fixtures loaded in shear .5
6 Verification of ultimate limit state by elastic analysis .6
6.1 General .6
6.2 Tension load .6
6.2.1 Required verifications .6
6.2.2 Detailing of supplementary reinforcement .7
6.2.3 Steel failure of fastener .8
6.2.4 Pull-out failure of fastener .8
6.2.5 Concrete cone failure .8
6.2.6 Splitting failure . 14
6.2.7 Blow-out failure . 15
6.2.8 Steel failure of the supplementary reinforcement . 18
6.2.9 Anchorage failure of the supplementary reinforcement in the concrete cone . 18
6.3 Shear load . 19
6.3.1 Required verifications . 19
6.3.2 Detailing of supplementary reinforcement . 19
6.3.3 Steel failure of fastener . 20
6.3.4 Concrete pry-out failure . 22
6.3.5 Concrete edge failure . 23
6.4 Combined tension and shear load . 30
6.4.1 Fastenings without supplementary reinforcement . 30
7 Fatigue . 31
8 Seismic . 31
2
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Foreword
This Technical Specification (CEN/TS 1992-4-2:2009) has been prepared by Technical Committee
CEN/TC 250 “Structural Eurocodes”, the secretariat of which is held by BSI.
Attention is drawn to the possibility that some of the elements of this document may be the subject of patent
rights. CEN [and/or CENELEC] shall not be held responsible for identifying any or all such patent rights.
The Technical Specification CEN/TS 1992-4–2 — Headed fasteners, describes the principles and
requirements for safety, serviceability and durability of headed fasteners for use in concrete. It is based on the
limit state concept used in conjunction with a partial factor method.
This Technical Specification does not provide information about the use of National Determined Parameters
(NDP).
CEN/TS 1992-4 'Design of fastenings for use in concrete' is subdivided into the following parts:
Part 1: General
Part 2: Headed fasteners
Part 3: Anchor channels
Part 4: Post-installed fasteners — Mechanical systems
Part 5: Post-installed fasteners — Chemical systems
Relation to Part 1 of this Technical Specification TS
The principles and requirements of Part 2 of this CEN/TS are additional to those in Part 1, all the clauses and
subclauses of which also apply to Part 2 unless varied in this Part. Additional information is presented under
the relevant clauses/subclauses of Part 1 of the CEN/TS. The numbers for the clauses/sub-clauses of Part 2
continue from the number of the last relevant clauses/sub-clauses of Part 1.
The above principles also apply to Figures and Tables in Part 2.
According to the CEN/CENELEC Internal Regulations, the national standards organizations of the following
countries are bound to announce this Technical Specification: Austria, Belgium, Bulgaria, Cyprus, Czech
Republic, Denmark, Estonia, Finland, France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia,
Lithuania, Luxembourg, Malta, Netherlands, Norway, Poland, Portugal, Romania, Slovakia, Slovenia, Spain,
Sweden, Switzerland and the United Kingdom.
3
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1 Scope
1.1 General
1.1.6 This document relies on characteristic resistances and distances which are stated in a European
Technical Specification. In minimum the following characteristics should be given in a European Technical
Specification as base for the design methods of this CEN/TS:
N , N , V
Rk,p Rk,s Rk,s
0
M
Rk,s
c , s
cr,N cr,N
c , s
cr,sp cr,sp
c , s , h
min min min
limitations on concrete strength classes of base material
k , k , k , k , k , k
cr ucr 2 4 6 7
d , d , h , l
h nom ef f
γ partial factors for material see also CEN/TS 1992-4-1:2009, clause 4.
Mi
2 Normative references
This European Standard incorporates by dated or undated reference, provisions from other publications.
These normative references are cited at the appropriate places in the text and the publications are listed
hereafter. For dated references, subsequent amendments to or revisions of any of these publications apply to
this European Standard only when incorporated in it by amendment or revision. For undated references the
latest edition of the publication referred to applies.
NOTE The following references to Eurocodes are references to European Standards and European Prestandards.
These are the only European documents available at the time of publication of this TS. National documents take
precedence until Eurocodes are published as European Standards.
EN 1992-1-1, Eurocode 2: Design of concrete structures — Part 1-1: General rules and rules for buildings
CEN/TS 1992-4-1:2009, Design of fastenings for use in concrete — Part 4-1: General
EN 10080, Steel for the reinforcement of concrete — Weldable reinforcing steel — General
EN ISO 13918, Welding — Studs and ceramic ferrules for arc stud welding (ISO 13918:2008)
3 Definitions and symbols
Definitions and symbols are given in CEN/TS 1992-4-1.
4 Basis of design
4.5.4 Design of welding should be in accordance with EN 1993-1.
4
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4.5.5 The following assumptions in respect to installation have been made in this CEN/TS. The installation
instructions should reflect them:
1) The fastener should be fixed to the formwork or auxiliary constructions in a way that no movement of the
fastener will occur during placing of reinforcement or during pouring and compacting of the concrete.
2) Requirements for
adequate compaction particularly under the head of the stud or fastener and under the fixture,
provisions for vent openings in fixtures larger than 400 mm × 400 mm.
3) Requirement for inspection and approval of the correct installation of the fasteners by qualified personnel.
4) The following conditions should be observed if the fasteners are vibrated (not just punched) into the wet
concrete immediately after pouring:
The size of the fixture does not exceed 200 mm × 200 mm and the number of fastenings is limited to
4 fasteners, so that it can be placed simultaneously during vibrating by the available personnel.
The installation is done according to a quality system.
The fastenings should not be moved after vibrating has been finished.
The concrete under the head of the headed stud or anchor as well as under the base plate should be
properly compacted.
5) The welding procedure for studs should be done in accordance with the provisions given in the relevant
European Technical Specification.
6) Inspection and approval of the correct installation of the fasteners is carried out by appropriately qualified
personnel.
