CHAPTER 2 NOTATION AND DEFINITIONS

farctatemountainousΠολεοδομικά Έργα

29 Νοε 2013 (πριν από 3 χρόνια και 6 μήνες)

294 εμφανίσεις


442

CHAPTER 2



NOTATION AND DEFINITIONS

1


2

Adhesive


Chemical components

formulated from organic polymer
s,

or a combination of
3

organic
polymers
and inorganic
materials, that cure when blended together.

4


5

Adhesive anchor



A post
-
installed anchor, inserted into hardened concrete with an anchor hole
6

diameter not greater than 1.5 times the anchor diameter, that transfers loads to the concrete by
7

bond between the anchor and the adhesive, and bond between the adhesive and the

concrete.

8


9

Anchor



A steel element either cast into concrete or post
-
installed into a hardened concrete
10

member and used to transmit applied loads
to the concrete. Cast
-
in anchors include

headed bolts,
11

hooked bolts (J
-

or L
-
bolt),
and

headed studs.
Post
-
installed anchors include

expansion anchors,
12

undercut anchors,
and adhesive anchors. Steel elements for adhesive anchors include threaded
13

rods, deformed reinforcing bars, or internally threaded steel sleeves with external deformations.


14


15

Anchor group



A number of
similar

anchors
having

approximately e
qual effective embedment
16

depth
s

with spacing
s

between adjacent anchors such that the projected areas overlap. See
18.2
.1.1.


17


18

Anchor pullout strength



The strength correspond
ing to the anchoring device

or a major
19

component of the device sliding out from the concrete without break
ing out a substantial portion
20

of the surrounding con
crete.

21


22

Anchor reinforcement


Reinforcement used to transfer the full design load from the anchors
23

into the structural mem
ber. See
18
.
4.2.6

or
18
.
5
.2.
6
.

24


25

Attachment



The structural assembly, external to the surface of the concrete, that transmits
26

loads to or receives loads from the anchor.

27


28

Brittle steel element



An element with a tensile test elongation of less than 14 per
cent, or
29

reduction in area of less than
30

percent, or both.

30


31

Cast
-
in anchor



A headed bolt, headed stud, or hooked bolt installed before placing concrete.

32


33

Concrete breakout strength



The strength corre
sponding to a volume of concrete surrounding
34

the a
nchor or group of anchors separating from the member.

35


36

Concrete pryout strength



The strength corre
sponding to formation of a concrete spall behind
37

short, stiff anchors displaced in the direction opposite to the applied shear force.

38


39

Distance sleeve



A

sleeve that encases the center part of an undercut anchor, a torque
-
40

controlled expan
sion anchor, or a displacement
-
controlled expansion anchor, but does not
41

expand.

42


43

Ductile steel element



An element with a tensile test elongation of at least 14 percent

and
44

reduction in area of at least
30

percent. A steel element meeting the requirements of ASTM
45

A307 shall be considered ductile.

46


443


1

Edge distance



The distance from the edge of the concrete surface to the center of the nearest
2

anchor.

3


4

Effective embedment
depth



The overall depth through which the anchor transfers force to or
5

from the surrounding concrete. The effective embedment depth will normally be the depth of the
6

concrete failure sur
face in tension applications. For cast
-
in headed anchor bolts and h
eaded
7

studs, the effective embedment depth

is measured from the bearing contact surface of the head.

8


9

Expansion anchor



A post
-
installed anchor, inserted into hardened concrete that transfers
10

loads to or from the concrete by direct bearing or friction or
both. Expansion anchors may be
11

torque
-
controlled, where the expansion is achieved by a torque acting on the screw or bolt; or
12

displacement
-
controlled, where the expansion is achieved by impact forces acting on a sleeve or
13

plug and the expansion is controll
ed by the length of travel of the sleeve or plug.

14


15

Expansion sleeve



The outer part of an expansion anchor that is forced outward by the center
16

part, either by applied torque or impact, to bear against the sides of the predrilled hole.

17


18

Five percent fract
ile



A statistical term meaning
90

percent confidence that there is
95

percent
19

probability of the actual strength exceeding the nominal strength.

20


21

Headed stud



A steel anchor conforming to the requirements of AWS D1.1 and affixed to a
22

plate or similar st
eel attachment by the stud arc welding pro
cess before casting.

23


24

Hooked bolt



A cast
-
in anchor anchored mainly by bearing of the
90
-
degree bend (L
-
bolt) or
25

180
-
degree bend (J
-
bolt) against the concrete, at its embedded end, and having a mini
mum

e
h

of
26

3
d
a
.

27


28

Horizontal and upwardly inclined

anchor



An anchor installed in a hole drilled horizontally
29

or in a hole drilled at any orientation above horizontal.

30


31

Post
-
installed anchor



An anchor installed in hardened concrete. Expansion anchors,
32

undercut,
and ad
hesive

anchors are examples of post
-
installed anchors.

33


34

Projected area



The area on the free surface of the concrete
member that is used to represent
35

the larger base of the assumed rectilinear failure surface.
See
18.4.2.1 and 18
.
5
.2.1.

36


37

Projected influence area


The rectilinear area on the free surface of the concrete member that
38

is used to calculate the bond strength of adhesive anchors. See
18.4.5.1
.

39


40

Side
-
face blowout strength



The strength of anchors with

deeper embedment but thinne
r side
41

cover corresponding to concrete spalling on the side face around the embedded head while no
42

major brea
kout occurs at the top concrete surface.

43


44

Specialty insert



Predesigned and prefabricated cast
-
in anchors specifically designed for
45

attachment of

bolted or slotted connections. Specialty inserts are often used for handling,
46


444

transportation, and erection, but are also used for anchoring structural elements. Specialty inserts
1

are not within the scope of this
appendix.

2


3

Stretch length


Length of ancho
r, extending beyond concrete in which it is anchored, subject
4

to full tensile load applied to anchor, and for which cross
-
sectional area is a minimum and
5

constant.

6


7

Supplementary reinforcement



Reinforcement that acts to restrain the potential concrete
8

br
eakout but is not designed to transfer the full design load from the anchors into the structural
9

member.

10


11

Undercut anchor



A post
-
installed anchor that develops its tensile strength from the
12

mechanical inter
lock provided by undercutting of the concrete
at the embedded end of the
13

anchor. The undercutting is achieved with a special drill before installing the anchor or
14

alternatively by the anchor itself during its installation.

15


16

CHAPTER 18



ANCHORING TO CONCRETE

17


18

18
.
1



Scope

19


20

18.1
.1



This appendix
provi
des

governs

design requirements for anchors in concrete used to
21

transmit structural loads by means of tension, shear, or a combination of tension and shear
22

between
:

(a) connected structural elements; or (b) safety
-
related attachments and struc
tural
23

elemen
ts. Safety levels specified are intended for in
-
service conditions, rather than for short
-
term
24

han
dling and construction conditions.

<D.2.1>

25


26

18.1.2



This appendix applies to cast
-
in anchors
,

and
to

post
-
installed
expansion (torque
-
27

controlled and
displacement
-
controlled), undercut, and adhesive

anchors.
Adhesive anchors shall
28

be installed in concrete having a minimum age of 21 days at time of anchor installation.

Specialty
29

inserts, through
-
bolts, multiple anchors connected to a single steel plate a
t the embedded end of the
30

anchors, grouted anchors, and direct anchors such as powder or pneumatic actuated nails or bolts
31

are not included
in the provisions of Chapter 18
. Reinforcement used as part of the embedment
32

shall be designed in accordance with ot
her parts of this Code. <D.2.2>

33


34

18.1.3



Design provisions are included for the following types of anchors:
<D.2.3>

35


36

(a)
Headed studs and headed bolts having a geometry that has been demonstrated to result in
37

a pullout strength in uncracked concrete equal

to or exceeding
1.4
N
p
, where
N
p

is given in Eq.
38

(
18.4.3.4
);

39


40

(b)
Hooked bolts having a geometry that has been demonstrated to result in a pullout strength
41

without the benefit of friction in uncracked concrete equal to or exceeding
1.4
N
p
, where
N
p

is
42

given in Eq. (
18.14.3.5
);

43


44

(c)
Post
-
installed expansion and undercut anchors that meet the assessment criteria of ACI
45

355.2; and

46


445


1

(d)
Adhesive anchors that meet the assessment criteria of ACI 355.X.

