Civ
Eng 771
Advanced Design of
Reinforced Concrete Structures
Design of Concrete Anchors
Dr.
Jian
Zhao
Spring 2010
Outlines
•
Brief History of Anchor Design
•
ACI 318

08, Appendix D
Design Equations
Phi (Ф) Factors
Interaction Equation
Seismic Provisions
Reinforcements to Prevent Breakout
Edge Distances, Thicknesses &
Spacings
•
When to design per Appendix D
•
Adhesive Anchors and Concrete
•
The Future of Anchor Design
Spring 20
2
Civ
Eng 771 Advanced Concrete Design
Spring 2010
3
Civ Eng 771 Advanced Concrete Design
Concrete Anchors
Spring 2010
4
Civ Eng 771 Advanced Concrete Design
Concrete Anchor Failures
Demonstrations of anchor connections
Spring 2011
5
Civ Eng 771 Advanced Concrete Design
Prior to ACI 318

02
•
Cast

In

Place anchors:
PCI / ACI 349
UBC / IBC codes listed
allowable stress
capacities
for CIP bolts
•
Design of Post

Installed anchors:
Individual manufacturers supplied load values
based on testing
Values found in catalogs and ICBO/ICC reports
Methodology was
allowable stress
and assumed an
uncracked
and unreinforced section.
Spring
2011
6
Civ
Eng 771 Advanced Concrete Design
ACI 318

08
•
Strength design
for anchorage to concrete
N
ua
≤
ΦN
n
or
V
ua
≤
ΦV
n
Cast

In

Place (CIP) anchors
Post

Installed (PI) anchors
o
Undercut anchors
o
Torque

controlled anchors
o
Deformation

controlled anchors
o
PI anchors must be prequalified per ACI 355.2
Spring
2011
7
Civ Eng 771 Advanced Concrete Design
Design Equations & Failure
Modes
Design equations check
5
failure modes
•
Steel capacity
Tension and Shear
•
Concrete breakout capacity
Tension and Shear
•
Pullout/Pull

through capacity
Tension only
•
Concrete
Pryout
Shear only
•
Concrete side

face blowout
Tension and CIP only.
Spring
2011
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Civ Eng 771 Advanced Concrete Design
Failure Modes
Spring
2011
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Civ Eng 771 Advanced Concrete Design
Design Equations
Tension Capacities
•
N
sa
=
nA
se,N
f
uta
•
N
cb
=
A
Nc
/
A
Nco
(
Ψ
ec,N
Ψ
ed,N
Ψ
c,N
Ψ
cp,N
)
N
b
•
N
pn
=
Ψ
c,P
N
p
•
N
sb
= (160c
a1
√A
brg
)
λ√f’
c
Shear Capacities
•
V
sa
= n 0.6
A
se,V
f
uta
•
V
cbg
=
A
Vc
/
A
Vco
(
Ψ
ec,V
Ψ
ed,V
Ψ
c,V
Ψ
h,V
)
V
b
•
V
cpg
=
k
cp
N
cbg
Spring
2011
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Civ Eng 771 Advanced Concrete Design
Steel Strength In Tension
–
D.5.1
N
sa
=
nA
se,N
f
uta
(Eq. D

3)
•
N
sa
–
Nominal tensile strength of
an anchor group
•
n
–
Number of anchors
•
A
se,N
–
Effective cross sectional
area of anchor in tension
•
f
uta
–
Specific ultimate tensile
strength of anchor
Spring
2011
11
Civ Eng 771 Advanced Concrete Design
Concrete Breakout In Tension
–
D.5.2
Ncb
=
A
Nc
/
A
Nco
(
Ψ
ec,N
Ψ
ed,N
Ψ
c,N
Ψ
cp,N
)
N
b
Spring
2011
12
Civ Eng 771 Advanced Concrete Design
Concrete Breakout In Tension
–
D.5.2
N
cb
=
A
Nc
/
A
Nco
(
Ψ
ec,N
Ψ
ed,N
Ψ
c,N
Ψ
cp,N
)
N
b
A
Nc
= Projected failure area of group
A
Nco
= 9h
ef
, Projected failure area of one anchor
(Eq. D

6)
Spring
2011
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Civ
Eng 771 Advanced Concrete Design
Concrete Breakout In Tension
–
D.5.2
N
cb
=
A
Nc
/
A
Nco
(
Ψ
ec,N
Ψ
ed,N
Ψ
c,N
Ψ
cp,N
)
N
b
Ψ
ec,N
: Modification for eccentric load
Ψ
ec,N
= 1/[1+(2e’
N
/3h
ef
)] (Eq. D

