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TR 029 Edition June 2007
TABLE OF CONTENTS Design method for bonded anchors Introduction …………………………………………………………………………………………………………………..4 1 Scope ...............................................................................................................................................................2 1.1 Type of anchors, anchor groups and number of anchors ......................................................................2 1.2 Concrete member...................................................................................................................................3 1.3 Type and direction of load ......................................................................................................................3 1.4 Safety class ............................................................................................................................................3 2 Terminology and Symbols ................................................................................................................................4 2.1 Indices ....................................................................................................................................................4 2.2 Actions and resistances .........................................................................................................................4 2.3 Concrete and steel .................................................................................................................................4 2.4 Characteristic values of anchors (see Figure 2.1)..................................................................................5 3 Design and safety concept ...............................................................................................................................6 3.1 General...................................................................................................................................................6 3.2 Ultimate limit state ..................................................................................................................................6 3.2.1 Design resistance...............................................................................................................................6 3.2.2 Partial safety factors for resistances ..................................................................................................6 3.2.2.1 Concrete cone failure, splitting failure and pull-out failure, pry-out failure and edge failure......6 3.2.2.2 Steel failure................................................................................................................................7 3.3 Serviceability limit state ..........................................................................................................................7 4 Static analysis...................................................................................................................................................7 4.1 Non-cracked and cracked concrete .......................................................................................................7 4.2 Loads acting on anchors ........................................................................................................................8 4.2.1 Tension loads.....................................................................................................................................8 4.2.2 Shear loads ......................................................................................................................................10 4.2.2.1 Distribution of shear loads.......................................................................................................10 4.2.2.2 Determination of shear loads ..................................................................................................11 4.2.2.3 Shear loads without lever arm .................................................................................................13 4.2.2.4 Shear loads with lever arm ......................................................................................................14 5 Ultimate limit state ..........................................................................................................................................15 5.1 General.................................................................................................................................................15 5.2 Design method .....................................................................................................................................15 5.2.1 General ............................................................................................................................................15 5.2.2 Resistance to tension loads .............................................................................................................15 5.2.2.1 Required proofs.......................................................................................................................15 5.2.2.2 Steel failure..............................................................................................................................15 5.2.2.3 Combined pull -out and concrete cone failure.........................................................................15 5.2.2.4 Concrete cone failure ..............................................................................................................19 5.2.2.5 Splitting failure due to anchor installation ................................................................................22 5.2.2.6 Splitting failure due to loading .................................................................................................22 5.2.3 Resistance to shear loads................................................................................................................23 5.2.3.1 Required proofs.......................................................................................................................23 5.2.3.2 Steel failure..............................................................................................................................23 5.2.3.3 Concrete pry-out failure ...........................................................................................................24 5.2.3.4 Concrete edge failure ..............................................................................................................26 5.2.4 Resistance to combined tension and shear loads ...........................................................................32 6 Serviceability limit state ..................................................................................................................................33 6.1 Displacements......................................................................................................................................33 6.2 Shear load with changing sign..............................................................................................................33 7 Additional proofs for ensuring the characteristic resistance of concrete member..........................................33 7.1 General.................................................................................................................................................33 7.2 Shear resistance of concrete member .................................................................................................34 7.3 Resistance to splitting forces................................................................................................................35
74533.07
Introduction The design method for bonded anchors given in the relevant ETA’s is based on the experience of a bond 2 resistance for anchors in the range up to 15 N/mm and an intended embedment depth of 8 to 12 anchor diameter. In the meantime anchors are on the market with significant higher bond resistance. Furthermore the advantage of bonded anchors, to be installed with varying embedment, needs a modified design concept. This concept is given in this Technical Report. It covers embedment of min hef to 20 d. The minimum embedment depth is given in the ETA, it should be not less than 4d and 40mm. Restriction of the embedment depth may be given in the ETA. Also the assessment and some tests in Part 5 need modifications, because it may be difficult to develop the characteristic bond resistance. Following the concept of Part 5 predominantly steel failure and concrete cone failure may be observed for shallow and deep embedment. These results are of minor interest. The design method given in this Technical Report is based on Annex C with necessary modifications. It is valid for anchors with European Technical Approval (ETA) according to the new approach with characteristic bond resistance (τRk) and it is based on the assumption that the required tests for assessing the admissible service conditions given in Part 1 and Part 5 with modifications according to this Technical Report have been carried out. The use of other design methods will require reconsideration of the necessary tests. The ETA’s for anchors give the characteristic values only of the different approved anchors. The design of the anchorages e.g. arrangement of anchors in a group of anchors, effect of edges or corners of the concrete member on the characteristic resistance shall be carried out according to the design methods described in Chapter 3 to 5 taking account of the corresponding characteristic values of the anchors. Chapter 7 gives additional proofs for ensuring the characteristic resistance of the concrete. The design method is valid for all types of bonded anchors except undercut bonded anchors, torque controlled bonded anchors or post installed rebar connections. If values for the characteristic resistance, spacing, edge distances and partial safety factors differ between the design methods and the ETA, the value given in the ETA governs. In the absence of national regulations the partial safety factors given in the following may be used. 1 1.1 Scope Type of anchors, anchor groups and number of anchors
The design method applies to the design of bonded anchors (according to Part 1 and 5) in concrete using approved anchors which fulfil the requirements of this Guideline. The characteristic values of these anchors are given in the relevant ETA. The design method is valid for single anchors and anchor groups. In case of an anchor group the loads are applied to the individual anchors of the group by means of a rigid fixture. In an anchor group only anchors of the same type, size and length should be used. The design method covers single anchors and anchor groups according to Figure 1.1 and 1.2. Other anchor arrangements e.g. in a triangular or circular pattern are also allowed; however, the provisions of this design method should be applied with engineering judgement. In General this design method is valid only if the diameter df of the clearance hole in the fixture is not larger than the value according to Table 4.1. Exceptions: • For fastenings loaded in tension only a larger diameter of the clearance hole is acceptable if a correspondent washer is used. • For fastenings loaded in shear or combined tension and shear if the gap between the hole and the fixture is filled with mortar of sufficient compression strength or eliminated by other suitable means.