2


3

18.1.4



Load applications that are predominantly hi
gh cycle fatigue or impact loads are not
4

covered by this appendix.

<D.2.4>

5


6

18.2



General requirements

7


8

18.2
.1


Anchors and anchor groups shall be designed for critical effects of factored loads as
9

deter
mined by elastic analysis. Plastic analysis
approaches are permitted where nominal strength
10

is controlled by ductile steel elements, provided that deformational compatibility is taken into
11

account.

<D.3.1>

12


13

18.2.1.1


Anchor group effects shall be considered wherever two or more anchors have
14

spacing less than the critical spacing
given in Table 18.2.1.1.
as follows:

15


16

Table 18.2.1.1


Critical spacing in anchor groups

17

Failure mode under investigation

Critical spacing

Concrete breakout in tension

3
h
ef

(a)

Bond strength in tension

2
c
Na

(b)

Concrete breakout in shear

3
c
a1

(c)


18

Only those anchors susceptible to the particular failure mode under investigation shall be
19

included in the group. <D.3.1.1>

20


21

18.2
.
2



The

design strength of anchors shall equal or exceed the largest required strength
22

calculated from the applicable load combinations in
6.4
.

<D.3.2>

23



24

18.2.3


Seismic design requirements

25


26

18.2.3.1



Anchors
in

structures assigned to Seismic Design Cate
gory C, D, E, or F
shall
27

satisfy

the additional requirements of 18.2.3.2 through 18.2.3.7. <D.3.3.1>

28


29

18.2
.3.2



The provisions of
Chapter 18

do not apply to the design of anchors in plastic hinge
30

zones of concrete structures under earthquake forces. <D.3.
3.2>

31


32

18.2
.3.3



Post
-
installed anchors shall be qualified for
earthquake loading

in accordance with
33

ACI 355.2
or ACI 355.X
.
The

pullout strength
N
p

and steel strength in shear
V
sa

of expansion
34

and undercut anchors

shall be based on the results of the ACI 355.2 Simulated Seismic Tests.
For
35

adhesive anchors, the steel strength in shear
V
sa

and the characteristic bond stresses

uncr

and

cr

36

shall be based on results of the ACI 355.X Simulated Seismic Tests.

<D.3.3.3>

37


38

18.2
.3.4


Requirements for tensile loading

39


40

18.2
.3.4.1


Where the tension component of the strength
-
level earthquake force applied to
41

anchor

or group of anchors

is equal to or less than

20 percent of the total factored anchor tensile
42


446

force
,

the
provisions of 18.2.3.4.2 through 18.2.3.4.5 shall

not apply

it shall be permitted to
1

design the anchor or group of anchors to satisfy 18.4 and 18.3.1.1
.

<D.3.3.4.1>

2


3

18.2
.3.4.2


Where the tension component of the strength
-
level earthquake force applied to

4

anchor
s

exceeds 20 percent of the total factored anchor tensile force

for the same load
5

combination, anchors and their attachments shall be designed in accordance with 18.2.3.4.
3
. The
6

anchor design tensile strength,

N
n,e
, shall be determined using
18.2.3.4.
4
.

<D.3.3.4.2>

7


8

18.2.3.4.
3



Anchors and their attachments shall be designed using one of options (a) through
9

(d):
<D.3.3.4.3
>

10


11

(a) The anchor or group of anchors shall have a concrete
-
governed design strength in tension
12

not less than 1.2 times
the steel
-
governed design strength of the anchor

or group. The concrete
-
13

governed design strength shall be calculated from
18.2
.3.4.4

(b), (c) and (d). Anchors shall have
14

a ductile steel element with a stretch length of at least eight anchor diameters unl
ess otherwise
15

determined by analysis. Where anchors are subject to load reversals the anchor shall be
16

protected against buckling. The ratio of
f
uta
/ f
ya

shall not be less than 1.3
for threaded connections
17

unless the threaded portions are upset
.

It shall b
e permitted to include threads in the stretch
18

length.


19


20

(b) The anchor or group of anchors shall have

N
n,e


not less than the maximum force that
21

can be transmitted to the anchor or group of anchors based on the development of a ductile yield
22

mechanism in
the attachment in flexure, shear, or bearing, or a combination of those conditions,
23

and considering both material overstrength and strain hardening effects for the attachment.

24


25

(c) The anchor or group of anchors shall have

N
n,e


not less than the maximum tension that
26

can be transmitted to the anchors by a non
-
yielding attachment.

27


28

(d) The anchor or group of anchors shall have

N
n,e


not less than the maximum tension
29

obtained from design load combinations that include
E
, with
E

increased by Ω
0
. The anchor
30

design tensile strength shall satisfy
Table
18.3.1.1

18.3.3
. Where adhesive anchors are used to
31

resist sustained tension loads the anchor design tensile strength shall also satisfy
Eq. (
18.3.1.2

32

18.3.3.1
)
.

33


34

18.2
.3.4.
4



The anchor design tensile strength for resisting earthquake forces,

N
n,e
, shall be
35

the lowest design strength in tension of a single anchor or group of anchors as determined from
36

consideration of (a) through (d) and assuming the concrete is cracked unles
s it can be
37

demonstrated that the concrete remains uncracked:
<D.3.3.4.4
>

38


39

(a)

N
sa

for a single anchor,

or for the most highly stressed individual anchor in a group of
40

anchors,

41


42

(b)
0.75

N
cb

or
0.75

N
cbg
, except that
N
cb

or
N
cbg

need not be computed where anchor
43

reinforcement satisfying
18.4.2.6

is provided,

44


45


447

(c)

0.75


N
pn

for a single anchor, or for the most highly stressed individual anchor in a group
1

of anchors, and

2


3

(d)
0.75

N
sb

or
0.75

N
sbg


4


5

where


is in accordance with
18.3.
3 or 18.3.
4

18.3.3.6
.

6


7

18.2
.3.4.5


Where anchor reinforcement is provided in accordance with
18.4.2.6
, no
8

reduction in design tension strength beyond that specified in
18.4.2.6

shall be required.
9

<D.3.3.4.5>

10


11

18.2
.3.5


Requirements for shear
loading

12


13

18.2.3.5.1


Where the shear component of the strength
-
level earthquake force applied to the
14

anchor or group of anchors is equal to or less than 20 percent of the total factored anchor shear
15

force,
the provisions of
18.2.3.5
.2

through 18.2.3.5
.
4

s
hall

not apply

it shall be permitted to
16

design the anchor or group of anchors to satisfy 18.5 and
the shear strength requirements of
17

18.3.1.1
.

<D.3.3.5.1
>

18


19


18.2
.3.5.
2



Where the shear component of the strength
-
level earthquake force applied to
20

anchors exceeds 20 percent of the total factored anchor shear force, anchors and their
21

attachments shall be designed in accordance with
18.2
.3.5.
3
. The anchor design shear strengt
h
22

for resisting earthquake forces shall be determined in accordance with
18.5
.
<D.3.3.5.2
>

23


24

18.2
.3.5.
3



Anchors and their attachments shall be designed using one of options (a) through
25

(c):
<D.3.3.5
.3
>

26


27

(a)

The anchor or group of anchors shall have

V
n

not less than the maximum force that can
28

be transmitted to the anchor or group of anchors based on the development of a ductile yield
29

mechanism in the attachment in flexure, shear, or bearing, or a combination of those conditions,
30

and considering both mat
erial overstrength and strain hardening effects in the attachment.

31



32

(b)

The anchor or group of anchors shall have

V
n

not less than the maximum shear that can
33

be transmitted to the anchors by a non
-
yielding attachment.


34


35

(c)

The anchor or group of anchors shall have

V
n

not less than the maximum shear obtained
36

from design load combinations that include
E
, with
E

increased by Ω
0
. The anchor design shear
37

strength shall satisfy
the shear strength requirements of
18.3.1.1

18.3.3
.

