Headed Steel Stud Anchors in Composite Structures

Journal of Constructional Steel Research 66 (2010) 198–212

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Journal of Constructional Steel Research

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Headed steel stud anchors in composite structures, Part I: ShearLuis Pallarés a, Jerome F. Hajjar b,∗a Universidad Politécnica de Valencia, Valencia, 46022, Spainb Department of Civil and Environmental Engineering, University of Illinois at Urbana-Champaign, Urbana, IL 61801-2352, USA

a r t i c l e i n f o

Article history:Received 25 February 2009Accepted 18 August 2009

Keywords:Composite constructionComposite columnSteel anchorShear studHeaded studShear connector

a b s t r a c t

The formula in the 2005 American Institute of Steel Construction Specification to compute the strength ofheaded steel stud anchors (shear connectors) in composite steel/concrete structures has been used in theUnited States since 1993, after being proposed based primarily on the results of push-out tests. In the pastseveral decades, the range of members used in composite structures has increased significantly, as hasthe number of tests in the literature on the monotonic and cyclic behavior of headed studs in compositeconstruction. This paper reviews 391 monotonic and cyclic tests from the literature on experiments ofheaded stud anchors and proposes formulas for the limit states of steel failure and concrete failure ofheaded stud anchors subjected to shear force without the use of a metal deck. Detailing provisions toprevent premature pryout failure are also discussed. This paper also reviews proposals from severalauthors and provides recommended shear strength values for the seismic behavior of headed studs. Thelimit state formulas are proposed within the context of the 2005 AISC Specification, and comparisons aremade to the provisions in the ACI 318-08 Building Code, the PCIHandbook, 6th Edition, and Eurocode 4. Thescope of this research includes composite beam–columns [typically concrete-encased steel shapes (SRCs)or concrete-filled steel tubes (CFTs)], concrete-encased and concrete-filled beams, boundary elements ofcomposite wall systems, composite connections, composite column base conditions, and related forms ofcomposite construction.

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1. Introduction

Headed steel stud anchors (shear connectors) welded to a steelbase and encased in concrete have been themost commonmethodfor transferring forces between the steel and concrete materialsin composite construction. This type of anchor has been inves-tigated by numerous researchers worldwide. For steel and com-posite steel/concrete construction, the focus of the work has beenpredominantly on composite beams with and without a metaldeck. Much less comprehensive assessment has been conductedfor the strength of headed steel anchors in composite components.For such alternative configurations, the focus of much prior

work has been on reinforced or prestressed concrete construction.The main approaches regarding anchors in reinforced concrete areoutlined in [1] and Appendix D of ACI 318-08 [2]. Recently, Ander-son and Meinheit [3–5] developed a comprehensive research pro-gram to assess the shear strength of headed studs in prestressedconcrete. As a result of this work, the 6th Edition of the PCI Hand-book [6] incorporated new alternative approaches for computingthe shear strength of headed studs.

∗ Corresponding author. Tel.: +1 217 244 4027; fax: +1 217 265 8040.E-mail address: [email protected] (J.F. Hajjar).

0143-974X/$ – see front matter© 2009 Elsevier Ltd. All rights reserved.doi:10.1016/j.jcsr.2009.08.009

Research on headed studs in composite structures extends backto the 1950’s. A brief summary is presented here. The first push-outtest for studying the behavior of headed studs was conducted byViest [7], who performed 12 tests at the University of Illinois withvarying ratios of effective depth-to-stud diameter (hef /d), wherehef is the studheight from its base to the underside of the studhead.Viest [7] observed three types of failure: steel failures, where thestud diameter reached its yield point and failed; concrete failures,where the concrete surrounding the headed stud crushed; andmixed failures that included failure of bothmaterials. Furthermore,Viest proposed one of the first formulas to assess the shear strengthof headed studs of composite structures (see Table 1).Driscoll and Slutter [8] proposed a modification of Viest’s

equation (Table 1) and observed that the total height-to-diameterratio (h/d) for studs embedded in normal-weight concrete shouldbe equal to or larger than 4.2 if the full shear strength of the anchorhad to be developed. Chinn and Steele [9,10] developed push-outtests on lightweight composite slabs. Davies [11] studied groupeffects for several headed studs in push-out tests. Mainstone andMenzies [12] carried out tests on 83 push-out specimens coveringthe behavior of headed anchors under both static and fatigueloads. Goble [13] investigated the effects of flange thickness onthe strength of composite specimens. Topkaya et al. [14] tested24 specimens in order to describe the behavior of headed studs atearly concrete ages.

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L. Pallarés, J.F. Hajjar / Journal of Constructional Steel Research 66 (2010) 198–212 199

Notation

As Area of the headed stud anchorAvg. (µ) AverageCv Coefficient for shear strengthsC .O.V . Coefficient of variationEc Modulus of elasticity of the concreteEcm Secant modulus of elasticity of concreted Diameter of the headed stud anchorf ′c Specified compressive strength of the concretef ′cr Average measured compressive strength of the

concretef ′c,sp Specified splitting tensile strength of concretef ′s Yield stress of the steelFu Specified minimum tensile strength of a stud shear

connectorh Height of the studhef Effective embedment depth anchorkcp Coefficient to compute pryout by ACI 318-08; it

equals 1 for hef < 2.5 and 2 for hef ≥ 2.5Nb Nominal concrete breakout strength of a single

anchor in tension in cracked concreteP Load applied in the testQnv Nominal shear strength of anchorQnvc Nominal shear strength in the concreteQnvs Nominal shear strength in the steelRg , Rp Metal deck coefficients in composite slabsRm/Rn Average of the ratios between the test result and the

predicted valueSt.D. (σ ) Standard deviationVcp Concrete pryout strength of a single anchor in shearVR Coefficient of variation of resistanceVF Coefficient of variation on fabricationVP Coefficient of variation of Rm/RnVM Coefficient of variation of materialsα Linearization approximation constant used to sepa-

rate the resistance and demand uncertaintiesβ Reliability indexλ Modification factor for lightweight concreteξ Reduction factor for cyclic loadingφv Resistance factor for shear strength

In the figures

• Steel failure in test◦ Concrete failure in test× Mixed failure in test

Ollgaard et al. [15] proposed the first formula adopted by theAISCManual in 1993 to compute the shear strength of headed studs(see Table 1). They tested 48 push-out tests in lightweight andnormal-weight concrete with an effective embedment depth ratio,hef /d, of 3.26. Failures were noted in both the steel and concretematerial.Oehlers and Bradford [16] indicate that short studs experimen-

tally show a lower shear strength than long steel stud anchors. Thevariation in the shear strength with height has been recognizedin some national standards. For example, the British Standards forbridges (e.g., [17]) have given the strength of 19 × 100 mm steelstud anchors as 14%–18% stronger than 19 × 75 mm steel studanchors depending on the strength of the concrete. Furthermore,[18], as a result of a finite element analysis, pointed out the rapidincrease in strength with the height of the steel anchor. These au-thors noted that at a ratio of 7 between the height and the diam-

Table 1Proposed equations for headed steel anchor strength in composite structures.