. 1. 1.1).2 shear loading. otherwise it has to be shown that the concrete is non-cracked (see 4.-3-
Figure 1. if anchors are situated close to an edge ( c < 10 hef and < 60 d )
The concrete member should be of normal weight concrete of at least strength class C 20/25 and at most strength class C 50/60 to ENV 206 [8] and should be subjected only to predominantly static loads.4 Safety class
Anchorages carried out in accordance with these design methods are considered to belong to anchorages.
74533.2 Anchorages covered by the design methods 1. In general for simplification it is assumed that the concrete is cracked.1 Anchorages covered by the design methods all loading directions. The concrete may be cracked or non-cracked. if anchors are situated close to edges ( c < 10 hef and < 60 d )
Figure 1.3 Type and direction of load
The design methods apply to anchors subjected to static or quasi-static loadings and not to anchors subjected to impact or seismic loadings. if anchors are situated far from edges ( c > 10 hef and > 60 d ) tension loading only. the failure of which would cause risk to human life and/or considerable economic consequences.
FRk (NRk . Further notations are given in the text.1 S R M k d s c cp p sp u y Indices = = = = = = = = = = = = action resistance material characteristic value design value steel concrete concrete pry-out pull-out splitting ultimate yield
2.3 fck. MSd . shear force) design value of resistance
FSk (NSk .cube fyk fuk As W el
Concrete and steel = = = = = characteristic concrete compression strength measured on cubes with a side length of 150 mm (value of concrete strength class according to ENV 206 [8]) characteristic steel yield strength (nominal value) characteristic steel ultimate tensile strength (nominal value) stressed cross section of steel elastic section modulus calculated from the stressed cross section of steel ( section with diameter d)
74533. VRd)
2. torsion moment) design value of actions design value of tensile load (shear load) acting on the most stressed anchor of an anchor group calculated according to 4. MT. MSk .2 F N V M
Actions and resistances = = = = = force in general (resulting force) normal force (positive: tension force.-4-
The notations and symbols frequently used in the design methods are given below.07
. VSk . 2. MT.2 characteristic value of resistance of a single anchor or an anchor group respectively (normal force. shear load. bending moment. VRk) FRd (NRd . VSd .Sk)
FSd (NSd .2 design value of the sum (resultant) of the tensile (shear) loads acting on the tensioned (sheared) anchors of a group calculated according to 4. negative: compression force) shear force moment bond strength = characteristic value of actions acting on a single anchor or the fixture of an anchor group respectively (normal load.
1b and Figure 5. in case of anchorages close to an edge loaded in shear c1 is the edge distance in direction of the shear load (see Figure 2.sp cmin d do h hef hmin s s1 s2 scr.Np scr.-5-
2.Np ccr.7) edge distance in direction 2. direction 2 is perpendicular to direction 1 edge distance for ensuring the transmission of the characteristic tensile resistance of a single anchor without spacing and edge effects in case of pullout failure edge distance for ensuring the transmission of the characteristic tensile resistance of a single anchor without spacing and edge effects in case of concrete cone failure edge distance for ensuring the transmission of the characteristic tensile resistance of a single anchor without spacing and edge effects in case of splitting failure minimum allowable edge distance diameter of anchor bolt or thread diameter.07
.sp smin
Characteristic values of anchors (see Figure 2.1) = = = = = = = = = = = = = = = = = = = = = = = spacing between outer anchors of adjoining groups or between single anchors spacing between outer anchors of adjoining groups or between single anchors in direction 1 spacing between outer anchors of adjoining groups or between single anchors in direction 2 width of concrete member edge distance edge distance in direction 1.N ccr. in case of internally threaded sockets outside diameter of socket drill hole diameter thickness of concrete member effective anchorage depth minimum thickness of concrete member spacing of anchors in a group spacing of anchors in a group in direction 1 spacing of anchors in a group in direction 2 spacing for ensuring the transmission of the characteristic resistance of a single anchor without spacing and edge effects in case of pullout failure spacing for ensuring the transmission of the characteristic tensile resistance of a single anchor without spacing and edge effects in case of concrete cone failure spacing for ensuring the transmission of the characteristic tensile resistance of a single anchor without spacing and edge effects in case of splitting failure minimum allowable spacing
74533.4 a a1 a2 b c c1 c2 ccr.N scr.
Figure 2. pry-out failure and edge failure (γMc).2. Sd ≤ Rd (3.2.1
Concrete member. splitting failure (γMsp) and pull-out failure (γMp) are given in the relevant ETA. γ2
partial safety factor for concrete = 1. pry-out failure and edge failure The partial safety factors for concrete cone failure. For anchors to according to current experience the partial safety factor γMc is determined from:
γMc γc γ2
γc . The design resistance is calculated as follows: Rd = Rk/γM Rk = γM 3. splitting failure and pull-out failure.1 Design resistance The design resistance is calculated according to Equation (3.5 partial safety factor taking account of the installation safety of an anchor system The partial safety factor γ2 is evaluated from the results of the installation safety tests.2) characteristic resistance of a single anchor or an anchor group partial safety factor for material
3. 3. The partial safety factors for actions may be taken from national regulations or in the absence of them according to EN 1990.1 3 3.2).1) Sd = value of design action Rd = value of design resistance Actions to be used in design may be obtained from national regulations or in the absence of them from the relevant parts of EN 1991.2.
74533. anchor spacing and edge distance
Design and safety concept General
The design of anchorages shall be in accordance with the general rules given in EN 1990.2 Partial safety factors for resistances In the absence of national regulations the following partial safety factors may be used: 3.2. It shall be shown that the value of the design actions Sd does not exceed the value of the design resistance Rd.2 = (3.07
.1 Concrete cone failure.