38


39

18.2
.3.5.4


Where anchor reinforcement is provided in accordance with
18.5.2.6
, no
40

reduction in design shear strength beyond that specified in
18.5.2.6

shall be required.
41

<D.3.3.5.4>

42


43

18.2
.3.6


Single anchors or groups of anchors that are subjected to both tension and shear
44

forces shall be designed to satisfy the requirements of
18.6
, with

N
n,e

substituted for

N
n
.
45

<D.3.3.6>

46


448


1

18.2
.3.7


Anchor reinforcement used in structures assigned to Seismic

Design Category C,
2

D, E or F shall be deformed reinforcement satisfying requirements of
19
.1.5.2.
<D.3.3.7>

3


4

18.2
.4



Adhesive anchors installed horizontally or upwardly inclined shall be qualified in
5

accordance with ACI 355.X requirements for sensitivity to installation direction. <D.3.4>

6


7

18.2
.5



For adhesive anchors subjected to sustained tension loading,
18.3
.1.2
shall

be satisfied.
8

For groups of adhesive
anchors, Eq. (
18.3.1.2
) shall be

satisfied
for the anchor that resists the
9

highest sustained tension load.
Installer certification and inspection requirements for horizontal
10

and upwardly inclined adhesive anchors
subjected to sustained tension loading shall be in
11

accordance with
18.8.2.2

through

18.8
.2.
4
, respectively
. <D.3.5>

12


13

18.2
.6



Modification factor
λ
a

for
anchors in

lightweight concrete shall be
in accordance with
14

(a), (b), (c)
taken as
:

15


16

(a)

Cast
-
in and
undercut anchor concrete failure

................................
.

1.0
λ

17


18

(b)

Expansion and adhesive anchor concrete failure

...........................

0.8
λ

19


20

(c)

Adhesive anchor bond failure per Eq
. (
18.4.2.2.a
)

.........................

0.6
λ

21


22

where
λ

is determined in accordance with
5.2.4
. It shall be permitted to use an alternate value
23

of
λ
a

where tests have been performed and evaluated in accordance with ACI 355.2 or ACI
24

355.X.

<D.3.6>

25


26

18.2
.
7



The values of
f
c

used for calculation pur
poses in this appendix shall not exceed
10,000

27

psi for cast
-
in anchors, and
8000

psi for post
-
installed anchors. Testing is required for post
-
28

installed anchors when used in concrete with
f
c


greater than
8000

psi.

<D.3.7
>

29


30

18.3



General requirements for strength of anchors

31


32

18.3
.1



Strength design of anchors shall be based either on
calculations

using

design models
33

that satisfy the
requirements of
18.3
.2,
or

the design requirements of 18.3.3
.

on test evaluation
34

using the
5
percent fractile of

applicable

test results for the followi
ng:

<D.4.1>

35


36

(a) Steel strength of anchor in tension (18.4.1);

37


38

(b) Concrete breakout strength of anchor in tension (18.4.2);

39


40

(c) Pullout strength of cast
-
in, post
-
installed expansion or undercut anchor in tension (18.4.3);

41


42

(d) Concrete side
-
face blowout

strength of headed anchor in tension (18.4.4);

43


44

(e) Bond strength of adhesive anchor in tension (
18.4
.5);

45


46


449


(f) Steel strength of anchor in shear (18.5.1);

1


2


(g) Concrete breakout strength of anchor in shear (18.5.2);

3


4

(h) Concrete pryout

strength of anchor in shear (18.5.3).

5


6

In addition, anchors shall satisfy the required edge distances, spacings, and thicknesses to
7

preclude splitting failure, as required in 18.7.

8


9

18.3.1.1


The

design of anchors, except as noted in 18.2.3, shall be in accordance with Table
10

18.3.1.1.

<D.4.1
.1>

11


12

Table 18.3.1.1


Required strength of anchors, except as noted in 18.2.3

13

Failure mode

Single
anchor

Anchor group*

Individual
anchor in a
group

Anchors
as a
group

Steel strength in tension (
18.4
.1)


N
sa


N
ua


N
sa


N
ua,i


Concrete breakout strength in
tension (
18.4
.2)


N
cb


N
ua



N
cbg


N
ua,g

Pullout strength in tension (
18.4
.3)


N
pn


N
ua


N
pn


N
ua,i


Concrete side
-
face blowout strength
in tension

(
18.4
.4)


N
sb


N
ua



N
sbg


N
ua,g

Bond strength of adhesive anchor in
tension (
18.4
.5)


N
a


N
ua



N
a
g


N
ua,g

Steel strength in shear (
18.5
.1)


V
sa


V
ua


V
sa


V
ua,i


Concrete breakout strength in shear
(
18.5
.2)


V
cb


V
ua



V
cbg


V
ua,g

Concrete
pryout strength in shear
(
18.5.
3)


V
cp


V
ua



V
cpg


V
ua,g

*

Required strengths of anchors in groups shall resist applicable failure modes for
individual anchors and for the group.


14

18.3
.1.2


For the design of adhesive anchors to resist sustained

tension loads, in addition to
15

18.3
.1.1,

16


17


0.55

N
ba


N
ua,s


(18.3.1.2
)

18


19

where
N
ba

is determined in accordance with
18.4
.5.2.

<D.4.1.2>

20


21

18.3
.1.3


When both
N
ua

and
V
ua

are present, interaction effects shall be considered

using an
22

interac
tion expression
that results in computation of strength in substantial agreement with
23

results of comprehen
sive tests. This requirement shall be considered satis
fied by 18.6

.

<D.4.1.3>

24


25

18.3
.2


The nominal strength for any anchor or group of anchors shall be based on design
26

models that result in predictions of strength in substantial agreement with results of
27


450

comprehensive tests. The materials used in the tests shall be compatible with the mater
ials used
1

in the structure. The nominal strength shall be based on the
5

percent fractile of the basic
2

individual anchor strength. For nominal strengths related to concrete strength, modifications for
3

size effects, the
number

of anchors, the effects of clo
se spacing of anchors, prox
imity to edges,
4

depth of the concrete member, eccen
tric loadings of anchor groups, and presence or absence of
5

cracking shall be taken into account. Limits on edge distances and anchor spacing in the design
6

models shall be consi
stent with the tests that verified the model.

<D.4.2>

7


8

18.3
.2.1


The effect of reinforce
ment provided to restrain the concrete brea
kout

shall be
9

permitted to be included in the design models used to
satisfy
18.3
.2.

Where anchor reinforcement
10

is provided

in accordance with
18.4
.2.
6

and
18.5
.2.
6
, calculation of the concrete breakout
11

strength in accordance with
18.4
.2 and
18.5
.2 is not required.

<D.4.2.1>

12


13


14

18.3.1.1

18.3.3



The design of anchors
, except as noted in 18.2.3,

shall be in accordance with
15

Table
18.3.1.1

18.3.3
. <D.4.1.1>

16


17

Table
18.3.1.1

18.3.3



Required

Design

strength of anchors
, except as noted in 18.2.3

18

Failure mode

Single anchor

Anchor group
*
[1]

Individual
anchor in a
group

Anchors as a
group

Steel
strength in tension
(
18.4
.1)


N
sa


N
ua

(a)


N
sa


N
ua,i


(i
)



Concrete breakout strength
in tension (
18.4
.2)


N
cb


N
ua

(b)




N
cb
g


N
ua,g

(l
)

Pullout strength in tension
(
18.4
.3)


N
pn


N
ua

(c)


N
pn


N
ua,i

(j
)



Concrete side
-
face blowout
strength
in tension (
18.4
.4)


N
sb


N
ua

(d)




N
s
b
g


N
ua,g

(m
)

Bond strength of adhesive
anchor in tension (
18.4
.5)


N
a


N
ua

(e)




N
ag


N
ua,g

(n)

Steel strength in shear
(
18.5
.1)


V
sa


V
ua

(f)


V
sa


V
ua,i

(k
)



Concrete breakout strength
in shear (
18.5
.2)


V
cb


V
ua

(g)




V
cb
g


V
ua,g

(o
)

Concrete pryout strength in
shear (
18.5.
3)


V
c
p


V
ua

(h)




V
cpg


V
ua,g

(p
)

*
[1]

Required strengths of anchors in groups shall resist applicable failure modes for
individual anchors and for the group.


