Design of Fastenings for Use in Concrete – the CEN/TS 1992-4 ProvisionsRainer Mallée, Werner Fuchs, Rolf Eligehausen

Design of Fastenings for U

se in Concrete –

the CE

N/TS

1992-4 Provisions

Contents

Editorial .................................................................................. XI

1 Introduction................................................................................. 1

2 Fields of application ................................................................... 3

3 Basis of design ........................................................................... 133.1 General................................................................................................ 133.2 Verifications........................................................................................ 143.3 Partial factors ...................................................................................... 153.3.1 General................................................................................................ 153.3.2 Actions................................................................................................ 153.3.3 Resistance ........................................................................................... 163.3.3.1 Ultimate limit state ............................................................................. 163.3.3.2 Serviceability limit state ..................................................................... 18

4 Derivation of forces acting on fasteners ................................... 194.1 General................................................................................................ 194.2 Tension loads ...................................................................................... 194.2.1 Tension loads on fastenings with post-installed fasteners and headed

fasteners .............................................................................................. 194.2.2 Tension loads on fastenings with anchor channels ............................. 214.3 Shear loads.......................................................................................... 234.3.1 Shear loads on fastenings with post-installed and headed fasteners... 234.3.2 Shear loads on fastenings with anchor channels................................. 354.4 Tension forces in a supplementary reinforcement .............................. 36

5 Verification of ultimate limit state by elastic analysis forpost-installed fasteners (mechanical systems) ........................ 41

5.1 General................................................................................................ 415.2 Tension load........................................................................................ 425.2.1 Required verifications......................................................................... 425.2.2 Steel failure......................................................................................... 445.2.3 Pull-out/pull-through failure............................................................... 445.2.4 Conical concrete break-out failure ..................................................... 455.2.4.1 Characteristic resistance of a single fastener ...................................... 465.2.4.2 Effect of spacing and edge distance.................................................... 485.2.4.3 Effect of heavy surface reinforcement (shell spalling)....................... 555.2.4.4 Effect of the eccentricity of the load................................................... 575.2.4.5 Special cases: three or four edges with ci < ccr,n ................................ 595.2.5 Splitting .............................................................................................. 615.2.5.1 Splitting failure during installation of post-installed fasteners........... 615.2.5.2 Splitting failure of loaded post-installed fasteners ............................. 615.3 Shear load ........................................................................................... 635.3.1 Required verifications......................................................................... 635.3.2 Steel failure without lever arm............................................................ 64

V

5.3.3 Steel failure with lever arm................................................................. 645.3.4 Pry-out failure..................................................................................... 655.3.5 Concrete edge failure.......................................................................... 685.3.5.1 Characteristic resistance of a single fastener ...................................... 695.3.5.2 Effect of spacing ................................................................................. 705.3.5.3 Effect of edge distances parallel to the load direction........................ 735.3.5.4 Effect of member thickness ................................................................ 735.3.5.5 Effect of the eccentricity of the load................................................... 745.3.5.6 Effect of load direction ....................................................................... 765.3.5.7 Effect of the position of the fastening................................................. 775.3.5.8 Special case: narrow thin member...................................................... 775.4 Combined tension and shear load ....................................................... 805.4.1 Steel failure decisive for tension and shear load................................. 805.4.2 Other modes of failure decisive .......................................................... 81

6 Verification of post-installed fasteners (chemical systems) forthe ultimate limit state based on the theory of elasticity.......... 83

6.1 General................................................................................................ 836.2 Tension load........................................................................................ 836.2.1 Required verifications......................................................................... 836.2.2 Steel failure......................................................................................... 846.2.3 Combined pull-out and concrete failure ............................................. 846.2.3.1 Characteristic resistance of a single fastener ...................................... 866.2.3.2 Edge distance and spacing.................................................................. 866.2.3.3 Effect of closely spaced fasteners....................................................... 876.2.3.4 Effect of heavy reinforcement (shell spalling) ................................... 886.2.3.5 Effect of the eccentricity of the load................................................... 896.2.3.6 Special case: three or four edges with ci < ccr,Np ............................... 896.2.4 Concrete cone failure.......................................................................... 896.2.5 Splitting .............................................................................................. 896.3 Shear load ........................................................................................... 896.3.1 Required verifications......................................................................... 896.3.2 Steel failure due to shear load without and with lever arm ................ 906.3.3 Concrete pry-out ................................................................................. 906.3.4 Concrete edge failure.......................................................................... 906.4 Combined tension and shear............................................................... 90

