20Design of resin anchors in comparisonTR 029 can do moreDr. Rainer Malle>Intermsoftheirload-bearingperformance,resin anchorsdifferinanumberofpropertiesfromundercut and expansion anchors. This means that specific rules and regulations must be taken into account and observed in their design. The Technical Report 029 lists these diffe-rences and new findings drawn from basic research in a separate document.Metal fixings with European Technical Approval (ETA) for use in concrete are designed and dimensioned according to Guideline ETAG 001, Annex C1) (in this article referred toasAnnexC).Thismethod,knownasCCMethod, applies to all types of fixings listed and specified in the Guide line and hence also to resin anchors (capsule and injection systems). However, it was found quite early on that resin anchors differ in their load-bearing performance from under cut and expansion anchors. One essential dif-ference lies in the load introduction. Whereas undercut and expansion anchors introduce focused tensile loads into the concrete in the zone of the undercut or the expan-sion shells, resin anchors introduce the load continually over the entire length of the anchoring. This special load-bear ingmechanismisthecauseforthetypeoffailure known as combined failure through pull-out and concrete pry-out which is not observed in the other anchor types. There is no need to prove straight pull-out in resin anchors. Regardless of the carrying mechanism, it is also assumed that resin anchors have no higher concrete pry-out load thanundercutandexpansionanchorssetatthesame anchoring depth. This assumption is taken into account in thedesign by meansofan additionalproofforstraight concrete pry-out.Existing regulations for resin anchors account for these differences from the known design methods1) by way of specialregulationsinthetextoftheapproval.This approach is unsatisfactory and prone to errors because twodocumentsneedtobeobservedandcombined. Fig. 1: Group of 8 anchors covered by TR 029. Fig. 2:Steel failure and concrete failure on the side facing away from the load (pry-out): all anchors take the load.VSd,h VSd VSd,v VSd,v /4VSd,h /4VSd,h /4VSd,v /4VSd,h /4VSd,h /4Anchor plateAnchor21 DESIGNThis is why the Anchors study group at the European Organisation for Technical Approvals (EOTA) has worked out a separate document known as the Technical Report TR 029 Design of Resin Anchors2). Next to the above departures from the previous design methods, the report alsoaccountsfornewfindingsandresultsfrombasic research which have evolved over the past ten years since the publication of Annex C. The most important changes in TR 029 versus Annex C are discussed below.ScopeThedesignconceptappliedtodaterestsonempirical data with resin anchors which have a bonding strength of as much as 15 N/mm2 and with an anchoring depth of about eight to twelve times the anchor diameter. In con-trast,theTR029isalsovalidforresinanchorswitha higher bonding strength, and the scope has been enlarged to include anchoring depths ranging from 4 d to 20 d. This regulation allows injection anchors to be set at vari-able anchoring depths and so to use an important advan-tage over other types of anchors. AnnexCappliesbothtosingleanchorsandtoanchor groups with 2, 3, 4 and 6 fixings. As the distribution of the shear loads over the individual anchors of group can-not be predicted clearly because of the usual hole clea-rance, groups of three or six may be used only if their edge spacing c in all directions is c 10 hef. Comparative com-putations have shown that, with such large edge spac ings, anchors exposed to shear loads fail through steel failure and not as a result of concrete edge failure.The scope of the TR 029 has been enlarged to include groups with 8 fixings (Fig. 1) set in square or rectangular configuration. Also, groups with 3, 6 and 8 fixings can be arranged near the edge (c cmin) if no shear loads act on the fixings. As before, the edge spacing in this group under shear loads must be c 10 hef in all directions and an additional c 60 d (d = diameter of the threaded rod). The second condition has been introduced because short and thick resin anchors are permitted due to the variable anchoring depth. Limiting the edge spacing to multiples of the anchoring depth alone would in these cases not guarantee steel failure.Fig. 3:Concrete edge failure under shear load at right angle to the edge: only the most unfavourable anchors take the loads.Fig. 4:Concrete edge failure under shear load parallel to the edge: all anchors take the load.EdgeVSd,v VSd,v /2VSd,h EdgeVSd,h /4 VSd,h /4Loads not taken into account in the proofforconcreteedgefailure.22Distribution of shear loadsThe distribution of the shear loads over the individual fix-ings of a group is more clearly defined in the TR 029 than inAnnexC.Althoughtheauthorbelievesthatthereis nochangefromAnnexC,thisregulationwillagainbe describ ed in detail.The distribution of the shear loads depends on the type of failure. In the event of steel failure and concrete failure on the side facing away from the load (pry-out), it is assum-ed that all the fixings of the group will take up shear loads (Fig. 2) provided that the diameter of the holes in the fix-ture does not exceed the values specified in TR 029, Table 4.1. The theory of elasticity applies in the event of eccen-tric load exposure.For