19

18.3.1.2

18.3.3.1



For the design of adhesive anchors to resist sustained tension loads, in
20

addition to 18.3.1.1,

In addition to Table 18.3.3
, the
basic bond strength of a
n

adhesive anchor in
21

tension,
N
ba
, shall satisfy:

22


23


0.55

N
ba


N
ua,s


(
18.3.1.2

18.3.3.1
)

24


451


1

where
N
ba

is determined in accordance
with 18.4.5.2.

<D.4.1.2>

2


3

18.3.1.3

18.3.3.
2



When both
N
ua

and
V
ua

are

present, interaction effects shall be considered

4

using an interac
tion expression that results in computation of strength in substantial agreement

5

with results of comprehen
sive tests. This requirement shall be considered satis
fied by 18.6
.

6

<D.4.1.3>

7

18.3.3.3


In addition, anchors shall satisfy the required edge distances, spacings, and
8

thicknesses to preclude splitting failure, as required in
18.7.

9


10

18.3.
3
.3


Where anchor reinforcement is provided in accordance with 18.4.2.6 and 18.5.2.6,
11

calculation of the concrete breakout strength in accordance with 18.4.2 and 18.5.2 is not
12

required.

<D.4.2.1>

13


14

18.3.2.2

18.3.3.
4



For anchors with diameters not exceeding
4

in.
,
the concrete breakout
15

strength requirements shall be considered satisfied by the design procedure of 18.4.2 and 18.5.2.
16

<D.4.2.2>

17


18


18.3.2.3

18.3.3.
5



For adhesive anchors with embedment depths
4
d
a


h
ef


20
d
a
, the bond
19

strength requirements shall be considered satisfied by the design procedure of
18.4
.5.

<D.4.2.3>

20


21

18.3
.
3

18.3.3.
6



Strength reduction factor


景爠
a湣桯牳r楮ic潮c牥te
獨a汬扥
楮iacc潲oa湣e


睩瑨⁔w扬敳b
ㄸ⸳
.
㌮3
⹡,
1㠮8
⸳⸶
⹢Ⱐ.湤n
ㄸ⸳
.
㌮3


ta扵污瑥搠cco牤楮朠瑯⁴桥⁣潲oe獰潮摩湧⁦a楬畲u


浯摥m

<䐮㐮D
>

<䐮㐮㐠De浯癥搠m楴栠䅰灥湤楸⁃>






Table
18.3
.
3.6
.a


Reduction factors for steel

element failure modes for cast
-
in and post
-
26

installed anchors

27

Strength
type

Type of steel element



Tension

Ductile anchor

0.75

Brittle anchor

0.65

Shear

Ductile

0.65

Brittle

0.60


28

Table
18.3
.
3
.
6
b


Reduction factors for concrete
failure modes
with cast
-
in anchors

29

Strength
type

Concrete
failure mode

Reinforcement



Tension

Breakout

Supplementary

0.75

None

0.70

Pullout

All cases

0.70

Side
-
face
blowout

Supplementary

0.75

None

0.70

Shear

Breakout

Supplementary

0.75

None

0.70

Pryout

All cases

0.70


452


1

Table
18.3
.
3.6
.
c



Reduction factors for concrete
failure modes
with
post
-
installed

anchors

2

Strength
type


Concrete
failure mode

Reinforcement

Anchor
category per
ACI 355.2

or
ACI 355.X





Tension

Breakout

Supplementary

1

0.75

2

0.65

3

0.55

None

1

0.65

2

0.55

3

0.45

P
ullout

All cases

1

0.65

2

0.55

3

0.45

Shear

Breakout

Supplementary

All

0.75

None

All

0.70

Pryout

All cases

All

0.70


3

18.4



Design requirements for tensile loading

4


5

18.4
.1


Steel strength of anchor in tension

6


7

18.4
.1.1


The nominal strength of an anchor in ten
sion as governed by the steel,
N
sa
, shall be
8

evaluated by calculations based on the properties of the anchor material and the physical
9

dimensions of the anchor.

<D.5.1.1>


10


11

This provision states in words what is required in 18.4.1.2. Recommend moving this wording to
the commentary.


12

18.4
.1.2


The nominal strength of
a
n

anchor in tension,
N
sa
, shall not exceed

13


14


N
sa

=
A
se,N
f
uta

(
18.4
.1.2
)

15


16

where
A
se,N

is
the
effective cross
-
sectional area of
a
n

anchor in tension, in.
2
,
and

f
uta

shall not

17

exceed the lesser

be taken greater than the smaller

of
1.9
f
ya

and
125,000

psi.

<D.5.1.2>

18


19

18.4
.2


Concrete breakout strength of anchor in tension

20


21

18.4
.2.1


The nominal concrete breakout strength

in tension
,
N
cb
,

of a single anchor
or
,

N
cbg
,
22

of
a

group of anchors
, s
hall not exceed

(a) or (b):

<D.5.2.1>

23


24

(a)
For
a single anchor

25


26


N
cb

= (
A
Nc

/

A
Nc
o
)
Ψ
ed,N

Ψ
c,N

Ψ
cp,N

N
b

(
18.4
.2.1.a
)

27


453


1

(b)
For
a group of anchors

2


3


N
cb

= (
A
Nc

/

A
Nc
o
)
Ψ
ec,N

Ψ
ed,N

Ψ
c,N

Ψ
cp,N

N
b


(
18.4
.2.1.b
)

4


5

Factors
Ψ
ec,N
,

Ψ
ed,N
,
Ψ
c,N
, and
Ψ
cp,N

are defined in
18.4
.2.4
, D.5.2.5, D.5.2.6, and D.5.2.7,
6

respectively
.
A
Nc

is the projected concrete failure area of a single anchor or group of anchors
7

that shall be approximated as the base of the rectilinear geometrical figure that results from
8

projecting the failure surface outward
1.5
h
ef

from the centerlines of the anchor, o
r in the case of
9

a group of anchors, from a line through a row of adjacent anchors.
A
Nc

shall not exceed
nA
Nco
,
10

where
n

is the number of anchors in the group

that resist tension
.
A
Nco

is the projected concrete
11

failure area of a single anchor with an edge d
istance equal to or greater than
1.5
h
ef


12


13


A
Nc
o

=
9
h
ef
2

(
18.4
.2.1.c
)

14


15

18.4
.2.2


The basic concrete breakout strength of a single anchor in tension in cracked
16

concrete,
N
b
, shall not exceed

<D.5.2.2>

17


18


N
b

=
k
c
λ
a
(√
f
c

)

h
ef
1.5

(
18.4
.2.2.a
)

19


20

w
here

21


22

k
c

=

24

for cast
-
in anchors; and

23

k
c

=

17

for post
-
installed anchors.

24


25

Alternatively,

t
he value of
k
c

for post
-
installed anchors shall be per
mitted to be increased
26

above
17

based on ACI 355.2
or ACI 355.X

product
-
specific tests, but shall
in no case

not

27

exceed
24
.

28


29

Alternatively, for cast
-
in headed

anchors

studs and headed bolts

with
11

in. ≤
h
ef


25

in.,
N
b

30

shall not exceed

31


32


N
b

=
16
λ
a
(√
f
c

)

h
ef
5
/3

(
18.4
.2.2.b
)

33


34

18.4
.2.3


Where anchors are located less than

1.5
h
ef

from three or more edges, the value of
35

h
ef

used

in 18.4.2
for the calculation of

A
Nc

in accordance with 18.4.2.1, as well as

in Eq.
36

(
18.4
.2.1.a)

through
(
18.4
.2.
4.d
)

shall be the
larger

of
c
a,max
/1.5

and
s
/3
, where

s

is
the maximum
37

spacing between anchors within the group.

