DESIGN OF ANCHOR REINFORCEMENT FOR SEISMIC SHEAR LOADS

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18 Ιουλ 2012 (πριν από 5 χρόνια και 2 μήνες)

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1

DESIGN OF ANCHOR REINFORCEMENT

FOR SEISMIC SHEAR LOADS

1

Derek Petersen
and
Jian Zhao

2


3

B
iography:

ACI student member
Derek Petersen

is a former
g
raduate
r
esearch
a
ssistant at the
4

University of Wisconsin
at

Milwaukee where he received his MS degree in Civil/S
tructural
5

Engineering. He is now working as a
s
tructural
e
ngineer with Osmose Railroad Services Inc. in
6

Madison,
WI
.

7

ACI member
Jian Zhao

is
an assistant professor in
UWM
Department of Civil Engineering and
8

Mechanics
.

He received his PhD from the Universi
ty of Minnesota, Minneapolis, MN

and served
9

as a post
-
doctoral researcher at
Iowa State University
, Ames, IA.
He is a member of ACI
10

C
ommittees 355 (Anchorage to
C
oncrete) and 447 (
Finite
E
lement Analysis
o
f Reinforced
11

Concrete Structures
-
Joint ACI
-
ASCE
)
.

H
is research interests include behavior of reinforced
12

concrete structures
, concrete
-
steel connections,

and earthquake engineering.

13


14

ABSTRACT

15

E
xisting

design code
s
recommend hai
rpins and surface reinforcement

consisting of
hooked
16

bars

encasing an edge reinfo
rcement
to improve the behavior of anchor connections

in shear
.
17

C
oncrete breakout
is assumed to
occur

before
anchor

reinforcement

take
s

effect

in the current
18

design method
.
This paper presents a
n alternative

design method for anchor
shear reinforcement
.


19

The proposed anchor
shear
reinforcement

consist
s

of a group of closed stirrups
proportioned to
20

resist the
code
-
specified
anchor steel capacity in shear and
placed within a distance from the
21

anchor bolt equal to the
front
edge distance.

Steel fracture was

achieved in the
tests of
twenty

22

25
-
mm [1
-
in.]
reinforced anchor
s
with a front edge distance of 152 mm [6in.].

Meanwhile, t
he
23

observed anchor
capacities

were
smaller than the code
-
specified anchor steel capacity

in shear

24

2

because c
oncrete cover
spalling

ca
us
ed

combined bending and shear action
in

the anchor
bolts
.
1

R
e
bars
are needed
along all concrete surfaces to minimize
concrete damage in front of reinforced

2

anchor
s for
consistent

seismic behavior

in shear
.


3


4

Keywords:
Cast
-
in anchors
;
headed studs;
anch
or co
nnections; anchor reinforcement
; fastening
5

to concrete; composite construction; and
seismic

design
.

6


7

INTRODUCTION

8

Concrete anchor connections are a critical component of load transfer between steel and
9

concrete members affecting structural performance

during
earthquake events
. Observations of
10

damage

in recent major earthquakes have raised concerns about the seismic performance of
11

anchor connections.
1
-
4

C
ast
-
in
-
place anchors

may experience steel fracture or
concrete breakout
12

failure

when subjected to
a shear force

towards a free edge
.
5

The failure modes are mainly
13

dependent upon
the front edge distance,
c
a
1
,
when the anchor bolt is placed in plain concrete.

14

C
oncrete break
out cones
such
as
the one
shown in

Fig
. 1
vary in

shape

while
a
n

idealized
15

break
out
cone
6

encased in the dashed lines

is generally
assumed

in calculating the anchor
16

breakout
capacity.
With the breakout cone partially formed, the anchor bolt may lose
concrete
17

support when subjected to
reversed
cyclic shear loads
, leading to
unreliable

seismic performance
.

18

Building codes
5

and design guidelines
7,8

allow e
ngineers to use steel r
einforcement
to
19

increase the
shear
capacity of

anchors placed near an edge.

The
recommended
anchor shear
20

reinforcement

usually consist
s

of
horizontal
hairpins
tha
t wrap around the anchor shaft
or
hooked
21

bars
along the direction of the shear force
close to

the top
concrete
surface as illustrated in Fig. 2.
22

T
he existing design method
s
5,7,8

assume

that
the concrete breakout similar to that
observed

for
23

3

anchors
in pla
in concrete oc
curs before steel reinforcement

take
s

effect.

With this assumption,
1

the
shear
resistance of the anchor is
exclusively
provided by the
anchor

reinforcement.

Anchor
2

reinforcement in terms of hooked bars is required to

be fully developed
in th
e

assumed breakout
3

cone
5

or the

contribution from each bar is calculated according to its development length in the
4

assumed breakout cone.
7,8


The
development length
requirements
limit

the distance from the
5

anchor bolt,

within which the reinforcement

can b
e deemed effective as illustrated in Fig. 2.



6


7

RESEARCH SIGNIFICANCE

8

S
ignificant
effort
s

h
ave

been invested
to
testing anchors reinforced
with

hairpins
.

L
aboratory
9

test
s

of anchors reinforced with
other types of reinforcement

is scarce, especially for
a
nchors

10

under cyclic shear loading.
T
his
paper
present
s tests of cast
-
in
-
place anchors
reinforced using
11

closed
stirrups

under both monotonic and cyclic
shear
loading
.

C
losed stirrups
encasing bars
12

placed at
the
corners and distributed along concrete surfa
ces
can
restrain concrete breakout such
13

that the shear load is transferred to the structure through the confined concrete
.


A design method
14

was proposed

for anchor shear reinforcement

based on

the observed anchor behavior
.

15


16

BACKGROUND

17

Various types of anch
ors have been developed over the past
4
0 years.

Numerous studies
18

have been performed to develop the
design method
of
anchor
s in plain concrete

corresponding to
19

various identified failure modes
.
6


The behavior of anchors
and headed studs
in plain concrete
20

has been discussed at length
,
7,9
-
12

and the test
s

have been
summarized

in several databases.
13
-
15


21

On the other hand
, studies are limited on
the performance of anchor
s with

reinforcement
.

The
22

existing studies
on anchor
shear
reinforcement

are reviewed
and

the
available

design methods
23

4

summarized below.

1

Previous

Studies

2

The most investigated
anchor
reinforcement
for resisting shear forces is
horizontal
hairpin
s

3

that wrap

around the anchor

as
illustrated

in
Fig.

2
.

Swirsky

et al.
16

tested

24 cast
-
in
-
place
4

an
chors
,

consisting

of
25
-

and
51
-
mm

[1
-

and 2
-
in.]
diameter A307 or A449 bolt
s

reinforced
5

with
No.
4 or
No.
5 hair
pin
s
,

under monotonic and cyclic loading.

The hairpins had
a
12
0
-
6

degree
ben
d

wrapping around the bolts
51 mm [2 in.]
below the concrete surfac
e.

A
capacity
7

increase
of
15
to
87 percent

was observed
at
a
displacement

about

25 mm

[1 in.]
.

Only s
ix

8

anchors

were reported to fail

with anchor shaft fracture
, in part
because the
development length
9

for
the

hairpins was
20
d
b

(
d
b

is the diameter
of the
hairpin
s
), which is

not sufficient
.

M
a
n
y tests
10

were terminated

after bond failure
of hairpins
was observed.

Two additional tests were
11

conducted with
two

No.
4
vertical
stirrup
s

placed
51 mm

[2 in.]
away from the bolt.