5 Determination of action effects
5.3 Tension forces in a supplementary reinforcement
5.3.1 General
Where supplementary reinforcement is provided, the design tension forces in the supplementary
reinforcement should be established using an appropriate strut and tie model. The supplementary
reinforcement should be designed to resist the total external load on the fastening.
5.3.2 Fasteners loaded in tension
The design tension forces N in the supplementary reinforcement should be calculated using the design
Ed, re
load on the fastener.
5.3.3 Fixtures loaded in shear
The design tension force N in the supplementary reinforcement caused by the design shear force V
Ed, re Ed
acting on a fixture is given by Equation (1).
e
s
N 1⋅V
= + (1)
Ed, re ed
z
5
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with (see Figure 1):
e = distance between reinforcement and shear force acting on a fixture
s
z = internal lever arm of the concrete member
≈ 0,85d
2 h
ef
d ≤ min
2 c
1
If the supplementary reinforcement is not arranged in the direction of the shear force (see Figure 10c)) then
this must be taken into account in the calculation of the design tension force of the reinforcement.
In the case of different shear forces on the fasteners of a fixture, Equation (1) should be solved for the
h h
shear load V of the most loaded fastener resulting in N .
Ed Ed,re
Figure 1— Detailing of reinforcement to take up shear forces
6 Verification of ultimate limit state by elastic analysis
6.1 General
6.1.5 This section applies when forces on the fasteners have been calculated using elastic analysis.
Annex B of Part 1 should be used for plastic analysis.
6.1.6 The spacing between outer headed fasteners of adjoining groups or the distance to single fasteners
shall be a > s .
cr,N
6.2 Tension load
6.2.1 Required verifications
The required verifications are given in Table 1.
6.2.1.1 For fasteners without supplementary reinforcement the verifications of Table 1, lines 1 to 5 apply.
6.2.1.2 For fasteners with supplementary reinforcement the verifications of Table 1, lines 1, 2 and 4 to 7
apply.
6
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6.2.2 Detailing of supplementary reinforcement
When the design relies on supplementary reinforcement, concrete cone failure according to Equation (4)
needs not to be verified but the supplementary reinforcement should be designed to resist the total load.
The supplementary reinforcement to take up tension loads should comply with the following requirements (see
also Figure 2):
a) In general, the same diameter of the reinforcement should be provided for all fasteners of a group. The
2
reinforcement should consist of ribbed reinforcing bars (f ≤ 500 N/mm ) with a diameter d not larger
yk s
than 16 mm and should be detailed in form of stirrups or loops with a mandrel diameter according to
EN 1992-1-1.
Table 1 — Required verifications for headed fasteners loaded in tension
Fastener group
Single fastener
most loaded fastener fastener group
N N
Rk, s Rk, s
Steel failure h
1 N ≤ N = N ≤ N =
Ed Rd, s Rd, s
Ed
of fastener
γ γ
Ms Ms
N N
Rk, p Rk, p
Pull-out failure h
N ≤ N = N ≤ N =
2
Ed Rd, p Rd, p
Ed
of fastener
γ γ
Mp Mp
N N
Rk, c Rk, c
Concrete g
N ≤ N = N ≤ N =
3
Ed Rd, c Rd, c
Ed
cone failure
γ γ
Mc Mc
N N
Rk, sp Rk, sp
g
N ≤ N = N ≤ N =
4 Splitting failure
Ed Rd, sp Rd, sp
Ed
γ γ
Msp Msp
N N
Rk, cb Rk, cb
a g
5 Blow-out failure N ≤ N = N ≤ N =
Ed Rd, cb Rd, cb
Ed
γ γ
Mc Ms
N N
Rk, re Rk, re
Steel failure of h
N ≤ N = N ≤ N =
6
Ed,re Rd, re Rd, re
Ed, re
reinforcement γ γ
Ms, re Ms, re
Anchorage failure
h
N ≤ N
N ≤ N
7
Ed,re Rd, a
Rd, a
Ed, re
of reinforcement
a
Not required for fasteners with c > 0,5 h
ef
Figure 2 — Example for a multiple fastening with supplementary reinforcement to take up tension
loads and corresponding strut and tie model
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b) The supplementary reinforcement should be placed as close to the fasteners as practicable to minimize
the effect of eccentricity associated with the angle of the failure cone. Preferably, the supplementary
reinforcement should enclose the surface reinforcement. Only these reinforcement bars with a distance
≤ 0,75 h from the fastener should be assumed as effective.
ef,
c) The minimum anchorage length of supplementary reinforcement in the concrete failure cone is
min l = 4d (anchorage with bends, hooks or loops) or min l = 10d (anchorage with straight bars with or
1 s 1 s
without welded transverse bars).
d) The supplementary reinforcement should be anchored outside the assumed failure cone with an
anchorage length l according to EN 1992-1-1.
bd
e) A surface reinforcement should be provided as shown in Figure 2 designed to resist the forces arising
from the assumed strut and tie model, taking into account the splitting forces according to 6.2.6.
6.2.3 Steel failure of fastener
The characteristic resistance of a fastener in case of steel failure N is given in the relevant European
Rk,s
Technical Specification. The strength calculation is based on f .
uk
6.2.4 Pull-out failure of fastener
The characteristic resistance in case of pull-out failure N is given in the relevant European Technical
Rk,p
Specification.
NOTE The characteristic resistance N is limited by the concrete pressure under the head of the fastener according
Rk,p
to Equation (2):
N = 6 ⋅ A ⋅ f ⋅ ψ (2)
Rk, p h ck, cube ucr, N
with
A = load bearing area of the head of the fastener
h
π
2 2
= ()d − d (3)
h
4
f characteristic cube strength of the concrete strength class but noting the limitations
ck,cube,
given in the relevant European Technical Specification
ψ = 1,0 for fasteners in cracked concrete
ucr, N
= 1,4 for fasteners in non-cracked concrete
6.2.5 Concrete cone failure
The characteristic resistance of a fastener, a group of fasteners and the tensioned fasteners of a group of
fasteners in case of concrete cone failure may be obtained by Equation (4).
