failure analysis of anchors in shear under simulated seismic

1

Failure Analysis of Anchors in Shear under Simulated Seismic Loads 1

Zhibin Lin1*

, Jian Zhao2, and Derek Petersen

3 2

1: Department of Civil, Architectural and Environmental Engineering, Missouri University of Science and 3

Technology, Rolla, MO 65401, USA 4

2: Department of Civil Engineering and Mechanics, University of Wisconsin, Milwaukee, WI 53201, USA 5

3:Osmose Railroad Services Inc. Madison, WI 53716, USA 6

Abstracts: This paper presents a study of the failure analysis of anchors in shear in simulated 7

seismic loads. Ductile failure is critical for anchor design in seismic applications to avoid brittle 8

catastrophe while existing design codes and guidelines that usually accept steel failure as ductile 9

failure are insufficient, and may overestimate shear capacities and ductility. In this study 10

ductility was evaluated based on both effective confinement due to anchor reinforcement and 11

ductile steel. Those anchors with the proposed reinforcement showed a significantly high 12

strength and exhibited great ductility due to effective confinement. Three types of anchor steel 13

were also evaluated. The influences of failure modes, shear capacities and ductility of anchors 14

were taken in account by defining exposed length. Test results indicated both effective 15

confinement and specified ductile steel could ensure anchor have good seismic performance. 16

Keywords: Concrete anchors; headed studs; anchor connections; fastening to concrete; anchor 17

reinforcement; and ductility. 18

19

1. Introduction 20

The behavior of cast-in-place anchors and headed studs subjected to static loading has been 21

studied [1-5], and the results have been implemented in design codes (e.g., ACI 318 [6]; FIB [7]). 22

Anchors and headed studs work as essential elements for shear transfer in connections for 23

* Corresponding author. Tel: +1 414 229 1119; fax: +1 414 229 6958

E-mail address: [email protected] (Zhibin Lin).

2

buildings and bridges when subjected to seismic loading. Dysfunction/damages in concrete 1

anchors due to seismic loading, as reported during major earthquakes (Northridge, 1994; 2

Wenchuan, 2008; Haiti, 2010; Chile, 2010, and Christchurch, 2011), have raised concerns in both 3

experimental research and post-earthquake investigations for seismic performance of anchors. 4

For example, brittle concrete breakout in bridge anchor connections (Fig. 1a) was observed in 5

current post-earthquake investigations of Chile earthquake [8] while Figure 1b presented two 6

fractured anchor shafts, which was used in the connection of shear keys in bridges. It is well 7

known that the behavior of anchors under seismic loading could be affected by loading history, 8

concrete and steel materials, and etc. Among them the requirement of ductility in anchor design 9

is particularly important in earthquake-prone areas. The corresponding ductility-related 10

provisions have been specified for the design of anchors. For example, ACI 318-08 stipulates the 11

steel having a tensile elongation of at least 14 percent and 30 percent reduction in area can be 12

defined as a ductile steel element. Also, the previous observations by Silva and Hoehler [9] 13

revealed that using the concept of steel failure equivalent to ductile failure, as specified in 14

existing design codes and guidelines (e.g., ACI 318-11 Appendix D and FIB), is inadequate in 15

some cases. It is because ductile steel element only may not be sufficient to ensure ductile steel 16

failure of anchor, which is also largely associated with anchors under different load cases [9, 10]. 17

To ensure ductile response corresponding to the desired behaviors, however, it is insufficient to 18

only use the specified minimum elongation without specifying failure modes and confinement 19

from concrete which may significantly affect the strength capacity and ductility of anchor bolts 20

[11]. 21

Moreover, most studies which investigated anchor rods in concrete anchors focused on 22

concrete failure modes, rather than the failure of anchor rods. Few documented studies examined 23

