anchor bolts - concrete capacity design.pdf

I Title n o 9269

Code Background Paper:*

Concrete Capacity Design (CCD) Approach for Fastening to Concrete

A tucrfiendh high/) rransparenr modeljor rhc design ofpossinnalIed specified installation torque is applied Ihereby. one cone or rs or cnrt.hploce headed sruds or bola renned rhe concrete, sign ICCD) oppmoch ispnscrircd. Tu appmach ircompared

*nown pmvisionr o/'AC,!,34fE T h r ~ c of both nuthods to rr conc~i~/ni l trre load of'/faeningr i= y + k r c d r o n m t i under

o r ~ i c loa& for iizporra"r & ~ ~ C ~ I I O N u crnp~md %riables rded si& anchors a$+ f&K&d ;l+ori 10 I@ edge. &chm gmups.

re~rr io~ loading and ihea<ldnding Ad+ b~thcludfig a p p m d ~ e l y 12W Eirmpcnn nndAtnericM'r~5rsw~ ~13ufc'$ F e c+puiwn shows rltm rhe C'CD,,prhod y accumrely prcdicl h e con~n(c/allrur loud of

enbtgs /or the full range ?/ Invcrrigmed npplicorions On Jle orhcr d. de&dina dn rhc a ~ o l i c d . r i o ~ I ~ oucsrion. the ~ i i d i d o ~ $ACX 349

" increased use of metallic anchoring systems Currently em-

' ployed are cast-in situ anchors such ? headed studs [Fig l(a)] or headed bolts and fastening systems to be in-. stalled in hardened concrete. such as torqueanrrotled expansion anchors [Fig l(b)l. deformation-controlled expan.. sion anchors [Fig. I(c)], undercut anchors f ig . 1(d)], and adhesive anchors [Fig. I(e)l

-elements are fastened to the formwork &d cart into the concrete. A common example is a plate with weided-on headed studs Fig,: ](a)] which produces he- chanicai interlocking with the concrete., f&&&&& anchors can be fasrencd in almost any posi-

tion desired in hardened concrete by installing them in a hole drilled after concrete curing. A distinction is dra& between

@eta1 exbansion ancho@ndercut anchor?@nd , . . bonded in- chon. according to their principles of'opention.

produce expansion forces &d thereby (frictional) holding forces in the conk te base &erial,, Wirh torque.controlled expansion anchors f i g , l(b)!. a - . . .$;::.,;:;i.:,.:.: i,...., :,. ,;;; , , : . ;;,.;.., :.<%;;<,~; :.;.< :::~,;, .:

ACI .. Structural . ., Journal / January-Feb~ary !995 .__. . ,.

- . . . two cones. &co+ng to the type of anchor, idare drawn into the expandins sleeve, or segments Tbrque~controlled an- chok should expand further under load ~efomation trolled anchors [(Fig l(c)] are expanded by driving the into the sleeve [dropin anchor,'~ig l(cJ or onto the con [Fig, i(cz), (self-drilling inchor) and Fig. 1(c3) (steel chor)] through a specified displacement Deformation-con trolled anchon cannot exuand further under. load., 0 are anchors with parts that spread and

mechanically interlock with the concrete base material Af- ter ~roductidn of the cvlindrical hole bv drillinrr. the under- -. . : ., cutting is produced in a second opention before installation ,$. of the anchor Fig. I(d,) chiough l(dJ or during ihtallation '2 : of the anchor$@(&f~&$~d5)] . . *.. . ... ' ~ u c h lower expansion forces are hdduced duling installation andloading than with expansion anchors.. In fact, certain undercut anchors can act. . - ' virtually identically to cabin anchors if' the angle and diam- : eter at the undercut are within certain limits., 0 q [Fig l(e)] de-

pends on gluing together a threaded rod and the wall of the drilled hole with reacting resins Ihe load is transferred to the concrete base material by chemical bonding. Adhesive anchors ar i not covered in this paper:.

Fig 2). each with very different loaddefomtion patterns, as shown in Fig 3 Fig 3 is valid for anchors with relatively low remaining pmtnssing

%rmr I h h s i.7 A l ~ m o x ~ ~ i m m n i t ~ r ~ ,y ,he Ilrl,; 11, ~~1~~~~~~~~~~~ C,,?IV, K,n,fcrin~, Gllman?. ilr rrrrilrrl h h df;!ltmm JCRW hl <isilrnfi~srr;nx fmnr rho Uniwrdc~ of

Xorl.!nthhr and P1,lJ fnmr thr U u i w r ~ i r ~ Swpnn Genna,,c Ajlrr a purrdodnrol /dl"" d>ip 01 ,In< uUiver,rit! <f n,rtu 0, A"n i ,~ he ]##i",d iri11i. it< I,<,., <,",d"c,,cr rcscwx h md ,, dnm * ~ I o w i % <I! on to~?ics m h t d t,, rc, hr8;qws fo,Jmt# ah8 to con.. rnrr llc ir snrn!br r f lA( l V 5 In.l?oln$r to C'iw,m

Ifa) -Fa'orre~ttr~g I) steins headed rmds

. ,, b t 1 bz b 3 )

. rg I(h) ---Ftelre,tirrg s,yrte~rrs: rorqlte-corr!rolled espairsio~l rtchor (ifpper sketcher rltolv arrerrrbled ortchorr, lower letcher slto~v a ~ ~ c l t o r nretl~a~rien acriotrr)

xce after losses due to rcla.talion and other similar effects lie rnaznilude of the prestressing force will id-e the h v i o r of the anchor RL(~TY~CC levels but has practi. ~ l l y no influence at failurc load I& Prillol~t orprrllrhrouqh failures are failure by sliding outof

-

e fasteni~ig device or parts of it h& concrete (pullQIID by pulling the cone tlp~~&hJ~e sleeve l o u l l t l i r o ~ w i l l ~

11 thc breaking out of a fairly substantial portioti of the sur- undinr! concrete [Fig 2(c)J For defor~~~ation-co~~trolled stcners, only thepullout failure mode is possible,

Fig. I(e) -Fosrenb~g syrrerm boitdedoradl~esive orrctor:s (1~9-dde sketcher sltu~v hole slrape; righr..,ride sketclte,~ rhow iirsrnllcd antho; s)