The u
s
e of

12

stirrups is similar to t
he anchor reinforcement
proposed
in this paper
;

however the amount
of the

13

reinforcement
was not sufficient
, and
both

tests stopped after concrete cracked and a large
14

displacement was observed.

15

Th
e

behavior of anchor bolts
reinforced
with hairpins
was
furth
er
s
tudied by Klingner et al.
17

16

through 12 monotonic tests and 16 cyclic tests of
19 mm

[3/4 in.]
diameter A307 bolts.

A
No.
5
17

hairpin with a 180
-
degree

ben
d

and a development length about 37
d
b

was placed
19

or
51

mm

18

[3/4 or 2 in.]
below

the top surface
.

The t
ests showed that th
e most effective
way to transfer
19

anchor shear force

to the
hairpin

is
through the contact between the anchor
shaft
and the
hairpin

20

near the surface
.

H
airpins
that were not in contact with

the anchor shaft

were found

effective

in
21

m
onotonic tests
,
but
unreliable
under

cyclic loading.
T
he
No.
5 hairpin provided sufficient
shear
22

5

resistance

compared to the anchor steel capacity; however most tests
were terminated

before
1

anchor

fracture
was achieved
likely because a capacity drop was ob
served during the tests
.

2

Lee et al.
18

conducted

10 tests of
64 mm [
2.5 in
.]

diameter anchor bolts
with a
381
-
mm

[15
-
3

in.]
edge distance and
a 635
-
mm

[25
-
in.]
embedment depth

reinforced with U
-
shaped hai
rpins
4

and
hooked

reinforcing bars
.

T
he reinforcement

was
proportioned to carry the shear capacity of
5

anchor steel,
result
ing

in

a
combination of
No.
6 hairpins and
No.
8
hooked

bar
s dispersed within
6

381 mm

[15 in.]
from the anchor bolt

with a 152
-
mm [6
-
in.] spacing
.

Three layers of
No.
8
7

hairpins were used
in
some

specimens.

M
ost tests
were terminated

before a peak load was
8

observed due to the limited stroke of the
loading device
.

T
he unfinished tests were not able to
9

fully
demonstrate the
effectiveness of the

various anchor reinforcement designs.


10

In Eur
ope

as documented
by

Schmidt
,
19

Paschen and
Schönhoff
20

examined ten types of
11

anchor reinforcement

layouts
.

H
airpins touching anchor shaft
s

and
reinforcing bars
distributed
12

near
the top surface

as illustrated in Fig.

2 were found most effective.

Similar c
onclusions were
13

made by
Ramm and
Greiner
21

based on their
test
s

of anchor
s

reinforced with
five
types of

14

reinforcement
.
Randl and John
22

observed a capacity increase of 300

percent

in their tests of
15

post
-
installed anchor bolts with hairpins. It was conclud
ed that the thickness of concrete cover
16

affect
ed

the effectiveness of hairpins

as anchor shear
reinforcement
.

Recently,
Schmidt
19

17

conducted tests
on
five types of
anchors with
hooked
reinforcing bars,
which simulated the
18

rebars in an existing concrete ele
ment.

A model was proposed for determining

the
shear
capacit
y

19

of
reinforced
anchors, which can be obtained from the
summation of
the
contribution
s

from
all
20

reinforcing bars

bridging the
assumed
35
-
degree

breakout
crack
. The
contribution
from each

21

reinfor
c
ing bar

included

the bearing force of the bent leg and the bond force of the straight part
22

within the breakout cone
.
Schmidt
’s equation
for the capacity of reinforced anchors in shear
is a
23

6

refined version of the equation proposed by Fuchs and Eligehausen
,
23

who clearly defined the
1

assumption
that a

concrete
cone
must
form

before
steel
reinforcement
takes effect
.

On the other
2

hand,
many
of
Schmidt
’s tests
were terminated

after the
spalling of the
concrete cover
,

which
3

might have

not indicate
d

the
final
fa
ilure of the specimen
s
.

4

Existing
Design
R
ecommendation
s


5

The methods for pro
portioning anchor
shear
reinforcement

are summarized in Table 1. Note
6

that many design methods that focused on
the
capacity calculation for
anchors with
a known
7

configuration of
a
nchor
reinforcement, such as that
proposed
by Schmidt,
19

were not included

in
8

Table 1
.

In summary, m
ost
existing

desig
n methods require the reinforcement

to provide more
9

resistance

than the anchor steel capacity in shear.

This is achieved

by
either
incre
asing the
10

design force
5

or reducing the effect
iveness of anchor reinforcement

based on

their
relative
11

vertical
locations
.
7,8


Note that
there are few tests with
such
over
-
designed reinforcement
, and
12

many
such
tests
were terminated

before
a

true

ultimate lo
ad

was achieved.


13

Hairpins are deemed effective
as anchor shear reinforcement
because they
can be

placed
14

close to the anchor shaft
using

a small bending radius

on the hairpin
.
17,18


The
transfer of
shear
15

load
to surface reinforcement

shown in Fig. 2
is us
ually visualized using a strut
-
and
-
tie model

16

(STM)
.
23,24


S
trut
-
and
-
tie model
s

permit

large size
reinforcing
bars located at a
large
distance
17

from the anchor
bolt

as anchor reinforcement
as long as the angle between the concrete strut and
18

the applied shear

force is small (e.g
.
,

less than
5
5

degrees
)
.

However,
tests
18,25

have
indicate
d

19

that
reinforcing bars

placed close
r

to the anchor
are more

effective.

As a result
, the existing
20

design guideline
s
5,7,8
require

the anchor reinforcement
to be

within
a distan
ce equal to half of the
21

front
edge distance (
0.5
c
a
1
)
as illustrated in Fig. 2. Such

requirement
s

leave
a small window of
22

applicability
for practical implementations

of the anchor reinforcement
.

Often time t
he
front
23

7

edge distance need
s

to be increased

to
accommodate the anchor reinforcement
, which

in turn

1

increases the concrete breakout capacity such that
the
anchor reinforcement
may be

no longer
2

needed
.


3

Anchor reinforcement design for shear in this study considered the following four aspects: 1)
4

an effec
tive reinforcement layout that
restrains concrete breakout failure
; 2) a
proper
design
5

force for proportioning
the
anch
or reinforcement
; 3) a
reasonable

distance on each side of anchor
6

bolt, within which
the
anchor reinforcement

is deemed

effective; and 4)

an accurate

estimation of
7

shear
capacity of
reinforced
anchors.

8


9

PROPOSED
ANCHOR SHEAR REINFORMENT DESIGN

10

The proposed anchor reinforcement is shown in Fig. 3 for anchors with both unlimited and
11

limited side edge distances.
The goal of the proposed
desig
n for
anchor
shear
reinforcement is to
12

prevent

concrete breakout using closely

spaced
stirrups

placed parallel to the plane of the applied
13

shear force and the anchor
.
With
the
concrete confined around the anchor, it
i
s expected that the
14

concrete
will rest
rain the anchor shaft

and provide shear resistance
.
The stirrups should be
15

proportioned using the anchor steel capacity in

shear as specified by the equation in the last row
16

of Table 1. The nominal yield strength of reinforcing steel
should

be used in th
e calculation.
17

T
wo stirrups
should be

placed
next to

the anchor shaft, where the
breakout
crack
in concrete
may
18

initiate

under a shear load.