A
c, N
o
N = N ⋅ ⋅ψ ⋅ψ ⋅ψ [N] (4)
Rk, c s, N re, N ec, N
Rk, c
0
A
c, N
The different factors of Equation (4) are given below.
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6.2.5.1 Characteristic resistance of a single fastener
Cracked concrete:
The characteristic resistance of a single fastener placed in cracked concrete and not influenced by
adjacent fasteners or edges of the concrete member is obtained by:
o 1,5
N = k ⋅ f ⋅ h [N] (5)
cr ck,cube
Rk,c ef
with k factor to take into account the influence of load transfer mechanisms for
cr
applications in cracked concrete, the actual value is given in the corresponding
European Technical Specification.
2
f [N/mm ], characteristic cube strength of the concrete strength class but noting the
ck,cube
limitations given in the relevant European Technical Specification.
h [mm], see CEN/TS 1992-4-1:2009, Figure 5, the actual value is given in the
ef
corresponding European Technical Specification.
NOTE For headed fasteners according to current experience the value is 8,5. The actual value for a particular
fastener may be taken from the relevant European Technical Specification.
Non-cracked concrete:
The characteristic resistance of a single fastener placed in non-cracked concrete and not influenced by
adjacent fasteners or edges of the concrete member is obtained by:
1,5
o
N = k ⋅ f ⋅ h [N] (6)
ucr ck,cube
Rk,c ef
with k factor to take into account the influence of load transfer mechanisms for
ucr
applications in non-cracked concrete, the actual value is given in the
corresponding European Technical Specification.
NOTE For headed fasteners according to current experience the value is 11,9. The actual value for a particular
fastener may be taken from the relevant European Technical Specification.
6.2.5.2 Effect of axial spacing and edge distance
The geometric effect of axial spacing and edge distance on the characteristic resistance is taken into account
0
by the value A /A , where
c, N
c, N
0
Α = reference projected area, see Figure 3
c,Ν
= s ⋅ s (7)
cr,N cr,N
A = actual projected area, limited by overlapping concrete cones of adjacent fasteners
c, N
(s < s ) as well as by edges of the concrete member (c < c ).
cr,N cr,N
Examples for the calculation of A are given in Figure 4
c,N
s , c given in the corresponding European Technical Specification
cr,N cr,N
NOTE For headed fasteners according to current experience s = 2 c = 3 h
cr,N cr,N ef.
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0
A = s ⋅ s
c,N cr,N cr,N
Key
1 Concrete cone
0
Figure 3 — Idealized concrete cone and area A of concrete cone of an individual fastener
c, N
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A = (c + 0,5 s ) ⋅ s
c, N 1 cr, N cr, N
if: c ≤ c
1 cr, N
a)
A = (c + s + 0,5 s ) ⋅ s
c, N 1 1 cr, N cr, N
if: c ≤ c
1 cr, N
s ≤ s
1 cr, N
b)
A = (c + s + 0,5 s ) ⋅ (c + s + 0,5 s )
c, N 1 1 cr, N 2 2 cr, N
if: c ; c ≤ c
1 2 cr, N
s ; s ≤ s
1 2 cr, N
c)
Key
a) Individual fastener at the edge of a concrete member
b) Group of two fasteners at the edge of a concrete member
c) Group of four fasteners at a corner of a concrete member
Figure 4 — Examples of actual areas A of the idealised concrete cones for different arrangements of
c, N
fasteners in case of axial tension load
6.2.5.3 Effect of the disturbance of the distribution of stresses in the concrete due to edges
The factor ψ takes account of the disturbance of the distribution of stresses in the concrete due to edges of
s, N
the concrete member. For fastenings with several edge distances (e.g. fastening in a corner of the concrete
member or in a narrow member), the smallest edge distance c should be inserted in Equation (8).
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c
ψ = 0,7 + 0,3 ⋅ ≤ 1 [-] (8)
s, N
c
cr, N
6.2.5.4 Effect of shell spalling
The shell spalling factor ψ takes account of the effect of a dense reinforcement for embedment depths
re, N
h < 100 mm:
ef
h
ef
ψ = 0,5 + ≤ 1 [-] (9)
re, N
200
with: h [mm]
ef
Irrespective of the embedment depth of the fastener, ψ may be taken as 1,0 in the following cases:
re, N
a) Reinforcement (any diameter) is provided at a spacing ≥ 150mm, or
b) Reinforcement with a diameter of 10 mm or less is provided at a spacing > 100 mm.
6.2.5.5 Effect of the eccentricity of the load
The factor ψ takes account of a group effect when different tension loads are acting on the individual
ec, N
fasteners of a group.
1
ψ = ≤ 1 [-] (10)
ec, N
1+ 2⋅ e /s
N cr, N
with
e eccentricity of the resulting tensile load acting on the tensioned fasteners
N
(see CEN/TS 1992-4-1:2009, 5.2).
Where there is an eccentricity in two directions, ψ should be determined separately for each direction and
ec, N
the product of both factors should be inserted in Equation (4).