In this check the partial safety factors on actions and on resistances may be assumed to be equal to 1.4 for systems with low but still acceptable installation safety Shear loading
fyk/fuk < 0.3c)
γMs = 1. In the absence of other guidance the following provisions may be taken. If no detailed analysis is conducted.2 fyk / fuk
> 1.3b) and
fuk < 800 N/mm
(3. 4 4.4
(3.1.2 for systems with normal installation safety = 1.g. Tension loading = 1.8 fuk > 800 N/mm fyk/fuk > 0.2. The admissible displacement depends on the application in question and should be evaluated by the designer. For anchorages subjected to a resultant load FSk < 60 kN non-cracked concrete may be assumed if Equation (4.5
(3.1 Static analysis Non-cracked and cracked concrete
If the condition in Equation (4.1) is observed: σL + σR < 0 σL σR = = stresses in the concrete induced by external loads. shrinkage of concrete) or extrinsic imposed deformations (e.0 for systems with high installation safety = 1.3a)
1. including anchors loads stresses in the concrete due to restraint of intrinsic imposed deformations (e.g.0 > 1.1) is not fulfilled or not checked.25 fyk / fuk
(3. according to EC 2 [1]. 3. then cracked concrete is assumed.0
For the partial safety factors γMsp and γMp the value for γ Mc may be taken. For anchors according to current experience the partial safety factors γMs are determined as a function of the type of loading as follows: Tension loading:
1. Non-cracked concrete may be assumed in special cases if in each case it is proved that under service conditions the anchor with its entire anchorage depth is located in non-cracked concrete.2. then σR = 3 N/mm should be assumed. 6.07
. (4.2.0. due to displacement of support or 2 temperature variations).2 Steel failure The partial safety factors γMs for steel failure are given in the relevant ETA.-7-
see Part 1. For the characteristic displacements see 6.1)
74533.2.3
In the serviceability limit state it shall be shown that the displacements occurring under the characteristic actions are not larger than the admissible displacement.2.
walls) Equation (4.2 Loads acting on anchors In the static analysis the loads and moments are given which are acting on the fixture. To design the anchorage the loads acting on each anchor are calculated. to enable a more accurate assessment of the anchor group resistance.-8-
The stresses σL and σR are calculated assuming that the concrete is non-cracked (state I).3 in the serviceability limit state.1 in the ultimate limit state and according to 3. If the tensioned anchors do not form a rectangular pattern.07
.1). b) The stiffness of all anchors is equal and corresponds to the modulus of elasticity of the steel.1b). taking into account partial safety factors for actions according to 3.2. for reasons of simplicity the group of tensioned anchors may be resolved into a group rectangular in shape (that means the centre of gravity of the tensioned anchors may be assumed in the centre of the axis in Figure 4.1 Tension loads In general. The modulus of 2 elasticity of concrete is given in. This distribution shall be calculated according to the theory of elasticity. 4. In the case of anchor groups with different levels of tension forces Nsi acting on the individual anchors of a group the eccentricity eN of the tension force N S of the group may be calculated (see Figure 4. bending and torsion moments acting on the fixture are distributed to tension and shear forces acting on the individual anchors of the group. the tension loads acting on each anchor due to loads and bending moments acting on the fixture should be calculated according to the theory of elasticity using the following assumptions: a) The anchor plate does not deform under the design actions. For plane concrete members which transmit loads in two directions (e. To ensure the validity of this assumption the anchor plate has to be sufficiently stiff. If in special cases the anchor plate is not sufficiently stiff. c) In the zone of compression under the fixture the anchors do not contribute to the transmission of normal forces (see Figure 4. then the flexibility of the anchor plate should be taken into account when calculating loads acting on the anchors.g. With anchor groups the loads. 4.1c)
74533. With single anchors normally the loads acting on the anchor are equal to the loads acting on the fixture.1) should be fulfilled for both directions. As a simplification it may be taken as Ec = 30 000 N/mm . slabs.
1 Example of anchorages subjected to an eccentric tensile load N S
g Figure 4.
4). Table 4.6). when all anchors take up shear loads
74533.1 (see Figure 4.2. Slotted holes in direction of the shear load prevent anchors to take up shear loads..2
4.7).3 and 4.2.2.2 and 4.07
4. All anchors take up shear loads acting parallel to the edge. b) Concrete edge failure Only the most unfavourable anchors take up shear loads if the shear acts perpendicular towards the edge (see Figure 4.1 the design method is only valid if the gap between the bolt and the fixture is filled with mortar of sufficient compression strength or eliminated by other suitable means.1 Diameter of clearance hole in the fixture (mm) 6 7 8 9 10 12 12 14 14 16 16 18 18 20 20 22 22 24 24 26 27 30 30 33
external diameter 1) 2) d or dnom
diameter df of clearance hole in the fixture (mm)
if bolt bears against the fixture if sleeve bears against the fixture
Figure 4. If the diameter df of clearance hole in the fixture is larger than given in Table 4. This can be favourable in case of fastenings close to an edge (see Figure 4.1 Distribution of shear loads The distribution of shear loads depends on the mode of failure: a) Steel failure and concrete pry-out failure It is assumed that all anchors of a group take up shear load if the diameter df of clearance hole in the fixture is not larger than the value given in Table 4.2
Examples of load distribution.
Figure 4. when only the most unfavourable anchors take up shear loads
Figure 4. Equilibrium has to be satisfied.07
.2.2 Determination of shear loads The determination of shear loads to the fasteners in a group resulting from shear forces and torsion moments acting on the fixture is calculated according to the theory of elasticity assuming equal stiffness for all fasteners of a group.7.