The rest of
the
required stirrups
should be

placed with a cent
er
-
on
-
19

center spacing of
51 mm
[2 in.]
to 76 mm

[3 in
.]
.

A smaller spacing may be used provided that
20

the clear spacing requirements
, such as those in ACI 318
-
11,

are satisfied.
The stirrups can be
21

distributed within a distance of
c
a
1

as shown in Fig. 3.
Note that the horizontal legs of the
closed
22

stirrups

are used as anchor
shear
reinforcement
while the vertical legs

close to the anchor shaft
24

23

8

may be used as anchor
tension
reinforcement as shown in Phase III tests of this study
.

For this
1

purpose, the depth of the stirrups
should be large enough such that

the vertical legs are fully
2

developed for
the tension load
.

3

T
he development length requirements
for the horizontal legs of the closed stirrups
are
4

satisfied similar to the transverse
reinforcement
in
a flexural member, where the stirrups
are fully
5

develop
ed at both sides of a shear crack through
the
interaction between the closed stirrups and
6

longitudinal b
ars at
all four
corners
.
26

Meanwhile

r
ebar pullout tests, in which
both legs of
No.
4
7

U
-
shaped
bars embedded
38 mm

[1.5 in.]
and
76 mm

[3 in.]
in concr
ete were loaded in tension,
8

indicated that
a
minimum
embedment
depth

of
6
d
b

wa
s needed
to develop

a
No.
4
stirrup

9

through the interaction
.

Therefore, the length of horizontal legs of the vertical closed stirrups
10

should be at least

8
d
b

on both sides of the anchor as shown in Fig.

3. This requirement results in
11

a minimum edge distance of 8
d
b

plus the concrete cover. Design of reinforced anchors should
12

also satisfy other
edge distance
requirements, such as those in Section D.8 of ACI
318
-
11
.

13

Bars at all four

corner
s

of the closed

stirrups (
referred to as

corner bars hereafter) restrain

14

splitting cracks
as well as

other bars distributed along the concrete surfaces (
referred to as
crack
-
15

controlling bars hereafter).
Therefore the corner bars
and crack
-
controlling bars
need to be ful
ly
16

developed at both sides of the anchor bolt, and a 90
-
degree

ben
d

as shown in dashed lines in Fig.
17

3 may be needed.

The selection of corner bars may follow
the
common practices in selecting
18

longitudinal corner bars for reinforced concrete beam
s
, such as

those specified in Section 11.5.6
19

of ACI
318
-
11
. Crack
-
controlling bars were not provided
in the tests

and the splitting cracks
20

were observed
as
presented below
.

Crack
-
controlling bars are
therefore
recommended

as shown
21

in Fig. 3, and the
determination o
f these bars can be based on

the well
-
recognized strut
-
and
-
tie
22

models
.
23,24


23

9

EXPERIMENTAL
INVESTIGATION


1

Specimens

2

This group of experimental tests is part of a research program
, which
focused on
the
behavior
3

and design of cast
-
in
-
place anchors under simu
lated seismic loads.
27

Sixteen

tests were
4

conducted using
25 mm

[1 in.]
diameter
anchors consisting of an
ASTM
A193
Grade B7
5

threaded rod
(
f
y
=
724

MPa
[105 ksi]
and

f
ut
=1069 MPa [131 ksi]) and a heavy hex nut welded to
6

the end
. Another

four

tests
using

19

mm

[3/4 in.]
diameter ASTM F1554
Grade 55
anchors
7

(
f
y
=43
4

MPa

[63 ksi]
and

f
ut
=524

MPa

[76 ksi]
)
were conducted with tw
o tests
each
under

8

monotonic shear and cyclic shear
loading
.
Ready
-
mixed concrete
with a targeted strength of
9

27.6

Mpa

[4000 psi]

was us
ed, and cylinder
tests

using three batches of three 100
×
200

mm
[4×8
10

in.]
cylinders tested throughout the anchor test period showed an average compressive strength
11

of 24.3

MPa

[3525 psi]
.

12

The dimensions of the test blocks
containing four anchors each
are
illustrated

in Fig.
4
.

One
13

block was prepared for Type 19
-
150
-
100 specimens,
and
two blocks for Type 25
-
150
-
150 and
14

Type 25
-
150
-
150H specimens. Another block similar to that for Type 25
-
150
-
150 specimens
15

was used for Type 25
-
150
-
150SG specimens. Strain g
ages were installed on the reinforcing bars
16

of the two anchors in this block. All anchors had an embedment depth of 152 mm [6 in.]. The
17

width and depth of the test blocks were
selected

such that the spacing between the anchors
was

18

larger than two times th
e
ir

front edge distances
.

Anchors in Type
25
-
150
-
150H specimens

had
19

two limited side edge distances equal to 1.5 times their front edge distance. The
height of the
20

block
s

w
as

432 mm [17 in.],
similar to all other anchor tests in the study.
27



21

The anchor

shear
reinforcement
was

proportioned to carry the
maximum
capacity of
the
22

anchor

bolts

in

shear:

68 kN
[15.3 kips]
for
the
19
-
mm
[3/4
-
in.]
anchors and 209kN
[47 kips]
for
23

10

the
25
-
mm
[1
-
in.]
anchors. Using the nominal
yield
strength of Grade 60 steel
,
t
he

required
1

anchor reinforcement
was

found as

164 mm
2

[0.25 in.
2
]
for
the
19
-
mm
[3/4
-
in.]
anchors
, and
503
2

mm
2

[0.78 in.
2
]
for
the
25
-
mm
[1
-
in.]
anchors
. Therefore two No. 4
bars

were provided for Type
3

19
-
150
-
100 specimens

as shown in Fig.
4
.
The required anchor r
einforcement for 25
-
mm [1
-
in.]
4

anchors
was provided using
four

No.
4

bars

with a
spacing of
51
-
mm
[2
-
in.]
for
Type
25
-
150
-
5

150 specimens,
two
No.
4 and
four
No.
3

bars

for
Type
25
-
150
-
150H specimens with a
spacing
6

of
76
-
mm
[3
-
in.]
, and
eight
No.
3

bars

for
Type
25
-
150
-
150SG specimens with a 51
-
mm
[2
-
in.]
7

spacing. Two
additional

No.
3
J
-
hooks

were
added besides the outmost bars

in
Type
25
-
150
-
8

150SG specimens
as shown in Fig.
4

to host two more strain gages
, which were

roughly 250 mm
9

[10

in.] away from the an
chor bolt
.

One straight bar was provided at each corner of the closed
10

stirrups. Note that some specimens had several narrow stirrups
placed behind the anchors, the
11

vertical legs of which were intended to be anchor tension reinforcement
,

in

w
hic
h

case

o
ne
12

additional co
rner bar was

provided along the top surface.
However,
the planned
tension tests
13

were not performed because the
concrete blocks were not
s
ufficient

for the large tension load
14

that would be carried by the reinforced anchors. The additional stirrups did not affect the shear
15

behavior of the anchors because they were placed behind the anchor bolts.
All reinforcing bars
16

were placed with a
cover of
38 mm

[1.5 in.]
.