6.2.5.6 Effect of the position of the fastening
The factor ψ takes account of the position of the fastening in cracked or non-cracked concrete.
ucr, N
ψ = 1,0 for fasteners in cracked concrete (11)
ucr, N
= 1,4 for fasteners in non-cracked concrete (12)
6.2.5.7 Effect of a narrow member
For the case of fasteners in an application with three or more edges distances less than c from the
cr, N
fasteners (see Figure 5) the calculation according to Equation (4) leads to conservative results. More precise
results are obtained if in the case of single fasteners the value h is substituted by
ef
c
' max
h = ⋅ h (13)
ef ef
c
cr, N
or in the case of groups h is substituted by the larger value of
ef
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c s
' '
max max
h = ⋅ h or h = ⋅ h (14)
ef ef ef ef
c s
cr, N cr, N
with c = maximum distance from centre of a fastener to the edge of concrete member ≤ c
max cr,N
s = maximum centre to centre spacing of fasteners ≤ s
max cr,N
' 0
The value h is inserted in Equation (5) or Equation (6) and used for the determination of A and
ef
c, N
A according to Figures 3 and 4 as well as in Equations (7), (8) and (9), where the values
c, N
'
h
' ef
s = s ⋅ (15)
cr,N cr,N
h
ef
'
h
' ef
c = c ⋅ (16)
cr,N cr,N
h
ef
are inserted for s or c , respectively.
cr,N cr,N
'
NOTE An example for the calculation of h is illustrated in Figure 6.
ef
Key
a) (c ; c ; c ) ≤ c
1 2,1 2,2 cr,N
b) (c ; c ; c ; c ) ≤ c
1,1 1,2 2,1 2,2 cr,N
' ' '
Figure 5 — Examples for fastenings in concrete members where h , s and c may be used
ef cr,N cr,N
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c = 110 mm
1
c = 100 mm
2
c = 120 mm = c
3 max
c = 80 mm
4
s = 210 mm
h = 200 mm
ef
'
h = 120/1,5 = 80 mm > 210/3 = 70mm
ef
'
Figure 6 — Illustration of the calculation of h for a double fastening influenced by 4 edges
ef
6.2.6 Splitting failure
6.2.6.1 Splitting failure due to installation
Splitting failure during installation e.g. by torquing of fasteners (see CEN/TS 1992-4-1:2009, Figure 3) is
avoided by complying with minimum values for edge distances c , spacing s , and member thickness h
min min min
and requirements for reinforcement as given in the relevant European Technical Specification.
NOTE Minimum values for edge distance, spacing and member thickness should also be observed for headed
fasteners not torqued to allow adequate placing and compaction of the concrete.
6.2.6.2 Splitting failure due to loading
No verification of splitting failure is required if one of the following conditions is fulfilled:
a) The edge distance in all directions is c > 1,0 c for fastenings with one anchor and c > 1,2 c for
cr,sp cr,sp
fastenings with more than one anchor.
The characteristic values c and s are given in the relevant European Technical Specification.
cr,sp cr,sp
b) The characteristic resistance for concrete cone failure and pull-out failure is calculated for cracked
concrete and reinforcement resists the splitting forces and limits the crack width to w ≤ 0,3 mm.
k
The required cross-section A of the splitting reinforcement may be determined as follows:
s
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ΣN
Ed
A = 0,5 [mm²] (17)
s
f /γ
yk Ms, re
with
ΣΝ = sum of the design tensile force of the fasteners in tension under the design value of the actions [N]
Ed
f = nominal yield strength of the reinforcing steel ≤ 500 N/mm²
yk
If the conditions a) and b) of 6.2.6.2 are not fulfilled, then the characteristic resistance of one fastener or a
group of fasteners should be calculated according to Equation (18).
A
c, N
0
N = N ⋅ ⋅ψ ⋅ψ ⋅ψ ⋅ψ [N] (18)
Rk, sp s, N ec,N re, N h, sp
Rk
0
A
c, N
0 0
with N = min(N , N )
Rk Rk,p Rk,c
N according to Section 6.2.4
Rk,p
0
N ,ψ ⋅ψ ⋅ψ ⋅ψ according to 6.2.5, however the values c and s should be
cr,N cr,N
Rk, c s, N re, N ec, N ucr, N
replaced by c and s . The values c and s are based on a member thickness h
cr,sp cr,sp cr, sp cr, sp min
The factor ψ takes into account the influence of the actual member depth h on the splitting resistance. For
h, sp
fasteners according to current experience it is given by Equation (19).
2/3 2/3
2 h
h
ef
ψ = ≤ (19)
h, sp
h h
min min
For fastenings with several edge distances (e.g. fastening in a corner of the concrete member or in a narrow
c shall be inserted in Equation (18).
member), the smallest edge distance
NOTE If in the European Technical Specification c for more than one member depth h is given, then the member
cr,sp
depth valid for the used c shall be inserted in Equation (4).
cr,sp
If the edge distance is smaller than
...
SLOVENSKI STANDARD
oSIST-TS prCEN/TS 1992-4-2:2008
01-september-2008
Projektiranje pritrjevanja za uporabo v betonu - 4-2: Glavna pritrjevala
Design of fastenings for use in concrete - Part 2: Headed Fasteners
Bemessung von Befestigungen in Beton - Teil 2: Kopfbolzen
Ta slovenski standard je istoveten z: prCEN/TS 1992-4-2
ICS:
21.060.01 Vezni elementi na splošno Fasteners in general
91.080.40 Betonske konstrukcije Concrete structures
oSIST-TS prCEN/TS 1992-4-2:2008 en
2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.
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oSIST-TS prCEN/TS 1992-4-2:2008
TECHNICAL SPECIFICATION
FINAL DRAFT
prCEN/TS 1992-4-2
SPÉCIFICATION TECHNIQUE
TECHNISCHE SPEZIFIKATION
June 2008
ICS 21.060.01; 91.080.40
English Version
Design of fastenings for use in concrete - Part 2: Headed
Fasteners
Bemessung von Befestigungen in Beton - Teil 2:
Kopfbolzen
This draft Technical Specification is submitted to CEN members for formal vote. It has been drawn up by the Technical Committee CEN/TC
250.
CEN members are the national standards bodies of Austria, Belgium, Bulgaria, Cyprus, Czech Republic, Denmark, Estonia, Finland,
France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta, Netherlands, Norway, Poland, Portugal,
Romania, Slovakia, Slovenia, Spain, Sweden, Switzerland and United Kingdom.
Warning : This document is not a Technical Specification. It is distributed for review and comments. It is subject to change without notice
and shall not be referred to as a Technical Specification.