7 Verification of ultimate limit state by elastic analysis forheaded fasteners ........................................................................ 91

7.1 General................................................................................................ 917.2 Tension forces in the supplementary reinforcement........................... 917.2.1 Detailing of supplementary reinforcement in case of tension loaded

fastenings ............................................................................................ 917.2.2 Detailing of supplementary reinforcement in case of shear loaded

fastenings ............................................................................................ 927.3 Tension load........................................................................................ 92

VI Contents

7.3.1 Required verifications......................................................................... 927.3.1.1 Fastening without supplementary reinforcement ............................... 927.3.1.2 Fastenings with supplementary reinforcement ................................... 937.3.2 Steel failure......................................................................................... 937.3.3 Pull-out failure.................................................................................... 937.3.4 Concrete cone failure.......................................................................... 937.3.5 Splitting .............................................................................................. 947.3.6 Local concrete break-out (blow-out) .................................................. 947.3.6.1 Characteristic resistance of a single headed fastener.......................... 957.3.6.2 Effect of spacing and further edge distances ...................................... 957.3.6.3 Free component edges ........................................................................ 977.3.6.4 Effect of the bearing area on the behaviour of groups........................ 977.3.6.5 Effect of load eccentricity................................................................... 977.3.6.6 Effect of the position of the fastening................................................. 987.3.7 Steel failure of the supplementary reinforcement............................... 987.3.8 Anchorage failure of the supplementary reinforcement in the

concrete cone ...................................................................................... 987.4 Shear load ........................................................................................... 997.4.1 Required verifications......................................................................... 997.4.1.1 Fastenings without supplementary reinforcement.............................. 997.4.1.2 Fastenings with supplementary reinforcement ................................... 997.4.2 Steel failure of the headed fastener..................................................... 997.4.3 Concrete pry-out failure...................................................................... 997.4.4 Concrete edge failure.......................................................................... 997.4.5 Steel failure of the supplementary reinforcement............................... 997.4.6 Anchorage failure of the supplementary reinforcement in the

concrete break-out body ..................................................................... 1007.5 Combined tension and shear load ....................................................... 100

8 Verification of ultimate limit state by elastic analysis foranchor channels ......................................................................... 101

8.1 General................................................................................................ 1018.2 Tension forces in the supplementary reinforcement........................... 1038.2.1 Detailing of supplementary reinforcement in case of tension loaded

anchor channels .................................................................................. 1038.2.2 Detailing of supplementary reinforcement in case of shear loaded

anchor channels .................................................................................. 1048.3 Tension load........................................................................................ 1048.3.1 Required verifications......................................................................... 1048.3.1.1 Anchor channels without supplementary reinforcement .................... 1048.3.1.2 Anchor channels with supplementary reinforcement ......................... 1058.3.2 Steel failure of channel bolt and channel............................................ 1058.3.3 Pull-out failure.................................................................................... 1058.3.4 Concrete cone failure.......................................................................... 1058.3.4.1 Characteristic resistance of a single anchor........................................ 1058.3.4.2 Effect of neighbouring anchors .......................................................... 106