17

Test Setup

18

The l
oading frame, actuator placement, and instrumentation setup used for
the
tests
are

19

shown

in Fig.
5
.
Instead of
a self
-
balanced

load frame
,

a
tie
-
down rod
381 mm

[15 in.]
behind
20

the test anchor was
used

to
fix the test block to the strong floor
. In additi
on, the concrete block
21

was wedged against the strong floor to minimize the slip of the test block under cyclic loads as
22

shown in Fig.
5
.
An
MTS Model 244.31, 245
-
kN
[55
-
kip]
actuator was used to apply shear
23

11

loading to the anchor bolt

through a loading pla
te
.
The actuator
body
was braced against the
1

floor
to eliminate the

downward
motion of actuator swivel head

and the
rotation of the loading
2

plate
. To
minimize

the friction between the load
ing

plate and the concrete top surface, a
net

3

tension force of
0.
8

kN

[0.2 kips]
was
applied to the load
ing

plate by an MTS Model 244.41,
4

489
-
kN
[110
-
kip]
actuator,
which was used for applyi
ng tension loads in other tests
.

The nut
5

fixing the load
ing

plate to the
anchor bolt was first hand tightened, and
then loosened 1/
8 of a
6

turn to allow slight vertical movement of the loading plate when the
0.8
-
kN
[0.2
-
kip]
tension
7

force was applied at the beginning of
a

test
.

The test anchors were inserted through a standard
3
-
8

mm

[1/8
-
in.]
oversized hole in the load
ing

plate
,

and

a
steel sleeve shim was inserted between
9

the anchor and the hole

to eliminate

the
clearance and
to
prevent

damage to the load
ing

plate.

10

Loading Protocol

11

M
onotonic
shear
tests were performed first to determine the
typical

actuator displacement
at
12

failur
e, and the tests indicated a failure

displacement
a
round

3
5

mm

[1.4 in.]
.
Hence,

the
cyclic
13

displacement steps for each
3
-
cycle
group
were chosen as
2
,
3, 4

(failure
displacements
for
14

typical
unreinforced anchors)
, 8, 16, and 32

mm

[0.08, 0.12, 0.16, 0.32, 0.
64,
and
1.28 in.]

as
15

shown in Fig. 5
.
The
l
oading rate

for
the
displacement cycles at or below 4 mm
[0.16 in.]
w
as

16

kept at 2

mm/min
[0.08 in./min]
while the load rate was increased to 10 mm/min
[0.4 in./min]
for
17

the
8, 16, and 32
-
mm
[0.32, 0.64, and 1.28
-
in.]
cycles in order to reduce test time.
Most

reversed
18

cyclic shear tests
were conducted following the loading pattern C1

shown in Fig. 5
,
in which
the
19

maximum displacement
was set as 4

mm

[0.16 in.]
when the shear
l
oading

was applied opposite
20

to the
front

edge.

This was to
prevent early anchor fracture under reversed loads and to
observe
21

the cyclic behavior over
a

full
displacement range.
Cyclic tests
following loading pattern C2
in
22

Fig.

5

with

equal
peak
displacement
s

in both directions of
shear
load
i
ng

w
ere conducted

for two
23

12

Type
25
-
150
-
150H specimens
.
Note that the control of actuator was based upon the actuator
1

piston motion instead of anchor displacement; hence the
actual
anchor displacements were
2

smaller than

the above
target

displacements.

3

Instrume
ntation

4

String pots
(Celesco PT510DC)
and linear variable differential transformers (LVDT’s)
5

(Trans
-
tek Model 245)
were used to measure the anchor displacements
as
illustrated

in Fig.

5
.
6

The displacement
s

of the load plate w
ere

actually
used as the anchor

displacement

because the
7

anchor shaft just above the concre
te surface was not assessable.

An IO Tech DaqBook 2000 was
8

used to collect data from all
sensors

as well a
s
the
force and displacement output
s from the
9

actuators.
The sampling frequency was 5

Hz

and the collected data was filtered
using an in
-
10

house program with a cutoff frequency of
0.
1

Hz
.

The
observed

anchor behavior
i
s discussed
11

below.

12


13

EXPERIMENTAL RESULTS AND DISCUSSION

14

Behavior of Anchors
u
nder Monotonic Loading

15

The load versus displacemen
t behavior
is shown in Fig. 6 for
the reinforced
anchors
16

subjected to monotonic shear
along with

selected images of failed specimen
s
. For comparison
17

purpose,
t
he load versus displacement behavior

for
a 19
-
mm
[3/4
-
n.]
anchor

with a
front
edge
18

distance of 100 mm
[4 in.]
in

plain concrete
is shown in Fig. 6a

and
the result of
another anchor
19

with a

front

edge distance of 150 mm
[6 in.]
in the rest of Fig. 6
.
The u
nreinforced anchors

were
20

tested with a concrete strength of 39 MPa
[5656 psi]
while the reinforced anchor tests ha
d a
21

concrete strength of 24.3 MPa

[3525 psi]
,
therefore

the load values
for the unreinforced anchors
22

were
normalized using

a factor of







in Fig. 6.

I
n
General
the

reinforced
anchor
s

failed
23

13

by anchor shaft fracture while
the unreinforced
anchors
with simil
ar edge distances failed by
1

concrete
breakout.
The failure loads for
t
he

reinforced anchors

increased by about 100

percent

2

and the displacement
s

corresponding to the peak load
s

increased more than six times

compared
3

with that of the unrein
forced anchor
s
.

4

The

load
-
displacement
behavior of
19
-
mm
[3/4
-
in.]
anchor
s

in reinforced concrete did not
5

show much difference from that in plain concrete (Fig. 6a) before a crack was observed at the top
6

surface

at a load about 45 kN

[10 kips]
.

Rather th
an propagating vertically along the anchor
7

shaft as observed in
the tests of unreinforced anchors as represented by
Fig. 1, the crack
8

propagated around the corner
of

the
stirrups

(
see the inserted figure in
Fig. 6a)
. The loss of the
9

38
-
mm
[1.5
-
in.]
thick
c
oncrete cover in front of the anchor
caused a
small
capacity loss

for the
10

19
-
mm
[3/4
-
in.]
anchor
s

as

shown in Fig. 6a
.

B
ecause the
19
-
mm
[3/4
-
in.]
anchor

only mobilize
11

the top concrete before cracking
, similar to that suggested by
Randl and John
22

(roughly 2
d
a

12

d
eep
)
, the anchor shaft in bending was not able to resist the
same amount of
load until a larger
13

displacement was applied.

Such post
-
spalling load drop has been observed in
other tests of
14

anchors reinforced with hairpins
.
17,18


The failure load exceeded the code
-
specifie
d anchor shear
15

capacity because the failure
wa
s caused by the fracture of anchor shaft largely under tension

as
16

shown in Fig. 7a
though the fracture may have started
from

a flexural crack.


17

The
shear

load
did not
drop
noticeably
after concrete cover spall
ed
in the tests of 25
-
mm
[1
-
18

in.]
anchors
as shown in Fig
s
. 6b through 6d
.

The 25
-
mm [1
-
in.] anchors
mobilized deeper
19

concrete such that the loss of bearing support from the cover
concrete
was immediately
resisted

20

by
lower concrete
restrained by

the anchor

reinforcement
. Another contributing factor is that the
21

25
-
mm
[1
-
in.]
anchor
s
had
a
larger
bending
stiffness
such that a small displacement was needed
22

to mobilize their load carrying capacities
.