Author Equationa

Viest (1956) [7] If d < 1 in, then Qnv = 5.25d2f ′c√4000f ′c

If d > 1 in, then Qnv = 5df ′c√4000f ′c

Driscoll and Slutter (1961) [8] Long studs (h/d > 4.2): Qnv =932d2√f ′c

As

Short studs (h/d < 4.2): Qnv =222hd√f ′c

AsButtry (1965), Baldwin et al. Steel failure: Qnvs = Asf ′s(1965), Dallam (1968) [22–24] Concrete failure:

Qnvc = 0.0157hdf ′c,sp + 6.80Ollgaard et al. (1971) [15] Qnvs = 0.5As

√f ′c Ec < AsFu

a Units: pounds, inches for [7]; Units: kips, inches for [8,23,22,24,15].

eter of the shank, the strength is 98% of the maximum attainablestrength.The AISC Specification has included provisions for composite

structures since 1936. Tables providing allowable horizontal shearload of headed studs as a function of the stud diameter andconcrete strength appeared in the AISC Specification of 1961[19]. The effects of a metal deck on the shear strength of theheaded studs were added in 1978 [20] and the AISC Specificationadopted Ollgaard’s formula [15] to compute the shear strength ofheaded steel studs in 1993 [21]. In Europe, codifying provisionsfor composite construction as part of Eurocode (EC) culminatedwith an initial version of the provisions being issued in the 1990’s,followed by issuing of Eurocode-4 (2004) more recently.Composite beams, specifically hot-rolled steel shapes with a

concrete floor slab either with or without metal deck formwork,have received extensive coverage in the literature (e.g., [8,22–29])and are not within the scope of this paper.This paper reviews 391 monotonic and cyclic tests from the

literature on experiments of headed stud anchors and proposesformulas for the limit states of steel failure and concrete failureof headed stud anchors subjected to shear force without the useof a metal deck. Detailing provisions to prevent premature pry-out failure are also discussed. This paper also reviews proposalsfrom several authors and provides recommended shear strengthvalues for the cyclic seismic behavior of headed studs. The limitstate formulas are proposed within the context of the AISC Specifi-cation [30,31] and EC-4 (2004) [32], and comparisons are made tothe provisions in the ACI 318-08 Building Code [2] and the PCIHand-book, 6th Edition [6]. The scope of this research includes compositebeam–columns [typically concrete-encased steel shapes (SRCs) orconcrete-filled steel tubes (CFTs)], concrete-encased and concrete-filled beams, boundary elements of composite wall systems, com-posite connections, composite column base conditions, and relatedforms of composite construction. Pallarés and Hajjar [33] cover theresponse of steel stud anchors subjected to tension force and com-bined tension and shear.This paper also reviews cyclic tests under high-amplitude

loading simulating seismic excitation. Hawkins and Mitchell [34],Gattesco and Giuriani [35], Bursi and Gramola [36], Zandoniniand Bursi [37], and Civjan and Singh [38] performed a range ofdifferent types of push–pull tests on headed steel studs underhigh amplitude cyclic shear loading for slabs in composite beams.Saari et al. [39] reported the headed stud anchor behavior ofpartially-restrained steel frames with reinforced concrete infillwalls, looking at both static and cyclic loads. Saari et al. [39] studiedshear, tension, and shear/tension interaction response for headedstuds with two types of confining reinforcing patterns. These testsshowed that if sufficient confinement is included, concrete failureis precluded.

2. Objectives

This paper reports on the behavior of headed studs embeddedin solid concrete slabs subjected to shear force, including both

200 L. Pallarés, J.F. Hajjar / Journal of Constructional Steel Research 66 (2010) 198–212

static and large-amplitude cyclic (i.e., seismic) forces, withoutsteel profile sheeting or a metal deck. The results given inthis work are applicable to composite elements including steelreinforced concrete columns (SRCs) or concrete-filled tubes(CFTs), concrete-encased and concrete-filled beams, boundaryelements of composite wall systems, composite connections,composite column base conditions, and related forms of compositeconstruction. In this work, the limit states of failure in the steelanchor and concrete pryout are accounted for in the assessmentsmade and the recommendations put forward. As discussed below,the limit state of concrete breakout, as defined for stud anchors inshear in ACI 318 Appendix D [2], is assumed not to be a governinglimit state for these forms of composite construction. An extensiveset of test results of headed steel anchors in configurationsapplicable to composite construction has been collected andanalyzed relative to the design provisions put forward in AISC[30], EC-4 (2004) [32], ACI 318-08 Appendix D [2], and PCI 6thEdition (PCI, 2004) [6]. Recommendations and design guidelinesare thenproposed for headed steel anchors subjected to shear forcein composite construction. Approximately 27% of the test resultsutilized in this work include lightweight concrete so as to get acomprehensive set of test results for composite construction.

3. Monotonic behavior of headed studs subjected to shearforces

A comprehensive collection of headed steel anchors tests understatic loads may be found in [4]. The present work is based mainlyon that collection with added test data found in the literature,including [40,41,12,42,39,43]. In total, 391 tests were consideredwhen examining the monotonic behavior of headed steel anchors.There are three main failures that may occur in a headed stud

anchor for composite structures, namely: steel failure,weld failure,and failure of the concrete surrounding the headed stud. In thiswork,weld failure is included as a steel failure, since the distinctionbetween weld and steel failure is often difficult to ascertain in theexperiments.Of the 391 tests on headed steel studs, 114 tests were classified

as concrete failure and 202 were classified as steel failure. The restof the failureswere not reported by the author orwere classified asmixed failure. Within this data set, 286 tests used normal-weightconcrete and 105 of the tests used lightweight concrete.Schematics of the tests are presented in Table 2. Generally,

there are three types of tests. The first type is a push-out test[e.g., [7,15], etc.]. The second type is conducted horizontally withedge conditions far away from the tested steel anchor [e.g., [4,35]].The third type takes into account special conditions such as ininfill walls (e.g., [39]). The push-out test usually simulates wellthe conditions in composite structures, producing pryout or steelfailure of the anchor between the steel and concrete.The collected tests have been used to assess the approaches