Contents VII

8.3.4.3 Effect of edges of the concrete member ............................................. 1088.3.4.4 Effect of a corner of the concrete member ......................................... 1098.3.4.5 Effect of dense surface reinforcement (shell spalling) ....................... 1098.3.4.6 Effect of the anchor channel position ................................................. 1098.3.4.7 Effect of a narrow member ................................................................. 1108.3.5 Splitting of the concrete...................................................................... 1118.3.6 Blow-out failure.................................................................................. 1118.3.7 Steel- and anchorage failure of the supplementary reinforcement ..... 1128.4 Shear loads.......................................................................................... 1128.4.1 Required verifications......................................................................... 1128.4.2 Channel bolt (special screw) and local flexure of channel lip............ 1128.4.3 Concrete pry-out failure...................................................................... 1128.4.4 Concrete edge failure.......................................................................... 1138.4.4.1 Characteristic resistance of one anchor (basic resistance).................. 1138.4.4.2 Influence of neighbouring anchors ..................................................... 1138.4.4.3 Effect of a corner ................................................................................ 1158.4.4.4 Effect of the thickness of the structural component ........................... 1168.4.4.5 Effect of load parallel to the edge....................................................... 1178.4.4.6 Effect of the anchor channel position ................................................. 1178.4.4.7 Effect of a narrow member ................................................................. 1188.4.4.8 Steel and anchorage failure of the supplementary reinforcement ...... 1198.5 Combined tension and shear loads ..................................................... 119

9 Plastic design approach, fastenings with headed fastenersand post-installed fasteners ...................................................... 121

9.1 General................................................................................................ 1219.2 Conditions of application.................................................................... 1219.3 Distribution of external forces to the fasteners of a group.................. 1239.4 Design of fastenings............................................................................ 125

10 Durability ..................................................................................... 12710.1 General................................................................................................ 12710.2 Fasteners in dry, internal conditions ................................................... 12710.3 Fasteners in external atmospheric or in permanently damp internal

exposure and high corrosion exposure ............................................. 12710.3.1 Fastenings in external atmospheric or in permanently damp internal

exposure.............................................................................................. 12810.3.2 Fasteners in high corrosion exposure by chloride and sulphur

dioxide ................................................................................................ 128

11 Exposure to fire........................................................................... 13111.1 General................................................................................................ 13111.2 Basis of design.................................................................................... 13211.3 Resistances under tension and shear load........................................... 13511.3.1 Steel failure under tension load and shear load .................................. 13511.3.2 Steel failure under shear load with lever arm ..................................... 136

VIII Contents

11.3.3 Pull-out under tension load................................................................. 13611.3.4 Concrete break-out under tension load and concrete pry-out failure

under shear load.................................................................................. 13611.3.5 Concrete edge failure under shear load .............................................. 137

12 Seismic loading .......................................................................... 13912.1 General................................................................................................ 13912.2 Additions and alterations to EN 1998-1:2004 (Eurocode 8) .............. 13912.3 Verification of seismic loading ........................................................... 14112.3.1 General................................................................................................ 14112.3.2 Derivation of actions........................................................................... 14212.3.3 Resistance ........................................................................................... 142

13 Outlook........................................................................................ 145

References.......................................................................................... 147

Index................................................................................................... 153

Contents IX

5 Verification of ultimate limit state by elastic analysisfor post-installed fasteners (mechanical systems)

5.1 General

The design provisions of CEN/TS, Part 4, described in the following are valid for post-installed fasteners as shown in Figure 2.1, with exception of bonded fasteners afterFigure 2.1e1. This type of fasteners transfers the loads – in contrast to the remainingfasteners of Figure 2.1 – continuously along the entire embedment depth in theconcrete. This anchorage principle requires special design rules which are describedin Section 6.

For the design of post-installed fasteners (mechanical systems) in the ultimate limitstate, there are three different design methods available in CEN/TS. The methodsdiffer significantly in the degree of simplification at the expense of conservatism. Inmethod A the resistance is established for all load directions and all modes of failure,using actual values of edge distance c to the fasteners and spacing s between fastenersin a group which might be smaller than characteristic values. Characteristic spacingand edge distances are the distances for ensuring the maximum characteristicresistance of a single fastener. Method A is most complex, however, offers almostfor any application possibilities and leads to the best results. In method B one singlevalue of resistance is used for all load directions and modes of failure. This resistanceis related to the characteristic spacing and edge distances and it is permitted to usesmaller values for c and s than these but the resistance should then be modified asindicated – as for method A. Method B is less complex than method A, however,yields more conservative results. The most simple and most conservative designprocedure is method C. It corresponds, in principle, to method B, however, spacingand edge distances below the characteristic values is not permitted. Method C ishardly applied in practice due to its uneconomical results. Though method B offersless uneconomical solutions than method C, nevertheless, compared with method A,method B owns in particular in the design of shear-loaded fastenings considerabledisadvantages. Therefore, method B is infrequently used in practice. Hence, in thefollowing sections only design procedure A is presented.