proofs of concrete edge failure and shear loads per-pendicular to the edge, the hole clearance causes only the most unfavourable fixings to take up the shear loads (Fig. 3). If the shear load acts parallel to the edge, all the fixings of the group will be involved in taking up the load (Fig. 4), and only the shear loads near the edge (red) will be used for proving the concrete edge failure. Both the shear loads remote from the edge have no influence on the failure load of the unfavourable fixings close to the edge. Fig. 5 shows the distribution for a shear load inclined in relation to the edge of the component. For the proof of the concrete edge failure, it is again only the loads in the figure on the right (red) which are taken into account.Shear loads with lever armWith a mortar compensating layer between concrete and fixture greater than 3 mm, the existing regulation provides for a bending proof to be made for the fixings. This is often difficult in practice as such thin layers can be achiev ed and maintained only in rare cases. In the TR 029 this limit thickness has been enlarged to d/2, but it is still relatively small. There is an urgent need for further research in this field.In stand-off or spaced installations, the degree of restraint M allows a restraint of the fixing into the fixture to be taken into account, provided that the fixture is capable of taking up the developing moment. With a full restraint (M = 2.0) this leads to the halving of the bending moment acting on the fixing. Although this regulation has not been changed with respect to Annex C, experience has shown that it often leads to misinterpretations in practice be cause it is often assumed that an anchor plate resting on a pres-sure-resistant mortar compensating layer already causes the full restraint of the fixing. In the opinion of the author, which is shared by others, this cannot be assumed if a hole clearance exists between the fixing and the fixture. This hole clearance can cause the fixing to rotate to some degree in the region of the fixture, with the effect that the restraintmomentisnoticeablyreduced.Thedegreeof restraint should in these cases not differ substantially from the value of free rotation (M = 1.0), and the fixing would be overloaded if full restraint is assumed in arithmetical terms. This is the reason why Annex C and the TR 029 specifyfurtherconditionsforthedegreesofrestraint M > 1.0. The hole clearance must be smaller than the maximum value given in Table 4.1 of the Guidelines, or the fixing must be clamped (countered) against the fix-ture using a nutand washer. Thefirstof these require-ments is most likely quite difficult to observe in building practice, and the second requirement can, by the nature ofthings,notbemetforananchorplaterestingona mortar layer.Fig. 5:Concrete edge failure under inclined shear load: Load component at right angle to the edge is taken up by the anchors set close to the edge parallel to the edge by all anchors.Fig. 6:Failure of a group of two resin anchors with small axial spacing; combined failure through pull-out and concrete break-out3).EdgeVSd,h VSd VSd,v VSd,v /2VSd,h /4 VSd,h /4Loads not taken into account in the proof for concrete edge failure.Surface of the break-out element23 DESIGNProof of combined failure through pull-out and concrete pry-out under tensile loadThe equation for the characteristic resistance NRk,p with the combined failure by pull-out and concrete breakout is similar to the equation for the characteristic resistance in concrete breakout according to Annex C:(1)It differs from the equation for concrete breakout only by the group factor g,Np and by the absence of the factor ucr,N,whichaccountsforthepositionofthefixingin crack ed or non-cracked concrete. The position of the fixing istakenintoaccountinthebasevalueN0Rk,pofthe resis tance of a single anchor which, assuming a constant bond ingtensionovertheentireanchoringlength,is calculated according to the following equation:(1a)For the application in non-cracked concrete Rk = Rk,ucr is used, and Rk = Rk,cr in cracked concrete. The influenc-ingareasAp, NandA0p, Naredeterminedasbefore, al thoughthecharacteristicaxialspacingscr,Npisnota multiple of the anchoring depth hef, but instead depends on the characteristic bonding tension Rk,ucr The assump-tionsaccordingtoAnnexCremainunchangedforthe factors s,Np, ec,Np and re,Np.The group factor g,Np accounts for the influence of the surface of the breakout body in groups of anchors. If two resin anchors are arranged at an axial spacing of s = d (Fig. 6),thecharacteristicresistanceofthisgroupoftwois roughly equal to the value of a single anchor according to equation (1). In reality however, the bonding area is larger than that of a single anchor. This is taken into account by means of the group factor according to3) which is:(2)where: s = axial spacing, for anchor groups with several differentaxialspacings(e.g.groupsoffourorsix),the mean axial spacing is used(2a)n = number of anchors in the groupk = 3.2 for applications in non-cracked concretek = 2.3 for applications in cracked concreteRk and fck,cube [N/mm], hef and d [mm] acc. to ap provalProof of concrete pry-out under tensile loadAs mentioned above, the TR 029 demands an additional proof for concrete breakout to limit the resistance of resin anchors to the value of undercut and