3

the effects of ductile anchor used for ductility requirement in design codes for the strength 1

capacity of anchors. Thus, there is a lack of research which investigates anchor steel failure 2

modes that may characterize the shear capacity of anchors. Based on the current design 3

specifications, for anchors controlled by steel failure in shear, no reduction is required for the 4

anchor capacities corresponding to steel failure. Strength reductions under cyclic loading against 5

the static loading, however, have been recognized in the literature [12, 13]. For example, Pallarés 6

and Hajjar [12] suggested that the steel capacity of anchor in shear shall have a reduction by a 7

factor of 0.76 while Petersen’s experimental tests [13] indicated a 0.85 reduction factor for 8

anchor steel failure under cyclic loading. Such deviation iterated that extensive studies are 9

required to appropriately characterize the effects of cyclic loading on the capacity of anchor rods 10

in shear. 11

It is therefore useful to carry out an investigation to assess potential interaction between 12

ductility and shear strength for anchor design to verify the effectiveness of those ductility-related 13

provisions and also anchor design practice in earthquake design requirements. 14

15

2. Behavior of anchor bolts in shear and ductility 16

Based on ACI 318 Appendix D for the seismic design of anchors, current design regulations, 17

as documented in Moheler [10] and Derek et al. [14], recommend three options for seismic design 18

of anchor connections: a) to design for ductile anchor steel failure as anchor capacity; b) to design 19

for ductile connection failure below the anchor capacity; and c) to design for brittle failure of 20

anchor using increased seismic force. Ductile anchor steel failure in shear in the first case was only 21

discussed in this paper. To better understand shear capacity, and ductility of anchors in seismic 22

performance, the behavior of anchor with and without anchor shear reinforcement was reviewed 23

4

and discussed below. 1

2

2.1 Anchor in shear in plain concrete 3

Research on behavior of anchors/headed studs in shear in plain concrete has been conducted 4

extensively [1, 4-7] while anchor may end up with steel fracture or concrete breakout, as shown 5

in Figs 1a and 1b. Without introduction of any reinforcement, plain concrete, a quasi-brittle 6

material, may suffer sudden failure when anchor was subjected to shear loads, thus causing 7

significant reduction of shear capacity of anchor. The post-earthquake observations (e.g., photos 8

shown in Figure 1a) showed that anchor connection failed by large pieces of concrete breakout in 9

front of anchors, thereby causing dysfunction of the connection between superstructure and 10

bridge column. It was suggested that impacts of brittle failure on shear capacity could have 11

played a significant role in contributing to the failure of connection. It is well known that the 12

concrete breakout leads to unreliable seismic performance and must be prevented in seismic 13

design because of its nature of brittle failure. Such concrete failure modes may be associated 14

with embedment length and the front edge distance from the anchor. Increasing anchor 15

embedment length or the front edge distance may switch failure modes from concrete failure to 16

steel fracture. 17

Unlike concrete breakout, shear fracture of anchor shaft should behave in ductile manner. 18

Existing building codes and design guidelines, such as ACI 318-11 Appendix D [6] and FIB [7], 19

commonly accept steel fracture failure modes for the design of fastenings [9]. Additional 20

ductile-based provisions are stipulated to ensure ductile steel failure of anchors for seismic 21

applications. For example, elongation of anchor steel greater than 14 percent, as well as 22

reduction of its cross section larger than 30 percent, is required for ductile element in ACI 318-08 23

5

Appendix D. 1

However, steel failure is not equivalent to ductile failure [9] and the ductile performance of 2

anchor may also correlate with loading cases and confinement from concrete. For example, 3

ASTM A193 Grade B7 threaded rods are widely accepted as ductile steel in tension with an 4

elongation of up to 16 percent. The shear tests of 19-mm (3/4-in.) diameter anchor rods with 5

152-mm (6-in.) embedment length in concrete, however, showed that the rods were failed by 6

steel fracture with only averaged 7 mm (0.3 in.) brittle shear deformation, as shown in Figure 2a. 7

Fracture surface of the rod, as illustrated in a photo in Figure 2b, displayed an obviously brittle 8

failure, similar to the observations in the shear tests in Kwon et al. [15] and Lin et al. [11]. The 9

backscattered electron image of a sample cut from fracture anchor shafts was shown in Figure 3. 10

Micro-scale dimples in grains slipped and oriented uniformly parallel to the shear deformation 11

direction, which correlated with the observed smooth and shining surface in fractured anchors. 12