For post-installed chemical systems, CEN/TS, Part 5 provides only one design method.Its philosophy corresponds to method A for post-installed mechanical systems. Thesame is valid for headed fasteners (CEN/TS, Part 2).

The distance between the external post-installed fasteners of neighbouring post-installedfastener groups or the distance between single fasteners or the external post-installedfasteners of groups and single fasteners shall be a> scr,N (scr,N¼ characteristic spacing).This corresponds to the necessary minimum distance, to prevent that the load bearingbehaviour of adjacent post-installed fastener groups or single post-installed fastenersdoes not influence mutually (e.g. in case of conical concrete break-out).

The following assumptions in respect to installation have been made in CEN/TS. Priorto drilling of the borehole via visual check it shall be ensured that the concrete has beencompacted adequately in the area of the fastening. The holes are drilled perpendicular

Design of Fastenings for Use in Concrete – the CEN/TS 1992-4 Provisions. First edition.Rainer Mall�ee, Werner Fuchs, Rolf Eligehausen.� 2013 Ernst & Sohn GmbH & Co. KG. Published 2013 by Ernst & Sohn GmbH & Co. KG.

41

to the surface of the concrete by the drilling method specified by manufacturer’sinstructions since the drilling method can essentially influence the load-bearingbehaviour of post-installed fasteners. Deviations from the drilling directions areonly admissible if specifically required by the manufacturer’s instructions. Whenhard metal hammer-drill bits are used, they should comply with ISO or NationalStandards. When diamond core drilling is permitted, the diameter of the segmentsshould comply with the diameter prescribed in the manufacturer’s installation instruc-tions. Reinforcement shall not be damaged during drilling. In prestressed concretestructures it shall be ensured that the distance between the drilling hole and theprestressed reinforcement is at least 50mm. Boreholes are to be cleaned according tothe manufacturer’s installation instructions. Aborted drill holes which are filled withhigh strength non-shrinkage mortar do not have to be considered in the design of thefasteners. This assumption is acceptable because the filled borehole for example in caseof a shear load directed to the aborted hole will have similar characteristics as the intactadjacent concrete.

As a matter of principle inspection and approval of the correct installation of thefasteners is carried out by appropriately qualified personnel.

5.2 Tension load

5.2.1 Required verifications

Post-installed fasteners fail under tension load by steel rupture, pull-out/pull-through,originate a conical concrete break-out or split the concrete component (Figure 5.1). Steelfailure (Figure 5.1a) is characterized by fracture in the shaft or the thread area or byrupture the sleeve. Steel failure constitutes to the greatest possible resistance of a fastener.

Pull-out failure (Figure 5.1b1) is a failure mode where the complete fastener is pulledout of the borehole. The concrete close to the surface might be also damaged. Theinfluence on the resistance of this secondary damage can be neglected. Pull-outfailure can be expected for torque-controlled expansion fasteners in which theexpansion force is too small to anchor the fastener in the borehole or for fastenerswith insufficient follow-up expansion. Furthermore pull-out failure can occur if theexpansion force of displacement controlled fasteners is too small. Pull-throughfailure (Figure 5.1b2) appears only in case of properly functioning torque-controlledexpansion fasteners. Then the expansion cone is pulled through the expansion sleeveor expansion segments. This behaviour complies with the working principle of thistype of fasteners. Due to reasons of simplification CEN/TS does not distinguishbetween the failure modes pull-out and pull-through. The common term used for bothfailure modes is pull-out.

In case of conical shaped concrete break-out the fastener separates a concrete conefrom the base material (Figure 5.1c1). If, however, fasteners are commonly loaded by asteel plate and grouped with small spacing the individual failure cones overlap and acommon concrete break-out cone develops (Figure 5.1c2). If a fastener is positionedclose to the edge of a concrete component, then a complete concrete cone cannot form(Figure 5.1c3).