74533. to enable a more accurate assessment of the anchor group resistance.5). Examples are given in Figs 4..4
Examples of load distribution for a fastening with slotted holes
In the case of anchor groups with different levels of shear forces Vsi acting on the individual anchors of the group the eccentricity ev of the shear force VS of the group may be calculated (see Figure 4.6 and 4.5
Example for a fastening subjected to an eccentric shear load
Determination of shear loads when all anchors take up loads (steel and pry-out failure)
74533.v /4
VSd.07
.h /4 c) Group of four anchors under an inclined shear load Vanchor
Vanchor TSd s1 Vanchor
Vanchor =
TSd ⋅ (s1 / 2)2 + (s2 / 2)2 Ip
0 ..v /4 VSd.h
VSd.12 -
VSd / 3
a) Group of three anchors under a shear load VSd / 4
VSd / 4
b) Group of four anchors under a shear load VSd.5
with: Ip = radial moment of inertia (here: Ip = s1 + s2 )
d) Group of four anchors under a torsion moment
Figure 4.h /4 VSd.v /4 VSd.h /4
VSd.v VSd VSd.v /4 VSd.h /4
b) The fixture shall be in contact with the anchor over its entire thickness.
74533..7
Determination of shear loads when only the most unfavourable anchors take up loads (concrete edge failure)
In case of concrete edge failure where only the most unfavourable anchors take up load the component of the load acting perpendicular to the edge are taken up by the most unfavourable anchors (anchors close to the edge). while the components of the load acting parallel to the edge are – due to reasons of equilibrium – equally distributed to all anchors of the group.13 -
Load not to be considered VSd VSd/2 b) Group of two anchors loaded parallel to the edge Load to be considered
VV = VSd ⋅ cos αV
αV VV/2 Load not to be considered VH = VSd ⋅ sin αV Load to be considered
VH/4 Edge c) Group of four anchors loaded by an inclined shear load
.2.3 Shear loads without lever arm Shear loads acting on anchors may be assumed to act without lever arm if both of the following conditions are fulfilled: a) The fixture shall be made of metal and in the area of the anchorage be fixed directly to the concrete either 2 without an intermediate layer or with a levelling layer of mortar (compression strength ≥ 30 N/mm ) with a thickness < d/2. 4.2.
If restraint of the anchor is assumed the fixture shall be able to take up the restraint moment.2.3 are not fulfilled the lever arm is calculated according to Equation (4.4 Shear loads with lever arm If the conditions a) and b) of 4.2.2.5 d 0 if a washer and a nut is directly clamped to the concrete surface (see Figure 4.1 or the anchor is clamped to the fixture by nut and washer (see Figure 4.3)
The value αM depends on the degree of restraint of the anchor at the side of the fixture of the application in question and shall be judged according to good engineering practice.07
4.8b) nominal diameter of the anchor bolt or thread diameter (see Figure 4.
(4. Full restraint (αM = 2.
Figure 4.8) l = a3 + e1 with e1 = a3 = a3 = d = (4. No restraint (αM = 1.0) may be assumed only if the fixture cannot rotate (see Figure 4.8).3) MSd = VSd
Fixture without (a) and with (b) restraint
74533.8
Definition of lever arm
The design moment acting on the anchor is calculated according to Equation (4.9a). This assumption is always on the safe side.2) (see Figure 4.0) shall be assumed if the fixture can rotate freely (see Figure 4.9b) and the hole clearance in the fixture is smaller than the values given in Table 4..2.8a)
distance between shear load and concrete surface 0.
.s = As fuk [N] NRk. ψec.Np .sp / γMsp
5.2 Resistance to tension loads
5.sp / γMsp
N Sd < NRk.2 Design method
5.2a)
74533. ψre.2 Steel failure The characteristic resistance of an anchor in case of steel failure.Np
(5.3 Combined pull -out and concrete cone failure The characteristic resistance in case of combined pull -out and concrete cone failure.s. hef and d [mm]
. concrete edge failure and concrete pry-out failure). splitting failure.2.1) it has to be shown that the design value of the action is equal to or smaller than the design value of the resistance.s / γMs
N Sd < NRk.
[N/mm ]. shear) as well as all failure modes (steel failure. combined pull-out and concrete cone failure.2. is NRk. τRk
(5.p
. N Rk.1) is observed for all loading directions (tension.1
Ultimate limit state General
According to Equation (3. 5.p / γMp
NSd < NRk.2. ψg.2. The spacing between outer anchor of adjoining groups or the distance to single anchors should be a > scr. Spacing. concrete cone failure. NRk.2) for anchors according to current experience are given below: a) The initial value of the characteristic resistance of an anchor is obtained by:
0 .p = N Rk.1)
Ap.2.N .ψs.p = π ⋅ d hef .1 Required proofs single anchor anchor group
NSd < NRk. In case of a combined tension and shear loading (oblique loading) the condition of interaction according to 5.Np .p.15 -
5 5. 5. The characteristic values of the anchor to be used for the calculation of the resistance in the ultimate limit state are given in the relevant ETA.4 should be observed.2)
The different factors of Equation (5. 5.1 General It has to be shown that Equation (3.2. is . edge distance as well as thickness of concrete member should not remain under the given minimum values.2.2. NRk.2.c / γMc
NSd < NRk.p / γMp
N Sd < NRk.Np .s / γMs
combined pull-out and concrete cone failure
NSd < NRk.N
0 Ap..s is given in the relevant ETA. NRk.c / γMc
2c) and (5. N
influence area of an individual anchor with large spacing and edge distance at the concrete surface. where:
0 Ap.ucr ) in the
relevant ETA b) The geometric effect of spacing and edge distance on the characteristic resistance is taken into account
0 by the value Ap.ucr for C20/25 [N/mm ].Np ⋅ scr.07
.1). Examples for the calculation of Ap.N are given in Figure 5.N
scr.16 -
τRk characteristic bond resistance. depending on the concrete strength class.Np 2
0. d [mm]
c cr . it is limited by overlapping areas of adjoining anchors (s < scr.2.Np
 τ Rk . N of an individual anchor
74533.Np).2c)
with τRk.2d)
Note: The values according to Equations (5.2d) are valid for both cracked and non-cracked concrete.
s cr .Np (5..5
≤ 3 ⋅ hef
(5.cr ) or for applications in non-cracked concrete (τRk.Np (see Figure 5.5 
s cr .N/ A p.Np =
(5.1 Influence area
Figure 5. N .2b) actual area. values given for applications in cracked concrete (τRk.Np) as well as by edges of the concrete member (c < ccr. idealizing the concrete cone as a pyramid with a base length equal to scr.