EUROPEAN COMMITTEE FOR STANDARDIZATION
COMITÉ EUROPÉEN DE NORMALISATION
EUROPÄISCHES KOMITEE FÜR NORMUNG
Management Centre: rue de Stassart, 36 B-1050 Brussels
© 2008 CEN All rights of exploitation in any form and by any means reserved Ref. No. prCEN/TS 1992-4-2:2008: E
worldwide for CEN national Members.
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Contents Page
Foreword.3
1 Scope .4
1.1 General.4
2 Normative references .4
3 Definitions and symbols .4
4 Basis of design .4
5 Determination of action effects.5
5.3 Tension forces in a supplementary reinforcement .5
5.3.1 General.5
5.3.2 Fasteners loaded in tension .5
5.3.3 Fixtures loaded in shear .5
6 Verification of ultimate limit state by elastic analysis .6
6.1 General.6
6.2 Tension load.6
6.2.1 Required verifications .6
6.2.2 Detailing of supplementary reinforcement .7
6.2.3 Steel failure of fastener .8
6.2.4 Pull-out failure of fastener .8
6.2.5 Concrete cone failure .8
6.2.6 Splitting failure.13
6.2.7 Blow-out failure.14
6.2.8 Steel failure of the supplementary reinforcement.17
6.2.9 Anchorage failure of the supplementary reinforcement in the concrete cone .17
6.3 Shear load.18
6.3.1 Required verifications .18
6.3.2 Detailing of supplementary reinforcement .18
6.3.3 Steel failure of fastener .19
6.3.4 Concrete pry-out failure .21
6.3.5 Concrete edge failure .22
6.4 Combined tension and shear load.29
6.4.1 Fastenings without supplementary reinforcement .29
7 Fatigue .30
8 Seismic .30
2
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Foreword
This document (prCEN/TS 1992-4-2:2008) has been prepared by Technical Committee CEN/TC 250
“Structural Eurocodes”, the secretariat of which is held by BSI.
This document is currently submitted to the Formal Vote.
The Technical Specification CEN/TS 1992-4–2 — Headed fasteners, describes the principles and
requirements for safety, serviceability and durability of headed fasteners for use in concrete. It is based on
the limit state concept used in conjunction with a partial factor method.
CEN/TS 1992-4 'Design of fastenings for use in concrete' is subdivided into the following parts:
Part 1: General
Part 2: Headed fasteners
Part 3: Anchor channels
Part 4: Post-installed fasteners — mechanical systems
Part 5: Post-installed fasteners — chemical systems
Relation to Part 1 of this Technical Specification TS
The principles and requirements of Part 2 of this TS are additional to those in Part 1, all the clauses and sub-
clauses of which also apply to Part 2 unless varied in this Part. Additional information is presented under the
relevant clauses/sub-clauses of Part 1 of the TS. The numbers for the clauses/sub-clauses of Part 2 continue
from the number of the last relevant clauses/sub-clauses of Part 1.
The above principles also apply to Figures and Tables in Part 2.
3
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1 Scope
1.1 General
1.1.6 This document relies on characteristic resistances and distances which are stated in a European
Technical Specification. In minimum the following characteristics should be given in a European Technical
Specification as base for the design methods of this CEN/TS:
N , N , V
Rk,p Rk,s Rk,s
0
M
Rk,s
c , s
cr,N cr,N
c , s
cr,sp cr,sp
c , s , h
min min min
limitations on concrete strength classes of base material
k , k , k , k , k , k
cr ucr 2 4 6 7
d , d , h , l
h nom ef f
γ partial factors for material see also CEN/TS 1992-4-1:XXXX, clause 4
Mi
2 Normative references
This European Standard incorporates by dated or undated reference, provisions from other publications.
These normative references are cited at the appropriate places in the text and the publications are listed
hereafter. For dated references, subsequent amendments to or revisions of any of these publications apply to
this European Standard only when incorporated in it by amendment or revision. For undated references the
latest edition of the publication referred to applies.
NOTE The following references to Eurocodes are references to European Standards and European Prestandards.
These are the only European documents available at the time of publication of this TS. National documents take
precedence until Eurocodes are published as European Standards.
EN 1992-1-1, Eurocode 2: Design of concrete structures - Part 1-1: General rules and rules for buildings
CEN/TS 1992-4-1:XXXX, Design of Fastenings for use in Concrete — Part 1: General
EN 10080, Steel for the reinforcement of concrete — Weldable reinforcing steel — General
EN ISO 13918, Welding — Studs and ceramic ferrules for arc stud welding (ISO 13918:2008)
3 Definitions and symbols
Definitions and symbols are given in CEN/TS 1992-4-1.
4 Basis of design
4.5.4 Design of welding should be in accordance with EN 1993-1.
4
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4.5.5 The following assumptions in respect to installation have been made in this CEN/TS. The installation
instructions should reflect them:
1) The fastener should be fixed to the formwork or auxiliary constructions in a way that no movement of the
fastener will occur during placing of reinforcement or during pouring and compacting of the concrete.
2) Requirements for
adequate compaction particularly under the head of the stud or fastener and under the fixture,
provisions for vent openings in fixtures larger than 400 mm × 400 mm.
3) Requirement for inspection and approval of the correct installation of the fasteners by qualified personnel.
4) The following conditions should be observed if the fasteners are vibrated (not just punched) into the wet
concrete immediately after pouring:
The size of the fixture does not exceed 200mm × 200mm and the number of fastenings is limited to
4 fasteners, so that it can be placed simultaneously during vibrating by the available personnel.
The installation is done according to a quality system.
The fastenings should not be moved after vibrating has been finished.
The concrete under the head of the headed stud or anchor as well as under the base plate should be
properly compacted.
5) The welding procedure for studs should be done in accordance with the provisions given in the relevant
European Technical Specification.