42 5 Verification of ultimate limit state by elastic analysis for post-installed fasteners

Fig. 5.1 Failure modes of post-installed fasteners under tension load

(a) steel failure

(b1) pull-out failure

(b2) pull-through failure

(c) conical concrete break-out failure

(d) splitting failure

5.2 Tension load 43

Splitting failure is a failure mode in which the concrete component splits completely(Figure 5.1d1) or the concrete fractures along the fastening and the edge of theconcrete element (Figure 5.1d2). In case of large distances to the edge splittingcracks might develop between closely spaced fasteners during installation(Figure 5.1d3).

In general, it cannot be predictedwhich of the abovementioned failuremodeswill governthe load-bearing capacity of a fastening. Therefore all failure modes must be verified fordesign method A. In case of steel failure and pull-out or pull-through the resistanceis neither influenced by neighbouring post-installed fasteners nor by component edges.For fastener groups the verification of these failure modes is performed for the mostloaded single fastener. On the other hand spacing and edge distances are of majorinfluence on the load-bearing capacity of fasteners in case of conical concrete break-outas well as splitting failure. Therefore, the verification shall be done for thewhole fastenergroup if these failure modes occur.

5.2.2 Steel failure

The characteristic resistance of a post-installed fastener in case of steel failure is givenin the relevant European Technical Approval. The strength calculations are based onfuk. The steel resistance of a fastener is:

NRk;s ¼ As � f uk (5.1)

with:

As net cross section of the post-installed fastener, tensioned cross section for threadedparts

fuk tensile steel strength

Bolt-type post-installed fasteners show a non-uniform cross section along the fastenerlength. In the upper area these post-installed fasteners have a thread with a smoothshaft following below. At the end of the bolt there is a conical segment with reducedcross section. All three areas can show different cross sections which for cold-formedfasteners might also indicate different tensile strengths. This is checked in theapproval tests and the typical resistance given in the ETA is the smallest resistanceof these three areas.

5.2.3 Pull-out/pull-through failure

The characteristic resistance in case of pull-out/pull-through failure is given in therelevant ETA. This value cannot be calculated but only determined in elaborate testseries. In general, the value of the ETA is valid for the concrete strength class C20/25.For higher concrete strength classes (in general up to C50/60) the ETAs provideindividual enlargement factors for each concrete strength class.

In the ETA it is noted, if no pull-out or pull- through failure appears. Then thisverification does not have to be performed.

44 5 Verification of ultimate limit state by elastic analysis for post-installed fasteners

5.2.4 Conical concrete break-out failure

Most post-installed mechanical fasteners subjected to tension loads fail by cone-shapedconcrete break-out. The break-out bodies of different post-installed fasteners aresimilar. The slope of the surfaces of the cones is not constant over the embedmentdepth and the circumference and varies from test to test. The average slope as measuredfrom the horizontal lies between 30 � and 40 � and is on average about 35 �. As depth ofthe break-out cones the anchorage depth hef can be assumed as simplification. Then thediameter of a break-out cone is about three times the embedment depth of the post-installed fastener (Figure 5.2, on top).

The characteristic resistance of a group with post-installed fasteners failing by conicalconcrete break-out is influenced by numerous parameters. First there are the concretestrength and the condition of the concrete (cracked or uncracked) as well as theembedment depth of the post-installed fastener. Moreover, the spacing to neighbouringfasteners within a fastener group as well as the distances to the free edges of theconcrete component affects the characteristic resistance. Finally a possible eccentricityof the load within a group as well as an unfavourable strong surface reinforcement

A c,N

3 · hef

N

1.5 · hef 1.5 · hef

3 · hef

hef 35°

°

Fig. 5.2 Concrete break-out cone (schematically)

(Fuchs, Eligehausen, and Breen (1995))

5.2 Tension load 45

shall be taken into account. The characteristic resistance of a group with post-installedfasteners can be calculated after Equation 5.2:

NRk;c ¼ N0Rk;c �

Ac;N

A0c;N

� cs;N � cre;N � cec;N N½ � (5.2)

The different factors of Equation 5.2 are explained in the following.