Ap.ucr = 20 ⋅ d ⋅   7 .
g.Np takes account of the disturbance of the distribution of stresses in the concrete due to edges of the concrete member. ψs.2 c)
Examples of actual areas Ap.. c.2e)
74533.Np
(5.7 + 0. shall be inserted in Equation (5.07
.N for different arrangements of anchors in the case of axial tension load
The factor ψs.
c c cr. the smallest edge distance. anchorage in a corner of the concrete member or in a narrow member). For anchorages with several edge distances (e.Np = 0.2e).17 -
a) individual anchor at the edge of concrete member
b) group of two anchors at the edge of concrete member
Np = 0.
hef or
h 'ef =
s max s cr .18 -
The factor. 5
≥ 1. Np
0 ⋅ψg .Np
' . ψg.07
.2h) the values
A0 c.Np
 s − s  cr . hef and d [mm] τRk characteristic bond resistance.
depending on the concrete strength class is taken from the
relevant ETA: k = 2.Np
0 .2b) to (5. in case of anchor groups with s1 ≠ s2 the mean value of all spacings s1 and s2 should be taken with
0 n− ψg .0
(5.cube [N/mm2]. ψre. Np =
 d ⋅ τ Rk n −1 ⋅  k⋅ h ⋅ f ef ck .N and Ac.Np
are inserted for scr.0 may be applied independently of the anchorage depth.1).5 s’cr.Np = ψ
0 g . More precise results are obtained if for hef the larger value of
c max c cr .
The shell spalling factor.5 +
h ef < 1 200
(5.2a)and (5. ψec. Np
. c cr.Np. respectively.Np or ccr..cube 
1.2i)
hef [mm] If in the area of the anchorage there is a reinforcement with a spacing > 150 mm (any diameter) or with a diameter < 10 mm and a spacing > 100 mm then a shell spalling factor of ψre.
74533.Np takes account of a group effect when different tension loads are acting on the individual anchors of a group.2h)
eccentricity of the resulting tensile load acting on the tensioned anchors (see 4.2 leads to results which are on the safe side.2.Np =
c max c cr.2). takes account of the effect of the failure surface for anchor groups
ψ g .2 as well as in Equations (5.2f)
= spacing.Np = 1.Np (cmax = largest edge distance) (see Figure 5.
scr. Where there is an eccentricity in two directions. g) Special cases For anchorages with three or more edges with an edge distance cmax < ccr. Np = 0.
is inserted in Equation (5.0
(5.3 (for applications in cracked concrete) k = 3.3) the calculation according to Equation 5. takes account of the effect of a dense reinforcement ψre.Np.Np = eN =
1 1 + 2eN /s cr.N shall be determined separately for each direction and the product of both factors shall be inserted in Equation (5.Np
τRk and fck.2 (for applications in non-cracked concrete) e) The factor of ψec. ψec.1 and 5.Np − 1 ≥ 1.N according to Figures
s 'cr.Np.2i) and for the determination of 5.
The different factors of Equation (5.N).2.19 -
Figure 5. hef1.c = N Rk.N .1 for applications in non-cracked concrete b) The geometric effect of spacing and edge distance on the characteristic resistance is taken into account by the value Ac. It is limited by overlapping concrete cones of adjoining anchors (s < scr. idealizing the concrete cone as a pyramid with a height equal to hef and a base length equal to scr.
74533.4 Concrete cone failure The characteristic resistance of an anchor or a group of anchors.cube [N/mm ].2.c = k1 ⋅
fck.N) as well as by edges of the concrete member (c < ccr. Np
5.N ⋅ scr.3b)
actual area of concrete cone of the anchorage at the concrete surface. hef [mm] k1 = 7.N .N .N/ A c.ψs. ψre.
A c. s cr.3a)
fck. [N] A0 c.N are given in Figure 5. ψec.2 for applications in cracked concrete k1 = 10.N
= Ac. in case of concrete cone failure is: NRk.N (see Figure 5.07
area of concrete of an individual anchor with large spacing and edge distance at the concrete surface.4a).Np and
' c cr.c
.N .. Examples for the calculation of Ac.3
Examples of anchorages in concrete members where h’ef.N
with scr.3) for anchors according to current experience are given below: a) The initial value of the characteristic resistance of an anchor placed in cracked or non-cracked concrete is obtained by:
N0 Rk.N =
scr.4b.N .cube .N = 3 hef
(5. where:
A0 c. respectively.
..4a Idealized concrete cone and area
A0 c.20 -
Figure 5.N of concrete cone of an individual anchor
.N of the idealized concrete cones for different arrangements of anchors in the case of axial tension load
c) group of four anchors at a corner of concrete member Figure 5.4b Examples of actual areas Ac.
3e) the values
s 'cr.N
eccentricity of the resulting tensile load acting on the tensioned anchors (see 4. ψec.2.3).0 may be applied independently of the anchorage depth.1).22 -
The factor ψs.N = 0.N = 3 h 'ef
c'cr. spacing smin.5 +
(5.N takes account of the disturbance of the distribution of stresses in the concrete due to edges of the concrete member.sp shall be taken from the ETA as a function of the embedment depth. (5. Where there is an eccentricity in two directions.5 s’cr. takes account of the effect of a reinforcement ψre.7 + 0.07
74533.5 Splitting failure due to anchor installation Splitting failure is avoided during anchor installation by complying with minimum values for edge distance cmin.2. N
. ψs.