9)
Spring
2011
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Civ
Eng 771 Advanced Concrete Design
Concrete Breakout In Tension
–
D.5.2
N
cb
=
A
Nc
/
A
Nco
(
Ψ
ec,N
Ψ
ed,N
Ψ
c,N
Ψ
cp,N
)
N
b
Ψ
ed,N
: Modification for edge effects
•
If
c
a,min
>
1.5h
ef
then:
•
Eq. D

10
Ψ
ed,N
= 1.0
•
ƒIf
c
a,min
< 1.5h
ef
then
•
Eq. D

11
Ψ
ed,N
= 0.7 + 0.3(
c
a,min
/ 1.5h
ef
)
Spring
2011
15
Civ
Eng 771 Advanced Concrete Design
Concrete Breakout In Tension
–
D.5.2
N
cb
=
A
Nc
/
A
Nco
(
Ψ
ec,N
Ψ
ed,N
Ψ
c,N
Ψ
cp,N
)
N
b
•
Ψ
c,N
: Modification for cracking
•
ƒ
Ψ
c,N
=1.4 for
uncracked
section if
kc
= 17 in
eq. (D

7)
•
ƒ
Ψ
c,N
per evaluation report (ER) if
kc
from
ER
used in eq. (D

7)
•
ƒ
Ψ
c,N
=1.0 for cracked section
Spring
2011
16
Civ
Eng 771 Advanced Concrete Design
Concrete Breakout In Tension
–
D.5.2
N
cb
=
A
Nc
/
A
Nco
(
Ψ
ec,N
Ψ
ed,N
Ψ
c,N
Ψ
cp,N
)
N
b
•
Ψ
cp,N
: Modification for
Post

Installed Anchors
(
Uncracked
concrete, No
supplemental
reinforcements
to
control
splitting)
•
ƒ If
c
a,min
>
c
ac
then:
Ψ
cp,N
= 1.0 (Eq. D

12)
•
ƒ If
c
a,min
<
c
ac
then:
Ψcp,N
=
c
a,min
/
c
ac
(Eq. D

13)
Where
c
ac
=
2.5h
ef
(undercut
anchors)
4.0h
ef
(wedge anchors)
Spring
2011
17
Civ
Eng 771 Advanced Concrete Design
Concrete Breakout In Tension
–
D.5.2
N
cb
=
A
Nc
/
A
Nco
(
Ψ
ec,N
Ψ
ed,N
Ψ
c,N
Ψ
cp,N
)
N
b
•
N
b
=
k
c
λ √
f’
c
h
ef
1.5
(
Basic
concrete breakout
strength
)
•
k
c
–
Coefficient for basic concrete breakout
strength
Found
in either App. D or per product ER
•
λ
–
Modification factor for lightweight concrete
•
f’c
–
Concrete compressive strength
•
h
ef
–
Effective embedment depth
Spring
2011
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Civ
Eng 771 Advanced Concrete Design
Spring 2011
19
Civ Eng 771 Advanced Concrete Design
Spring 2011
20
Civ
Eng 771 Advanced Concrete Design
Pull

out Strength
–
D.5.3
•
N
pn
=
Ψ
c,P
N
p
(Eq. D

14)
•
N
pn
–
Nominal pullout strength
•
Ψ
c,P
–
Modification for cracking
–
1.0 for cracked
–
1.4 for
uncracked
•
N
p
–
Pullout strength in
tension
Spring
2011
21
Civ
Eng 771 Advanced Concrete Design
Pull

out Strength
–
D.5.3
•
Npn
=
Ψc,P
Np
(Eq. D

14)
•
Np
–
Pullout strength in tension
For PI anchors
N
p
based on ACI 355.2 test results
For CIP anchors,
Np
based on:
–
N
p
= 8
A
brg
f’
c
(Eq. D

15) headed bolts
–
N
p
=
0.9f’
c
e
h
d
a
(Eq. D

16) hooked bolts
Spring
2011
22
Civ
Eng 771 Advanced Concrete Design
Side

Face Blowout Strength
–
D.5.4
•
N
sb
= (160c
a1
√A
brg
)
λ√f’
c
(Eq. D

17)
•
N
sb
–
Side

face blowout strength
(headed anchors only)
•
c
a1
–
edge distance
•
A
brg
–
Net bearing area of the head of
anchor
•
λ
–
Modification factor for
lightweight concrete
Spring
2011
23
Civ
Eng 771 Advanced Concrete Design
Anchors in Shear
Spring 2011
24
Civ Eng 771 Advanced Concrete Design
Steel Strength In Shear
–
D.6.1
•
V
sa
= n
A
se,V
f
uta
(eq. D

19)
CIP
•
V
sa
= n 0.6
A
se,V
f
uta
(eq. D

20)
•
n
–
number of anchors
•
A
se,V
–
effective cross sectional area
of a single anchor in shear
•
f
uta
–
specified tensile strength of
anchor steel
Spring
2011
25
Civ
Eng 771 Advanced Concrete Design
Spring 2011
26
Civ Eng 771 Advanced Concrete Design
Concrete Breakout In
Shear
–
D.6.2
•
V
cbg
=
A
Vc
/
A
Vco
(
Ψ
ec,V
Ψ
ed,V
Ψ
c,V
Ψ
h,V
)
V
b
(
Eq. D