In general, shear capacity of anchor may not be fully developed due to concrete brittle 13

failure while correspondingly ductility of anchor may be limited to concrete strength against 14

anchor steel. Without the anchor reinforcement, anchor may either fail by brittle concrete 15

breakout or brittle steel shear fracture, as indicated in Figs. 2a and 2b. Neither of them was 16

reliable to provide a ductile manner, in particular under cyclic seismic loading. Without enough 17

confinement from concrete to allow anchor deform, anchor that tended to be designed by steel 18

fracture may lose support due to the crushing of concrete around the anchor shaft when subjected 19

to reversed seismic loads, which in turn resulted in the concrete failure, thereby ending up with 20

pulling out failure. 21

22

23

6

2.2 Anchor in shear with anchor shear reinforcement 1

To increase shear deformation and thus fully develop shear capacity of anchors, two types of 2

steel reinforcement are recommended in ACI 318-11 Appendix D [6]: using horizontal hairpins 3

wrapping around anchor (Figure 4a) or hooked bars along the direction of the shear force. It 4

should be noted that the concept of the anchor reinforcement in existing studies or existing codes 5

and guidelines, as revealed in Derek and Zhao [16], is based on the assumption that the 6

confinement of anchor reinforcement takes effect associated with the onset of the concrete 7

breakout forming. As such, the anchor reinforcement may directly carry shear force from anchor 8

but core concrete becomes ineffective after concrete spalling and breakout, as indicated by grey 9

areas in Figure 4a. 10

Most of limited research on anchor in shear reinforcement has been performed by using 11

hairpins [4, 17-20], as indicated in a detailed document by Derek and Zhao [16]. Swirsky et al. 12

[17] documented 24 experimental anchor tests under monotonic and cyclic shear loading using 13

hairpins as reinforcement. Much higher shear capacity and relatively large shear deformation (up 14

to 25 mm (1 in.)) in anchor tests were observed as compared to that in plain concrete. Such 15

improvement in shear capacity was further confirmed by Klingner et al. [4] on the investigation 16

of 28 anchors under monotonic and cyclic shear loading using U-shaped hairpins placed at 17

varying locations through depth. The test results, however, also revealed that hairpins may not 18

be effective to resist reversed cyclic shear loads. Crushed concrete through depth caused by the 19

previous cycles may result in a considerable decrease in the lateral support to the anchor shaft 20

such that the hairpins cannot provide effective load transfer to unrecovered crushed concrete 21

when the anchor was loaded toward the opposite direction of the hairpins head. Similar 22

conclusions were also drawn by Lee et al. [18], Paschen and Schönhoff [19], and Ramm and 23

7

Greiner [20]. Some unexpectedly terminated tests due to significant capacity reduction before 1

anchor fracture, as observed in Swirsky et al. [17], Klingner et al. [4], and Lee et al. [18], also 2

demonstrated that reliable shear deformation should be attributed to the effectiveness of the 3

anchor reinforcement, with which anchor could be allowed to fully develop its capacity and 4

experience large ductile shear deformation till steel fracture for seismic applications. 5

Clearly the important seismic design consideration for strength and ductility of anchor in 6

shear is to have sufficient reinforcement to confine the compressed concrete in front of anchor. 7

In addition to enhance strength, the requirements for ductile steel failure of an anchor should be 8

coupled with both ductile steel element and also a specific shear deformation capacity to achieve 9

ductility. Both good confined concrete and ductile anchor steel are essential to allow anchor have 10

adequate rotation capacity to fully develop shear capacity and present ductile behavior, which 11

were addressed in details followed by two sections below. 12

13

3. Strength enhancement and ductile deformation in proposed anchor reinforcement 14

The observations in aforementioned previous studies in behavior of anchor in shear with and 15

without reinforcement revealed that enhancement in strength and ductility of anchors in shear 16

should be attributed to effective confinement by anchor reinforcement to prevent concrete core 17

around the anchors from splitting, and breaking out. This understanding has led to alternative 18

designs and detailing for the anchor reinforcement [16]. The proposed anchor shear 19

reinforcement, shown in Figure 4b, consisted of: a) closed stirrups placed parallel to the plane of 20

the applied shear force and the anchor; and b) straight reinforcing bars at corners and evenly 21

distributed along the concrete surfaces. Two closed stirrups were installed next to the anchor 22

shaft separately at both sides while remaining stirrups were installed with a spacing of 51 mm (2 23

8

in.) to 76 mm (3 in.) within an effective distance about 0.5 times the front edge distance. A 1

distance of 8db on both sides of the anchor was required to have the development length of 2

horizontal legs of the vertical closed stirrups, where db denotes the reinforcement diameter. Full 3

details of the proposed anchor reinforcement and the corresponding behavior were discussed 4

elsewhere [14, 16]. 5

With the proposed shear reinforcement, Derek and Zhao [16] presented the investigation of 6