expansion anchors with the same anchoring depth. This proof does not differ from the corresponding assumption in Annex C, although the factor ucr,N. is ignored. The difference in resistance betweennon- crackedandcrackedconcreteisagain accountedforintheequationfortheresistanceofa single anchor.Fig. 7:Group of two, under torsion load: shear loads changing their direction.1 2Ts=> V1=T/sV2= T/s24Proof of splitting under tensile loadAnnex C states that proof of splitting in non-cracked con-crete may be waived if the edge distance of the fixing in all directions is c 1.5 ccr,sp and if the component thick-ness is h 2 hef. This regulation makes sense for undercut and expansion anchors because their minimum compo-nent thickness is about twice the anchoring depth. Resin anchors, on the other hand, can be set in thinner building components. The required component thickness depends only on the cover of the drill hole on the side facing away from the anchor which, in turn, must be sufficiently large to avoid spalling or pry-out on the back of the component during the drilling operation. For this reason, the factor h,spfortheinfluenceofthecomponentthicknesson thesplittingresistanceandtheconditionsforwaiving the proof of splitting in non-cracked concrete has been chang ed from Annex C (c 1,2 ccr,sp and h 2 hmin).Proofofconcretefailureattheload-opposingside (pry-out) under shear loadThe proof of concrete failure on the side facing away from theloadhasbeensupplementedwithaproofforthe mostunfavourableanchorinagroup.Thisproofhas beenleftoutinAnnexCbecausenotorsionmoments were taken into account during its preparation. If shear loads and/or torsion loads act on a group of anchors, the direction of the forces acting on the anchors of the group may reverse. Fig. 7 shows this by way of a group of two, loaded with a torsion moment. The equation for the proof of the anchor group according to Annex C is unsuitable inthiscasebecausethetwoshearforcescanceleach other out and the impact effect is therefore VSd = 0. The TR 029 therefore introduces the proof for the most un-favourable anchor of the group. It uses the same equa tion as for the anchor group, although the influencing areas Ac,N and A0c,N are calculated for each single anchor in-cluding the edge distances and axial spacings. Examples are shown in the TR 029, Fig. 5.5b.Proof of concrete edge failure under shear loadThe known equation from Annex C essentially applies for the proof of the concrete edge failure, although the as-sumptions for V0Rk,c and ,V are changed and the factor ucr,V is renamed re,V. According to4), the characteristic resistance of a single anchor V0Rk,c is:(3)where: k1 = 2.4 for applications in non-cracked concretek1 = 1.7 for applications in cracked concrete(3a)(3b)d, hef and c1 [mm], fck,cube [N/mm]Equation(3)deliversmorerealisticresultsthanthe pre viousequationinAnnexCandnolongeroverrates the resistance for anchors with a diameter d > 25 mm. Diameters of this size are not unusual in resin anchors.Factor ,V according to4) is:(4)Fig. 8:Group of two set at the edge, exposed to inclined shear load and torsion moment.a) ImpactEdgeTVEdgeShear loads ignored. The sum of the components is directed away from the edge.b) Load acting on each anchor25 DESIGNIf one inserts the angle of the shear load at V = 90 in equation (4) (load parallel to the edge), then ,V = 2.5 and is therefore greater than the corresponding value accord-ing to Annex C (,V = 2.0). Also, unlike in Annex C, ,V is limited to the angle V 90 Shear load components pointing away from the edge (V = 180) may be ignored in the proof for concrete edge failure. An example is shown in Fig. 8. Under the previous regulation, they had to be takenintoaccountandthefactor,Vwassetfor ,V = 2.0.OutlookBesides a number of special features inherent in resin an-chors, the new Technical Report TR 029 Design of Resin Anchors also considers the state of engineering in the design and dimensioning of fixings. It seemed obvious, therefore, to transpose this state also to other metal an-chors such as undercut and expansion anchors. As a result, Annex C (1998) has meanwhile been revised by the EOTA Anchors study group and has since been approved in February 2008 by the Technical Steering Committee of the EOTA5).EuropeanOrganisationforTechnicalApprovals (EOTA):Leitliniefrdieeuropischetechnische ZulassungfrMetalldbelinBeton.AnhangC: BemessungsverfahrenfrVerankerungen.Mit-teilungen.DeutschesInstitutfrBautechnik, 28. Jahrgang, Sonderheft Nr. 16, Berlin, Dezember 1997. EuropeanOrganisationforTechnicalApprovals (EOTA):BemessungvonVerbunddbeln.EOTA Technical Report TR 029, Brssel 2007. Eligehausen, R.; Appl, J. J.; Lehr, B.; Meszaros, J.; Fuchs, W.: Tragverhalten und Bemessung von Be-festigungenmitVerbunddbelnunterZugbean-spruchung, Teil 2: Dbelgruppen und Befestigungen amBauteilrand.Beton-undStahlbetonbau100, Heft 10, S. 856 bis 864. Hofmann,J.:TragverhaltenundBemessungvon Befestigungen am Bauteilrand unter Querlasten mit beliebigem Winkel zur Bauteilkante. Dissertation, Lehrstuhl fr Werkstoffe im Bauwesen, Universitt Stuttgart, 2004. Bernholz, M.: Kurzbericht ber die 60. Sitzung des TechnischenLenkungsausschussesderEOTA (EOTA Technical Board) am 6./7. Februar 2008 in Brssel. Mitteilungen. Deutsches Institut fr Bau-technik, 39. Jahrgang, Heft 2, Berlin, April 2008..Edgec) Load acting on anchor group