Forexpansio~~ ancl~ors, thc failure load depcnds on the design of' the expansion nicclianisnl, method of drilling the hole, condition of tlie drilled liole, and deformability of the concrete Currently, i l w e is no esmblished procedure to determine theoretically the ultimate load to bc expected of fas.. teniligs in the pullout or pulltl~rough type of failure It nwst be determined ill co~liprel~ensive prequaiification tests, such ,

ACI Structural Journal 1 January-Feb . , , , , , . . ,.,, : , " , . ::'"',,.: Tm;mnn7n1:,77iii .., , , r , , . . , ,... , .., , . \ . .,,8,,lh;! .,,. ,., , ,. , (..:. .. ... , :r, : '

ing further and developing a higher load capacity. This be., havior is influenced considerably by the installation procedure and is highly undesirable It must be prohibited by performance requirements in prequalification testing of the fastening device

With expansion anchors, the depth of' embedment can control the type of failure. As shown in Fig. 4, there is a critical embedment depth later termed /I+ the effective embedment depth, at which the mode of failure changes fiom concrete failure to pullout. 'This depends on the expansion mechanism and he, is determined in prequnlification tests,,

The concrete bearing area of undercut anchors and headed studs is usually large enough to prevent pullout failure.

re failure by yielding of'the fastening de.. vice or system fastened to the concrete before any breakout of concrete occurs [Fig, 2(a)].

Under conditions that the steel miterial is sufficiently ductile aid the Ienothof the fasteneior attachment over which

Axial Deformation

Fig. 3-Ideali~edload.deformarion curves forfasrenerr under tension load

h e , Embedment Depth

Fig 4--Role oj'effecrive deprk her for expansion anchors

failures are failure by concrete breakout or splitting of the structural concrete member before yielding of the fastener or fastened element [Fig 2(b) and (d)] or by steel failure when the length over which inelastic steel suains appear is rather small..

For nonductile fasteners and cases where the concrete capacity is less ti-& the fastener device capacity, a brittle fail-

* to determine theoretically the failure in the '-type of failure

.. .

. . , . 75

L . 2 c..; c )

Fig. 5-Failrrre mo~felerforfnsto~i~~gr urtdcr. shear loading: (a) steelfniltrre preceded by co~rcrete spall, (6) concrete breakotrt; fc) cow edge . '

[ ~ i g 2(d)l 'This ty n~inintu~t~ values of center-torcenter and edge spacings, as well as c'omponcnt 'tliickness ;\gain, prequalification testing under ASTM ZXXX' is'designed to preclude such failures,

Concrete breakout failure [Fig 2(bI) through 2(b3)] is a very impor@nt practical dcsign case, because many fasteners are mnde such Illat a concrete failure will occur before yield.. ing of steel. lit fasteners with deeper embedment but thinner side cover, concrete blowout [Fig 2(b4)J can govem This latter case is not covered it;'this paper.

. . . .

loading can be observed.. H0wever.a pullout failure may theoretically occur only if the ratio of anchorage depth to anchor diameter is very small and the tensile capacity is very low In contrast. in shear. a brittle concrete failure will occur for fastenings located close to the edge [Fig 5(b)J and cannot be avoided by increasing anchorage deljth. Steel failure, often proceeded by a local concrete spill in 'front of the anchor [Fig S(a)], will be observed for fasteners sufficiently far away from the edge Forthat case, the load-displacement behavior will depend on ductility of tlie anchor steel A concrete-of fastenings located quite far away from the edge [Fig. 5(c)J ntay occur for single anchors and especially for groups of anchors with a small ratio ofembedment depth to anchor diameter and high tensile capacity The critical ratio depends on the anchor strengih. concrete strength, and nurnber and spacing of fasteners This failure mode is not covered in this paper,

I n pmc~icc, nt:t~ty fa~tc~tings or i l t l : ~ ~ l ~ ~ t t e ~ ~ l ~ arc lhccd on a rrour bed. h r this t y e of inst;~llalion. :I grout fa~lure niny occur beforc an! otl~er type of failurc I n this case. thc s1tc:tr 10.~1 tn~tst he tr;urd'erred into the base by bending the anchors 1ltis ma) reduce tltc 1o:td trnnsfcr cap:t<ity when con).. p~rcil to :I hstcning or :~lt:tcltnienl inst:~llcd di~cvtly on tl~e base 1n:1tcrial'1 11e effect of tlie grout bed on load tr:~nsfcr cnpacity is not discussed in this paper

fizm%e ...?.>".- *\,* 1 be ~clcvant literature contail~s several approacl~es for the

calculntion of concrete failure load i n uncrackcd concrete. The most inrportant examples are dcsign reco~~n~endations of ACI Committee 34gS4 PC1 design proccdurc~ that are son~cwltnr sintilnr to those of ACI 349? and tlie'co~tcrete capacity design (CCD) ntethod based on the so-called K-ntctli- od Jevcloped a! the University of S t u t t g i ~ l ~ ~ l'lte CCD method provides a clear visual expl:matio~~ of calculatio~i of the K-factors used in the ~-,method. It contbines~he trails.. parency (ease of visualization of a physical ntotlel. making it readily undc~stood by designers for application) uf the ACI 349 method, accuracy of the ~..nietl~od, and a user-friendly rectang&r failure surface calculalion procedtm.'A comparison of tltc CcD method with the K -method is given in Ref- erences 9 and 10, From this comparison. it is evident that the CCD and K-ntethods p;edict almost identical failure loads.

lniltis paper, t h i pro\;isions of ACI 349-85 in? he CCD metltdd to predict the fastening cap&& of britlle (c&;cte breakout) failures in &cracked concrete arc c,oinpa;ed with a large 'number pf test results 'To f$cilirate direct cotnpsri- son, the capacity reductionfactor $ of ACI 349 and pariinl material safety factor y, of the CCD method k c botil taken . . .. . as I 0 'I'he comparison is lnade for f&tenikgs both under tension load (single fasteners close to and f:tr from tlie'edge, as well as anchor groubs wiih up to 36 fa&ners far fro&the edge) and under shear load toward the edge (single fasteners ind double f'astenings installed close to the edge in wide and narrow as well as thick and thin ntenibcrs) Rased on this comparison, tile accuracy of the two design app~oaches is determined,, . ,

Wl~ile ductility is hiphly desirn e III npplications where there are substantial lire safety concerns. a brittle failure mode covered by a sufficient safety factor is often accept- able In both cases. concrete capacity must be predicted as accurately as possible to insure a ductile failure (ductile de. sign) or sufficiently low probability of failure (hrittlc design). respectively. In many applications, the relevant design methods (ACI 349-85 and CCD method) will predict rather different concrete capacities Therefore, screening of both methods based on an extensive data base is netded Compa- rable earlier studies'' l 2 are based on a small number of test data and did 11; include the newly developed CCD tnct l t~l ,

DESIGN PROCEDURES Fig 6 shows concrete breakout cones for si~tgle anchors

under tension or shear load, respectively. idealized accord ing to ACI 349 From this figure, i t is evident that the concrete cone failure load depends on tensile capacity of the

ACI Structural Journal / January-February 1995

a ) tens ion M

2 axs T*' -..- ; ~ ( j ~ ~ ~ ~ ~ ~ y - br~) . II (4h4 r k & he! i d u 2 . dug 1

4 4 .4 Tr(h;+4duh,C). -tTb2(\tdU; heFi

5 1 2 b - e r

I 4. +.-&..a h..q ,,ze e I

X I * ..*-'&. 1.h. . d.