The
25
-
mm
[1
-
in.]
anchors failed at load
s

lower than
23

14

the
co
de
-
specified
anchor steel capacity

in shear
.
The fractured
25
-
mm
[1
-
in.]
anchor
s

in Fig. 7c
1

showed a different failure mode

from that of 19
-
mm
[3/4
-
in.]
anchors
: anchor shaft cracked
2

under a bending moment and the
rest
of the anchor shaft then fractured i
n shear. For the shear
-
3

dominant failure mode, the flexural cracking reduced the cross sectional area, thus leading to a
4

lower ultimate shear capacity.

5

A
nchor steel failure was achieved in all 25
-
mm
[1
-
in.]
diameter
anchor
s,
indicating that
6

reinforcing
ba
rs placed outside the code
-
specified effective distance
,

such as

0.5
c
a
1

in
T
ype
25
-
7

150
-
150SG and 0.3
c
a
2

in
T
ype
25
-
150
-
150H
,

can be effective as anchor shear reinforcement
.

8

However, r
einforcing bars must be
evenly distributed with a small

spac
ing

in order

for outside
9

bars
to
be
mobilize
d
.
The effective distance

was

verified

by the measured strains in the
10

reinforcing bars in Type 25
-
150
-
150SG specimens as

shown in Fig.
8
.

The
anchor reinforcement

11

consisted
of eight
No.
3

stirrups at a spacing of
51

mm
[2 i
n.]
and two additional
No.
3

J
-
hooks
.
12

The
thin
dashed lines
in Fig. 8
indicate

the assumed breakout crack at the concrete surface and
13

the strain gages were installed 25 mm
[1 in.]
behind the assumed breakout crack line o
n the
14

inside

face of the stirrups.

In genera
l, larger strains were observed in the
bars close
r

to t
he
15

anchor bolt
.


M
eanwhile
outside

bars
, as indicated by G
age
s

4S and 4N located 170 mm

[6.7 in.]
16

from the anchor bolt
,

also developed significant strains, especially after the surface crack
formed
.
17

Note that the gage positions relative to a crack
should

be considered to interpret the measured
18

strains. For example, the strains by

G
age 2N
may have been

affected by the crack passing the
19

gage location
as shown in Fig. 8
.
More importantly, smaller str
ains measured by the gages on
20

outsider bars may have been
due

to the fact that the gages were
away from the
actual
crack
.
In
21

addition, t
h
e

measured strain
s

indicate
d

that none of the Grade 60
bars yielded at the peak load;
22

hence the she
a
r capacity of reinforced anchors may not

be calculated as the summation of the
23

15

yield forces of
the
anchor reinforcement
.

The
shear force

w
as

actually
transferred to the
s
upport
s

1

(
e.g.,
the tie
-
down rods
on the back and the steel wedg
ing tube at the bottom in this case) through
2

the concrete confined by the closed stirrups
.

3

A
nchors in
T
ype 25
-
150
-
150H specimens had lower ultimate capacity

as shown in Fig. 6c
.
4

This might have been due to the poor confine
ment of concrete in front of the anchor bolt:
5

additional splitting crack
s

w
ere

observed and deeper concrete crushed in these tests, leading to
a
6

longer portion of

exposed and
unsupported anchor bolts (
e.g
.
,

up to
0.5
d
a

l
ar
ger than th
ose

in
7

T
ype 25
-
150
-
150
specimens
)
.

F
inite element analys
e
s indicated that
the anchor capacity

8

controlled by shear
fracture

can be affected by anchor diameter

and

concrete
cover depth.
28


It is
9

thus
envisioned that
t
he following measures
as illustrated in Fig. 3
can be
effective

in

improv
ing

10

the post
-
spalling
behavior
and the capacity
of
reinforced
anchors

in shear
: 1)
corner
bars

should
11

be fully developed
; 2)
crack
-
controlling bars
should be
provided

along

both
the
top and front
12

surfaces

of

concrete; and 3) a
separate

bar can be

placed
right
in front of the anchor bolt to
13

alleviate

the
large local
compressive

stress in

concrete.

14

Anchor Shear Capacit
y

15

Most anchor bolts in this group of tests failed by shear
fracture of
a reduced
anchor shaft
16

cross section as shown b
y the typical f
ractured sections
in Fig. 7
.
This

failure mode occurred
17

when a short portion of the anchor bolt was
exposed

and
a lever arm developed

in the anchors

18

after cover concrete spalled.


The
effect of

lever arm
s

in anchor bolts
is reco
gnized in
existing
19

design
c
odes
.
5
,8

F
or example,
ACI
318
-
11

stipulates

that
the design capacity of
anchor
20

connections having grout
leveling
pads
should be
reduced by a factor of
0.8 for the anchor steel
21

strength in shear.

Such capacity reduction considers the combined bending and s
hear
in the

22

anchor shaft, but does not consider the thickness of the grout pads
, which is similar to
the
23

16

expo
sed length at the ultimate load
.

Eligehausen
et al.
12

proposed an equation
for predicting the
1

strength of
an exposed anchor
assuming
that
the anch
or fails

by
pure
bending
.
This
equation
was
2

found not applicable for

predict
ing

the capacity of the anchors in this study likely due to
the fact
3

that the anchor failure was controlled
by shear fracture
.
Lin et al.
28

improved the equation by
4

Eligehausen
et
al.
12

by considering the contributions from flexural, shear and tensile resistance of
5

an exposed anchor shaft to the shear capacity of exposed anchors.
However

the equation was
6

based on double shear tests and finite element analyses of threaded rods, and
t
he lateral support
7

to the actual anchor shaft from partially damaged concrete was not considered. Therefore, the
8

equation may provide lower
-
bo
u
nd estimates of
the
actual anchor capacities.

9

The capacity of anchor bolts with a lever arm was
instead
examined usi
ng the
test d
ata
10

available in the literature as shown in Fig. 9.
The measured anchor capacit
ies

w
ere

normalized
11

by the
design capacity of
anchor

bolts
in shear
specified in

ACI
318
-
11
.
The exposed depth of
12

the anchors in other tests
16,25

was defined as t
he
distance between the
bottom face of
a

base plate
13

and the
lowest solid
concrete surface.
The anchor steel capacity observed in this study is low
14

compared with other
available
tests.
This might have been due to
the fact that friction between
15

the load plate and the co
ncrete surface was minimized as previously described in the test setup
16

section
.

17

The statistical analysis of the limited data in Fig. 9 did not follow the

procedures of
18

predictive inference,
29
,30

which are usually used to predict future occurrences based o
n the
19

existing observed data
. Instead,
a
5
-
percentile value of 0.73 was obtained using a
descriptive
20

statistic analysis
of

the twenty two collected
data points.

Considering the aforementioned
21

reasons for the low observed capacities in this study, it is p
roposed that t
he shear strength of
22

reinforced

anchors can be estimated as
75 percent

of the code specified
steel
capacity for anchors
23

17

without a lever arm. This is slightly lower than the
reduction factor in
ACI
318
-
11

because of
1

two data points observed i
n specimens with limited side edge distances

(
T
ype 25
-
150
-
150H)
. It
2

is envisioned that as more data points become available in future tests with the
recommended

3

anchor shear reinforcement
shown in Fig. 3
; the
statistical
importance

of these t
wo

data point
s
4

can be
reduced. Using the suggested capacity reduction for
exposed
anchors should be limited to
5

those with
an
expose
d

length less than
three

times the anchor diameter

(3
d
a
)
.

Beyond this limit,
6

the anchor steel failure
in shear needs

furthe
r study
.