6) Inspection and approval of the correct installation of the fasteners is carried out by appropriately qualified
personnel.
5 Determination of action effects
5.3 Tension forces in a supplementary reinforcement
5.3.1 General
Where supplementary reinforcement is provided, the design tension forces in the supplementary
reinforcement should be established using an appropriate strut and tie model. The supplementary
reinforcement should be designed to resist the total external load on the fastening.
5.3.2 Fasteners loaded in tension
The design tension forces N in the supplementary reinforcement should be calculated using the design
Ed, re
load on the fastener.
5.3.3 Fixtures loaded in shear
The design tension force N in the supplementary reinforcement caused by the design shear force V
Ed, re Ed
acting on a fixture is given by Equation (1).
e
s
(1)
N = + 1
Ed, re
z
5
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with (see Figure 1):
e = distance between reinforcement and shear force acting on a fixture
s
z = internal lever arm of the concrete member
≈ 0,85d
2 h
ef
d ≤ min
2 c
1
If the supplementary reinforcement is not arranged in the direction of the shear force (see Figure 10c)) then
this must be taken into account in the calculation of the design tension force of the reinforcement.
In the case of different shear forces on the fasteners of a fixture, Equation (1) should be solved for the shear
h h
load V of the most loaded fastener resulting in N .
Ed Ed, re
Figure 1— Detailing of reinforcement to take up shear forces
6 Verification of ultimate limit state by elastic analysis
6.1 General
6.1.5 This section applies when forces on the fasteners have been calculated using elastic analysis.
Annex B of Part 1 should be used for plastic analysis.
6.1.6 The spacing between outer headed fasteners of adjoining groups or the distance to single fasteners
shall be a > s .
cr,N
6.2 Tension load
6.2.1 Required verifications
The required verifications are given in Table 1.
6.2.1.1 For fasteners without supplementary reinforcement the verifications of Table 1, lines 1 to 5 apply.
6.2.1.2 For fasteners with supplementary reinforcement the verifications of Table 1, lines 1, 2 and 4 to 7
apply.
6
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6.2.2 Detailing of supplementary reinforcement
When the design relies on supplementary reinforcement, concrete cone failure according to Equation (4)
needs not to be verified but the supplementary reinforcement should be designed to resist the total load.
The supplementary reinforcement to take up tension loads should comply with the following requirements (see
also Figure 2):
a) In general, the same diameter of the reinforcement should be provided for all fasteners of a group. The
2
reinforcement should consist of ribbed reinforcing bars (f ≤ 500 N/mm ) with a diameter d not larger
yk s
than 16 mm and should be detailed in form of stirrups or loops with a mandrel diameter according to
EN 1992-1-1.
Table 1 — Required verifications for headed fasteners loaded in tension
Fastener group
Single fastener
most loaded fastener fastener group
N N
Rk,s Rk,s
Steel failure h
1 N ≤ N = N ≤ N =
Ed Rd,s Rd,s
Ed
of fastener
γ γ
Ms Ms
N N
Rk, p Rk, p
Pull-out failure h
N ≤ N = N ≤ N =
2
Ed Rd, p Rd, p
Ed
of fastener γ γ
Mp Mp
N N
Rk, c Rk, c
Concrete g
N ≤ N = N ≤ N =
3
Ed Rd, c Rd, c
Ed
cone failure
γ γ
Mc Mc
N N
Rk,sp Rk,sp
g
N ≤ N = N ≤ N =
4 Splitting failure
Ed Rd,sp Rd,sp
Ed
γ γ
Msp Msp
N N
Rk, cb Rk, cb
a g
5 Blow-out failure N ≤ N = N ≤ N =
Ed Rd, cb Rd, cb
Ed
γ γ
Mc Ms
N N
Rk, re Rk, re
Steel failure of h
N ≤ N = N ≤ N =
6
Ed,re Rd, re Rd, re
Ed, re
reinforcement γ γ
Ms, re Ms, re
Anchorage failure
h
N ≤ N
N ≤ N
7
Ed,re Rd, a
Rd,a
Ed, re
of reinforcement
a
Not required for fasteners with c > 0.5 h
ef
Figure 2 — Example for a multiple fastening with supplementary reinforcement to take up tension
loads and corresponding strut and tie model
7
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b) The supplementary reinforcement should be placed as close to the fasteners as practicable to minimize
the effect of eccentricity associated with the angle of the failure cone. Preferably, the supplementary
reinforcement should enclose the surface reinforcement. Only these reinforcement bars with a distance
≤ 0,75 h from the fastener should be assumed as effective.
ef,
c) The minimum anchorage length of supplementary reinforcement in the concrete failure cone is
min l = 4d (anchorage with bends, hooks or loops) or min l = 10d (anchorage with straight bars with or
1 s 1 s
without welded transverse bars).
d) The supplementary reinforcement should be anchored outside the assumed failure cone with an
anchorage length l according to EN 1992-1-1.
bd
e) A surface reinforcement should be provided as shown in Figure 2 designed to resist the forces arising
from the assumed strut and tie model, taking into account the splitting forces according to 6.2.6.
6.2.3 Steel failure of fastener
The characteristic resistance of a fastener in case of steel failure N is given in the relevant European
Rk,s
Technical Specification. The strength calculation is based on f .
uk
6.2.4 Pull-out failure of fastener
The characteristic resistance in case of pull-out failure N is given in the relevant European Technical
Rk,p
Specification.
NOTE The characteristic resistance N is limited by the concrete pressure under the head of the fastener according
Rk,p
to Equation (2):
N = 6 ⋅ A ⋅ f ⋅ ψ (2)
Rk, p h ck, cube ucr, N
with
A = load bearing area of the head of the fastener
h
π
2 2
= ()d − d (3)
h
4
f characteristic cube strength of the concrete strength class but noting the limitations
ck,cube,
given in the relevant European Technical Specification
ψ = 1,0 for fasteners in cracked concrete
ucr, N
= 1,4 for fasteners in non-cracked concrete
6.2.5 Concrete cone failure
The characteristic resistance of a fastener, a group of fasteners and the tensioned fasteners of a group of
fasteners in case of concrete cone failure may be obtained by Equation (4).