, . . . ,

the capaciiy when used in uncracked concrete This paper presents the resulu for uncracked concrete only and should be compared with design expressions for uncracked concrete The behavior of anchor groups is infuenced by stiffness of the base plate In this paper, a rigid base plate is presumed and no plastic action of the anchor group is considered

with nuclear.related structures Because of concern with nuclear safety. the phi- losophy of ACI 349 is to design ductile fastenings 10 obtain a limit to guard against brittle concrete failure, the cone model was developed.!,r4 l5

Under tension loading, the concrete capacity of' an arbi.. trary fastening is calculated assuming a constant tensile stress equal to Q . 4 f l acting on the projected area of the failure cone, taking the inclination between the failure sur.. face and concrete surface as 45 deg

Fig 7-Projected areas for mulriple fastenings under tensile loading according to ACI 349 (a) double fastening, (b) quadruple fmtening

N" = fc, AN (1)

with

fc, = 0 4 E = capacity reduction factor, here taken as 1 0

AN i. actual projected area of stress cones radiating '

toward attachment from bearing edge of anchors Effective area shall be limited by overlapping stress cones, intersection of cones with concrete surfaces, bearing area of anchor heads, and overall thickness of concrete member

In the following, it is assumed that member thickness is sufficiently large to avoid any reduction of the concrete cone failure load

For a single anchor unlimited by edge influences or overlapping cones p i g 6(a)I

with

ANo= projected area of a single anchor

?he SI equivalent of Eq (2) was determined assgning that

77

f i g &Projected arear forfasteningr under shear loading according to A U ,349, (a) single fastening installed in thick concrete member;. (b) .single fastening in.stolled in thin concrete member (h S c,); (b) double fastening installed in thick concrete member is, < Zc,)

1 i n = 25 4 mm, 1 si = 0,006895 N/mm2, 1 lb = 4448 N, P a n d E = l , i 8 f,' t N" = (4a)

Nno = 0 96 h ( 1 + 5 ) , N (3) - AN - -. ,, N n ~ ~ ~ g t z ) ~ (4b)

AN0 For fastenings with edge effects (c < h,/) andlor affected

C 4 (?)I, N

by other concrete breakout cones (s < 2 he/). the average To obtain the-failure load in SI units (N), Eq ( 3 ) may be failure load follows from Eq (4) use$ in place of E q (2) in Eq (4b)., , , 7 , : * > : ! , : ! , .

Fig 7 shows the detemlination of the projected areas AN for double and quadruple fastenings Note the computational complexity of determining O and AN

ndividual anchor failing the concrete (Fig 8). provided that the concrete half-cone is fully developed, is

Again. with r$ = I and the conversion factors given. the SI equivalent is

~f the depth of the concrete member is small (h < ~ 1 ) andl or the spacing is close ( s < 2 c , ) andor the edge distance perpendicular to the load direction is small (c2 < cl). then the load has to be reduced with the aid of the projected areas On the side of the concrete member

V, = A, 4 ;', l b

where AV = actual projected area

A , ~ = projected area of one fastener unlimited by edge influences, cone ove SS

[Fig 8(a)I 2

= n/2 c ,

10 obtain the failure load in SI units (N). Eq (6) may be used in place of Eq (5) in Eq 7(b)

Fig 8 shows the determination of Ihe projected areas Av for shear loading using the cone concept of ACI 349 Again. the computations are complex for the examples shown in Fig 8(b) and 8(c)

-J= The concrete capacity of arbitrary fastenings under tension

or shear load can be calculated with the CCD method 1'0

predict the steel capacity, additional design models are nec- essay. such as the one proposed in Reference 8 for elastic design or ductile and nonductile fasteners, or in Reference 16 for plastic design of ductile m ~ l t i p k fisten- ings. Note that failure load of anchors by pullout is lower than the concrete breakout capacity. Equations for calcul* tion of pullout cap;sity are available but are not sufficiently accurate or general 'Therefore, the pullout failure loads must be evaluated and regulated by prequalification testing,

ACI Structural Journal I January-February 1995

~ ig . 94deal ized concrete conefor individual fastening . :;: under tensile loading after CCD method ... . .

.. . ,,

fjstening is calculated assuming an inclination between

horizontal extent of' the failure surface is abo the effective embed

given by E q (8)

where kl, k2 k, are calibration factors, with

where k,,, = 35. post-installed fasteners

k,,, = 40 cast-in situ headed studs and headed anchor bolts

79

hef = effbctive anchorage depth (Fig. 10) For fastenings with three or four edges and c, 5 15hd(cm= largest edge distance), the embedment depth to be insened in Eq (10a) and (lob) is limited to htf= c,,&5., This gives a constant failure load fordeep embedments2?

Examples for calculation of projected areas are given in Fig 1 1 Note the relatively simple calculation for the CCD method compared to Fig 7 illusrnting the ACI 349 m e w .