proposed by AISC [30], EC-4 (2004) [32], PCI 6th Edition [6], andACI 318-08 [2]. All four of the provisions use a general formof φvCvAsFun to predict the strength of the headed stud whenthe failure occurs in the steel shank, where φv is the resistancefactor, Cv is a reduction factor of the strength, As is the cross-sectional area of the headed stud and Fu is the specified (nominal)minimum tensile strength of the headed stud anchor, and n is thenumber of studs. The coefficient values from the three standardsare presented in Table 3.The general form of the formulas to compute the nominal

strength of an individual headed stud anchor when failure is inthe concrete, as provided by ACI 318-08 [2] and PCI 6th Edition[6], is φvCvRvn. These formulas are based on the 5% fractile; thatis, the formulas are developed such that there is a 90% confidencelevel that over 95% of the failures occur above the calculated limit

state value for an individual anchor [48]. The ACI 318-08 averagestrength formulas are given in [49]. The PCI 6th Edition averagestrength formulas are given in [4].The most likely concrete failure modes that may occur in com-

posite construction given by ACI 318-08 Appendix D are breakoutand pryout. Breakout is a type of failure occurring when free edgeconditions govern the failure. In these cases, failure planes form avolume of concrete surrounding the anchor, separating this con-crete from the member. In contrast, pryout failure happens in a lo-cal area surrounding the anchor corresponding to a formation of aconcrete spall in the direction perpendicular to the applied shearforce. It is likely that breakout failure rarely occurs in compositestructures and is assumed in this work not to be a governing limitstate since there are not appropriate failure planes for front-edgeor side-edge breakout in the vast majority of composite members,particularly if typical reinforcement detailing is used. The tests re-ported by Ollgaard et al. [15] are representative of the fact thatpryout, following the terminology of ACI 318-08, or ‘‘in the field’’following the terminology of PCI 6th Edition, is the concrete failuremode that is most likely to occur in composite structures.ACI 318-08 proposes a formula to compute the pryout failure

(Vcp) based on the basic concrete breakout strength in tension(Nb), which necessitates the computation of several intermediatequantities. However, PCI 6th Edition provides a direct formula tocompute the pryout failure when the ratio hef /d is less than 4.5.This assumes that when the ratio hef /d is larger than 4.5, the mostlikely failure is in the steel shank. The formulas from ACI 318-08and PCI 6th Edition to compute the pryout failure are summarizedin Table 3.AISC [30] provides a formula to compute the shear strength in

composite components other than composite beams. This formulais an adaptation of the formula for headed steel anchors incomposite beams proposed by Ollgaard et al. [15], who calibratedit by adjusting different models to the 48 test results developedin their research. Currently, reliability of the headed steel anchoragainst premature failure is taken into account as a part of thedesign of the composite component, such as a composite column;hence, the headed steel anchor strength typically does not have itsown resistance factor in AISC [30]. The resulting formula (EquationI2-12 in [30]) is presented in Table 1 (as [15]). Eurocode-4 (2004), incontrast, proposes a similar formula to compute the shear strengthin compositemembers, but this formula is affected by partial safetyfactors (Table 3) that provide more conservative results than [30].

4. Comparison of AISC 2005, EC-4, ACI 318-08, AND PCI 6thEdition

The current formula for the nominal shear strength of asteel anchor (other than in composite beams) in AISC [30](0.5As

√f ′c Ec < AsFu) andEC-4 [32] (Cv0.5As

√f ′c Ecm)was computed

for each of the 391 tests (using the minimum value of the steeland concrete failure modes) and compared to the experimentallyobtained load. In these formulas,measured values of Ec are used, orin caseswhere themeasured values are not provide, Ec is calculatedper ACI 318-08 [2] using measured properties of the concretestrength. Ecm is calculated per [50] using measured properties ofthe concrete strength. Measured Fu values were not provided bythe authors in a very small number of cases. In these cases, for thisstudy, the specified (nominal) values of Fu given by the authorswere used.The results are shown in Fig. 1(a, e).1 The ratio of experimental

strength to predicted strength, Vtest/Vpredicted, was less than 1 for235 of the 391 tests for AISC 2005, indicating that the formula is

1 The legend for the markers in the figures is identified in the list of notation.


Table 2Headed steel anchor test configurations.

Reference hef /d #Tests

Type Type of test Type of concrete Range of f ′c ksi (MPa)

Viest (1956) [7] 2.47, 2.55, 3.23, 3.22, 4.53,4.67, 4.77, 5.50, 7.00 12 1 4 studs (2 per side) Normal: 12 tests 3.19–4.39

8 studs (4 per side) Lightweight: 0 tests (22.0–30.2)

Shoup and Singleton (1963) [40] 8.00, 6.30, 5.20, 6.67, 9.33,9.65 9 2 8 studs (4 per side) Normal: 9 tests 3.43–4.89

Lightweight: 0 tests (23.6–33.7)

Chapman and Balakrishnan(1964) [41] 2, 3.29, 4.67, 7.29 9 1 4 studs (2 per side) Normal:9 tests 3.64–6.10


Buttry (1965) [22] 2.00, 3.33, 3.50, 4.67, 5.38,5.90, 7.38 22 1 4 studs (2 per side) Normal:9 tests 3.02–6.22


Chinn (1965) [9] 3.33, 3.38, 3.41, 4.00, 4.67,5.38, 4.67 10 1 4 studs (2 per side) Normal:8 tests 3.99–5.48


Mainstone and Menzies (1967)[12] 4.67 11 1 4 studs (2 per side) Normal:11 tests 3.74–5.02


Davies (1967) [11] 4.67 19 1, 2,3

4, 6, or 8 studs Normal:19 tests 3.76–5.52(2, 3, or 4 per side) Lightweight: 0 tests (25.9–38.0)

Steele (1967) [10] 3.50 18 1 4 studs (2 per side) Normal:3 tests 2.98–4.37Lightweight: 15 tests (20.5–30.1)

Dallam (1968) [24] 4.00, 4.67, 5.90, 7.38 17 1 4 studs (2 per side) Normal:2 tests 3.89–6.11Lightweight: 15 tests (26.8–42.1)

Baldwin (1970) [25] 3.50, 4.00, 4.67, 5.90, 7.38 26 1 4 studs (2 per side) Normal:2 tests 2.99–8.07Lightweight: 24 tests (20.6–55.6)