A
c, N
o
N = N ⋅ ⋅ψ ⋅ψ ⋅ψ [N] (4)
Rk, c Rk, c s, N re, N ec, N
0
A
c, N
The different factors of Equation (4) are given below.
6.2.5.1 Characteristic resistance of a single fastener
Cracked concrete:
8
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The characteristic resistance of a single fastener placed in cracked concrete and not influenced by
adjacent fasteners or edges of the concrete member is obtained by:
o 1,5
N = k ⋅ f ⋅ h [N] (5)
Rk,c cr ck,cube
ef
with k factor to take into account the influence of load transfer mechanisms for
cr
applications in cracked concrete, the actual value is given in the corresponding
European Technical Specification.
2
f [N/mm ], characteristic cube strength of the concrete strength class but noting the
ck,cube
limitations given in the relevant European Technical Specification.
h [mm], see CEN/TS 1992-4-1:XXXX, Figure 5, the actual value is given in the
ef
corresponding European Technical Specification.
NOTE For headed fasteners according to current experience the value is 8,5. The actual value for a particular
fastener may be taken from the relevant European Technical Specification.
Non-cracked concrete:
The characteristic resistance of a single fastener placed in non-cracked concrete and not influenced by
adjacent fasteners or edges of the concrete member is obtained by:
o 1,5
N = k ⋅ f ⋅ h [N] (6)
Rk,c ucr ck,cube
ef
with k factor to take into account the influence of load transfer mechanisms for
ucr
applications in non-cracked concrete, the actual value is given in the
corresponding European Technical Specification.
NOTE For headed fasteners according to current experience the value is 11,9. The actual value for a particular
fastener may be taken from the relevant European Technical Specification.
6.2.5.2 Effect of axial spacing and edge distance
The geometric effect of axial spacing and edge distance on the characteristic resistance is taken into account
0
by the value A / A , where
c, N c, N
0
Α = reference projected area, see Figure 3
c,Ν
= s ⋅ s (7)
cr,N cr,N
A = actual projected area, limited by overlapping concrete cones of adjacent fasteners
c, N
(s < s ) as well as by edges of the concrete member (c < c ).
cr,N cr,N
Examples for the calculation of A are given in Figure 4
c,N
s , c given in the corresponding European Technical Specification
cr,N cr,N
NOTE For headed fasteners according to current experience s = 2 c = 3 h
cr,N cr,N ef.
9
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0
A = s ⋅ s
c, N cr, N cr, N
Key
1 Concrete cone
0
Figure 3 — Idealized concrete cone and area A of concrete cone of an individual fastener
c, N
A = (c + 0,5 s ) ⋅ s
c, N 1 cr, N cr, N
if: c ≤ c
1 cr, N
a)
A = (c + s + 0,5 s ) ⋅ s
c, N 1 1 cr, N cr, N
if: c ≤ c
1 cr, N
s ≤ s
1 cr, N
b)
10
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A = (c + s + 0,5 s ) ⋅ (c + s + 0,5 s )
c, N 1 1 cr, N 2 2 cr, N
if: c ; c ≤ c
1 2 cr, N
s ; s ≤ s
1 2 cr, N
c)
Key
a) Individual fastener at the edge of a concrete member
b) Group of two fasteners at the edge of a concrete member
c) Group of four fasteners at a corner of a concrete member
Figure 4 — Examples of actual areas A of the idealised concrete cones for different arrangements of
c, N
fasteners in case of axial tension load
6.2.5.3 Effect of the disturbance of the distribution of stresses in the concrete due to edges
The factor ψ takes account of the disturbance of the distribution of stresses in the concrete due to edges of
s, N
the concrete member. For fastenings with several edge distances (e.g. fastening in a corner of the concrete
member or in a narrow member), the smallest edge distance c should be inserted in Equation (8).
c
ψ = 0,7+ 0,3⋅ ≤ 1 [-] (8)
s, N
c
cr, N
6.2.5.4 Effect of shell spalling
The shell spalling factor ψ takes account of the effect of a dense reinforcement for embedment depths
re, N
h < 100 mm:
ef
h
ef
ψ = 0,5+ ≤ 1 [-] (9)
re, N
200
with: h [mm]
ef
Irrespective of the embedment depth of the fastener, ψ may be taken as 1,0 in the following cases:
re, N
a) Reinforcement (any diameter) is provided at a spacing ≥ 150mm, or
b) Reinforcement with a diameter of 10 mm or less is provided at a spacing > 100 mm.
6.2.5.5 Effect of the eccentricity of the load
The factor ψ takes account of a group effect when different tension loads are acting on the individual
ec, N
fasteners of a group.
1
ψ = ≤ 1 [-] (10)
ec, N
1+ 2⋅ e / s
N cr, N
11
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with
e eccentricity of the resulting tensile load acting on the tensioned fasteners
N
(see CEN/TS 1992-4-1:xxxx, 5.2).
Where there is an eccentricity in two directions, ψ should be determined separately for each direction and
ec, N
the product of both factors should be inserted in Equation (4).