In E q (10). i t is assumed that the failure load is linearly proponional to the projected area Ihis is &en into account by the fact0rA~4A,~, For fastenings close to an edge. the ax- isymmetric state of stress. which exists in concrete in the - case of fastenings located far from theedge, will be dis- turbed by the e' dge. Due to this disturbance. the conmte cone failure load will be rehuced. (Ihis also occun in cracked concrete82-') 'Ihis is taken into account by the Nn- ing factor yt . A linear reduction from y2 = 1.0 for c1 2 15hd(no edge influence) to v2 = 0 7 forthe theoreticalme c, = 0 has been assumed,,

Up to this point, it has been assumed that anchor ,pups areloaded concentrically in tension. However.-

with AN, AN,,. v2. and N,, as defined in Eq (10)

A. . Is, r 15h.112 1m.l

* 5 1 1%.

a l

Fig Il--Projecredareas for different fasrenings under ren.. rile loading according lo CCD method

reiationship of the concrete capacity is proposed between these limiting cases f ig 14)

y I = factoftaking into account the eccentricity of the , : -.. ...I.I~-.~~c..~P

resultant tensile force on tensioned fasteners..ln the ; m q r . i ! o a d s ! $ cask wheieeccentric Ioadine exists about two axis ' ., .-

The concrete c x & % individual anchor in a ,, uncracked suuctu.d meinber under shear loading towar

free edge (Fig 15) is

- (Fig 11). the modification factor y 1 shall be corn- puted for each axis individually and the product of the factors used as y in Eq (I la)

e,' = distance between the resultant tensile force of ten..

sioned fasieners of'a group and centroid of ten. sioned fasteners (Fig,. 12)

Fig. 12 shows examples of an eccentricaly loaded quadruple fsstening under tensile loading located close to a corner In Fig. 13. E q (Ila) is applied for the case of a double fastening. In this figure (as in Fig 12). it is assumed that the eccentricity e,; of the resultant tension force on the fistenen is equal to eccentricity e ~ o f the applied load. 'Ibis is valid fbr eh, 5 r, 16 and for e,, > r, 16 if the fatener . . . . . . displacements are neglected. If the load acrs concentrically on the anchor plate, Eq. (10) is valid ( y I = I) [Fig 13(a)l If only one fastener is loaded p i g 13(c)J, the failure load of' . . . . . the erouo is eaual to the conciiie $pacity of' one fastener

where

do = outside diameter of fastener. in: 1 = activatedload-bearing length of' fstener, in , 5 8d,

(Reference 25) = he,forfastencrs with a constant overall stiffness,

such as headed studs, undercut anchors, and torque- controlled expansion anchors, where there is no disrance sleeve or the expansion sleeve also has the function of the dismce sleeve

= 2 4 for t'otque~conuolled expansion anchors with distance sleeve separated from the expansion sleeve

c, ,= edge dismce in loading direction, in m?. 1n=$ith length quantities in:qnpd stress =%' -.

=;%is equation becomes m*?

located c10,se to corner

ACI Structural Journal 1 Janua . . . . . . . . ............ . , . . . . . . . . . . ....,. .( .L,r-., _. _... , .......... ? .-.,. ryrr : , , - . * , , . . . - . . . . ,: . , '...".! . . . " . . . . . : ,-; . . . . : . , . , , . !

According to E~:. ( failure load does not incr;ase with the hilu which is proponional to c.; .. Rather, it is pro .. Ibis is again due to size effect Funhermor.e, the failure load is influenced by the anchor. stiffness and diameter The size effect on the shew failure load has been verified theoretically and experimentally .?

The shear load capacity of. single anchors and anchor groups loaded toward the edge can be evaluated from Eq, (13a) in the same general manner. as for tension loading by taking into account that the size of the failure cone is dependent on the edge distance in the loading direction. while in tension loading it is dependent on the anchonge depth Ftg, 16)

where A, = actual projected area at side of concrete member

idealizing the shape of the fracture area of individ- Fig IbCbmparison of'rension andshear loading for CCZ) method

ACI Structural Journal I JanuaryFebruary 1995 a 83

C::

' I

A V = A,. (single fastening] = 15c,(2 15cJ = 4 5 4

A, = 15c,(15c, t cz) if: c, s 1 Sc,

A, = 2 1 Sc, h

if: h s 15c,

unl nr1c.ho1 s as n l1nl6pyran1id with sidc length I 5 c I nnd 3cl (Fig 17)

.I,, = projected area of one fhstener unli~nitcd by corner influences. spacing. or. member thickness, idealizing the sl~npe of the fracture area as a 11alf.pyramid with side length 1 5 q and 3 q [Fig 15(b) and 1 W l

y r , = effect o f eccentricity of shear load

' = distatice between resultant shear force of f x t e n e ~ s

of group rcsisti~ig shear and centroid of slleared fils- tencrs (Fig 18)

y = tuning factor co~~side~ir lg disturb:mce of synmelric

stress dist~ibution csilscd by a corner

q = edgedistan& in loading dircction, in (F ig 1'7): for k~stenings in a narrow, thin inember with e2.,,c 1 5c1 (q,,,, = maximunr value dredge distnnces perpendicular to the Ioxling direction) and 11 < 1 5c1, the edge distance to bc insertcd in E q (131).

( I lb) , anti (I 3c) is limited to c l = max (c2,,,/1 5; Irll 5 ) 1 his gives a constant fnilurc load intlepen- dent of'lllc edge distance c l (Refcrencc 21) '


.

Fig 18-Caniple o/'~ultrple faiteiing with cast..in rim headed sttrds close to edge under eccentric shear loading

c2 = edge distance perpendicular to load direction (Fig

17) Examples for calculation of projected areas are shown in ,

Fiz 17 Note the relatively simple calculation com~ared lo , % - the more complex geomeuy of the ACI 349 procedures illus- 0 J

, 19-~&ble fartening: (a) rhear 1oadperpendic.ular to ; (b) shear load parallel to edge

.. The assumption of. ;lope of the f'iilure cone surface, his leads to different minimum spacings and distances , , . .. . . . .

load that can b.ikesisted iitiiediridtion perpeidiiular to &d . to divelop full anchor hpacily,: toward the kdge (Fig. 19) A similai value can be conserva- 3.. The assumption about' the shape of the fracture area tively used for resistance to loads in the direction perpendic- (ACI 349: cone, CCD method: pyramid approximating an ular to but away f idealized cone). In both methods. the influence of' edges and

overlapping cones is lakeninto account by projected ireas, Comparison. of bqed on circles (ACI 349) or rectangles (CCD method), re..

The main differences between these design approaches are . spectively due to.this, calculation of' the projected area is summarized in Table 1 Thky are as follbws:

, . . rather simple in the case of the.CCD method and ofien rather 1 The way in which they consider influence of anchorage iom$icated in rhe case of ACI 349

depth hg(tensile 'loading) and edge distance C I (shear load- , 4, The CCD method takes intb a c c o k disturbance of the ing),, suesses in concrete caused by edges and influence of load

Table 1--Comparison of the influence of main parameters on maximum load predicted by ACI 349 and CCD methods . .