Special cases For anchorages with three or more edges with an edge distance cmax < ccr.N = 0.N according to Figures
5.2.N
are inserted for scr.N.3a)and (5.6 Splitting failure due to loading For splitting failure due to loading the values ccr.2. 5. member thickness hmin and reinforcement as given in the relevant ETA. respectively.N. a) It may be assumed that splitting failure will not occur.N
(5.N (cmax = largest edge distance) (see Figure 5.3 mm. e) The factor of ψec. ψec. the calculation of the characteristic splitting resistance may be omitted if the following two conditions are fulfilled: − − a reinforcement is present which limits the crack width to wk ∼ 0. shall be inserted in Equation (5.N or ccr.N takes account of a group effect when different tension loads are acting on the individual anchors of a group.3
. ψre.N = eN =
1 1 + 2eN / scr. anchorage in a corner of the concrete member or in a narrow member).3 the characteristic resistance for concrete cone failure and pull-out failure is calculated for cracked concrete.g.3 and 5.sp and the member depth is h > 2 hmin.3d) and for the determination of
A0 c. 5.4 as well as in Equations (5.3c).sp and scr.
s max s cr . c.3d)
hef [mm] If in the area of the anchorage there is a reinforcement with a spacing > 150 mm (any diameter) or with a diameter < 10 mm and a spacing > 100 mm then a shell spalling factor of ψre.3) the calculation according to Equation 5.
c ccr.N = 1.3c)
The shell spalling factor..3b).N and Ac.2.3c) and (5. the smallest edge distance.N = 0. if the edge distance in all directions is c > 1.3 leads to results which are on the safe side.
is inserted in Equation (5. More precise results are obtained if for hef the larger value of
cmax ccr .N shall be determined separately for each direction and the product of both factors shall be inserted in Equation (5. For anchorages with several edge distances (e. b) With anchors suitable for use in cracked concrete. taking into account the splitting forces according to 7.2 ccr.
c with ψh.N.s / γMs
concrete pry-out failure concrete edge failure
VSd < VRk.4 b).2. 5.s / γMs
steel failure. ψec.5 ·As · fuk VRk.2.2. In case of current experience it is given by Equation (5.s is taken from the relevant ETA.ψs.
If the edge distance of an anchor is smaller than the value ccr. ψre.sp = N Rk.2.. shear load without lever arm
VSd < VRk.sp
 2 ⋅ hef ≤  h  min
(5..3a) to (5.N.1 Required proofs
steel failure.4)
0 N0 Rk.5)
In case of anchor groups.N . however the values ccr.
A c.4a)
1 ≤ ψ h . ψre. shear load with lever arm
VSd < VRk.N .2 Steel failure a) Shear load without lever arm The characteristic resistance of an anchor in case of steel failure. then the characteristic resistance of a single anchor or an anchor group in case of splitting failure should be calculated according to Equation (5. the characteristic shear resistance given in the relevant ETA is multiplied with a factor 0.N
.N.N should be replaced by ccr. ψh.3e) and Ac.sp A0 c.c . if the anchor is made of steel with a rather low ductility (rupture elongation A5 < 8%)
74533.s / γMs
V Sd < VRk.N .2.23 -
If the conditions a) or b) are not fulfilled.3 Resistance to shear loads
5.4b). VRk.4) NRk. on the splitting resistance for anchors according to current experience
 h  =  h    min 
(5. ψec. = factor to account for the influence of the actual member depth.3.sp then a longitudinal reinforcement should be provided along the edge of the member.3.cp / γMc V Sd < VRk.N according to Equations (5.c / γMc
5.sp and scr.s / γMs
V Sd < VRk. N as defined in
5.N .cp / γMc
V Sd < VRk.sp.s is given in the relevant ETA.8. ψs.s = 0.
VRk. h.
(5.N and scr. Ac .sp
p and NRk.NSd/NRd.07
M0 Rk. For anchors according to current experience failing under tension load by concrete cone failure the following values are on the safe side k = 1 k = 2 hef < 60mm hef > 60mm (5.7a)
where k = factor to be taken from the relevant ETA NRk.7a).2.2.6)
MRk.2.7c)
Figure 5. . the lowest value of (5. γMs
to be taken from the relevant ETA characteristic bending resistance of an individual anchor
0 Rk.3 Concrete pry-out failure Anchorages with short stiff anchors can fail by a concrete pry-out failure at the side opposite to load direction (see Figure 5.2 ·W el · fuk
5.2. VRk.2.24 -
Shear load with lever arm The characteristic resistance of an anchor.s
The characteristic bending resistance The value of
M0 Rk.
[Nm] (5.5 Concrete pry-out failure on the side opposite to load direction Verification of pry-out failure for the most unfavourable anchor
74533.6a)
NRk.cp = k .. NRk.s.s .c according to 5.7a) is decisive.s =
α M ⋅ M Rk. The corresponding characteristic resistance VRk.3 and 5.s (1 .2.2.4
(5. NRk.6).s / γMs
(5.s shall be taken from the relevant ETA.3.cp may be calculated from Equation (5.s = 1. VRk.s
lever arm according to Equation (4.7) and (5.
M0 Rk. VRk.7) and (5.s for anchors according to current experience is obtained from Equation (5.c (5.6b).p (5.cp = k .5).s
= = = = = see 4. is given by Equation (5.7) VRk.4 determined for single anchors or all anchors of a group loaded in shear.7b) (5.s)
NRk.s NRd.6b)
Examples for the calculation of Ac..
74533.7a) are not suitable for this application. shear loads acting on the individual anchors of the group alter their directions In cases where the horizontal or vertical components of the shear loads on the anchors alter their direction within a group the verification of pry-out failure for the entire group is substituted by the verification of pry-out failure for the most unfavourable anchor of the group. Fig. It is self-explanatory that Equation (5. 5.25 -
In cases where the group is loaded by shear loads and/or external torsion moments.5a demonstrates this for a group of two anchors loaded by a torsion moment.07
Group of anchors loaded by a torsion moment.N are given in Fig. When calculating the resistance of the most unfavourable anchor the influences of both. 5. the direction of the individual shear loads may alter.7) and (5. The shear loads acting on the individual anchors neutralise each other and the shear load acting on the entire group is VSd = 0.5b. edge distances as well as anchor spacing should be considered.
V1 = T / s
V2 = -T / s
c1 [mm].