Menzies (1971) [42] 4.67 6 1 4 studs (2 per side) Normal:6 tests 2.47–7.33Lightweight: 0 tests (17.0–50.5)

Hawkins (1971) [44] 2.00, 2.33, 2.86, 3.00, 3.51,4.00, 4.67 22 2 4 studs (2 per side) Normal:22 tests 2.89–5.04

8 studs (4 per side) Lightweight: 0 tests (19.9–34.7)

Ollgaard et al. (1971) [15] 3.50, 4.21 48 1, 2 4 studs (2 per side) Normal:18 tests 2.67–5.088 studs (4 per side) Lightweight: 30 tests (18.4–35.0)

Klingner and Mendonca (1982)[45] 11 8 5 ‘‘In the field’’ Normal:8 tests 4.28

Lightweight: 0 tests (29.5)

Hawkins and Mitchell (1984)[34] 3.33 2 5 ‘‘In the field’’ Normal:2tests 1.97–8.98


Jayas and Hosain (1989) [26] 4.30 1 3 12 studs (6 per side) Normal:1tests 4.37Lightweight: 0 tests (30.1)

Zhao (1993) [46] 2.27, 2.96, 4.09 18 5 ‘‘In the field’’ Normal:18 tests 3.13–3.36Lightweight: 0 tests (21.6–23.1)

An and Cederwall (1996) [47] 3.51 8 2 8 studs (2 per side) Normal:8 tests 4.46–13.2Lightweight: 0 tests (30.7–90.9)

Gattesco et al. (1996) [35] 6.58 1 5 ‘‘In the field’’ Normal:1 tests 3.77Lightweight: 0 tests (25.9)

Saari et al. (2004) [39] 6.67 2 4 4 studs (2 per side) Normal:2 tests 4.44–5.04Lightweight: 0 tests (30.6–34.7)

Shim et al. (2004) [43] 5.68, 5.22, 4.70 17 2 8 studs (4 per side) Normal:17 tests 5.13–9.35Lightweight: 0 tests (35.3–64.4)

Anderson and Meinheit (2005)[4]

3.62, 4.21, 4.81, 5.32, 5.93,9.84 105 5 ‘‘In the field’’ Normal:105 tests 5.15–7.15


unsafe for 60% of the tests. The results for EC-4 (2004) are moreconservative, since 309 of the 391 tests resulted in ratios less than1, indicating that the formula is unsafe for 21% of the tests.

Additional insight can be gained by separating the testsbased on the failure mode before computing the average test-to-predicted ratio. For steel failures, the AISC 2005 prediction is


Table 3Steel and concrete strength by AISC, PCI 6th Edition, and ACI 318-08.

Steel failureφQnvs = φvCvAsFun

Concrete failure (pryout, or ‘‘in the field’’) φQnvc = φvCvRvn

φv Cv φvCv φv Cv φvCv Rvb

Average formula 5% fractile

AISC 1.00 1.00 1.00 1.00 1.00 1.00 0.5As√f ′c Ec

EC-4 0.80 0.80 0.64 0.80 0.66 0.48 0.5As√f ′c Ecm

0.74c 0.60

PCI 6th 1.00 0.75 0.75 0.70 1.00 0.70 317.9λ√f ′c (d)

1.5 (hef )0.5 215λ√f ′c (d)

1.5 (hef )0.5ACI 318-08a Ductile steel element 0.65 1.00 0.65 0.70 1.00 0.70 kcp40λ

√f ′c(hef)1.5 kcp24λ

√f ′c(hef)1.5

Brittle steel element 0.60 1.00 0.60a The formulas for a ductile headed steel anchor have been used in this work.b Units: pounds, inches for ACI 318-08 and PCI 6th Edition; Units: kips, inches for AISC. N, mm for EC-4.c The Cv factor depends on the height of the stud.

Table 4Test-to-predicted ratios for steel failure in tests using the minimum strength provided by the standards.

Shear forces 202 tests Without resistance factor With resistance factorAISC EC-4 ACI 318-08 PCI 6th AISC EC-4 ACI 318-08 PCI 6th

Average 0.986 1.215 1.150/1.344a 1.051/1.498a 0.986 1.518 1.974 2.142Stand. dev. 0.158 0.195 0.560/0.815a 0.183/0.311a 0.158 0.244 1.141 0.441a γ 1/γ 2 : γ 1: uses the average value; γ 2: uses the 5% fractile formula.

Table 5Test-to-predicted ratios for concrete failure in tests using the minimum strength provided by the standards.

Shear forces 114 tests Without resistance factor With resistance factorAISC EC-4 ACI 318-08 PCI 6th AISC EC-4 ACI 318-08 PCI 6th

Average 0.849 0.996 1.576/2.097a 1.011/1.495a 0.849 1.245 2.997 2.127St. dev. 0.244 0.245 0.766/1.026a 0.168/0.249a 0.244 0.307 1.465 0.363a γ 1/γ 2: γ 1: uses the average value; γ 2: uses the 5% fractile formula.

accurate and safe (Fig. 1(b)), with EC-4 showingmore conservativeresults due to the 0.8 reduction factor (Fig. 1(f)). For tests in whichthe concrete failed, the scatter is much larger and many test-to-predicted ratios are less than 1 (Fig. 1(c)) for AISC 2005; EC-4 againpresents a more conservative range of results (Fig. 1(g)).The comparison between the different provisions for concrete

failure modes has been carried out using the average formula, the5% fractile formula provided by ACI 318-08 and PCI 6th Edition, andtaking into account the resistance factors specified in Table 3, inorder to assess the accuracy of the different approaches. The test-to-predicted ratios for ACI 318-08 Appendix D and PCI 6th Editionare shown in Fig. 2. The headed stud strength plotted in Fig. 2 isthe minimum of the strength of the steel (AsFu) and the strengthcomputed for pryout (‘‘in the field’’) failure mode.Based on using the average formula for predicting stud strength

in shear, it can be seen that PCI 6th Edition (Fig. 2(b)) is moreaccurate than ACI 318-08 Appendix D (Fig. 2(a)) in predicting thelocal failure of the concrete surrounding stud, and its standarddeviation shows less scattered results. ACI 318-08 is moreconservative than PCI 6th Edition due primarily to the auxiliarycoefficient kcp equaling 1 in ACI 318-08 when the headed studis less than 2.5 in (63 mm), as pointed out by Anderson andMeinheit [4]. AISC has lower average ratios thanACI 318-08 andPCI6th Edition, and the scatter is larger, with a considerable numberof tests (approximately 60%) having a test-to-predicted ratio lessthan 1.0 (Fig. 1(a)).The results derived from applying 5% fractile formulas for

pryout strength given by ACI 318-08 and PCI 6th Edition are shownin Fig. 2(c) and (d). The scatter of the results applying the 5% fractileformulas, both with and without resistance factors (Fig. 2(e) and(f)) is larger than results given by average values (Fig. 2(a) and (b)),and ACI 318-08 provides more conservative results in comparisonto PCI 6th Edition. The differences between [30], ACI 318-08 and