22)
•
Vcbg
–
Concrete breakout strength in shear
Spring
2011
27
Civ
Eng 771 Advanced Concrete Design
Concrete Breakout In
Shear
–
D.6.2
Spring
2011
28
Civ
Eng 771 Advanced Concrete Design
•
V
cbg
=
A
Vc
/
A
Vco
(
Ψ
ec,V
Ψ
ed,V
Ψ
c,V
Ψ
h,V
)
V
b
A
Vc
–
projected concrete failure area of a
group of anchors
Concrete Breakout In
Shear
–
D.6.2
Spring
2011
29
Civ
Eng 771 Advanced Concrete Design
•
V
cbg
=
A
Vc
/
A
Vco
(
Ψ
ec,V
Ψ
ed,V
Ψ
c,V
Ψ
h,V
)
V
b
A
Vco
–
maximum
projected concrete failure
area of a single anchor
Concrete Breakout In
Shear
–
D.6.2
Spring
2011
30
Civ
Eng 771 Advanced Concrete Design
•
V
cbg
=
A
Vc
/
A
Vco
(
Ψ
ec,V
Ψ
ed,V
Ψ
c,V
Ψ
h,V
)
V
b
Ψ
ec,V
–
Modification for eccentric load
(
Eq.
D

26)
Concrete Breakout In
Shear
–
D.6.2
Spring
2011
31
Civ
Eng 771 Advanced Concrete Design
•
V
cbg
=
A
Vc
/
A
Vco
(
Ψ
ec,V
Ψ
ed,V
Ψ
c,V
Ψ
h,V
)
V
b
Ψ
ed,V

Modification
for edge effects
ƒ If c
a2
> 1.5c
a1
Ψ
ed,V
= 1.0 (Eq. D

27
)
ƒ If ca2 < 1.5ca1
Ψ
ed,V
= 0.7 +
0.3c
a2
/1.5c
a1
(
Eq. D

28)
Concrete Breakout In
Shear
–
D.6.2
Spring
2011
32
Civ
Eng 771 Advanced Concrete Design
•
V
cbg
=
A
Vc
/
A
Vco
(
Ψ
ec,V
Ψ
ed,V
Ψ
c,V
Ψ
h,V
)
V
b
Ψ
c,V

Modification factor for cracking
ƒ
Ψ
c,V
= 1.4 for anchors located in a region
where analysis indicates
no cracking
at
service
loads
Ψ
c,V
= 1.0 for anchors in cracked concrete
with no supplemental reinforcement or
edge reinforcement
smaller than
a #4 bar
ƒ
Concrete Breakout In
Shear
–
D.6.2
Spring
2011
33
Civ
Eng 771 Advanced Concrete Design
•
V
cbg
=
A
Vc
/
A
Vco
(
Ψ
ec,V
Ψ
ed,V
Ψ
c,V
Ψ
h,V
)
V
b
Ψ
c,V
= 1.2 for anchors in cracked concrete
with reinforcement of
a #
4 bar or greater
between the anchor and the edge
ƒ
Concrete Breakout In
Shear
–
D.6.2
Spring
2011
34
Civ
Eng 771 Advanced Concrete Design
•
V
cbg
=
A
Vc
/
A
Vco
(
Ψ
ec,V
Ψ
ed,V
Ψ
c,V
Ψ
h,V
)
V
b
Ψ
c,V
= 1.4 for anchors in cracked concrete
with reinforcement of
a #
4 bar or greater
between the anchor and the edge, and with
the reinforcement enclosed within
stirrups
spaced at not more than 4”.
ƒ
Concrete Breakout In
Shear
–
D.6.2
Spring
2011
35
Civ
Eng 771 Advanced Concrete Design
•
V
cbg
=
A
Vc
/
A
Vco
(
Ψ
ec,V
Ψ
ed,V
Ψ
c,V
Ψ
h,V
)
V
b
Ψ
h,V
Modification factor for shear strength
of anchors located in concrete members
with h
a
<
1.5c
a1
ƒ
Ψ
h,V
= √1.5c
a1
/ha but not less than 1.0
When
h
a
< 1.5c
a1
,
A
Vc
is reduced.
However, breakout strength is not
directly proportional to member
thickness.
Ψ
h,V
adjusts for this.
ƒ
Concrete Breakout In Shear
–
D.6.2
N
cb
=
A
Nc
/
A
Nco
(
Ψ
ec,N
Ψ
ed,N
Ψ
c,N
Ψ
cp,N
)
N
b
•
Ψ
cp,N
: Modification for
Post