20 cast-in-place anchors, including sixteen 25 mm (1 in.) diameter ASTM A193 Grade B7 7

threaded rods and four 19 mm (3/4 in.) diameter ASTM F1554 Grade 55 anchors. Number of 8

anchor reinforcement was designed in accordance with nominal strength of anchor in shear. Two 9

closed No.4 reinforcing bars were placed to both sides of the 19 mm (3/4 in.) diameter F1554 10

anchors while three different types of evenly distributed stirrups wrapping 25 mm (1 in.) 11

diameter A193 anchors were used to account for the effects of varying stirrups spacing from 51 12

mm (2 in.) to 76 mm (3 in.) and effective distance from 51 mm (2 in.) to 250 mm (10 in.). 13

Figure 5 plotted the tests results with the proposed anchor reinforcement. The measured 14

shear forces vs. shear deformation of anchor with three types of reinforcements were compared 15

with that in unreinforced concrete breakout in Figure 5. Note that results were normalized by 16

nominal shear capacity of anchor (209 kN (47 kips)). Figure 5 showed that anchor steel failure 17

was achieved in all cases and resulted in a significant increase in strength compared to that in 18

unreinforced concrete breakout, indicating that the confinement of concrete core by proposed 19

arranged anchor reinforcement was effective. In particular, with the introduction of the proposed 20

anchor reinforcement, the anchors exhibited a considerable improvement in ductility, with up to 21

40-mm (1.5-in) shear deformation, as compared to only 2.5 mm (0.1 in.) deformation in brittle 22

concrete breakout. Unlike a significant strength drop with the increase of the shear deformation 23

9

in the most previous studies, strain hardening behavior during the relative large deformation also 1

confirmed that the proposed anchor reinforcement design was reliable in seismic applications. 2

Similar observation was found in all cases under reversed cyclic loading [14, 16]. 3

To demonstrate the effects of reinforcement on strength and ductility, the test results were 4

also compared with three tests of anchor/headed studs without reinforcement: a) in pure shear 5

test [21], b) in the nearly pure shear tests from 19-mm diameter A193 threaded rods in 6

unreinforced concrete (Fig. 2), and c) in the nearly pure shear tests of 22-mm (7/8-in.) diameter 7

A193 steel by Kwon et al. [15], which were used in the design of headed studs in composite 8

structures. All measured shear force were normalized by the design capacity of anchor bolts in 9

shear in ACI 318-11, that is, shear force over 0.6Ase,vfuta, where Ase,v is the effective area of 10

anchor in shear; and futa is ultimate tensile strength of anchor steel. Pure shear failure had an 11

only 3.8 mm (0.15 in.) deformation, though it had the highest shear capacity among all cases, a 12

slightly higher than unity. Nearly pure shear tests cases displayed a slightly larger deformation, 13

with up to 7.6 mm (0.3 in.) displacement while the strength had a slight drop to some extent. 14

Thanks to confinement of the reinforcement, the specimens presented a different behavior. The 15

load vs. displacement curves indicated an initial flexural-dominant behavior for the specimens 16

with reinforcement. It was likely because concrete cover, due to the lack of confinement, was 17

spalled off early when the anchors are subjected to shear, leading to an exposed portion in the 18

anchors, as shown in Figure 4b. The exposed portion of an anchor (lever arm in Eligehausen et 19

al., [5]) may undergo larger deformation. The stiffness regained at such larger displacements. 20

As described in elsewhere (Lin et al., [11]), the strain hardening behavior was likely due to 21

tension-dominant fracture, which was further explored and discussed in details below. As such, it 22

was observed that the proposed anchor reinforcement provided over 400 percent increase in 23