5.2.4.1 Characteristic resistance of a single fastenerActually by use of realistic assumptions for the concrete characteristics it is possibleto calculate numerically the load-bearing capacity of a single post-installed fastenerwith the failure mode concrete break-out with sufficient accuracy. Indeed, the effortsfor these numerical investigations (e.g., calculations FEM) are very high. Hence,usually the resistance for concrete break-out failure is determined empirically on thebasis of test results. The results of a very big number of test series and single testsform the basis of the approach for the characteristic resistance of a post-installedfastener with conical concrete break-out used in CEN/TS (Equations 5.2a1 and5.2a2). Furthermore they consider the knowledge of the non-linear fracture mechan-ics (Rehm, Eligehausen, and Mall�ee (1992)). The equations are valid for single post-installed fasteners which are not influenced by neighbouring fasteners or componentedges.

Cracked concrete:

N0Rk;c ¼ kcr �

ffiffiffiffiffiffiffiffiffiffiffiffiffif ck;cube

q� h1:5ef ½N� (5.2a1)

Uncracked concrete:

N0Rk;c ¼ kucr �

ffiffiffiffiffiffiffiffiffiffiffiffiffif ck;cube

q� h1:5ef ½N� (5.2a2)

with:

kcr product specific factor for cracked concretekucr product specific factor for uncracked concretefck,cube characteristic concrete compressive strength [N/mm2] for cubes with a side length

of 150mm considering the limitations given in the relevant ETAhef embedment depth of the fastener [mm]

The product specific factors kcr and kucr are given in the respective ETA. They differ notsubstantially for the individual types and sizes of post-installed fasteners. As a rule formechanical post-installed fasteners they are kcr¼ 7.2 und kucr¼ 10,1. The characteris-tic resistance in cracked concrete is lower than in uncracked concrete. This is causedmainly by the disturbance of the stress condition in the cracked concrete in the vicinityof the fastener. In uncracked concrete a tension load on a fastener generates arotationally symmetric stress pattern around the fastener. Equilibrium is provided

46 5 Verification of ultimate limit state by elastic analysis for post-installed fasteners

by the hoop stresses in the concrete (Figure 5.3a). If the fastening element is located in awide crack, no tension forces can be transferred vertically to the crack. Hence, the crackcauses a change of the stress distribution in the concrete (Figure 5.3b) and reduces thesurface area available for the transfer of the tension forces. After this model onereceives two independent concrete break-out bodies which are in contact in the area ofthe crack in the component.

Besides the described disturbance of the rotation-symmetrical stress condition incracked concrete for undercut fasteners and displacement controlled fasteners theinterlocking surface is decreased by the crack. In case of torque controlled expansion

(a) N

Crack plane

(b)N

Fig. 5.3 Influence of a crack on the stress distribution in the area of a headed fastener under tensionload

(a) uncracked concrete

(b) cracked concrete

5.2 Tension load 47

fasteners the opening of the crack causes a reduction of the expansion forces. In case ofpost-installed expansion fasteners suitable for applications in cracked concrete,however, the reduction of the expansion forces is compensated by the fact that theexpansion plug is pulled further into the expansion sleeves while the crack opens. Thisbehaviour is called follow-up expansion.

5.2.4.2 Effect of spacing and edge distance

SpacingThe term Ac;N=A

0c;N in Equation 5.2 considers the effect of spacing and edge distances

on the characteristic resistance for conical concrete break-out.

If fasteners within a group are installed with spacing that corresponds at least to thediameter of the break-out cone, then the break-out cones of neighboring fasteners(Figure 5.4a) do not overlap and the characteristic resistance of the group correspondsto n-times the resistance of a single fastener (n¼ number of the post-installed fastenersof the group). The corresponding characteristic spacing is scr,N and amounts toscr,N¼ 3 � hef. If the spacing is smaller than the characteristic value, the concretebreak-out cones overlap (Figure 5.4b) and a common break-out body develops. Thenthe fractured surface available for the load introduction into the concrete is smaller thanthe sum of the fractured surfaces of the same number of single fasteners. Therefore thecharacteristic resistance decreases.