(5. c = k1 ⋅ d ⋅ hef ⋅ 1.5
(5. The characteristic resistance for an anchor or an anchor group in the case of concrete edge failure corresponds to: VRk.5b
Examples for the calculation of the area Ac.V
.V ψh.2.4 Concrete edge failure Concrete edge failure need not to be verified for groups with not more than 4 anchors when the edge distance in all directions is c > 10 hef and c > 60 d.cube [N/mm2] with k1 = 1..V ψα. 1 ⋅  c  1
0 .5 f ck . fck.
Ac . hef.8b)
74533. .8) for anchors according to current experience are given below: a) The initial value of the characteristic resistance of an anchor placed in cracked or non-cracked concrete and loaded perpendicular to the edge corresponds to:
0 α β VRk . .
ψs.8)
The different factors of Equation (5.7 for applications in cracked concrete k1 = 2.3.N of the idealised concrete cones
5.V ψre.V
.V ψec.c =
0 VRk.26 -
.V Ac0. cube ⋅ c1
(5. .4 for applications in non-cracked concrete
 hef α = 0.8a)
of concrete cone for a single anchor
74533.1 ⋅  c    1
A0 c.07
. member thickness or adjacent anchors.V and Ac. assuming the shape of the fracture area as a half pyramid with a height equal to c1 and a base-length of 1.V/ A c.
Idealized concrete cone and area A
0 c.6).V
area of concrete cone of an individual anchor at the lateral concrete surface not affected by edges parallel to the assumed loading direction.V it is assumed that the shear loads are applied perpendicular to the edge of
the concrete member..5 c1).5 c1 and 3 c1 (Figure 5.5 c1 (5.8c)
b) The geometrical effect of spacing as well as of further edge distances and the effect of thickness of the concrete member on the characteristic load is taken into account by the ratio Ac.8d) actual area of concrete cone of anchorage at the lateral concrete surface.V are given in Figure 5.5 c1) and by member thickness (h < 1. 2 4.27 -
d  β = 0 .V .
(5. Examples for calculation of Ac. It is limited by the overlapping concrete cones of adjoining anchors (s < 3 c1) as well as by edges parallel to the assumed loading direction (c2 < 1. where:
A0 c.
Examples of actual areas of the idealized concrete cones for different anchor arrangements under shear loading
8e)..V = 0.5 
≥ 1 . ψh. in a narrow concrete member) the smaller edge distance shall be inserted in Equation (5.V/ A c. VSd or both are given in Fig. ψs.V takes account of the fact that the shear resistance does not decrease proportionally to the member thickness as assumed by the ratio Ac. and the direction .
c2 < 1 1.8f)
The factor ψαV takes account of the angle αV between the load applied. In case of αV > 90° it is assumed that only the component of the shear load parallel to the edge is acting on the anchor. see Figure 4.V takes account of the disturbance of the distribution of stresses in the concrete due to further edges of the concrete member on the shear resistance. For anchorages with two edges parallel to the assumed direction of loading (e.
74533.8g)
The maximum value αv to be inserted in equation (5.9. c1 1/2 ) > 1 h
(5. VSd.V = (
15 .5.7c).8g) is limited to 90°.7 + 0. perpendicular to the free edge of the concrete member (αv ≤ 90°
ψ α .8 and Fig.V =
 sin αV  (cos αV )2 +    2 .29 -
The factor ψs. The component acting away from the edge may be neglected for the proof of concrete edge failure.g. 5. Examples of anchor groups loaded by MTd .V .5 c1
(5.8e)
The factor ψh.3
. components directed away from the edge
a) group of anchors at an edge loaded by VSd with an angle αV = 180°
load on each anchor
components neglected. because directed away from the edge
load on anchor group for calculation
b) group of anchors at an edge loaded by VSd with an angle 90 < αV < 180°
Component neglected.30 -
no proof for concrete edge failure needed. because directed away from the edge
eV load on anchor group for calculation
c) group of anchors at the edge loaded by a torsion moment MTd
Examples of anchor groups at the edge loaded by a shear force or a torsion moment
Examples of anchors groups at the edge loaded by a shear force and a torsion moment
neglected because sum of components is directed away from the edge
load on anchor group
VSd load on anchor group for calculation a)
shear component due to torsion moment larger than component of shear force directed
Considered because sum of components is directed towards the edge
VSd load on anchor group for calculation
shear component due to torsion moment smaller than component of shear force directed towards the edge
2.V and Ac.2.V takes account of a group effect when different shear loads are acting on the individual anchors of a group.2.3. narrow member where the value c’1 may be used
5.max < 1.V eV = = = 1.2.9b) (5.9c)
74533.6 and 5.. In Equation (5. Special cases For anchorages in a narrow.5 c1 (see Figure 5.9) the largest value of β N and β V for the different failure modes shall be taken (see 5.8) leads to results which are on the safe side. ψec.1).32 -
The factor ψec.0 = 1. More precise results are achieved if in Equations (5.4
1 1 + 2 eV / ( 3c1 )
(5.8a) to (5.2 where β N (β V) ratio between design action and design resistance for tension (shear) loading.V ψre.11) shall be satisfied: βN < 1 βV < 1 β N + β V < 1. thin member with c2.5 and h/1.max = greatest of the two edge distances parallel to the direction of loading) and h < 1.07
.10) the calculation according to Equation (5.10
Example of an anchorage in a thin.1 and 5. c’1 being the greatest of the values c2max/1.V takes account of the effect of the type of reinforcement used in cracked concrete. ψre. the resistances for both edges shall be calculated and the smallest value is decisive. anchorage in non-cracked concrete and anchorage in cracked concrete without edge reinforcement anchorage in cracked concrete with straight edge reinforcement (> Ø12 mm)
The factor ψre.4 Resistance to combined tension and shear loads For combined tension and shear loads the following Equations (see Figure 5.8f) as well as in the determination of the areas
A0 c.2).2.V
anchorage in cracked concrete with edge reinforcement and closely spaced stirrups (a < 100 mm) For anchorages placed at a corner.7 the edge distance c1 is replaced by the value of
c’1.8h)
eccentricity of the resulting shear load acting on the anchors (see 4.2 = 1.9a) (5.5 c1 (c2. (5.V according to Figures 5.V ψre.5 or s2max/3 in case of anchor groups
appropriate measures shall be taken to avoid a fatigue failure of the anchor steel (e. the displacements for the tension and shear component of the resultant load should be geometrically added.minσ in the 2 serviceability limit state caused by temperature variations should be limited to 100 N/mm .11 Interaction diagram for combined tension and shear loads In general. In case of shear loads the influence of the hole clearance in the fixture on the expected displacement of the whole anchorage shall be taken into account.1 Additional proofs for ensuring the characteristic resistance of concrete member General
The proof of the local transmission of the anchor loads into the concrete member is delivered by using the design methods described in this document.10)
Serviceability limit state Displacements
The characteristic displacement of the anchor under defined tension and shear loads shall be taken from the ETA.