I ACI 349-85 1 CCD ~&thcd Anchorage dcprh, tension IJ hi. k.,

I I Edge dismcc shur 4 c:J

Sloped fa~luue cone a = 45&s a - 3 5 d e g . Rquind spacing to devclop full anchor clpacity Zh,!, tension 3k,,.tcluion

? c , rhcu 3c. . s k I . . ~ ~ I .

Required edxe diiuncc to develop full anchor upcity I h , , tension 1.5 h,.msion

. . I c, shear 15 c, .shear

Smallspacing or ' I dirccrion Nonlinear (area-proponiond) Linev rcduclion do= to edge 2 dirrcrions reducdan Nonlineunducrion

Eccenlricity of load .' : ' - -.; .%Taken into account . . I ... . . ... .. . . .. .,,. ... ., .

ACI Structural Journal I January-February 1995 > - 85

Table 2---Single fas tenings with post-Installed fas teners far from edge, t e s t series-'Tenslle loadlng

e c c c ,hies These influe&ing factors are neptected hy ACI 349

TEST DATA In the following sections, some extracts of'the data base

Ire reproduced to give the reader a sense ofthe large number 11' test series, individual tests. and range of' variables consid- :red The original sumnary of' test results is pixen in ieference 1 0 Only tests where a concrete breakout fXlure xcurred were taken into account In respnse to review omalents after submission of' this paper for. publication, hta from the Pragne tests reported by Eligeliausen et a1 .nd the Arkansas Nuclear One tests28 were added

-ensile loadlng 'Tables 2 tl~rougll 5 give an overvicw of the number of ten.,

ile tests and range of the varied paranleters No diflcrence 7 the procedure of perf'orming tests with anchors under tcn.. ile loading between Europe and the U S could be discov- red,, \

8 give an overvicw of the number of

I I

shear tests and ralge ofthe varied parameteis - In European tests with anchors under sllear loading, a flu- oropolylner sheet was always inserted between the concrete surface and steel plate Illis is to sitnulale reduction in friction betwee11 the steel plate and concrcte surface caused by reduction of thc prestressing force with time9 and by use of a plate wit11 a relatively smooth surface (c g . a painted, cold- drawn, or greased plate) In the U S , tests are usunlly performed with an unpainted steel plnte attncl~cd directly on the concrete surface with no fluoropolymer sheet in between Illis increases friction resistance and causes the U S test values to be higher,

ACI Slructural Journal I JanuaryFebruary 1995 .. , . . . - -

COMPARISON O F DESIGN METHODS WITH TEST DATA

111 this section. test data from the wide range of tcsts shown in t$e previous section will be cotnpared with the CCD and ACI design procedures \!

'Table 4-Single fastenings with post-installed fasteners close to edge, test series-Tensile loading

L.::~. ~ / m m ~ h,j mm C, mm Edxe Country

spacing of lc r l n Mnimum Avcnpe hlzximum Minimum Avenge ZIximum Minimum Avernge blximum

GB 3 3 0 2 , s 25 5 37 0 67 3 100 0 50 0 83 3 1200 F 2 IS4 184 18 4 63 5 63 5 63 5 63 5 63 5 63 5 D 36 24.0 25.7 59.0 30.0 81.5 220.0 30.0 95.6 330.0

CI s 1.54, EL'R 41 184 l 7 9 590 30 0 79 6 2200 300 931 330 0

us.+ 17.2 1 17.1 34.1 34.2 118.0 12.3 31.8 1 96.0 1n.8 172

240

nj 590 300 99 0 2 3 3 300 ' 946 1 3300

cl 5 I 0 hd 26 3 37 7 53 0 I W 9 2200 30 0 93 5 220 0 USA 30 18.6 27.7 W. I 34.2 137.8 2213 31.8 1W.8 158.8 - 2 , 1 ‘lo 18 6 27 3 377 342 128 6 2 2 3 30 0 989 1 2200

Table +Quadruple fastenings with cast-in situ headed studs, single tests-Tensile loading -- &,, . X/mm2 Itel, mm c 1 mm, I, mm Edqe Counrzy

rpau~ng of lest n Minimum/ AvarJgc ~I&ximun(hlinimum AverJpe Plasimumhlinimum Avengc j\l&ximumhlinimuml Avenge hluimurn

Quad- 3 - 101 6 -

1 I 35 179 1 281 1 389 1 673 177 9 360 3 - - - 508 1 1 4 6 0 '4330

. . Table 7-Single fastenings with post-installed fasteners in concrete members with limited thickness, single tests-Shear loading

1 1 . f r :~~ . l v /mm~ I . hd. mm ......

I I

Country Mmi- Maxi- Mini- Maxz- Mini- 1 Ma,i- h.lini- Maw Mint- Avensc Mzxi- ot'tcrt n mum Avcmcc mum mum Avcnne mum mum Avenne mum mum Averaqe mum mum mum

Tabie 8-Double fasteninas in thick concrete members. sinole tes t s

Tensile loading In Fig. 20 and 21. measured failure loads of' individual an..

chors are plotted as a function ofembedment depth. The tests !\ere pertormed on concrete with dimrent compression strengths. Iherefbre. the measured failure loads were nor- malized to /',: = 25 Nlmm' (f,' = 3070 psi) by multiplying them with the factor(2~//,,,,~,,)~~, In addition predicted failure loids according to ACI and the CCD methods are plot-

- ~~ -~~ ~, - ~ ~ ~ - ~ - - - -

ACI Structural Journal / Januarv-Februaw 1995

Anchor.. age

device Expan- sion

anchor

ted As can be seen, the tension failure loads predicted by the CCD method compare rather well with the mean test results over the total m g e of embedmentdepths, with the exception ofthe tuo post-insralled fasteners at the deepest embedment,, In conmst. anchor suengths predicted by ACI 349 can be considered as a lower bund for shallow embedments and give quire unconservatiue results for the deepest embedded headed studs 'This is probably due to the fact that size effect

Cduntry oftesr

D

n

36

fc&. N/m2 h 4 m

Mini- mum

20.5

Mini- mum

80.0

d m

Averrge Mini- mum

18.0

Avmpc

81.7

Maxi- mum

c , m

iVa.xi- mum

100.0 I 24.8 27.1

Average

20.7

Mini- mum

80.0

c? mm

Maxi- mum

24.0

Wini- mum

80.0

Avmgs

172.1

Average

190.0

x i - mum

200.0

M u i - mum

1W.O

';i'g, 20-~orrorle Oreokorrr load for,mr. Brsmlled fnslcn- r r, mrtrfle~~ed /Ir. edges o t spzcitrg ej/ror-7knrilc resf csrrlrs ondpr.cdic~i(m

s neglected by ACI 349, Suhstaatial scatter exists wit11 the leep embedment data. jostifj:ing a conservative approach irt his region.