Theoretically it is possible to determine the effect of spacing within a fastener group onthe characteristic resistance by comparison of the fractured surface of the group withthe sum of the fractured surfaces of the same number of single fasteners. However, thecalculation of overlapping cone surfaces is rather complex. Therefore, the approachdescribed in CEN/TS assumes simplified and idealized concrete break-out bodies. It isbased on a proposal by Fuchs (1991) and Fuchs, Eligehausen, and Breen (1995). Thedesign method is called CC-method (Concrete Capacity Method) and has been adoptedin many design provisions since then. It is based on k – method which is described inEligehausen, Mall�ee, and Rehm (1997).

The CC-method substitutes the break-out cone with a pyramid with the base lengthscr, N and the height hef. For the idealized break-out body the base area A0

c;N on theconcrete surface is quadratic (Figure 5.2). Is this area available on the surface of thecomponent, a fastener reaches his maximum resistance for concrete break-out afterEquation 5.2a1 or Equation 5.2a2. The influence of spacing on the characteristicconcrete break-out resistance of a fastener group is taken into account by the factorAc,N/A

0c;N . Then the break-out resistance increases in proportion to the base area of the

fastener group. Figure 5.5 shows examples for the determination of the base areas of theidealized break-out bodies for different fastener groups. In CEN/TS the base areas ofone pyramid or the base areas of overlapping pyramids are called projected area.

In the following the CC-method is explained with the help of an example (Figure 5.6a).The embedment depth of the post-installed fasteners is hef¼ 80mm. Then thecharacteristic spacing is scr,N¼ 3 � hef¼ 240mm. The projected area of the idealizedbreak-out body of the group shown in Figure 5.6a amounts to Ac,N¼ 171 600mm2 and

48 5 Verification of ultimate limit state by elastic analysis for post-installed fasteners

theprojectedareaofasinglepost-installedfastenerisA0c;N ¼ (scr,N)

2¼ 2402¼ 57 600mm2.With this, the factor Ac;N=A

0c;N ¼ 2:98, that is the characteristic resistance of this

fastener group is 2.98-times the value of the resistance of a single fastener. Thereforein this example the effect of the spacing in two directions compared with the sum ofthe resistance of 4 single fasteners reduces the resistance of the quadruple fasteningby approximately 25%.

This approach is only valid if the spacing between the individual anchors of a group isless than scr,N¼ 3 � hef. For greater spacing the break-out cones of adjacent fastenersdo not overlap and the spacing is without effect on the resistance of the fastening.

1.5 · hef s < 3 · hef 1.5 · hef

hef

N

(b)

3 · hef

Ac,N

Ac,N(a)

hef

N

1.5 · hef 3 · hef 1.5 · hef

3 · hef

Fig. 5.4 Influence of fastener spacing on the break-out body of a double fastening

(a) spacing s¼ 3 � hef(b) spacing s< 3 � hef

5.2 Tension load 49

Ac,N = (scr,N + s) · scr,N

s scr,N

s 0.5·scr,N0.5·scr,N

scr,N

Ac,N

(a)

Ac,N = (scr,N + s1) · (scr,N + s2)s1, s2 scr,N

0.5·scr,N

0.5·scr,N

s2

s1 0.5·scr,N0.5·scr,N Ac,N

(b)

Ac,N = (scr,N + s1,1 + s1,2) · (scr,N + s2)s1,1, s2,2, s2 scr,N

0.5·scr,N

0.5·scr,N

s2

s1,1 0.5·scr,N0.5·scr,N s1,2 Ac,N

(c)

Fig. 5.5 Definition of the base area of the idealized concrete break-out body for different

arrangements of fasteners

(a) double fastening

(b) quadruple fastening

(c) fixture with six fasteners and with different spacing s1,1 and s1,2

50 5 Verification of ultimate limit state by elastic analysis for post-installed fasteners

An example is given in Figure 5.6b. The horizontal spacing is s1¼ 300mm. This valueis greater than the characteristic spacing scr,N¼ 240mm. This means that the base plateis fastened by two double fastenings which act independently. The base areas of each ofthe two double fastenings is Ac,N¼ 93 600mm2 and A0

c;N ¼ 2402 ¼ 57 600mm2. Theratio of the base areas is Ac;N=A

0c;N ¼ 1:63; that is, the characteristic resistance of each

double fastenings is 1.63-times the value of a single fastening.