6.2.5.6 Effect of the position of the fastening
The factor ψ takes account of the position of the fastening in cracked or non-cracked concrete.
ucr, N
ψ = 1,0 for fasteners in cracked concrete (11)
ucr, N
= 1,4 for fasteners in non-cracked concrete (12)
6.2.5.7 Effect of a narrow member
For the case of fasteners in an application with three or more edges distances less than c from the
cr, N
fasteners (see Figure 5) the calculation according to Equation (4) leads to conservative results. More precise
results are obtained if in the case of single fasteners the value h is substituted by
ef
c
' max
h = ⋅ h (13)
ef ef
c
cr, N
or in the case of groups h is substituted by the larger value of
ef
c s
' '
max max
h = ⋅ hor h = ⋅ h (14)
ef ef ef ef
c s
cr, N cr, N
with c = maximum distance from centre of a fastener to the edge of concrete member ≤ c
max cr,N
s = maximum centre to centre spacing of fasteners ≤ s
max cr,N
' 0
The value h is inserted in Equation (5) or Equation (6) and used for the determination of A and A
c, N
ef c, N
according to Figures 3 and 4 as well as in Equations (7), (8) and (9), where the values
'
h
ef
'
s = s ⋅ (15)
cr,N cr,N
h
ef
'
h
ef
'
c = c ⋅ (16)
cr,N cr, N
h
ef
are inserted for s or c , respectively.
cr,N cr,N
'
NOTE An example for the calculation of h is illustrated in Figure 6.
ef
12
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Key
a) (c ; c ; c ) ≤ c
1 2,1 2,2 cr,N
b) (c ; c ; c ; c ) ≤ c
1,1 1,2 2,1 2,2 cr,N
' ' '
Figure 5 — Examples for fastenings in concrete members where h , s and c may be used
ef cr, N cr, N
c = 110 mm
1
c = 100 mm
2
c = 120 mm = c
3 max
c = 80 mm
4
s = 210 mm
h = 200 mm
ef
h = 120/1,5 = 80 mm > 210/3 = 70mm
ef
'
Figure 6 — Illustration of the calculation of h for a double fastening influenced by 4 edges
ef
6.2.6 Splitting failure
6.2.6.1 Splitting failure due to installation
Splitting failure during installation e.g. by torquing of fasteners (see CEN/TS 1992-4-1:XXXX, Figure 3) is
avoided by complying with minimum values for edge distances c , spacing s , and member thickness h
min min min
and requirements for reinforcement as given in the relevant European Technical Specification.
NOTE Minimum values for edge distance, spacing and member thickness should also be observed for headed
fasteners not torqued to allow adequate placing and compaction of the concrete.
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6.2.6.2 Splitting failure due to loading
6.2.6.1 No verification of splitting failure is required if one of the following conditions is fulfilled:
a) The edge distance in all directions is c > 1,0 c for fastenings with one anchor and c > 1,2 c for
cr,sp cr,sp
fastenings with more than one anchor.
The characteristic values c and s are given in the relevant European Technical Specification.
cr,sp cr,sp
b) The characteristic resistance for concrete cone failure and pull-out failure is calculated for cracked
concrete and reinforcement resists the splitting forces and limits the crack width to w ≤ 0,3 mm.
k
The required cross-section A of the splitting reinforcement may be determined as follows:
s
Σ N
Ed
A = 0,5 [mm²] (17)
s
f /γ
yk Ms, re
with
ΣΝ = sum of the design tensile force of the fasteners in tension under the design value of the actions [N]
Ed
f = nominal yield strength of the reinforcing steel ≤ 500 N/mm²
yk
6.2.6.2 If the conditions a) and b) of 6.2.6.1 are not fulfilled, then the characteristic resistance of one
fastener should be calculated according to Equation (18).
A
c, N
0
N = N ⋅ ⋅Ψ ⋅ψ ⋅ψ [N] (18)
Rk, sp Rk s, N re, N h, sp
0
A
c, N
0 0
with N = min(N , N )
Rk Rk,c
Rk, p
N according to Section 6.2.4
Rk, p
0
N ,ψ ⋅ψ ⋅ψ ⋅ψ according to 6.2.5, however the values c and s should be
cr,N cr,N
Rk , c s, N re, N ec, N ucr, N
replaced by c and s . The values c and s are based on a member thickness h
cr,sp cr,sp cr, sp cr, sp min
The factor ψ takes into account the influence of the actual member depth h on the splitting resistance. For
h, sp
fasteners according to current experience it is given by Equation (19).
2/3
2/3
2 h
h
ef
ψ = ≤ (19)
h, sp
h h
min min
For fastenings with several edge distances (e.g. fastening in a corner of the concrete member or in a narrow
member), the smallest edge distance c shall be inserted in Equation (18).
NOTE If in the European Technical Specification c for more than one member depth h is given, then the member
cr,sp
depth valid for the used c shall be inserted in Equation (4).
cr,sp
If the edge distance is smaller than the value c then a longitudinal reinforcement should be provided along
cr,sp
the edge of the member.
6.2.7 Blow-out failure
Verification of blow-out failure is not required if the edge distance in all directions exceeds c = 0,5 h . If a
ef
verification is required, the characteristic resistance in case of blow-out failure is:
A
c, Nb
0
N = N ⋅ ⋅ψ ⋅ψ ⋅ψ ⋅ψ [N] (20)
Rk, cb s, Nb g, Nb ec, Nb ucr, N
Rk, cb
0
A
c, Nb
The different factors of Equation (20) are given below:
14
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oSIST-TS prCEN/TS 1992-4-2:2008
prCEN/TS 1992-4-2:2008 (E)
NOTE For groups of fasteners perpendicular to the edge, which are loaded uniformly, verification is only required for
the fasteners closest to the edge.
6.2.7.1 Characteristic resistance of a single anchor
The characteristic resistance of a single anchor, not influenced by adjacent fasteners or free structural
component edges placed in cracked concrete is obtained by:
0
N = 8⋅ c ⋅ A ⋅ f [N] (21)
1 h ck,cube
Rk, cb
with
2
f [N/mm ], characteristic cube strength of the concrete strength class but noting the limitations
ck,cube
given in the relevant European Technical Specification
2
A [mm ], see Equation (3)
h
c [mm], edge distance, see Figure 7
1
0
Figure 7 — Idealized concrete break-out body and area A of an individual fastener in case of blow-
c, Nb
out failure
6.2.7.2 Geometric effect of
...
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