10

ductility compared to pure shear tests while strength maintained over 80 percent of nominal 1

shear capacity. 2

Comparison of tests results with pure and nearly pure shear tests without reinforcement 3

indicated that closed stirrups can effectively confine concrete breakout such that the confined 4

concrete can transfer shear force to the rest of structure. In this way, rather concrete splitting by 5

relying on the tensile properties of concrete, concrete core under the confinement due to the 6

proposed anchor reinforcement, shaded blue areas within closed stirrups shown in Figure 4b, 7

could continue to carry shear forces at higher strains with the benefit of compressive properties 8

of concrete. Effective confinement also allowed the anchor shaft to undergo larger shear 9

deformation without apparent strength reduction. Such potential benefits in turn resulted in 10

higher deformation capacity of the anchor, which correlated with the contribution of the concrete 11

compressive stress distribution through concrete core under high confinement. 12

13

4. Ductile element in anchor bolt 14

Failure analysis of anchor with anchor reinforcement showed that anchor can display 15

different behavior under varying confinement, which was schematically summarized in Figure 6. 16

To behave in effective ductile manner, the rotation capacity, shown in Figure 6, may be largely 17

correlated with confinement from the reinforcement and ductile material. Therefore, in addition 18

to the proposed anchor reinforcement offering effective confinement to allow anchor to behave 19

in ductile manner, the ductility of anchor steel itself also play another key role in ensuring anchor 20

achieve ductile performance in seismic design. 21

With effective confinement to ensure anchor deform, the capacity of ductile deformation of 22

anchor steel not only affects the failure modes, but also may cause differences in ultimate shear 23

11

capacity. For example, a coefficient in shear capacities ( ) with different 1

values of 0.375 and 0.25 are used for different grade steels (metric Grade 4.6 and 8.8 anchor steel, 2

respectively) in Dutch Standard (NEN 6770, 1990). ACI-318 Code [6] specifies the design factor 3

to account for the effects for the ductility. However, such factor is only to avoid the brittle failure 4

instead of explaining the difference in strength due to ductility of steel. A review of such 5

existing design guidelines reveals that shear behavior of anchor bolts with different ductile 6

element are not well understood, and methods to characterize strength capacities in shear are not 7

adequately supported by experimental data. To evaluate the effects of ductility of anchor steel 8

material on the shear capacity and also provide data to verify current design guidelines and 9

capacity predictions (e.g., in the appendix D in ACI 318-08), A total of 18 double-shear tests 10

were conducted using three different types of 19-mm (3/4-in.) diameter ASTM threaded rods: a) 11

ASTM A193 Grade B7, referred as A193; b) ASTM A307 Grade 55, referred as A307; c) 12

stainless ASTM A304 Grade 105, referred as A304. 13

The observation in the anchor tests with reinforcement revealed that the portion of anchor, 14

due to the lack of confinement after concrete cover spalling, was exposed and may experience 15

relatively large deformation without lateral support when the anchors are subjected to cyclic 16

shear loading. Exposed length, as described in the previous study (Lin et al., [11]), is a critical 17

variable among the influential factors for the shear behavior of the anchor. In order to simulate 18

behavior of anchor under seismic loading to account for the impact of the anchor exposed length 19

to the ductility of anchor, hence, double-shear tests using ASTM threaded rods with various 20

exposed lengths were conducted: under monotonic shear displacement in the first group of tests 21

while under reversed cyclic shear load for the specimens in the second group. Fixed boundary 22

conditions at both ends of test anchors were used to simulate the effective confinement from 23

12

concrete. The exposed lengths in all of tests (i.e., the net distance between the load plates and the 1

fixed plates) varied from da to 4da. Nine standard 12.7-mm (1/2-in.) diameter coupons of A193, 2

A307 and A304 (three for each steel) were tested to derive the constitutive relationship for the 3

steel material. It was observed that the all steel coupons exhibited a local necking, and the 4

cup-cone tensile fracture surfaces, which is a typical feature for ductile metals. The elongation of 5

A193, A307 and A304 were 17%, 25% and 63%, respectively. The load vs. displacement 6

curves of A193 anchor rods under monotonic and cyclic shear loading were shown in Figure 7 7

and ultimate shear capacities for each case were listed in Table 1. Due to ignoring any lateral 8

support from partially damaged concrete during cyclic loading, the shear capacity for all cases 9

may derive a low bound for the actual anchor capacities application. 10

In general, the specimen with an exposed length of da represents anchors with a relatively 11

short exposed length (e.g., the cases in Kwon et al. [15] and in Fig. 2), and showed a 12

shear-dominant behavior. There was obvious shear deformation with sudden failure based on the 13

load-displacement curve. This was also confirmed by the fracture surfaces of the anchor, as 14

shown in Figure 8a. It illustrated that the fracture of the anchor rod initiated a flexural crack at 15

the location of yellow solid line (in Figure 8a) and then failed in shear fracture after crack 16

opening till purple dashed line (in Figure 8a). The fracture surface exhibited the shear-dominant 17

fracture with a shining flat zone due to crystal slip, as described in Figure 3. 18