7

Behavior of Anchors under Cyclic Loading

8

Seismic actions on structural components are mostly simulated in laboratories using
quasi
-
9

static

cyclic
tests with reversed loading.
3
1

Therefore, displacement
-
controlled loading
33

was

used
10

in this study
th
ough
many

c
yclic tests of anchors
have been conducted with

load
-
controlled
11

loading
.
16,
17
,3
2

The

load versus displacement behavior of two
19
-
mm

[3/4
-
in.]
anchors subject to
12

Type C1
cyclic shear loading

is plotted in Fig
. 10
a
.

The monotonic curve was close
ly followed
13

by cyclic curves
until

a displacement of 10 mm [0.4 in.]
, beyond which the cyclic loads
were

14

lower than that
of the monotonic test
. The slope of the
cyclic curves

again
had a sudden change

15

at a displacement around 2 mm [0.16 in.]
, indicating the con
crete cover spalling.
The difference
16

in the observed loads
at this displacement
may have been due to variation
s

in the specimen
s

such
17

as the actual edge distance
s

and cover depth
s
.
T
he first
three

displacement cycles

did

not
see
18

significant
degrad
ation

in

loads
with successive c
ycles to the same displacement while the
19

degradation was
obvious
at

the
larger
-
displacement cycles
.
This was because

the
displaced
20

cover concrete

during the first cycle of each three
-
cycle group was not able to rec
over, leadin
g to
21

reduced restraint

to the anchor
shaft
in the successive cycles
.
An a
verage
capacity
reduction
of
22

28

percent

was
observed
in the cyclic shear capacity
for 19
-
mm
[3/4
-
in.]
anchors. This reduction
23

18

was partly attributed to the change of failure modes as shown

by the fractured shape of anchor in
1

Fig
s
.
7
a and
7
b: the anchor failure was controlled by the shear fracture

under cyclic loading
2

while
the
tensile fracture controlled the
anchor
failure in the monotonic test
.
Note that t
he
3

reduced
cyclic shear
capacit
ie
s

of 19
-
mm
[3/4
-
in.]
anchors
w
ere

higher

than the
proposed
4

capacity

of exposed anchors under

monotonic loading

because of
the monotonic failure mode
.

5

The behavior of Type 25
-
150
-
150 specimens are

compared

in Fig. 10b.
T
he monotonic load
-
6

displacement curve
nicely envelope
s

the cyclic curve
s r
epresented

by the first
loading
cycle in
7

each three
-
cycle group.

T
he load degradation
s

during the

successive two cycles
was
again
due to
8

the irreversible
crushing

of
concrete
cover in front of the anchors
.
No capacity drop was
9

observed in the tests of Ty
pe 25
-
150
-
150 specimens. A
n average capacity drop
of 6.8 percent
10

was observed for
Type 25
-
150
-
150H
anchors with limited side edge distance

as shown in Fig.
11

10c
.

In this group of three
cyclic
tests, conc
rete
deeper than the
38
-
mm
[
1.5
-
in.]

cover
crushed
12

likely due to poo
r confinement
conditions

as indicated by splitting cracks.

The larger exposed
13

length

l
ed

to a larger moment under the same shear load and
thus
a lower
shear

capacity.

Not
e

14

that the poor confinement conditions can be improved by crack
-
controlling bars rec
ommended in
15

Fig. 3. In addition,
a

bar
placed
just in front of the anchor shaft
can

help distribute the localized
16

high compressive stresses such that the exposed length of the anchors
would

not
be
affected by
17

the cyclic loading.


Finally, the tests
of two

Type 25
-
150
-
150H anchors
with fully reversed
18

cyclic loading (Type C2 in Fig.

5
) ended with anchor fractured under a shear load applied
19

opposite to the front edge
. The ultimate load capacities were on average
5

percent

lower than the
20

code
-
specified anchor
steel capacity as shown in Fig. 10d.
Hence, it is reasonable to ignore
the
21

reduction
of steel capacit
ies

for reinforced anchors in
cyclic
shear
consider
ing

that the monotonic
22

capacity of
reinforced

anchors
ha
s
already
been
reduced
by
25 percent

as proposed

above.

23

19

CONCLUSIONS

1

A design method for

anchor
shear
reinforcement was

proposed and verified

using
2

experimental tests of single cast
-
in
-
place

anchors
.

With a goal
to
prevent concrete breakout

and

3

to confine concrete in front of a
n

anchor

bolt
, the proposed anc
hor shear
reinforcement
consisted

4

of
closely spaced stirrups
, corner
bars
, and crack
-
control
ling

bars distributed along all concrete
5

faces
. The horizontal leg
s

close to the concrete surface

of the closed stirrups

were

proportioned
6

to
carry a force equal t
o
the code
-
specified anchor steel capacity in shear
.

The needed
7

reinforcement was provided by closely spaced small size stirrups distributed
within a distance
8

from the anchor equal to its front edge distance
.
Although not specifically tested in the study
,
9

the selection of corner bars should follow the practices specified in Section 11.5.6
.2

of ACI
318
-
10

11

for corner bars in beams, and crack
-
controlling bars may be determined following the well
-
11

recognized strut
-
and
-
tie models.


12

With the proposed anchor shea
r
reinforcement
,

concrete breakout
was

prevented and anchor
13

shaft fracture was observed in all
the
tests

of single anchors

in this study
.
Cover concrete in
14

front of the anchor bolts
spalled
,
causing the
top
portion of the anchor shaft close to the concrete
15

surface
to b
ecome
exposed
.

T
he full anchor steel capacity in shear was not achieved because the
16

exposed anchor
s were subjected to a combination of shear, bending, and tension at failure. An
17

analysis of
the test results of exposed

anchors in the literatu
re indicated that a reduction facto
r

of
18

0.75, which is
slightly lower than that in ACI
318
-
11

on anchors with a grout pad
,

can be used to
19

determine the shear capacity of reinforced anchors.
In addition,
quasi
-
static cyclic tests of the
20

reinforced anchors
in shear showed insignificant capacity reduction, which is comparable to
21

other displacement
-
controlled cyclic tests
. Although
large capacity reductions were observed in
22

20

load
-
controlled cyclic tests

in the literature
,
n
o further capacity reduction was recommended
in
1

this study
for reinfor
ced anchors subjected to cyclic
shear
loading.

2


3

ACKNOWLEDGMENTS

4

The study reported in this paper is
from a project

supported by the National Science
5

Foundation (NSF) under Grant No.
0724097
.


The authors gratefully acknowledge

the support of
6

Dr.
Joy
Paus
chke
, who

served
as
the program director for this
grant
.


The authors also thank the
7

colleagues in ACI
C
ommittee 355

for their
valuable
inputs
.
Any opinions, findings, and
8

recommendations
or
conclusions
expressed in this m
aterial are those of the authors

an
d do not
9

necessarily reflect the views of NSF.

10

11

21

NOTATION

1




= area of
anchor reinforcement

2











= effective cross
-
sectional area of anchor in shear

and tension

3

1
a
c

=
front edge distance of anchor


4

2
a
c

=
side edge distance of anchor

5

a
d

=
anchor

diameter

6

b
d

= reinforcement diameter

7





= distance from shear force to surface reinforcement

8




= design bond strength of anchor reinforcement in
breakout cone

9

'
c
f

=
concrete compressive strength

10

y
f

= yield strength
of anchor steel

11

ys
F

= yield strength of steel
reinforcement

12

uta
f
= ultimate
tensile
strength

of anchor steel

13






=

development length of hooked bar in breakout cone


14

u

=
circumference of reinforcing bar


15

sd
V

=
Design shear capacity of anchor

16

s
V

=
Actual shear capacity of exposed anchor

17




= vertical reinforcement posit
ion

18





= stress in
anchor reinforcement

19

22

REFERENCES

1

1.