<D.5.2.3>

38


39

18.4
.2.
4



S
trength modification factors for concrete breakout modes
in tension
shall be
40

calculated

in accordance with Table
18.4
.2.4
.
<D
.5.2.4> <D.5.2.5> <D.5.2.6> <D.5.2.7>

41



42


454


Table
18.4
.2.4


Strength modification factors

1

Variable

Limitations

Strength
modification factor

Eccentric
loading
[1]

Ψ
ec,N

O
nly the anchors in tension shall be
considered when calculating
e′
N

and
N
cbg
.

N
ot exceed the greater of (a) and (b)
:

1

/

[1 + 2
e′
N

/
(3
h
ef
)
]

(a)

1.0

(b)

Edge effects

Ψ
ed,N

c
a,min

≥ 1.5
h
ef

1.0

(c)

c
a,min

< 1.5
h
ef

0.7 + 0.3
c
a,min

/

(
1.5
h
ef
)

(d)

Cracking
effects
[2]

Ψ
c,N

Cracked concrete

1.0

(e)

Uncracked
concrete

Cast
-
in anchors

1.25

(f)

Post
-
installed anchors

k
c

=

17

1.4


(g)

Post
-
installed anchors

17

<
k
c



24


Test results in accordance
with

ACI 355.2 or ACI 355.X

(h)

Splitting
effects

Ψ
cp,N

Uncracked
concrete
a
nd no
supplementary
reinforcement

c
a,min


c
ac

1.0

(i)

c
a,min

<
c
ac

A
t least the g
reater of (j) and (k)
:

c
a,min

/
c
ac

(j)

1.5
h
ef

/

c
ac

(k)

All other cases

1.0

(l)

[
1
]

In

the case where eccentric loading exists about two axes, the modification factor,
Ψ
ec,N
, shall be
calculated
computed

for each axis individually and the product of these factors
is
used as
Ψ
ec,N

in
Eq. (18.4.2.1.b). <D.5.2.4>


[
2
]

When analysis
indicates cracking at service load levels, the cracking in the concrete shall be con
-
trolled by flexural reinforcement distributed in accor
dance with 9.6.3, or equivalent crack control
shall be provided by confining reinforcement. <D.5.2.6>


2

18.4
.2.5



Where an additional plate or washer is added at the head of the anchor, it shall be
3

permitted to calculate the projected area of the failure surface by projecting the failure surface
4

outward
1.5
h
ef

from the effective perimeter of the plate or washer. The
effec
tive perimeter shall
5

not exceed the value at a section projected outward more than the thickness of the washer or
6

plate from the outer edge of the head of the anchor.

<D.5.2.8>

7


8

18.4
.2.6



Where anchor reinforcement is developed in accordance with
20.4

on both sides of
9

the breakout surface, the design strength of the anchor reinforcement shall be permitted to be
10

used instead of the concrete breakout strength
in determining


N
n
. A strength reduction factor of
11

0.75

shall be used in the design of the a
nchor reinforcement.

<D.5.2.9>

12


13

18.4
.3


Pullout strength of
cast
-
in, and post
-
installed expansion and undercut

anchor
s

in
14

tension

15


16

18.4
.3.1


The nominal pullout strength of a single
cast
-
in, post
-
installed expansion, and post
-
17

installed undercut
anchor in tension,
N
pn
, shall not exceed

18


19


N
pn

=
Ψ
c,P
N
p

(
18.4
.3.1)

20


21


455

where
Ψ
c,P

is defined in
18.4
.3.6.

<D.5.3.1>

1


2

18.4.3.2


The pullout strength of an anchor in tension,
N
p
, shall be in accordance with Table
3

18.4.3.2. <D.5.3.2>

4

Table 18.4.3.2


Maximum
pullout strength of anchor in tension

5

Anchor type

Maximum

N
p

Cast
-
in headed studs and
headed
bolts
[1]

8
A
brg

f
c


Ca獴
-
楮⁨潯步搠扯汴
s
[1
]

[2]

0.9
f
c

e
h
d
a

Post
-
installed expansion and
undercut anchors
[
3
]

Test results in accordance
with ACI 355.2

[1]

It shall be permitted to use values of
N
p

based on the

5

per
-
cent fractile of tests performed and evaluated in the same
manner as the ACI 355.2 procedures but without the benefit
of friction.

[2]

Hook extension shall be,
3
d
a


e
h


4.5
d
a
.

[
3
]

It is not permissible to calculate the pullout strength in
tension for such anchors.


6


7

18.4
.3.2


For post
-
installed expansion and under
cut anchors, the values of shall be based on
8

the
5

percent fractile of results of tests performed and evalu
ated
according to ACI 355.2. It is not
9

permissible to calculate the pullout strength in tension for such anchors.

<D.5.3.2>

10


11

18.4
.3.3


For single cast
-
in headed studs and headed bolts, it shall be permitted to evaluate
12

the pull
out strength in tension using
18
.4
.3.4. For single J
-

or L
-
bolts, it shall be permitted to
13

evaluate the pullout strength in tension using
18.4
.3.5. Alternatively, it shall be permitted to use
14

values of
N
p

based on the

5

per
cent fractile

of tests performed and evaluated in the same manner
15

as the ACI 355.2 procedures but without the benefit of friction.

<D.5.3.3>

16


17

18.4
.3.4


The pullout strength in tension of a single headed stud or headed bolt,

N
p
,

for use in
18

Eq.
(
18.4
.3.1)
, shall not exc
eed

<D.5.3.4
>

19


20


N
p

=
8
A
brg

f
c


(
18.4
.3.4)

21


22

18.4
.3.5


The pullout strength in tension of a single hooked bolt
,
N
p
, for use in Eq. (18.4.3.1
)
23

shall not exceed


24


25


N
p

=
0.9
f
c

e
h
d
a

(
18.4
.3.5)

26


27

where

3
d
a


e
h


4.5
d
a
.

<D.5.3.5>

28


29

18.4
.3.6


For an anchor located in a region of a concrete member where analysis indicates no
30

crack
ing at service load levels, the following modification factor shall be permitted

31


32

Ψ
c,P

=
1.4


33


456


1

w
here
analysis indicates cracking at service load levels,

Ψ
c,P

shall be

taken as
1.0
.

<D.5.3.6>

2


3

18.4
.4


Concrete side
-
face blowout strength of a headed anchor in tension

4


5

18.4
.4.1


For a single headed anchor with deep embedment close to an edge

(
h
ef

>
2.5
c
a1
)
,
6

the nomi
nal side
-
face blowout strength,
N
sb
,

shall not exceed

7


8



N
sb

=
(160
c
a1

A
brg
)
λ
a

f
c


(
18.4
.4.1)

9


10

If
c
a2

for the single headed anchor is less than

3
c
a1
, the value of
N
sb

shall be multiplied by the
11

factor
(
1

+
c
a2

/
c
a1
) /

4

where

1.0



(
c
a2

/
c
a1
)

3.0
.

<D.5.4.1>

12


13

18.4
.4.2



For multiple headed anchors with deep embedment close to an edge

(
h
ef

>
2.5
c
a1
)

14

and anchor spacing less than
6
c
a1
, the nominal strength of
those

anchors
susceptible to
a side
-
15

face blowout failure
N
sb

sha
ll not exceed


16


17


sbg sb
a1
s
N 1 N
6c
 
 
 
 

(
18.4
.4.2)

18


19

where
s

is
the distance between

the outer anchors along the edge
,
and
N
sb

is obtained from Eq.
20

Eq. (
18.4
.4.1)

without modification for a perpendicular edge distance.