PCI 6th Edition also typically become larger when the respectiveresistance factors are applied.The formulas used for stud strength in shear in AISC and EC-

4 were derived by looking at all tests in aggregate, regardless ofthe mode of failure. It is informative to compare the accuracy ofthe various formulas for predicting the steel or concrete failuremodes by comparing each formula only to tests failing in the steelor concrete, respectively. If only tests that failed in the steel areexamined (202 tests), EC-4 provides the most conservative results(Table 4). PCI 6th Edition provides the most conservative resultswhen using the 5% fractile equation or when resistance factors areapplied. Similarly, for headed stud anchors failing in the concrete(114 tests), ACI 318-08 is shown to be themost conservative, whilePCI 6th Edition is accurate with small scatter (Table 5). AISC is seento be unsafe for both groups of tests.The strength prediction (AsFu) for steel failure (202 tests) may

be seen in Fig. 3. This formula becomes more conservative whenthe specified (nominal) values of the steel strength are used ratherthan measured values.Fig. 4 shows the results of using concrete failures to assess

tests that failed in the concrete. It can be seen that PCI 6th Editionis more accurate than ACI 318-08 Appendix D, although PCI 6thEdition restricted its proposed formula for ‘‘in the field’’ cases, orpryout, for headed studs with the ratio hef /d < 4.5. ACI 318-08 Appendix D again provides very conservative results when theeffective height of the stud is less than 2.5 in (63 mm), due to thekcp coefficient, as discussed earlier. If the AISC formula for concretefailure is used similarly, the results are less conservative, especiallywithout resistance factors (Fig. 1(c)). For EC-4, the average result isconservative (Fig. 1(g)).


Fig. 1. Assessment of anchor strength using the minimum of steel and concrete failure formulas in AISC and EC-4.

5. Reassessment of headed steel stud strength in the AISCspecification

From Fig. 3 and Table 7, where the steel formula and concreteformula of EC-4 with resistance factors are assessed respectively,it is seen that EC-4 presents conservative results for design pur-poses, particularly when the resistance factor is applied, For AISC[30], the results are less conservative; as a result, new resistancefactors are assessed in this paper for these provisions based on useof the experimental database. Using recommendations byRavindra

andGalambos [51], resistance factors can be computed to compen-sate for the scatter and low mean values exhibited by the resultsfrom the current AISC [30] formulas, as seen in Fig. 1. Given a relia-bility index, β , the resistance factor can be computed using Eq. (1).

φ =RmRne(−αβVR), (1)

whereRmRnis the average of the ratio between the test result and the

predicted value;


Fig. 2. Assessment of anchor strength using the minimum of steel and concrete failure formulas in [2] Appendix D and [6].

α is equal to 0.55, given by Ravindra and Galambos [51];β is the reliability index; and

VR =√V 2F + V

2P + V

2M , where VF is the coefficient of varia-

tion on fabrication and is taken as VF = 0.05 as recommendedby Ravindra and Galambos [51], reflecting the strong control char-acteristics of stud manufacturing; VP is the coefficient of variationof RmRn ; VM is the coefficient of the variation of the materials and istaken as VM = 0.09 based on test data from [52–54].Ravindra and Galambos [51] recommend a reliability index β

of 3 for members and 4.5 for connections. In this work, a reliabilityindex of 4 has been targeted to compute the resistance factors.Resistance factors for steel strength prediction using only tests

that failed in the steel are computed for values of the Cv coefficientequal to 1.00, 0.75 and 0.65 (Table 6). Values of the resistance factorfor aβ value of both 3 and4 are presented. Eq. (2) presents a samplecalculation for Cv = 1.00 and β = 4.

φv =RmRne(−0.55βVR) = 0.933e(−0.55·4.0·0.160) = 0.65. (2)

With Cv = 0.65 the resistance factor computed by Eq. (2) is largerthan 1.0, so it should be taken as 1.0.

Table 6Resistance factors computed for CvAsFy for Cv = 1, Cv = 0.75 and Cv = 0.65 forsteel strength based on steel failure in tests.

202 tests Cv µ σ C.O.V. φ

β = 3 β = 4

S1 1.00 0.933a 0.150 0.161 0.68 0.61S2 0.75 1.224a 0.200 0.161 0.89 0.80S3 0.65 1.436a 0.231 0.161 – 0.94a With measured values reported by authors or nominal values if the measuredsteel strength was not reported.

6. Formulas for concrete failure

The concrete failure formulas of ACI 318-08 and PCI 6th Editionare geared for general conditions for preventing failure of headedsteel anchors, especially cases where free edges may be close tothe stud. Such free edges rarely occur in composite construction.Thus, several alternative formulas were developed in this workto compute the concrete strength surrounding headed studs forconditions commensurate with composite construction. Theseformulas are comparedwith the AISC and EC-4 formulas in Table 7.It can be seen that themean value of the test-to-predicted ratios fortheAISC formula in particular is quite low, coupledwith a relativelylarge coefficient of variation. Both the optimized formula and


Fig. 3. Steel failure formulas in comparison with steel failure in tests.

simplified versions of these formulas are shown. The equations arefunctions of the properties of the headed steel anchors, includingheight, shank diameter, and concrete strength. The proposedformulas have been calibrated using a least squares technique,constraining the average test-to-predicted ratio to equal 1.0 forall 114 tests failing in the concrete (Fig. 5). The statistical valuesfor optimized formulas and then their corresponding simplifiedformulas developed to predict concrete failures of anchors loadedin shear in composite construction are shown in Table 7.Proposals 1 and 2 have the same form as the current formula

of AISC and EC-4, without distinguishing the concrete weight.Proposal 3 takes into account the stud height, similar to PCI6th Edition and ACI 318-08. Proposal 4 takes into accountthe concrete weight (λ), with the result being similar to oneproposed by Anderson and Meinheit [4]. The coefficient λ =(f ′c,sp6.7

)1√f ′c≤ 1.0 (in psi) or λ =

(f ′c,sp0.046

)1√

f ′c /0.0069≤ 1.0

(in MPa) is a lightweight concrete factor. It can be computedfollowing either ACI 318-08 or PCI 6th Edition. If the valueof the splitting tensile strength f ′c,sp is not known, λ equals0.85 for sand–lightweight concrete and 0.75 for all-lightweightconcrete. Lightweight concrete according to ACI 318-08 is concretecontaining lightweight aggregate and having a density between90 lb/ft3 (1440 kg/m3) and 115 lb/ft3 (1840 kg/m3).Table 7 shows the resistance factors (φ) for reliability indices

of 3 and 4 for the tests that failed by the concrete. It can beseen that all four proposals result in similar resistance factors,equaling approximately 0.60 for a reliability index of 4 and 0.70for a reliability index of 3.