Lifeline Earthquake Engineering (ASCE)
,
“Northridge
Earthquake: Lifeline Performance
a
nd
2

Post
-
Earthquake Response
,”

A
R
eport to U.S.
D
epartment of
C
ommerce; NIST Building and
3

Fire Research Laborator
y. Gaithersburg, MD
,

1997
.

4

2.

Asia
-
Pacific Economic Cooperation
, “
Earthquake Disaster Management of Energy Supply
5

System of APEC Member Economies,


Energy Commission, Ministry of Economic Affairs,
6

Taipei, China
,

2002
.

7

3.

Grauvilardell, J.
;

Lee, D.
;

Hajjar, J.
;

a
nd Dexter, R
.
,

“Synthesis
o
f Design, Testing
a
nd
8

Analysis Research
o
n Steel Column Base Plate Connections
i
n High
-
Seismic Zones
.”
9

Structural Engineering Report No. ST
-
04
-
02, University of Minnesota, Minneapolis, MN
,

10

2005
.

11

4.

Tremblay, R
.;

Bruneau, M
.;

Nakashi
ma, M
.;

G.L. Prion, H
.;

Filiatrault, A
.;

and DeVall, R
.
,

12

“Seismic
Design
o
f Steel Buildings
Lessons
f
rom
Japan
Earthquake
,”
Canadian Journal of
13

Civil Engineering
. Vol. 23,
1996
,
pp.727
-
756.

14

5.

American Concrete Institute
,

“Building Code Requirements for Struc
tural Concrete (ACI
15

318
-
11
).” Farmington Hills, Michigan
,

20
1
1
.

16

6.

Fuchs, W
.;

Eligehausen, R
.;

and Breen, J
.
,

“Concrete capacity design approach for fastening
17

to concrete.”
ACI Structural Journal
, Vol. 92,
1995
,
No. 1, pp.73
-
94.

18

7.

Comité Euro
-
International du B
éton (CEB)
,
“Fastenings
t
o Concrete
a
nd Masonry
19

Structures:
State
o
f
t
he Art Report
.” Thomas Telford Service Ltd
.,

London
,

1997
.

20

8.

Federation Internationale du Beton (
fib
)
,
“Fastenings
t
o Concrete
a
nd Masonry Structures
.”
21

Special Activity Groups (SAG) 4 repo
rt
,

2008
,
Obtained from Dr. Eligehausen.

22

23

9.

Cook,

R
.;

Doerr, G
.;

and Klingner, R
.
,
"Design
Guide
f
or Steel
-
To
-
Concrete Connections
."
1

Research
R
eport No. 1126
-
4
, Center for Transportation Research, University of Texas at
2

Austin, Austin, TX
,

1989
.

3

10.

Cannon, R
.,


Straight
Talk
a
bout Anchorage
t
o Concrete
, P
art I.”
ACI Structural Journal
,
4

Vol.
92
,
1995
,
No. 5, pp.

1
-
7.

5

11.

Cannon, R
.,

“Straight
Talk
a
bout Anchorage
t
o Concrete
,
Part
II.”
ACI Structural Journal
,
6

Vol.
92
,
1995
,
No. 6, pp.

1
-
11.

7

12.

Eligehausen
, R
.;

Mallée,
R
.;

and Silva, J
.,

“Anchorage
i
n Concrete Construction
.” Wilhelm
8

Ernst & Sohn, Berlin, Germany
,

2006
.

9

13.

Muratli, H
.
, “
Behavior of Shear Anchors in Concrete: Statistical Analysis and Design
10

Recommendations,


MS Thesis, University of Texas at Austin, TX
,

1998
,

181 pp.

11

14.

Anderson, N. and Meinheit, D
.,

“Design
Criteria
f
or Headed Stud Groups
i
n Shear:
Part I


12

Steel Capacity
a
nd Back Edge Effects
.”
PCI Journal
, Vol. 45,
2000
,
No. 5, pp. 46
-
75.

13

15.

Pallarés, L. and Hajjar, J
.,

“Headed
Steel Stud Anchors
i
n Composite Str
uctures
, Part I:
14

Shear.”
Journal of Constructional Steel Research
. Vol. 66,
2009
,
pp. 198
-
212.

15

16.

Swirsky, R
.;

Dusel, J
.;

Crozier, W
.;

Stoker, J
.;

and Nordlin, E
.,

"Lateral
Resistance
o
f Anchor
16

Bolts Installed
i
n Concrete
,"
Report No. FHWA
-
CA
-
ST
-
4167
-
77
-
12
, C
alifornia Department
17

of Transportation, Sacramento, CA
,

1978
.

18

17.

Klingner, R
.;

Mendonca, J
.;

and Malik J
.,

“Effect
o
f Reinforcing Details
o
n
t
he Shear
19

Resistance
o
f Anchor Bolts
u
nder Reversed Cyclic Loading
,

ACI Journal
,
Vol.
79
,
1982
,
20

No. 1
,
pp.
471
-
479.

21

18.

L
ee, N.; Park, K.;

a
nd Suh, Y.,

"
Shear
B
ehavior
o
f
H
eaded
A
nchors
w
ith
L
arge
D
iameters
22

a
nd
D
eep
Embedment
."
ACI Structural Journal,
V
ol
. 108,
2010,
No. 1, pp. 34
-
41.

23

24

19.

Schmid, K
.,


Structural
Behavior
a
nd Design
o
f Anchor
n
ear
t
he Edge
w
ith Hanger Steel
1

u
nder Shear
,


PhD Thesis, University o
f Stuttgart
, Germany,
2010
.

2

20.

Pasch
en, H. and Schönhoff, T
.,


Untersuchungen über in Beton eingelassene Scherbolzen aus
3

Betonstahl
,”

Deutscher Ausschuss für Stahlbeton, Heft 346, Verlag Ernst & Sohn
.

1983

(
I
n
4

Schmid 2010).

5

21.

Ramm, W.

and Greiner, U
.,


Gutacht
en zur Bemessung von Kopfbolzenveran
-
kerungen, Teil
6

II, Verankerungen mit Rückhängebewehrung
,”

Fachgebiet Massivbau und Baukonstruktion,
7

Universität Kaiserslautern
,

1993
.

(
I
n Schmid 2010).

8

22.

Randl, N. and John, M
.,


Shear Anchoring
i
n Concrete Close
t
o
t
he E
dge
,


International
9

Symposium on Connections between Steel and Concrete
,
2001
,
pp. 251
-
260. Editor: R.
10

Eligehausen
.

11

23.

Fuchs, W.

and

Eligehausen, R
.,

“Zur Tragfähigkeit von Kopfbolzenbefestigungen unter
12

Querzugbeanspruchung am Rand,” Institut für Werkstoffe i
m Bauwesen, Bericht Nr. 20,
13

1986
.

(
I
n Schmid 2010).

14

24.

Widianto
;

Owen,
J
.;

and Patel,
C
.,

“Design of Anchor Reinforcement in Concre
te
Pedestals,”
15

Proceedings of
t
he 2010 Structures Congress, Orlando, F
L
,
2
010, pp. 2500
-
2511
.

16

25.