The behavior changed for specimens with larger exposed lengths. The load vs. displacement 19

curves, shown in Figure 7, indicated a flexural-dominant behavior for the specimens with an 20

exposed length of 2da. Flexural yielding of the specimens, shown by the stiffness degradation in 21

Figure 7, indicated a larger impact from bending and a larger reduction of cross sectional area, 22

which may explain the lower capacity observed in these specimens. Flexural crack initiation 23

13

sites were present, with one main crack that led to failure. The cracks initiated at a diameter 1

transition opposite to the support bearing and the most area of final failure (the area as shown 2

intersected by yellow solid line and purple dashed line (in Figure 8b), was caused by opening of 3

flexural crack associated with the major crack. There was a small fracture area near the fracture 4

edge along shear direction. This was most likely caused by mechanical damage of the fracture 5

surface that occurred due to tension prior to final failure (However, the area of tension was 6

relative small and thus final capacity had no apparent increase). 7

The initial part of the load vs. displacement behavior (Figure 7) for specimens with an 8

exposed length of 4da showed a flexural-dominant behavior as well. However the stiffness and 9

shear capacity increased at larger displacements. Such post-hardening/strain hardening type of 10

behavior was observed due to tension close to failure. Such understanding led to the explanation 11

of the observation of strain hardening behavior shown in those anchors with the proposed 12

reinforcement (Fig. 5). The fracture surface, shown in Figure 8c, exhibited an obvious transition 13

(in purple dashed line) from different fracture modes, which initially showed flexural-dominant 14

fracture and then end up with a failure mode with a 45 degree shear lip due to the tension. 15

Qualitatively, both anchor rod experiments (monotonic and cyclic loadings) followed a 16

similar progression of events, as presented in Figure 6. Flexural crack was triggered by initial 17

yielding. The damage to the anchor rods progressively increased due to the propagation of the 18

crack, resulting in lower strength and stiffness, compared to those results obtained under 19

monotonic loading. In fact, such degradation in strength and stiffness were not significant 20

because of the following post-hardening behavior as the exposed length increases. Compared to 21

the measured shear capacities of anchor rods under monotonic loading presented in Table 1, the 22

ultimate load (of all three anchor rods) was approximately 5% lower than those under monotonic 23

14

loading for A193 and A307 while over 12% for A304. Fatigue effects may account for such 1

reduction. No strength reduction was recommended in this study. 2

Table 1 displayed the comparison of three different steel specimens with various exposed 3

lengths. The stiffness and shear capacities may decrease with the increase of exposed lengths. 4

The initial yielding is followed by strength as well as stiffness degradation at repeated cyclic 5

loadings. However, with the relatively larger exposed lengths, an increase in strength due to 6

tension effects as the rods deformed further, thereby resulting in a post-yielding increase 7

(referred as strain-harden) in shear capacities. 8

9

5. Conclusions 10

In summary, with a goal to achieve anchor seismic performance in ductile manner and verify 11

the ductility-related provisions in existing design codes and guidelines, behavior of anchor in 12

shear with and without reinforcement was reviewed and ductility for seismic applications were 13

evaluated from both effective confinement due to anchor reinforcement and ductile steel. 14

The proposed reinforcement was based on the contribution of the concrete compressive stress 15

distribution through concrete core under high confinement to anchor. Such effective confinement 16

provided effectively lateral support to anchor shaft and allowed it to undergo larger shear 17

deformation without apparent strength reduction. Test results of anchor with the proposed anchor 18

reinforcement showed consistent strength enhancement and great ductile behavior under static 19

and cyclic shear loading. Steel fracture was achieved in all cases. Failure analysis of the fracture 20

mechanism of anchors demonstrated that the shear capacities, failure modes and ductility were 21

correlated each other. 22

15

Moreover, all of the three types of anchor steel widely used in anchor material exhibited 1

great ductile (ductile material is defined to have at least 14 percent elongation for anchor steel in 2