Fi 3: shows tlie results of all evaluations forte~isile load- ng ~~ l " t - i~~s t a l l cd fasteners far from [he edge Average alues of the ratios N u,,,,,, to N ,,,,,,, ,,, , , p , dnt~d corresponding co-

:ficients of variation for botli methods arc plotted The av- :rage and coefficient of variation are substantially beuer for he CCD tnetliod tlmi for ACI 349'This is also true when tlie lata arc subdivided into five different anchor types (fig 23) ind for headed studs without edge or spacing influences Fig 24). Eq (9) uses the same coefliciet~t k,, for undercut ~rrchors as for other post-instnlled anchors 'The results illown in Fig 23 support this procedure 'These undercut an- +or tests were typically for undcrcut anchors with l~ead learing pressures greater than 13f: Bclter values would be :xpectcd if the undercuts were proponioned for l owr bcar- ng pressures 1 he coelficient of variation ofthe r:~tios of measured fail..

Ire load to the value predicted by the CCD method is ahobt IS percent for headed studs and undercut anchors, nhich lgrees with the coefficient of variation of the concrcte tensile

Fig 21.-Cotroere 6rcoliorrr l&d for tosr-in si'rrr h d e d a~rds, trrro/fecred by edges or sjmcing cj/rc 1s.-'re res~rlrs amipredic~iorrs

tlie CCD method This is doe to !lie fact that tile majority of the ev;~lunted data 11ap an efkctive e~~l~edrncrit depth Ifcf s"ia1ler than 150 tnm (6 in) . F& headed studs with embed- me& greater t h i n 300 mtii (12 i n ), ACI 349 predictions he- come unco~iser~ative(Fig 21). Thus, the average vaiues do not indicate local unconservitive cases,

la Fi$ 25, results of tcsts with quadr~~plc fastenings with h&detl stnds are evalun t ed in the sa111e way as in Fig 2 2 The figure indicates that spacing irtflucnce is tnore easily arid accurately takci~ into account by the CCV mcth?d tlian by ACI 349, Wl~ile tlie average failure load is predicted correctly by the CCD method, it is significantly overestittmtcd by ACI 349 Tltis can also be seen from Fig 226, which sflows failure loads of groups as a function of the distarice r; betweeii the outermost anchors Groups with 4 lo 36 anchors were installed in very thick concrete spcci~nerls loaded concentrical-, ly in tension through a rigid load frame to assure an alniost equal load dist~ihution to tlre ancllors I.,ight skin rrinforce- ment was present near the top and 11ottot11 surfaces of the speciri~ens and light stint~ps were present near the cdges in some specimcnf for handling The sti~rups did not intcrsecl the concrete conc No rcinlorcc~ncnt w;:s present near the fastct~ing i~eads These specimens represent h e capacity of' groups of' I;is!cncrs iristalled in plain concrete 13nhcdment depth and concrete stre~igtl~ were kept colist:lnt 111 a11 tcsts a


ACI 349 CC-Method

lows from the assumption of'a45-deg cone is toosmall Ob- viously, provision of special reinforcement designed to engage the hilure cones and anchor fastenings back into the block could provide substantial increase in load. ?his was not investigated in these tests and such increases are not treated in this paper

In Fig' 27, resulu of' tests with single post-installed fasteners close to the edge are evaluated. The average ntio to I V , , , ~ ~ ~ ~ , is approximately the same for boh methods. Howeber. the coefficient of' variation is much smallei for the CCD method and amounts to about the same value as for single fbteners away' from edges 'This shows that assumptions about the critical edge distance c,= 1 Sh@ and the stress disturbance factor yf are correct Note that most of the tests were done with rather shallow anchors (Sable :4). For deeper anchors. it would be expected that the CCD method would predict more accurate capacities due to its consideration of

ACI Structural ~ 6 u r n a l l Janu&y-iebwary 1995

. .

Frg 23- Comparison o/ design procedures forposr- instalkd fnsreners. unaffecred b> edges or spacing effects. divided into different fastening sjsrems-Tensile loading

size effect and effect of stress disturbance. as well as itsas- sumption of a chamtenstic edge distance c;, = 1 5 hij , ,

Influence of' load eccentricity on the failure load of' anchor groups is shown in Fig. %'I heeccentricity e,' is calculated using the general assumptions of the theory of elasticity, ie.., stiff' anchorplate anchordisplacement equal to steel eioriga- tion. and linear elastic behavior. of concrete. It can be seen that the CCD method yields conservative results 'This effect is also neglected by ACI 349

Shea r loading F ig 29 shows a comparison of results of U S and Europe-

an shear t<srs performed with single post-installed anchor fastenings in thick concrete members with the design procedure of the CCD method and hd1349 'The tests were performed on concrete with different concrete suengths, different anchor diameters, and different ratios of embedment depth to anchor diameter 'T herefbre. the measured failure loads were cnnsf'ormed to a concrete strength /;,' = 25 Nlmm' ( j'.' = 3070 psi), anchor diameter do = IS mm (0 71 in) , and a ratio //do = 8 by multiplying them with the factor (25/f,, ,t,, )05 ( I U d o,,,,, ) 0 5 , [8/ ( l / d ) ] Ptt,. On the average the concrete breakout loads of dte U S tests are higher than those of the European tests. especially at smaller edge

ACI 349 CC-Method

230 400 600 800 1000[mm]

7.9 15.7 ' 23,s 31,5 39,4 [ i n ]

S t

ACI Slructural Journal 1 JanuaryFebruaty 1995 . ,, . ,. , , .. .. .,.,.. ., , . . , , . . .,

ler

Or. tar: ag; Du dal

1 B i t

SIB

res 7 h ed1 ti01

1 all1 tes! (Fi me

AC: w....