7. Headed steel stud shear strength for hef /d > 4.5

From the earliest tests carried out by Viest [7], it has been seenthat hef /d is a significant parameter that often delineates the typeof failure that occurs in tests that do not have free edge conditions.In the tests by Viest [7], for example, the failure normally occurredin the steel stud when hef /d was larger than 4.53. Driscoll and

Slutter [8] observed that, if h/d was greater than 4.2, they coulddevelop all the strength in tension (i.e., AsFu) rather than shear, andthe tensile strength then determined the ultimate strength of thestuds in their push-out tests. It was further noted that, for studsshorter than h/d = 4.2, the strength must be reduced because ofthe possibility of the ultimate strength being reduced by fractureof the concrete. Ollgaard et al. [15] tested studs with an effectiveembedment depth of 3.50 and 4.20. They indicated that in manytests both steel and concrete failures were observed in the samespecimen.A summary of failures found in the tests in the database

classified as having studs that are greater than or less than a givenhef /d ratio (including ratios of 4.00, 4.50, 5.50, and 6.50) is givenin Table 8. AISC [30] states that headed steel studs shall not beless than four stud diameters in length after installation and EC-4 applies a reduction factor on the stud strength for ratios of h/dbetween 3 and 4. Recognizing the h/d limitation in AISC [30] andassuming that h is a few percent larger than hef to account for thedepth of the stud head, it can be reasoned that for a headed studwhose h/d value is right at the limit, approximately 73% of thefailures are likely to occur in the steel. In contrast, 81% of the testshaving a ratio hef /d larger than 4.50 failed in the steel, and 91%failed in the steel for hef /d larger than 5.50.Based on these results, if the minimum h/d ratio limit of 4 in

AISC [30] is recommended for increase to 5 (i.e., hef /d equaling4.5 for a 3/4 in (19 mm) diameter headed stud having a 3/8in (9.5 mm) depth of the head), 81% of the 224 tests with ratioslarger than this limit failed in the steel. In order to predict thefailure of the remaining 19% of the tests that failed in the concrete,one of the proposed formulas in the prior section could be used,taking the minimum value of steel and concrete failures. However,as discussed below, checking the steel formula alone may beadequate for this minimum ratio of hef /d.The required resistance factor for headed studswith hef /d ratios

larger than 4 and 4.5 is presented in Table 9. Fig. 5 then plots thetest-to-predicted ratios, separating tests based on their value ofhef /d. Also, in these plots, both the measured material strengths


Fig. 4. Concrete failure formulas in comparison with concrete failure in tests.

(Fig. 5a, b, g) and the specified (nominal)material strengths (Fig. 5c,d, e, f) are used in the formulas for both steel and concretefailures so as to provide an indication of the test-to-predictedvalues using nominal values typical in design calculations. AWSD1.1/D1.1:2006 Structural Welding Code—Steel [55] specifies twotypes of headed stud, type A and type B, for use in compositesystems depending on their function within the structure. Themain difference between them is the ultimate tensile strength ofthe headed stud. Type A [Fu = 61 ksi (420 MPa)] are general-purpose headed studs of any type and size used for purposes otherthan shear transfer in composite beam design and construction.Type B [Fu = 65 ksi (450 MPa)] are studs that are headed, bent,or of other configuration, with diameter of 3/8 in (9.5 mm), 1/2in (12.5 mm), 5/8 in (16mm), 3/4 in (19mm), 7/8 in (22mm) or 1in (25mm), and that are used commonly in composite beamdesignand construction. The AISC [30] commentary provides steel anchormaterial specifications that include specified (nominal) yield andtensile strengths of typical ASTM A108 [56] Type B studs as 51 ksi(350 MPa) and 65 ksi (450 MPa), respectively (AWS 2004).ACI 301-08 [57] provides formulas for the average measured

concrete (f ′cr) strength given the specified (nominal) concretestrength (f ′c ); for example, f

′cr = f ′c + 1200 (in psi), for a

specified (nominal) concrete strength between 3000 and 5000 psi.In Fig. 5, the stud strength has then been computed using the

specified concrete strength derived from the average measuredconcrete strength reported in the test. An important conclusionfrom this figure is that if hef /d is restricted to being larger than4.5 (or, comparably, h/d is restricted to being larger than 5), usingthe steel formula alone is adequate to safely predict the shearstrengths of the studs. Even those tests that fail in the concrete aregenerally seen to have test-to-predicted ratios larger than 1, withlittle difference from the case where both the steel and concreteformulas are checked, and the minimum used (as seen in Fig. 5(d)and (f)). In Fig. 5(c) and (e), using only the steel formula withspecified (nominal) strength values results in test-to-predictedratios of 1.964 for studs with Fu of 51 ksi (350 MPa) and 1.541 forstuds with Fu of 65 ksi (450 MPa), based on using 0.65AsFu as thedesign strength of the headed stud failing in shear.Fig. 6 plots the test-to-predicted ratios for all tests using the

minimum of the steel strength (0.65AsFu) and concrete strengthformulas for several different concrete strength formulas. Thefigure compares steel (•) and concrete (×) formula predictions,distinguishing type of failure in the top of each figure (C.F. meansconcrete failure, M.F. means mixed failure, and no mark meanssteel failure). It may be seen that the concrete formula alwayscontrols the strength prediction for hef /d < 4.5, which iscommensurate with the type of failure (concrete failure or mixedfailure) found in most of those tests. In contrast, the concrete


Fig. 5. Test-to-predicted values using only the steel formula (a, c, e, g) or the minimum of the steel and concrete formulas (b, d, f).


Table 7Evaluation of concrete formulas for headed stud anchors in shear from AISC 2005, EC-4, and proposed concrete formulas.