74533.33 -
Figure 5. It may be assumed that the displacements are a linear function of the applied load. In case of a combined tension and shear load. β V α = 2.9c) yield conservative results.0 α = 1. 7 7. the shear load should be transferred by friction between the fixture and the concrete (e. Equations (5.9a) to (5. The transmission of the anchor loads to the supports of the concrete member shall be shown for the ultimate limit state and the serviceability limit state. due to a sufficiently high permanent prestressing force)).9) if NRd and VRd are governed by steel failure for all other failure modes (5.2 and 7. for this purpose. facade elements).07
. 6.3 should be taken into account. either these members are anchored such that no significant shear loads due to the restraint of deformations imposed to the fastened element will occur in the anchor or in shear loading with lever arm (stand-off installation) the bending stresses in the most stressed anchor ∆σ = maxσ . More accurate results are obtained by Equation (5.2 Shear load with changing sign
If the shear loads acting on the anchor change their sign several times.g.10) ( β N ) α + ( β V) α < 1 with: β N. the normal verifications shall be carried out under due consideration of the actions introduced by the anchors..g. For these verifications the additional provisions given in 7. Shear loads with changing sign can occur due to temperature variations in the fastened member (e. Therefore.1 see Equations (5.g.5 6 6.
between the outermost anchors of adjacent groups or between the outer anchors of a group and individual anchors satisfies Equation (7. of the tensioned fasteners is NSk < 30 kN and the spacing. In case of slabs and beams made out of prefabricated units and added cast-in-place concrete. 7.34 -
If the edge distance of an anchor is smaller than the characteristic edge distance ccr.N.0 kN/m may be anchored in the precast concrete.3) a > 200
. 2 [1] When calculating VSd. a. Its distance from an individual anchor or the outermost anchors of a group should be smaller than hef If under the characteristic actions. NSk.4 VRd1 (7. Equation (7.2 Shear resistance of concrete member
In general. the shear forces VSd.a = 0. if one of the following conditions is met a) The shear force VSd at the support caused by the design actions including the anchor loads is VSd < 0. the resultant tension force. Otherwise only the loads of suspended 2 ceilings or similar constructions with a load up to 1.
a [mm]. If this shear reinforcement between precast and cast-in-place concrete is not present. the anchors should be embedded with hef in the added concrete. which encloses the tension reinforcement and is anchored at the opposite side of the concrete member. then a longitudinal reinforcement of at least ∅ 6 shall be provided at the edge of the member in the area of the anchorage depth. anchor loads may be transmitted into the prefabricated concrete only if the precast concrete is connected with the cast-in-place concrete by a shear reinforcement. The necessary checks for ensuring the required shear resistance of the concrete member are summarized in Table 7. of the tensioned fasteners is NSk > 60 kN.
74533.2)
b) Under the characteristic actions.1) with: VRd1 = shear resistance according Eurocode No.. The active width over which the shear force is transmitted should be calculated according to the theory of elasticity.a the anchor loads shall be assumed as point loads with a width of load application t1 = st1 + 2 hef and t2 = st2 + 2 hef.8 h or a hanger reinforcement according to paragraph c) above should be provided. NSk [kN]
(7.a caused by anchor loads should not exceed the value VSd. with st1 (st2) spacing between the outer anchors of a group in direction 1 (2). the resultant tension force. NSk.1) may be neglected. then either the embedment depth of the anchors should be hef > 0.07
c) The anchor loads are taken up by a hanger reinforcement.1.8 VRd1 (7.
8 VRd1
.N and a > 200 ⋅
NSk [kN] < 60
Proof of calculated shear force resulting from anchor loads not required
a > scr.k and the characteristic tension load NSk may be taken as FSp.k = 0. but hanger reinforcement or hef > 0. for fastenings in slabs and walls a concentrated reinforcement in both directions is present in the region of the anchorage.35 -
7. If the characteristic tension load acting on the anchorage is NSk > 30 kN and the anchors are located in the tension zone of the concrete member the splitting forces shall be taken up by reinforcement.07
. The area of the transverse reinforcement should be at least 60 % of the longitudinal reinforcement required for the actions due to anchor loads.N
. As a first indication for anchors according to current experience the ratio between splitting force FSp.4 VRd1 or hanger reinforcement or hef > 0.N a > scr. b) The tension component NSk of the characteristic loads acting on the anchorage (single anchor or group of anchors) is smaller than 10 kN. This may be neglected if one of the following conditions is met: a) The load transfer area is in the compression zone of the concrete member. In addition.8 VRd1 < 60 a > scr.5 NSk for bonded anchors.3
In general.8 h > 60 not required. the splitting forces caused by anchors should be taken into account in the design of the concrete member.1 Necessary checks for ensuring the required shear resistance of concrete member Calculated value of shear Spacing between single force of the concrete member anchors and groups of under due consideration of anchors the anchor loads VSd < 0.. c) The tension component NSk is not greater than 30 kN.a < 0.8 h
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