Installed Anchors
(
Uncracked
concrete, No
supplemental
reinforcements
to
control
splitting)
•
ƒ If
c
a,min
>
c
ac
then:
Ψ
cp,N
= 1.0 (Eq. D

12)
•
ƒ If
c
a,min
<
c
ac
then:
Ψcp,N
=
c
a,min
/
c
ac
(Eq. D

13)
Where
c
ac
=
2.5h
ef
(undercut
anchors)
4.0h
ef
(wedge anchors)
Spring
2011
36
Civ
Eng 771 Advanced Concrete Design
Concrete Breakout In Shear
–
D.6.2
N
cb
=
A
Nc
/
A
Nco
(
Ψ
ec,N
Ψ
ed,N
Ψ
c,N
Ψ
cp,N
)
V
b
•
V
b
=(
7(
ℓe
/
da
)0.2√da)
λ√f’c
(ca1)1.5 (Eq. D

24)
•
–
ℓe
–
load bearing length of anchor
Same
as
h
ef
if there is no sleeve on anchor
Per
manufacturer if there is a sleeve
•
–
d
a
–
outside diameter of anchor
•
–
λ
–
adjustment for lightweight concrete
•
–
f’
c
–
concrete compressive strength
•
–
c
a1
–
edge distance
Spring
2011
37
Civ
Eng 771 Advanced Concrete Design
Spring 2011
38
Civ Eng 771 Advanced Concrete Design
Spring 2011
39
Civ
Eng 771 Advanced Concrete Design
Concrete
Pryout
In
Shear
–
D.6.3
•
V
cpg
=
k
cp
N
cbg
(Eq. D

30)
k
cp
= 1.0 for
h
ef
< 2.5”
k
cp
= 2.0 for
h
ef
>
2.5”
•
N
cbg
–
Nominal concrete breakout strength in
tension
Spring
2011
40
Civ
Eng 771 Advanced Concrete Design
Phi (Φ) factors
•
N
ua
≤
Φ
N
n
or
V
ua
≤
Φ
V
n
•
Ф

factors
are applied to nominal capacities
before comparing with factored forces
•
Based
on:
–
Supplemental reinforcement
–
Failure mode
–
Load type
–
Anchor property
Spring
2011
41
Civ
Eng 771 Advanced Concrete Design
Phi (Φ)
factors D.4.4
Spring
2011
42
Civ
Eng 771 Advanced Concrete Design
Phi (Φ)
factors D.4.4
Spring
2011
43
Civ
Eng 771 Advanced Concrete Design
•
Condition A
•
Applies
where supplementary reinforcement is
present except for pullout and
pryout
strengths.
•
Condition
B
•
Applies
where supplementary reinforcement is
not present, and for pullout or
pryout
strength.
Interaction of Tension and Shear
–
D.7
Spring
2011
44
Civ
Eng 771 Advanced Concrete Design
Seismic Provisions
Spring
2011
45
Civ
Eng 771 Advanced Concrete Design
•
–
Seismic Design Category C, D, E & F
•
–
No anchors in plastic hinge
•
–
PI anchors must pass Simulated
•
Seismic Test
•
–
Design strength reduced by 25%
•
–
Ductile steel failure of anchors shall control,
or
...
•
–
Ductile yielding of attachment,
or
...
•
–
Anchor capacity reduced by 60%
Anchor Reinforcements Introduction
•
Breakout cone
forms before
anchor
reinforcement in
effect.
•
Reinforcement
fully developed at
both sides of
breakout crack.
1
5
.
0
a
c
2
3
.
0
a
c
dh
l
d
l
d
l
1
a
c
2
1
,
min
a
a
c
c
b
d
8
b
d
8
b
d
8
b
d
8
Proposed
•
Breakout cone
restrained by
reinforcement.
•
Concrete
provides shear
resistance.
•
Cover
spalling
causes a new
failure mode
•
Proportioned to resist full anchor
steel capacity in tension or shear
•
Development lengths inside
assumed failure cone satisfied by
interaction with corner bars
•
Placed outside the limits of 0.5c
1
and 0.5h
ef
Limited side edge distance tests
Strain gauge tests
Reinforcement Design
Test Setup
Reinforced Shear Tests
•
Gages are 25
mm behind
the assumed
35
°
cone
Reinforced Shear Tests
Exposed anchor bolts in various
types of connections
Column base connection; Shear key on bridge cap; Bearing in bridge
Exposed anchors in shear
Exposed
anchors in
shear
End Rotation
β
Minimum
elongation of
anchor steel
•
Reinforced anchors in
tension (May

June,
2011)
•
Anchor groups in plastic hinge zone (summer, 2011)
Next
Complex Design Process!
Seminars and training courses are available
Computer codes available
Spring 2011
60
Civ Eng 771 Advanced Concrete Design
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