Formula for Qnvc a µ σ C.O.V. φ

β = 3 β = 4

AISC 2005 0.5As√f ′c Ec 0.827 0.250 0.302 0.49 0.41

EC-4 Cv0.5√f ′c Ecm 0.965 0.249 0.258 0.61 0.52

Proposal 1 17.000As(f ′c)0.452

(Ec)0.041

1.001 0.242 0.242 0.65 0.5617As

(f ′c)0.45

(Ec)0.04 1.013 0.245 0.242 0.66 0.57

Proposal 2 6.214As(f ′c Ec

)0.209

1.002 0.242 0.242 0.65 0.566.2As

(f ′c Ec

)0.2 1.098 0.265 0.242 0.71 0.62

Proposal 3 18.197As(f ′c)0.479

(h)0.215

0.999 0.237 0.237 0.65 0.5718As

(f ′c)0.5

(h)0.2 0.997 0.237 0.237 0.65 0.57

Proposal 4 8.915λ(f ′c)0.476

(d)1.373 (h)0.564

1.021 0.219 0.214 0.69 0.619λ(f ′c)0.5

(d)1.4 (h)0.6 0.955 0.206 0.216 0.64 0.56a Optimized formula/Simplified formula. Units: kips, inches.

formulas of Proposals 1–3 (Fig. 6(a)–(c)) incorrectly control forhef /d > 4.5, even though steel failure often occurs in those tests.In Proposal 4 (Fig. 6(d)) (which is similar to the concrete formulaof PCI 6th Edition) and in ACI 318-08 (Fig. 6(e)), prediction ofthe type of failure typically matches better with the actual failuremode. However, the results of using the minimum of the steeland concrete formulas tend to be unnecessarily conservative forhef /d > 4.5, and the prediction may be reasonable based upon

checking only the steel formula, as mentioned above, due to thelimited cases with concrete or mixed failures and the reasonablepredictions made for those specific cases using the steel formula.While Table 9 and Figs. 5 and 6 include tests with both

normal-weight and lightweight concrete, to be conservative, allof the recommendations discussed so far in this section could belimited to the use of normal-weight concrete. This is because forlightweight concrete, 35% of the tests have hef /d > 4.5, whereas


Table 8Summary of test failure for several hef /d ratios.

# tests S.F.a C.F.b M.F.c Comments

All tests

hef /d ≥ 4.00 251 184 51 16 73.33% failed in the steelhef /d < 4.00 140 18 63 54 87.14% failed in the concrete or mixed failurehef /d ≥ 4.50 224 182 29 13 81.25% failed in the steelhef /d < 4.50 167 20 85 62 88.02% failed in the concrete or mixed failurehef /d ≥ 5.50 69 63 6 0 91.30% failed in the steelhef /d < 5.50 322 139 108 75 56.83% failed in the concrete or mixed failurehef /d ≥ 6.50 43 42 1 0 97.67% failed in the steelhef /d < 6.50 348 160 113 75 54.02% failed in the concrete or mixed failure

Normal-weight concrete

hef /d ≥ 4.00 201 164 28 13 81.59% failed in the steelhef /d < 4.00 75 9 41 20 81.33% failed in the concrete or mixed failurehef /d ≥ 4.50 187 158 16 13 84.49% failed in the steelhef /d < 4.50 99 11 53 35 88.89% failed in the concrete or mixed failurehef /d ≥ 5.50 50 49 1 0 98.00% failed in the steelhef /d < 5.50 236 120 68 48 49.15% failed in the concrete or mixed failurehef /d ≥ 6.50 33 32 1 0 96.96% failed in the steelhef /d < 6.50 253 137 68 48 45.84% failed in the concrete or mixed failure

Lightweight concrete

hef /d ≥ 4.00 50 24 23 3 60.00% failed in the steelhef /d < 4.00 65 9 22 34 83.63% failed in the concrete or mixed failurehef /d ≥ 4.50 37 24 13 0 64.86% failed in the steelhef /d < 4.50 68 9 32 27 86.76% failed in the concrete or mixed failurehef /d ≥ 5.50 19 14 5 0 73.68% failed in the steelhef /d < 5.50 86 19 40 27 77.90% failed in the concrete or mixed failurehef /d ≥ 6.50 10 10 0 0 100% failed in the steelhef /d < 6.50 95 23 45 27 75.78% failed in the concrete or mixed failurea S.F.: Steel failure (weld failures are included as steel failures).b C.F.: Concrete failure.c M.F.: Mixed failure or not reported.

Table 9Resistance factors for tests with hef /d ratios larger than 4.5 and 4.0.

224 tests, hef /d > 4.5 φ 251 tests, hef /d > 4.0 φ

Cv µ σ C.O.V. β = 3 β = 4 Cv µ σ C.O.V. β = 3 β = 4

Option 1 1.00 0.910 0.158 0.174 0.65 0.58 1.00 0.890 0.172 0.193 0.62 0.55Option 2 0.75 1.213 0.211 0.174 0.87 0.77 0.75 1.186 0.229 0.193 0.83 0.73Option 3 0.65 1.399 0.244 0.174 – 0.90 0.65 1.369 0.264 0.193 0.95 0.85

for normal-weight concrete 65% of the tests have hef /d > 4.5,thus providing a much larger sample size (see the portions ofTable 8 that disaggregate the test data for different weights ofconcrete). Thus, it may be deemed less conclusive what value ofhef /d is required to ensure that just checking a steel failure formulais adequate for lightweight concrete. The results of Fig. 5 implythat the steel strength formula adequately predicts both normal-weight and lightweight concrete failures, but Table 8 shows that arelatively large percentage of failures are occurring in the concreteif a minimum value of hef /d is taken as 4.5. From Table 8, a value of6.5 for hef /d (i.e., or a value of h/d > 7)more clearly assures failurein the steel for lightweight concrete, and thus this is proposed astheminimum hef /d for lightweight concrete if only the steel failuremode is to be checked. However, it is noted that there are fewertests results to validate this conclusion as compared to normal-weight concrete. Alternatively, for composite components that uselightweight concrete, either Proposal 4 of Table 7 should also bechecked, or the provisions of ACI 318-08 Appendix D or similarshould be used in total.