<D.5.4.2>

21


22

18.4
.5


Bond strength of adhesive anchor in tension

23


24

18.4
.5.1


The nominal bond strength in tension,
N
a

of a single adhesive anchor or
N
a
g

of a
25

group of adhesive anchors, shall not exceed

<D.5.5.1>

26


27

(a) For a single adhesive anchor:

28


29


N
a

= (
A
Na

/

A
Nao
)

Ψ
ed,Na

Ψ
cp,Na

N
ba

(18.4.5.1.a
)

30


31

(b) For a group of adhesive
anchors:

32


33


N
a
g

= (
A
Na

/

A
Nao
)
Ψ
ec,Na

Ψ
ed,Na

Ψ
cp,Na

N
ba

(
18.4.5.1.b
)

34


35

Factors
Ψ
ec,Na
,
Ψ
ed,Na
, and
Ψ
cp,Na
,

are defined in
18.4
.5.3,
18.4
.5.4, and
18.4.
5.5, respectively.
36

A
N
a

is the projected influence area of a single adhesive anchor or group of adhesive anchors that
37

shall be approximated as a rectilinear area that projects outward
c
Na

from the centerline of the
38

adhesive anchor, or in the case of a group of adhesive anchors, f
rom a line through a row of
39

adjacent adhesive anchors.
A
N
a

shall not exceed
n
A
N
a
o
, where

n

is the number of adhesive
40

anchors in the group that resist tension loads.
A
N
a

is the projected influence area of a single
41

adhesive anchor with an edge distance equal

to or greater than
c
Na
:

42


43


A
N
a
o

=

(2
c
N
a
)
2


(
18.4.5.1.c
)

44


45


457

w
here

1


uncr
Na a
τ
c 10d
1100


(
18.4.5.1.d
)

2


3

and constant 1100 carries the unit of lb/in.
2

4


5

18.4
.5.2


The basic bond strength of a single adhesive anchor in tension in cracked concrete,

6

N
ba
,
shall not exceed

<D.5.5.2>

7


8


N
ba

=

λ
a

τ
cr

π

d
a

h
ef


(18.4.5.2
)

9


10

The characteristic bond stress,

τ
cr

shall be taken as the
5

percent fractile of results of tests
11

performed and evaluated according to ACI 355.X.

12


13

Where analysis indicates cracking at service
load levels, adhesive anchors shall be qualified for
14

use in cracked concrete in accordance with ACI 355.X.

15


16

For adhesive anchors located in a region of a con
crete member where analysis indicates no
17

cracking at service load levels,
τ
unc
r

shall be permitted to be used in place of
τ
cr

in Eq. (
18.4.5.2
)
18

and shall be taken as the
5

percent fractile of results of tests performed and evaluated according
19

to ACI 355.X
.

20


21

I
t shall be permitted to use the minimum characteristic bond stress values in Table
18.4
.5.2
22

provided (a) through (f) are satisfied:

23


24

(a)
Anchors shall meet the requirements of ACI 355.X;

25


26

(b)
Anchors shall be installed in holes drilled with a rotary impact

drill or rock drill;


27


28

(c)
Concrete at time of anchor installation shall have a minimum compressive strength of 2500
29

psi;

30


31

(d)
Concrete at time of anchor installation shall have a minimum age of 21 days;

32


33

(e)
Concrete temperature at time of anchor insta
llation shall be at least 50
o
F.

34


35

TABLE 18.4.5.2


MINIMUM CHARACTERISTIC BOND STRESSES
[1],[2]

36

Installation
and service

environment

Moisture content
of concrete at time
of anchor
installation

Peak in
-
service
temperature of
concrete

τ
c
r

τ
unc
r

°F

(psi)

(psi)

Outdoor

Dry to fully
saturated

175

200

650

Indoor

Dry

110

300

1000


458

[1]
Where anchor design includes sustained tension loading, multiply values of
τ
cr

and

τ
unc
r

by
0.4
.

[2]
Where anchor design includes earthquake loads for structures assigned to
s
eismic Design Category C, D, E, or F, multiply values of
τ
cr

by 0.8 and
τ
unc
r

by
0.4
.


1

18.4
.5.3


The modification factor for adhesive anchor groups loaded eccentrically in tension,

2

Ψ
ec,Na
, shall be
calculated
computed

as:

<D.5.5.3>

3

ec,Na
'
N
Na
1
ψ
e
1
c

 

 
 


(18.4.5.3
)

4

but
Ψ
ec,Na

shall not be taken greater than 1.0.

5


6

If the loading on an adhesive anchor group is such that only some adhesive anchors are in
7

tension, only those adhesive anchors that are in tension shall be considered when determining the
8

eccentricity
e′
N

for

use in Eq. (18.4.5.3
) and for the calculation of
N
ag

a
ccording to Eq.
9

(
18.4.5.1.b
).

10


11

In the case where eccentric loading exists about two orthogonal axes, the modification factor,
12

Ψ
ec,Na
, shall be
calculated
computed

for each axis individually and the product of these factors
13

used as
Ψ
ec,Na

in Eq. (
18.4.5.1.b
).

14


15

18.4
.5.4


The modification factor for edge effects for single adhesive anchors or adhesive
16

anchor groups loaded in tension,
Ψ
e
d
,Na
, shall be
calculated
comput
ed

as

<D.5.5.4>

17


18

If

c
a,min


c
Na
, t
hen
Ψ
e
d
,Na

=

1.0

(18.4.5.4.a)

19


20

If

c
a,min

<

c
Na
,
then

Ψ
e
d
,Na

=

0.7 + 0.3
c
a,min

/
c
Na

(
18.4.5.4.b
)

21


22

18.4
.5.5


The modification factor for adhesive anchors designed for uncracked concrete in
23

accordance with
18.4
.5.2 without supplementary reinforcement to control splitting,
Ψ
cp
,Na
, shall
24

be
calculated
computed

as:

<D.5.5.5>

25


26

If
c
a,min


c
a
c
,
then
Ψ
cp
,Na

=
1.0

(18.4.5.5.a
)

27


28

If

c
a,min

<

c
a
c
, then

Ψ
cp
,Na

=
c
a,min

/
c
ac

(
18.4.5.4.b
)

29


30

but
Ψ
cp
,Na

determined from Eq. (
18.4.5.4.b
) shall not be taken less than

c
Na

/
c
ac

where the
31

critical edge distance,
c
ac
, is defined in 18.7
.6.

32


33

18.5



Design requirements for shear loading

34


35

18.5
.1


Steel strength of anchor in shear

36


37


459

18.5
.1.1


The nominal strength of an anchor in shear as governed by steel,
V
sa
, shall be
1

evaluated by calculations based on the properties of the anchor material and the physical
2

dimensions of the anchor.

Where concrete breakout is a potential failure mode, the
required steel
3

shear strength shall be consistent with the assumed breakout surface.

<D.6.1.1>

4


5

The first sentence in the

provision states in words what is requi
red in 18.5
.1.2. Recommend
moving
the first sentence t
o the commentary

and the second sentence
to 18.5.1.2
.


6

18.5
.1.2


The nominal strength of a single anchor or group of anchors in shear,
V
sa
, shall not
7

exceed (a) through (c):

<D.6.1.2>

8


9

(a)
For
cast
-
in headed stud anchors

10


11


V
sa

=
A
se,V

f
uta

(
18.5
.1.2.a)

12


13

where

A
se,V

is the
effective cross
-
sectional area of
a
n

anchor in shear, in.
2
,

and
f
uta

shall not

14

ex
c
eed

the lesser

be taken greater
than the smaller

of
1.9
f
ya

and
125,000

psi.

15


16

(b)
For
cast
-
in headed bolt and hooked bolt anchors and for post
-
installed anchors where
17

sleeves
do not extend through the shear plane

18


19


V
sa

=
0.6
A
se,V

f
uta

(
18.5
.1.2.b)

20


21

where
A
se,V

is the
effective cross
-
sectional area of
a
n
anchor in shear, in.
2
,

and
f
uta

shall not
22

ex
c
eed

the lesser

be taken greater
than

the smaller

of
1.9
f
ya

and
125,000

psi.

23


24

(c)
For
post
-
installed anchors where sleeves extend through the shear plane,
V
sa

shall be based
25

on the results of tests performed and evaluated according to ACI 355.2. Alternatively, Eq.
26

(
18.5
.1.2.b)

shall be per
mitted to be used.