ACI 349 CC-Method

30 83

ropolymer sheet in the U S tests and resulting friction contribution leading to higher shear capacity The friction contcibution relative to the failure loadis large for small edge distances

- 1 Failure loads predicted by the CCD method agree well with the average failure loads measured in European tests. On the contrary, ACI 349 is conservative for small edge distances and unconservative for luge edge distances This is, again. probably due to the neglect of' size effect by AC1349,, Due to the fiction contribution just mentioned. the U S test data are predicted more conservatively by both methods

In ~ i ~ , 30 and 31. average values ofthe ntios V, ,JV ,,,,

dirtinn and corresponding coefficients of variation for post..installed fasteners are given for European and'^^ test data, respectively The ACI 349 averages are more conservative,, 'This is due to the fact that most tests were done with small edge distances However. the AC1349 coefficients of'varia.. lion are larger A similarresult was found for headed studs 'O

The results of' European tests with double fastenings parallel to the edge and loaded toward the edge (Fig 32) and tests with single fiistenings in thin concrete members (F ig 33) are similarly evaluated. As can be seen, the CCD method comphres more favorabl) with the test data For both

ACI Structural Journal 1 January-February 1995

Fig 28-Comparison of resf rerrrlrr on eccenrrically loaded line farreni~ur composed offi~rcr e m . in siru headed rntcls wirl; loadpredicted by ~ ~ ~ r n e r h o d - ~ u n r i l e loading"

applications, avenge ffailure loads predicted by ACI 349 . are . . : '-

unconservative and coefficients of variation are much larger':. ', . .

CONCL.USIONS In this study, the concrete capacity of fastenings with cast.' .,

in situ headed studs and post-installed anchors in uncracked plain concrete predicted by ACI' 349 and the CCD method has been compared with the results of a large number of tests (see Tables 2 through 8 ) Based on this comparison, the fbl- lowing conclusions can be drawn:

1 . 'The average capacities of' single anchors without edge and spacing effects loaded in tension are predicted accurately by the CCD method over a wide range of' embedment depths [20 mm (0 8 i n ) < h,,S525 mm (207 in )] Fora few post..installed anchors with embedment depths in the 250- mm (10-in.) range. the CCD method was quiie conservative. Conversely, ACI 349 underestimates the strength of'shallow anchors and is unconservative for quite a number of' deep embedments The same result was found f'or tlir predicted capacities of single anchors loaded in shear toward the edge with small or large edge distances, respectively,

This result is due to the fact that AC1349 assumes the fail.. ure load to be proponional to a failure area that increases with the square ofthe embedment depth On the other hand. the CCD method takes size effect into account and assumes

1750 -

t Y ) O -

5 100.0

75,O .,

w.0 - 10

.O w.0 t o o m . 0 100.0 -0 m.0

,

Fig 29-Compari~ron of shear test results wit11 ACI 349 and I?C member:^: (a) European rests;. (b) U S resrr

ZOO

- .v . .. . . . -. ..: -

, . : 1:so '0 u - - -2 $2 1.00 . .Z 2 "

00 ACI 349 CC-Mclhod ACI 349 CC.,Melhod

-, 84 84

s 0

C - .- l o o ..

0 , - 20.0 -

C Z " .- - ; 30,O 0 U

40 0

i g 30-Co~nparison of design procedurrs for. European Fig. 31-Co~npari:son of design prat e d u m for U S tests rrs ni111 sirtgleposr.~i'nna/led fasteners in thick concrere 1citIl s i~~glepost~~i~~rtal led fasrener:s in rllick concrete n~ern- ember:s-Shear loading roward edge berrS11ear loading roward edge

ACI Structural Journal / January-February 1995

rocedurer for double fa,$- steners in thick concrete mem- loading toward edge

. ,

failure load to be proponional to the embedment depth to the - - 1 5 power

2 In many applications (for example, anchor groups away from edges loaded in tension single anchors in thin concrete members loaded in shear. double fastenings in thick concrete members loaded in shear). the capacity is predicted more ac- curatcly by the CCD method Failureloads predicted by ACI 3-19 for these cases are significantly unconservative, This is mainly due to the fact that ACI 349 assumes a 45-deg failure cone. The CCD method is based on an assumed inclination of the failure surface of about 35 deg. which produces better agreement wirh test results, .

3 In some applications, such as single anchors at the edge loaded in tension. the mean capacity is predicted accurately by both methods However. thecoefficient of variation of the ratio of' measured failure load to the value predicted by ACI 349 is rather large ( V = 45 percent),

4 In all applications investigated. concrete capacity is predicted with consistent accuracy by the CCD method The co- et'ficient of' variation of' the ratios between measured and predicted chpacities is about 15 to 20 percent. 'This coefficient of variation is equal toor not much larger than the value expected for concrete tensile strength %hen the lest specimens are produced from many different concrete mixes.

ACI ,349 CC-Method

99 a9

Fig , .3.3-Cbmpari.son of design procedures for European tests wirh singlepost..i,~smlledfasrene~~ in rhin concrete members-Shear. loading toward edge

l y In contrast, the circular. areas of ACI 349 result in consi erable computational comple~ity,~

Summarizing. the CCD methodis a relatively sim transparent, user-friendly. and accurate method for efficient calculation of concrete f'ailuk loads for fastenings in un- crackedconcrete. It is based on a physical model to assist designers in extrapolating the empirical results to other applications, 'Iheref'ore, this method is recommended for the design of fastenings It is riot inco~ect to use the ACI 349 method for. many fastening applications,. However. since it does not seem universally advantageous and in some applications produces unconservative values, the authors suongly recommend use of' the CCD procedures

CAUTION It is known that the presence of tensile cracks :an subsran-

tially reduce the concrete capacity of fasteners Some fasteners are nor suimble for use in cracked concrete FOI those fasteners suitable for use in cracked concrete, it is possible to adjust the uncracked concrete failure loads predicted by the CCD method by using an additional multiplicative factor This factor results in cracked concrete capacities around 70 percent of uncracked concrete capacitiest Similarly, it is

k n o w t t 1It;tI t l tc cot tctc ie c:tp:tcily of f:~slettcts ~ 1 1 1 hc en.. It:tttced by p t t y x r l y del:tilctl l oca l ~ e i t ~ ~ o r c e t t t c t t ~ Such cn- h:tttcetacttl c a n he i t t c ludvd i n des ign provis iot ts b u t i s ou ts ide l l l c scopc nf t i t is p:tper,