Nakashima, S
.,

“Mechanical
Characteristics
o
f Exposed Portions
o
f Anchor Bolts Subject
ed
17

t
o Shearing Forces
” Summaries

of technical papers of Annual
Report, Architectural Institute
18

of Japan, Vol. 38,
1998
,
pp. 349
-
352
.

19

26.

American Concrete Institute
,

“Examples of Anchor Design ACI
318
-
11

Appendix D
,

20

R
eport of
ACI
Committee
355
,
Farmington H
ills, Michigan
,

2011
.

21

27.

Petersen, D
.,


Seismic Behavior and Design of Cast
-
in
-
Place Anchors in Plain and
22

Reinforced Concrete,


MS Thesis, University of Wisconsin, Milwaukee
,

WI,
2011
.

23

25

28.

Lin, Z
.;

Petersen, D
.;

Zhao, J. and
Tian, Y
.,

“Simulation
a
nd Design
o
f Ex
posed Anchor
1

Bolts
i
n Shear,”
International Journal of Theoretical and Applied Multiscale Mechanics
.

(in
2

print)
.

3

29.

Geisser, S
.,

Predictive Inference: An Introduction, Chapman & Hall, New York, NY
,

1993
,
4

265 pp.

5

30.

Wollmershauser, R. E
.,

“Anchor Performance and
the 5

percent

Fractile.” Hilti Technical
6

Services Bulletin, Hilti, Inc
.
,

Tulsa, Oklahoma
,
1997
.

7

31.

American Society for Testing and Materials
, “
Standard Test Methods for Cyclic (Reversed)
8

Load Test for Shear Resistance of Vertical Elements of the Lateral Forc
e Resisting Systems
9

for Buildings
,”

West Conshohocken, PA
,
2010
,
15 pp.


10

32.

Civjan
,

S
. and

Singh
,

P
.,

“Behavior
o
f Shear Studs Subjected
t
o Fully Reversed Cyclic
11

Loading
,”

Journal of Structural Engineering
, Vol. 129,
2003
,
No. 11, pp.1466

1474.

12

33.

Vintzelou, E. and Eligehausen, R
.,

“Behavior of Fasteners under Monotonic or Cyclic S
hear
13

Displacements,”
ACI Special Publication
SP130
,

1992
,
p
p. 180
-
204.

14

15

26

TABLES AND FIGURES

1

List of Tables:

2

Table 1
S
ummary of design equations for anchor
shear
reinforcement

3

Table 2 Summary of reinforced anchor tests in shear

4


5

List of Figures:

6

Fig. 1

Con
crete breakout failure under shear

7

Fig. 2

Schematics of existing anchor shear
reinforcement

8

Fig. 3

Proposed anchor shear reinforcement layout

9

Fig.
4

Configurations of anchor specimens

10

Fig.
5

Experimental test setup

11

Fig. 6

Monotonic shear test results of r
einforced anchors

12

Fig. 7

Typical fractured shape of anchor bolts

13

Fig. 8

Strains in anchor shear
reinforcement

(25
-
150
-
150SG1)

14

Fig. 9

Capacity of anchor bolt with a lever arm

15

Fig. 10


Cyclic behavior of
reinforced
anchor bolts

16


17

27

Table 1
S
ummary of design eq
uations for anchor
shear
reinforcement

1

Reference

Design equation

for



given load



Development in cone

Actual s
hear capacity

(
V
s
)

Notes

Shipp and
Haninger (1983)



















Not needed

Design based on
equivalent tension

Hairpins

Klingner et al.
(1983)













Not needed














Hairpins

CEB

(1997)
















Considered in
capacity calculation













Bars within

0.5
c
a
1

ACI 318

(2008)





























*









Bars within
0.5
c
a
1

or 0.3
c
a
2

Widianto

et al.
(2010)

























reduced for not fully developed bars

Not considered in

Strut
-
and
-
tie model







Stirrups
,
ties

and
J
-
hooks

Fib design guide

(
to be
published)




















Considered in
capacity calculation














Bars wi
thin
0.5
c
a
1

Proposed




















on both sides














Closed s
tirrups

within
c
a
1



: area of anchor reinforcement
;


:
yield strength of
reinforcement
;




,




: effective cross
-
sectional area of anchor;

2




,



:
edge distances of

anchor
;


:
distance from shear to reinforcement
;



: design bond strength;



: ultimate strength of anchor;

3








: development le
ngth of hooked bar in breakout cone;

u
:
circumference of reinforcing bar
;


:
design shear force
;

4


:

reinforcement position
;



: modification factor;



:
stre
ss in anchor reinforcement
;

*: see Chapter
12

of ACI
318
-
11

for details.

5


6


7

28

Ta
ble
2

S
ummary

of
reinforced anchor tests in shear

1

Specimen
ID

Block
Type

d
a

(in.)

c
a
1

(in.)

Load

Type

Peak load

(kips)

9132010

-

0.75

4

M

22.19

9132010_2

-

0.75

4

M

22.47

9172010

-

0.75

4

C1

16.69

9202010

-

0.75

4

C1

15.50

9282010

-

1.0

6

M

39.18

929
2010

-

1.0

6

M

44.11

9302010

-

1.0

6

C1

38.71

10042010

-

1.0

6

C1

35.92

10052010

-

1.0

6

C
1

34.35

10062010

H

1.0

6

M

38.40

10062010_2

H

1.0

6

M

34.71

10072010

H

1.0

6

M

33.40

10082010

H

1.0

6

C1

33.62

10082010_2

H

1.0

6

C1

31.77

10122010

H

1.0

6

C
1

33.88

10132010

H

1.0

6

C2

-
42.68
*

10142010

H

1.0

6

C2

-
47.79
*

10292010

SG

1.0

6

M

36.13

11192010

SG

1.0

6

M

39.33

Note: 1 in. = 25.4 mm
;

1 kip = 4.45 kN;
*
: anchor fracture

2

occurred when shear was applied opposite to front edge.

3


4


5



6

29


1

Fig. 1

Concrete breakout failure under shear

2



3

102 mm

[4 in.]

1
52

mm

[
6

in.]

Idealized breakout cone

1
52

mm

[
6

in.]

35º

Top surface

Front surface

c
a
1
:

30


1

Fig. 2

Schematics of existing
anchor
shear
reinforcement

2



3

1
5
.
0
a
c

2
3
.
0
a
c

dh
l

d
l

d
l

31


1

Fig.
3

Proposed anchor shear reinforcement layout

2


3



4

1
a
c



2
1
,
min
a
a
c
c

b
d
8

b
d
8

b
d
8

b
d
8

32



1



2


3

Fig.
4

Configurations of anchor specimens

4


5

6

33


1

Fig.
5

Experimental test setup

2


3



4

34


1


2

Fig.
6

Monotonic shear test results

of reinforced anchors

3



4

35




1



2

Fig. 7

Typical fractured shape of anchor bolts

3



4

a
)

b
)

c
)

d
)

19
-
150
-
100
-
monotonic

19
-
150
-
100
-
cyclic

25
-
150
-
150
-
monotonic

25
-
150
-
150
-
cyclic

36


1


2

Fig.
8

Strains in anchor shear
reinforcement
(25
-
150
-
150SG1)

3



4

37


1

Fig.
9

Capacity of anch
or bolt with a lever arm

2


3



4

38




1



2

Fig.
10

Cyclic behavior of
reinforced
anchor bolts

3


4


5