27


28

18.5
.1.3


Where anchors are used with built
-
up grout pads, the nominal strengths of
18.5
.1.2
29

shall be multiplied by a
0.80

factor.

<D.6.1.3>

30


31

18.5
.2


Concrete breakout strength of anchor in shear

32


33

18.5
.2.1


The nominal concrete breakout strength

in shear
,
V
cb
,
of

a single anchor

or
,

V
cbg
, of

34

a

group of anchors shall not exceed:

<D.6.2.1>

35


36

(a)
For
shear force perpendicular to the edge on a single anchor

37


38


V
cb

= (
A
Vc

/

A
Vco
)
Ψ
ed,V
Ψ
c,V
Ψ
h,V

V
b


(
18.5
.2.1.a)

39


40

(b)
For
shear force perpendicular to the edge on a group
of anchors

41


42


V
cbg

= (
A
Vc

/

A
Vco
)
Ψ
ec,V
Ψ
ed,V
Ψ
c,V
Ψ
h,V

V
b


(
18.5
.2.1.b)

43


44


460

(c)
For
shear force parallel to an edge,
V
cb

or
V
cbg

shall be permitted to be twice the value of
1

the shear force determined from
Eq. (
18.5
.2.1.a) or (
18.5
.2.1.b)
, respec
tively, with the shear
2

force assumed to act perpen
dicular to the edge and with

Ψ
ed,V

taken equal to
1.0
.

3


4

(d)
For
anchors located at a corner, the limiting nom
inal concrete breakout strength shall be
5

determined for each edge, and the minimum value shall
be used.

6


7

Factors
Ψ
ec,V
,

Ψ
ed,V
,
Ψ
c,V
,
and
Ψ
h,V

are defined in
18.5
.2.5
, D.6.2.6, D.6.2.7,

and D.6.2.8,

8

respectively
.

V
b

is the basic concrete breakout strength value for a single anchor.
A
Vc

is the
9

projected area of the failure surface on the side of the
concrete member at its edge for a single
10

anchor or a group of anchors. It shall be permit
ted to evaluate
A
Vc

as the base of a truncated half
11

pyr
amid projected on the side face of the member where the top of the half pyramid is given by
12

the axis of the an
chor row selected as critical. The value of
c
a1

shall be taken as the distance from
13

the edge to this axis.
A
Vc

shall not exceed
nA
Vco
, where
n

is the number of anchors in the group.


14


15

A
Vco

is the projected area for a single anchor in a deep member with a d
istance from edges
16

equal or greater than
1.5
c
a1

in
the direction perpendicular to the shear force. It shall be permitted
17

to evaluate
A
Vco

as the base of a half pyramid with a side length parallel to the edge of
3
c
a1

and a
18

depth of
1.5
c
a1
.

19


20


A
Vco

=
4.5(
c
a1
)
2


(
18.5
.2.1.c)

21


22

Where anchors are located at varying distances from the edge and the anchors are welded to
23

the attach
ment so as to distribute the force to all anchors, it shall be permitted to evaluate the
24

strength based on the dis
tance to the farthest row of anchors from the edge. In this case, it shall
25

be permitted to base the value of
c
a1

on the distance from the edge to the axis of the far
thest
26

anchor row that is selected as critical, and all of the shear shall be assumed to be

carried by this
27

criti
cal anchor row alone.

28


29

18.5
.2.2


The basic concrete breakout strength in shear of a single anchor in cracked
30

concrete,
V
b
, shall
be the smaller of (a) and (b):

<D.6.2.2>

31


32

(a)

V
b

= [7 (

e

/
d
a
)
0.2


d
a
]

λ
a

(√
f
c

)(

c
a1
)
1.5


(
18.5
.2.2
.a
)

33


34

where

e

is the load
-
bearing length of the anchor for shear:

35


36


e

=

h
ef

for anchors with a constant stiffness over the full length of embedded section, such as
37

headed studs
and

post
-
installed anchors with one tubular shell over full length of the embedme
nt
38

depth,

39


40


e

=

2
d
a

for torque
-
controlled expansion anchors with a distance sleeve separated from
41

expansion sleeve
,

and

42


43


e



8
d
a

in all cases.

44


45

(b)
V
b

= 9
λ
a

(√
f
c

)(

c
a1
)
1.5

(18.5.2.2.b)

46


461


1

18.5
.2.3


For

cast
-
in headed studs, headed bolts, or hooked bolts that are continuously
2

welded to steel attachments having a minimum thickness equal to the greater of
3/8

in.
and

half
3

of the anchor diameter, the basic concrete breakout strength in shear of a single anchor in
4

cracked concrete,
V
b
, shall
be smaller of Eq. (18.5.2.2.b) and (18.5.2.3)
.

<D.6.2.3>

5


6


V
b

= [
8

(

e

/
d
a
)
0.2


d
a
]

λ
a

(√
f
c

)(

c
a1
)
1.5

(
18.5
.2.3)

7


8

where

e

is defined in
18.5
.2.2

9


10

provided that:

11


12

(a)

for groups of anchors, the strength is determined based on the strength of the row of
13

anchors farthest from the edge;

14


15

(b)

anchor spacing,

s
, is not less than
2.5

in.; and

16


17

(c) reinforcement

is provided at the corners if

c
a2


1.5
h
ef
.

18


19

18.5
.2.4


Where anchors are

located in narrow sections of limited thickness such that both
20

edge distances
c
a2

and thickness
h
a

are less than
1.5
c
a1
, the value of
c
a1

used
for the calculation
21

of
A
Vc

in accordance with 18.5.2.1 as well as
in
Eq. (
18.5
.2.1.c) through (
18.5
.2.5.d)

shall not
22

exceed the
largest

of:
<D.6.2.4>

23


24

(a)
c
a2
/1.5
, where
c
a2

is the largest edge distance;

25


26

(b)
h
a
/1.5
; and

27


28

(c)
s
/3, where
s
is the maximum spacing perpendicular to
direction of shear, between anchors
29

within a group.

30


31

18.5
.2.5


Anchor breakout strength modification factors for concrete shear breakout modes
32

shall be
calculated

in accordance with Table
18.5
.2.5.
<D.6.2.5> <D.6.2.6> <D.6.2.7> <D.6.2.8>

33


34

Table
18.5
.2.5


Strength modification factors

35

Effect

Member
condition at
service load

Other condition

Strength modification factor

Eccentric
loading
[1]

Ψ
ec,V

All

None

The lesser
of:

1
1
2'
1
3
V
a
e
c
 

 
 

(a)

1.0

(b)

Edge
All

c
a2


1.5
h
ef

1.0

(
c
)


462

effects

Ψ
ed,V

c
a2

<

1.5
h
ef

a
a
c
c

2
1
0.7 0.3
1.5

(
e
)

Cracking
effects

Ψ
c,V

Cracked
concrete

No supplementary
rebar or edge rebar
smaller than No. 4

1.0

(f)

Edge rebar

No. 4 or larger

1.2

(g)

Edge rebar at least No.
4, enclosed within
stirrups
s

≤ 4 in.

1.4

(h)

Uncracked
concrete

None

1.4

(i)

Really
close
effects

Ψ
h,V

All

h
a

<
1.5
c
a
1

The greater
of:

1
1.5
a
a
c
h

(j)

1.0

(k)

h
a


1.5
c
a
1

1.0

(l)

[1]
If the loading on an anchor group is such that only some anchors are loaded
in shear in the same
direc
tion, only those anchors that are loaded in shear in the same direction shall be considered when
determining the eccentricity of
e′
v

for use in Eq. (
18.5
.2.5.a
)

and for the calculation of
V
cbg

in Eq.
(
18.5
.2.1.b). <D.6.2.5>


1

18.5
.2.
6



Where anchor reinforcement is either developed in accordance with
20.4

on both
2

sides of the breakout surface, or encloses the anchor and is developed beyond the breakout
3

surface, the design strength of the anchor reinforcement shall be permitted

to be used instead of
4

the concrete breakout strength
in determining


V
n
. A strength reduction factor of
0.75

shall be
5

used in the design of the anchor reinforcement.