NO'TATION' r = dinanec frnw center a fa fassnrr to cdgc o f concrete 6 I = distnncr frwn centcr o fa fi~slener to edge ofconcrete in onc

dircct iu~~ \Vhm s h m is prcscnt,, c 1 is in thc dircctint~ of ~ h c shcm fonc

cz = diannce fnrm ccntrr nf a faslcncr to cdgc ofconcnte in dirce.. lion onhogwal lo rl Where shenr is prescnl, g is in the direc. lion perpcndiculnr to shear force

do = outsidcdinn~ctcr of fmtcncr or shnfi dinmttcr of iacadcd slnd or headed nnrlrw hslt

d, = head dinnwcr 6fhmJrd st~sls or hendcd =?chon

1,' = C O ~ C R ~ E ~ ~ n ~ p r c s s i v e strtngth measured an 6 hy 12 in cylin-

ders , = concrclc amprcssi\r strcng~h, rncmrcd on 2CU-mn1 cubcs

f = conerule tensile strength h = thickness ofconcrete memhcr in uhich a fasteuer is anchored

\ = cflective ~mbcdment tlepth (,3/ = nu,nhry or tcst rcsults s = distance ktween fasteners spacing

' , s, = distrnce bctwcn ?atermost fasteners o fa proup V = CocfIkient of vnriation r = ~ l i o o f nclual lo predicted load .x = tuenn value of r 4 = projected area tension A" = projected nrrn shear , .

C I 3 = Euro.hlcrnational Concrctc Comn~i~tee CS = Crceh~rslu\akin D = Gcrmony EUR = Europc F = France GB = Great llrilnin N = lc%silc I w d .5 = Snedcn LSA = United States o f Amrrica ' = shear load

a , = s l q x ofe;mcrete breakbut cone

r snfcty conridcratiow

, ,

ilicntion for Performance o f ~ n c b b r r cue lilr.twnlr." Dmfi I. hlnr 21. tY9,1,,

2. Furthc J and Eligelmuscn. K 'I.:sternl Rlowavl Failurc'of llended Stllds ncnr a fiec Edge " Arahorr i r r Conrnlr-Deri.q!r and &bowor,, SIL 130 Anicrican Concrete Institute iktroi t 1991, pp 2.35..252,

3 7hm. G ,, "'lJefcstigsnpen mi l Kopflrolzen itn ungerisscnen Brton t~aslcnings with llendcd Studs it! U w r x k e d Concrete)? I'ltl) thesis,, Uni.. Wrsily o f Slullg:rt,, 1993,

4 ACI Cnmmittcc 319 Cmlc Rcpuiren~cnls for Nr&r Safety Rclatrd C~ncretc SI~UCIIIICS fACI 319.85) " Alnrrieaa Coocrcle ltlailsle,, Detroit 1985

(hstcning Tichniqucl ' Rrmnloknd<, I Y V 2 V II firm1 8: Suhu I k r l i n 1992 pp 597.~7l.5 (in Grrmm)

9 Eligchnuscn R , , ""Vcrglciel~ dcs K .Verfahrens mil der CC..hlcthodc

(Compnriron ofthe K ,Jdelhnl r i l h lhc CC.Metlml),, 'Rrpovl No IU16.. 9 2 n lnrtilul filr \\crkstoffc iiln Dauucscn L~nivcrsilSt Stntlgan 1912 (in Gernran)

I 0 Fuchs W.. "Enluicklung cirlcs Vorschlogs fllr die Bctncssung ron Refestigungen (I>ereloprncnl o f r Proposal for the Dcrigtc o f Faacninpr lo Conrrcle)," Repon to the Deutschc Foncl~usgsgemeinscI~nft, Feh I991 (in German)

II Kiingner, R, E . nnd hicnd~mca J A . "lcnsilc Capacity o f Shod Anchor Bolls and Welded Studs: A Literalarc Rcvicw," ACI JOLIRNAI. Pm,. cwdings V 79, N o 4. July-Aug. 1982. pp 270..279,,

12 Klingncr R. E. and Mcntlonca J A,. "Shcar Cnpwily o f Shod Anchor Bola and Welded S~uds: A I.ilcrnture Revieu:' ACl Joyn~nt . Pm. crtdir~jis V. 7 9 Nd.5. Sept.-%I. 19

I 3 ACf Committee ,318. I.ctlc Chapter 22. Faslcning to . Concrclc. ~ I

14 ACI ~ ~ o i n m i ~ e e 349. ' Related Concrcte Structures (ACI 34976)" American Concrete Institute. Detroit, 1976. :

I S ACI Commitlei 349 Wesign Guide to ACI 319..85,' ~ k e r i c a n Concrca Iwtitute, Detroit. 1988.

16. C w k R A,. and Klingncr R E.. 'Uchmior dnd Design of Ductile hfultiplcAnchor~~ToOOSt~~IIIConnectio~ Rcsrorch, Report N o 1126..3, Ccnter for Tmsspoitation Rcwarclt. University of'Rxas 01 Austin. 1989

1 7 R m n t Z. P. "Size Elfccl i n Blunt Frncturc. Cbncrctc. Rock hktnl.

18, Bnle. li .and K o i L K . "llcid{d ~Iuds-~n&dded in c&& and Loaded in'Tcnsion~ncltorcrgc r o Cirtnrrti, ed . Amcn'can,'C?ncrctc Institute. Detroit.l98

:19. 'Eligchahen. R ; and ~awsdc. G.. "F Dc&ipiion'of~hc Pul lOnl Beltaviour of llcadcd Studs En~he+cd in Con. cretc.", From& hfcrbbni<:s of Conirere Structwrr, F k m Tltrorr. 10 Appli- cation~. L Elfgrm ed . Chapman & llall. I nndon 1989. pp 263-28 1

20. Elinebausen. R. and Orboll. J . 'Sizc Effccl in Anchorage Rchnv- iour.' Pmcndirgr Dmpcon Coufirc scr 08, f na twc hf<rhnnicr. Fmc

Udtmiow wd Dc+qn of hi<treridt md ~ t r ~ ~ t ~ ~ ~ ~ ~ l tv in. Oct I991

on the C ~ ~ I O F&;e Load o f Awhor~olts: Fna titre hlwhoni,:r o/ Concrete ~ ~ h r m ~ & E l s e y i e r Applied Sci:8?cc. 1997 pp. 517.425

22. El igehauscn. '~, and Rologh. T 'CC-hldhcd (Canc ie Cnpacity Mcthal):' R C ~ & No 12/15.92/). Inailnl fur \\'crkstoffc i m llnuwesen. UnivciritSt Stuttrm. 1992, .

ACI Struclural Journal / January-February 1995

anchor bolts - concrete capacity design.pdf

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