(a)

Ac,N = (0.5 · ssr,N + s1 + 0.5 · ssr,N) · (0.5 · ssr,N + s2 + 0.5 · ssr,N) = (120 + 200 + 120) · (120 + 150 + 120) = 171 600 mm2

200 120 120

120

150

120

(b)

Ac,N,1 = Ac,N,2 = ssr,N · (0.5 · ssr,N + s2 + 0.5 · ssr,N) = 240 · (120 + 150 + 120) = 93 600 mm2

300

150

120

120

240 240

Fig. 5.6 Determination of the base area of the idealised concrete break-out body at the example

of a quadruple fastening (embedment depth hef¼ 80mm)

(a) spacing s1 and s2 smaller than scr,N¼ 240mm

(b) spacing s1> scr,N¼ 240mm

5.2 Tension load 51

A simple and easy to understand geometrical model which can theoretically be usedto design a myriad of applications with post-installed fasteners even in cases, whichare beyond the area of application of CEN/TS (Figure 2.4) forms the basis of the CCmethod. Its validity was verified for groups with up to 36 fasteners (Eligehausenet al. 1992)). It is valid also for groups with variable spacing. Figure 5.7 showsexamples. In Figure 5.7a all spacing of the group are smaller than the characteristicvalue scr,N; in Figure 5.7b, however, the spacing s1,2 is bigger, that is, the base plate isfixed by two separate fastener groups.

(a) s1,1, s1,2, s2,1, s2,2 scr,N

s1,1 s1,2

s2,1

s2,2

Ac,N = (0.5·scr,N + s1,1 + s1,2 + 0.5·scr,N) · (0.5·scr,N + s2,1 + s2,2 + 0.5·scr,N)

(b) s1,1, s2,1, s2,2 scr,N; s1,2 > scr,N

Group 1: Ac,N = (0.5·scr,N + s1,1+ 0.5·scr,N) · (0.5·scr,N + s2,1 + s2,2 + 0.5·scr,N) Group 2: Ac,N = scr,N · (0.5·s cr,N + s2,1 + s2,2 + 0.5·scr,N)

s1,1 s1,2

s2,1

s2,2

Group 1

Group 2

Fig. 5.7 Examples of fastener groups with different spacing

52 5 Verification of ultimate limit state by elastic analysis for post-installed fasteners

Edge distancesThe geometrical influence of component edges on the characteristic resistance withconical concrete break-out (Figure 5.8) can be also described with the help of theCC-method. If the edge distance of a fastener corresponds to the radius of the failurecone, the cone is tangent to the edge (Figure 5.8a) and the load-carrying capacitycorresponds to the value of a one single fastener. If the edge distance is reduced (seeFigure 5.8b), then failure cone and edge overlap and the characteristic resistancedecreases. The influence can be described – as in case of spacing – by comparison ofthe base area of the idealized (truncated) break-out body with the base area of a singlefastener which is not influenced by spacing or edge distances. Figure 5.9 explains theapproach at the example of a single post-installed fastener at the component edge (Figure5.9a) and a quadruple fastening positioned in the corner of a component (Figure 5.9b).

Figure 5.10 shows the approach for a group with two post-installed fasteners in thecorner of a component. In the example post-installed fasteners with an anchorage depthhef¼ 80mm are assumed. In Figure 5.10a the spacing is s< scr,N and in Figure 5.10b thespacing is larger. In the first case the break-out cones of both fasteners overlap and inthe second they are separate.

The geometrical influence of the overlapping of the failure cones with componentedges is described by the comparison of the base areas. In addition, it is to be noted, that

(a)

c = 1.5 · hef 1.5 · hef

3 · hef

N

Ac,N

(b)

3 · hef

hef

c 1.5 · hef

N

Ac,N

Fig. 5.8 Influence of a component edge on the shape of the concrete break-out cone

(Fuchs, Eligehausen, and Breen (1995))

(a) fastening with an edge distance c¼ 1.5 � hef(b) fastening with an edge distance c< 1.5 � hef

5.2 Tension load 53

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