<
18.6
.2.9>

6


7

18.5
.3


Concrete pryout strength of anchor in shear

8


9

18.5.3.1



The nominal
pryout strength,
V
cp

for a single anchor

or
V
cpg

for a group of anchors
,
10

shall not exceed

(a) or (b)
: <D.6.3.1>

11


12

(a) For a single anchor

13


14



V
cp

=
k
cp
N
cp

(18.5.3.a)

15


16

For cast
-
in, expansion and undercut anchors,

N
cp

shall be taken as

N
cb

determined from Eq.
17

(
18.4.2.1.a
), and for adhesive anchors

N
cp

shall be the lesser of

N
a

determined from Eq.
18

(
18.4.5.1.a
) and

N
cb

determined from Eq. (
18.4.2.1.a
)
.

19


20

(b) For a group of anchors

21


22


V
cpg

=
k
cp
N
cpg

(18.5.3.b)

23


24


463

For cast
-
in, expansion and undercut anchors,

N
cpg

shall be taken as

N
cbg

determined from Eq.
1

(
18.4.2.1.b
), and for adhesive anchors

N
cpg

shall be the lesser of

N
ag

determined from Eq.
2

(
18.4.5.1.b
) and

N
cbg

determined from Eq. (
18.4.2.1.b
)
.

3


4

In Eq. (
18.5.3.a) and (18.5.3.b
)
,
k
cp
=
1.0

for
h
ef

<
2.5

in.; and
k
cp
=
2.0

for
h
ef



2.5

in.

5


6

18.6



Interaction of tensile and shear forces

7


8

Unless determined in accordance with
18.3
.
1.
3, anchors or groups of anchors that are subjected
9

to both shear and axial loads shall be designed to satisfy the requiremen
ts of
18.6
.1 through
10

18.6
.3. The value of

N
n

shall be as required in
18.3
.1.
1
. The value of

V
n

shall be as defined in
11

18.3
.1.
1
.

<D.7>

12



13

18.6
.1


If
V
ua
/

V
n


0.2
, then full strength in tension shall be permitted:

N
n


N
ua
.

<D.7.1>

14


15

18.6
.2



If
N
ua
/

N
n


0.2
, then full strength in shear shall be permitted:

V
n


V
ua
.

<D.7.2>

16


17

18.6
.3



If
V
ua
/

V
n

>
0.2

and
N
ua
/

N
n

>
0.2
, then

<D.7.3>

18


19


ua ua
n n
N V
.
φ N φ V
 
1 2

(
18.6
.3)

20


21

18.7



Required edge distances, spacings, and thicknesses to preclude

splitting
failure

22


23

Minimum spacings and edge distances for anchors and minimum thicknesses of members shall
24

conform to
18.7
.1 through
18.7
.5
, unless supplementary rein
forcement is provided to control
25

splitting. Lesser val
ues from product
-
specific tests performed i
n accordance with ACI 355.2
or
26

ACI 355.X

shall be permitted.

<D.8>

27


28

18.7
.1



Unless determined in accordance with
18.7
.3
,
minimum center
-
to
-
center spacing and
29

edge distances of cast
-
in anchors shall be in accordance with Table
18.7
.1
.

<D.8.1> <D.8.2>

30


31

Table
18.7
.1


Minimum spacing and edge distance for cast
-
in anchors

32

Anchor
type

Installation

Minimum

Spacing

s
, in.

Edge distance
c
a,min
, in.

Headed
?

Will not be
torqued

4
d
a

(a)

Section
18.8

(
e
)

Torqued

6
d
a

(b
)

6
d
a

(f
)

Hooked

Will not be
torqued

4
d
a

(c
)

?

(g
)

Torqued

6
d
a

(d
)

?

(h
)


33


464

18.7
.
2



Unless determined in accordance with

18.7
.3
, minimum edge distances for post
-
1

installed anchors shall be based on the greater of specified cover requirements for reinforcement
2

in
20.2
, or minimum edge distance
requirements for the products as deter
mined by tests in
3

accordance with ACI 355.2

or ACI 355.X
, and shall
not be less than

be
at least

twice

the
4

maximum aggregate size. In the absence of product
-
specific ACI 355.2

or ACI 355.X

test
5

information, the minimu
m edge distance shall
be in accordance with (a) through (d)
not
be
less
6

than
:

<D.8.3>

7


8

(a)

Adhesive anchors

................................
................................
............

6
d
a

9


10

(b)

Undercut anchors

................................
................................
............

6
d
a

11


12

(c)

Torque
-
controlled anchors

................................
..............................

8
d
a

13


14

(d)

Displacement
-
controlled anchors

................................
.................

10
d
a

15


16

18.7
.
3



For anchors where installation does not pro
duce a splitting force and that will
not be
17

torqued
, if the edge distance or spacing is less than those speci
fied in
18.7
.1
and

18.7
.2
,
18

calculations shall be performed by substituting for
d
a

a smaller value

d

a

that meets the
19

requirements of
18.7
.1
and
18.7
.2
. Calculated forces applied to the anchor shall be limited to the
20

values cor
responding to an anchor having a diameter of
d′
a
.

<D.8.4>

21


22

18.7
.
4



Unless determined from tests in accordance with ACI 355.2
, t
he value of
h
ef

for an
23

expansion or undercut post
-
installed anchor shall not exceed the greater of
2/3

of the member
24

thickness
,
h
a
,
and the member thickness
minus
4

in.

<D.8.5>

25


26

18.7
.
5



Unless determined from tension tests in accordance with ACI 355.2

or
ACI 355.X
, the
27

critical edge distance,
c
ac
, shall
be in accordance with (a) through (d)
not be taken less than
:

28

<D.8.6>

29


30

(a)

Adhesive anchors
................................
................................
............

4
h
ef

31


32

(b)

Undercut anchors
................................
................................
.........

2.5
h
ef

33


34

(c)

Torque
-
controlled
expansion
anchors

................................
............

4
h
ef

35


36

(d)

Displacement
-
controlled
expansion
anchors

................................
..

4
h
ef

37


38

18.8


Installation
and inspection

of anchors

39


40

18.8.1



Anchors shall be installed
by qualified personnel

in accordance with the
contract
41

documents
.
The contract documents shall require installation of post
-
installed anchors in
42

accordance with the manufacturer’s printed instructions. Installation of adhesive anchors shall be
43

performed by personnel trained to install adhesive anchors.

<D.9.1>

44


45

18.8.2


Installation of anchors shall be inspected in accordance with 1.
5

and the gener
al
46


465

building code. Adhesive anchors shall be subject to the following additional requirements:
1

<D.9.2>

2


3


18.8.2.1


For adhesive anchors, the contract documents shall specify proof loading where
4

required in accordance with ACI 355.X. The contract documents
shall also specify all parameters
5

associated with the characteristic bond stress used for the design according to
18.4.5

including
6

minimum age of concrete, concrete temperature range, moisture condition of concrete at time of
7

installation, type of lightwei
ght concrete if applicable, and requirements for hole drilling and
8

preparation. <D.9.2.1>

9


10


18.8.2.2


Installation of adhesive anchors horizontally or upwardly inclined to support
11

sustained tension loads shall be performed by personnel certified by an app
licable certification
12

program. Certification shall include written


and performance tests in accordance with the
13

ACI/CRSI Adhesive Anchor Installer Certification program, or equivalent. <D.9.2.2>

14


15


18.8.2.3


The acceptability of certification other than t
he ACI/CRSI Adhesive Anchor
16

Installer Certification shall be the responsibility of the
l
icensed
d
esign
p
rofessional. <D.9.2.3>

17


18


18.8.2.4



Adhesive anchors installed in horizontal and upwardly inclined orientations to
19

resist sustained tension loads shall be continuously inspected during installation by an inspector
20

specially approved for that purpose by the building official. The special i
nspector shall furnish a
21

report to the licensed design professional and building
official

that the work covered by the
22

report has been performed and that the materials used and the installation procedures used
23

conform with the approved contract documents a
nd the manufacturer’s printed installation
24

instructions. <D.9.2.4>

25


26


27