ACI standard). Ductility of steel not only provides enough deformation before failure to avoid 3

catastrophe, but also develops the strain hardening behavior, leading to different failure modes 4

(from shear or flexural failure to tension failure) and correspondingly resulting in higher 5

capacities and great ductility, which can be easily observed from all test results. It can be 6

envisioned that both effective confinement and specified ductile steel could ensure anchor have 7

good seismic performance. 8

9

Acknowledgements 10

The study reported in this paper is from a project supported by the National Science 11

Foundation (NSF) under Grant No. 0724097. The authors gratefully acknowledge the support 12

of Dr. Joy Pauschke, who served as the program director for this grant. The authors also thank 13

the colleagues in ACI committee 355 for their valuable inputs. Any opinions, findings, and 14

recommendations or conclusions expressed in this material are those of the authors and do not 15

necessarily reflect the views of NSF.16

16

Notation 1

The following symbols are used in this paper: 2

= area of anchor reinforcements 3

= effective cross-sectional area of single anchor in shear 4

1ac = front edge distance of anchor 5

2ac = side edge distance of anchor 6

ad = anchor diameter 7

bd = reinforcement diameter 8

utaf

= ultimate tensile strength of anchor steel 9

l = distance from the applied shear force to a fictitious fixed end 10

11

17

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List of Tables: 1

Table 1. Matrix of double-shear experimental tests for different types of anchor steel (kips) 2

3

List of Figures: 4

Figure 1. Anchor bolts damaged in bridge connection in Chile earthquake (Yen et al., [8]) 5

Figure 2. Shear steel failure of 19-mm diameter A 193 B7 threaded rods 6

Figure 3. Microstructure of a typical shear failure mode using SEM (50× and 1000×) 7

Figure 4. Schematics of a) Hairpins and b) the proposed anchor reinforcement 8

Figure 5. Normalized test results of anchor with and without shear reinforcement 9

Figure 6. Schematics of steel failure modes, shear capacity and ductility 10

Figure 7. Load vs. shear deformation curves of A193 Grade 7 threaded rods under monotonic 11

and cyclic shear loading 12

Figure 8. Fracture surfaces of A193 anchor rods in shear 13

14

21

1

Table 1. Matrix of double-shear experimental tests for different types of anchor steel (kips) 2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

*: Deviation of shear capacity of anchor under cyclic loading over monotonic loading. 25

1 kN=0.2248 kips 26

27

28

Steel l/da Load type Ultimate

Capacities Deviation

*

A

193

1 Mono. disp. 16.77 -

2 Mono. disp.. 12.98 -

4 Mono. disp. 17.00 -

1 Cyclic load 16.95 96%



A

307

1 Mono. disp. 10.82 -

2 Mono. disp. 12.50 -

4 Mono. disp. 9.84 -




A

304

1 Mono. disp. 24.30 -

2 Mono. disp. 15.40 -

4 Mono. disp. 17.95 -




22

1 (a) Concrete breakout (b) Fractured anchors 2

Figure 1. Anchor bolts damaged in bridge connection in Chile earthquake (Yen et al., [8]) 3

23

1

(a) Shear force vs. displacement curves (b) steel fracture 2

Figure 2. Shear steel failure of 19-mm diameter A 193 B7 threaded rods 3

24

1

Figure 3. Microstructure of a typical shear failure mode using SEM (50× and 1000×) 2

fracture

25

1

(a) (b) 2

Figure 4. Schematics of a) Hairpins and b) the proposed anchor reinforcement 3

26

1

Figure 5. Normalized test results of anchor with and without shear reinforcement 2

27

1

Figure 6. Schematics of steel failure modes, shear capacity and ductility 2

Unreinforced concrete

Tensile-dominant

steel fracture

Rotation capacity

Flexural-dominant

steel fracture

Shear resistance

Tensile resistance

Shear-dominant

steel fracture

Δc Shear deformation, Δ

Δs

28

1

Figure 7. Load vs. shear deformation curves of A193 Grade 7 threaded rods under monotonic 2

and cyclic shear loading 3

29

1

Figure 8. Fracture surfaces of A193 anchor rods in shear 2

a)A193-da

Flexural crack initiation

Crack opening

b)A193-2da c)A193-4da

failure analysis of anchors in shear under simulated seismic

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