8. Seismic behavior of steel anchors in shear

Results from the literature generally show that push-out speci-mens having headed steel stud anchors subjected to cyclic shearforce exhibited lower strength and ductility than correspondingmonotonic push specimens. A number of experiments on headed

steel anchors subjected to cyclic loading have been conducted tostudy the behavior of steel frames with reinforced concrete infills.For example, Makino [58] conducted experiments were performedon single-story, single-bay steel frames with reinforced concreteinfills at approximately a one-third scale. They estimated that thecyclic strength of the studs was approximately 50% of the pre-dicted strength from the formulas of Ollgaard et al. [15]. Civjanand Singh [38] conducted seven cyclic tests and concluded thatreversed cyclic loading resulted in nearly a 40% reduction in thestud shear strength compared to monotonic strengths computedby AISC 2005, attributing this reduction to low-cycle fatigue ofthe stud and weld materials as well as concrete degradation. Gat-tesco and Giuriani [35] tested two specimens under cyclic loadingand concluded that the accumulateddamageduring cycles reducedthe measured monotonic strength by almost 10%. Saari et al. [39]carried out eight tests under different combinations of shear andtension loads and both monotonic and cyclic loads with differentamounts of confining reinforcement around the anchors withina specimen modeling an infill wall. From their tests they deter-mined that when good detailing is provided surrounding the studsin the specimen, the cyclic failure always occurred in the steel. Also,under shear forces, a 21% reduction in measured monotonic studshear strength was found.These reduction factors for cyclic loading (ξ) for conditions rep-

resenting either infill wall specimens or composite slabs without


a b

c d

e

Fig. 6. Comparison between steel (0.65AsFu) and concrete predictions with resistance factors and type of failure.

Table 10Cyclic shear strength of headed studs.

Code ξ Reference ξ

AISC 341-05 [31] 0.75 Makino (1984) [58] 0.50ACI 318-08 [2]b 0.75 Civjan and Singh (2003) [38] 0.60a ,bNEHRP (2004) [59] 0.75 Gattesco and Giuriani (1996) [35] 0.90a

Saari et al. (2004) [39] 0.79a

a Failure of the steel.b Failure of the concrete.

metal decking are summarized in Table 10, along with the valuesassumed in several design provisions. While there is variation inthe recommendations (for example, ACI 318-08 does not require areduction for cyclic loading on the shear strength of steel anchors),it may generally be concluded that the 25% reduction inmonotonicshear strength to account for cyclic loading is reasonable so long asthemonotonic shear strength is predictedwithin reasonable statis-tical accuracy. For example, a reduction factor of 0.75 is appropriatewhen used in conjunction with a Cv coefficient or resistance factorof 0.65 applied to the nominal shear strength AsFu of a headed studanchor with hef /d ratios larger than 4.5.

9. Conclusions

In this work, limit state formulas for headed stud anchors inshear specifically in composite construction have been assessedversus 391 monotonic and cyclic experiments from the literaturewithin the context of the AISC Specification [30,31] and EC-4 (2004)[32], and comparisons have been made to the provisions in theACI 318-08 Building Code [2] and the PCI Handbook, 6th Edition [6].New formulas are proposed to predict concrete failure and exist-ing formulas for steel failure are evaluated based upon the com-prehensive experimental data set. The experimental results aredisaggregated to highlight tests that failed in the steel shank orweld, tests that failed in the concrete, or tests that are identified ashavingmixed failure. The scope of this research includes compositebeam–columns [typically concrete-encased steel shapes (SRCs) orconcrete-filled steel tubes (CFTs)], concrete-encased and concrete-filled beams, boundary elements of composite wall systems, com-posite connections, composite column base conditions, and relatedforms of composite construction; composite beams consisting ofsteel girders with composite lightweight concrete slab (with deck-ing) are out of the scope of this work. Several conclusions can bedrawn from this work.


• The most likely concrete failure mode in composite construc-tion is pryout failure, rather than breakout failure (with thesefailure modes being as described in ACI 318-08) since thereare not appropriate failure planes for front-edge or side-edgebreakout in the majority of composite structures. In this work,the concrete breakout strength is deemed not to be a governinglimit state; such conditions are thus beyond the scope of thiswork.• The AISC [30] formula for predicting the steel failure mode inheaded stud anchors (AsFu) is accurate for steel failures in an-chors only if a resistance factor is included to ensure an accept-able level of reliability, comparable to what is used in PCI 6thEdition andACI 318-08. A resistance factor of 0.65 provides a re-liability index β of approximately 4. Alternatively, a resistancefactor of 1.0 may be used if a reduction factor such as 0.65 isapplied to AsFu.• EC-4 (2004) provides conservative results inmost cases for steeland concrete failures when resistance factors are applied.• PCI 6th Edition and ACI 318-08 provide more conservative pre-diction for concrete failures thanAISC 2005,with PCI 6th Editionbeing the most accurate. AISC 2005 is generally unconservativewhen anchors fail in the concrete.• A selection of formulas to estimate pryout concrete failures areproposed as an alternative to the current prediction of concretefailure in AISC 2005. The choice of formula is dependent onwhich types of parameters are deemed appropriate to governthe concrete failure strength.• After assessing the literature regarding headed studs subjectedto shear, itwas deemed that the steel strength formulaAsFuwitha resistance factor equal to 0.65 is the only formula that needsto be checked for headed stud anchors that are not subject tobreakout failures in the concrete, if normal-weight concrete isused and if the effective height-to-depth ratio hef /d is largerthan 4.5 (where hef is measured to the underside of the studhead; a comparable minimum value of h/d is 5, where h is thetotal height of the stud). For the few experiments in this cate-gory that fail in the concrete, the steel strength formula provedto be conservative. For composite componentswith lightweightconcrete, a larger minimum value of the anchor height is rec-ommended because there is less data available for these longerlengths, and what data is available shows that the failure tendsto occur more in the concrete than for normal-weight concreteif hef /d is just above 4.5. Based on the limited data available todate, a value of hef /d > 6.5 (or a comparable value of h/d > 7)more clearly assures that failure will occur in the steel, and thusthis value is recommended for lightweight concrete if only asteel strength formula is to be checked. Additional test resultscould validate using a lower value of this minimum ratio in fu-ture research.• A reduction factor of 0.75 is adequate to design headed stud an-chors in shear subjected to seismic loads, so long as the mono-tonic steel strength of headed studs has a resistance factor onAsFu that is in the range of the values proposed in this work.

Acknowledgements

Funding for this research was provided by the Fundación CajaMadrid and theUniversity of Illinois at Urbana-Champaign. The au-thors thankMr. N. Anderson, Dr. D. Meinheit, and Dr. K. Rasmussenfor sharing their collected data and Mr. M. Denavit of the Univer-sity of Illinois at Urbana-Champaign for his contributions to thiswork. The authors thank the members of the American Institute ofSteel Construction Committee on Specifications Task Committee 5on Composite Construction for their comments on this research.

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Documents

Headed Steel Stud Anchors in Composite Structures