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
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Civ
Eng 771 Advanced Concrete Design
Spring 2010
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Civ Eng 771 Advanced Concrete Design
Concrete Anchors
Spring 2010
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Civ Eng 771 Advanced Concrete Design
Concrete Anchor Failures
Demonstrations of anchor connections
Spring 2011
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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
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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
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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.
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2011
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Civ Eng 771 Advanced Concrete Design
Failure Modes
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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
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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
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2011
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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
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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
A
Nc
= Projected failure area of group
A
Nco
= 9h
ef
, Projected failure area of one anchor
(Eq. D

6)
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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)
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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
)
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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
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
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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
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
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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
•
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
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Eng 771 Advanced Concrete Design
Spring 2011
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Civ Eng 771 Advanced Concrete Design
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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
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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
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Civ
Eng 771 Advanced Concrete Design
Anchors in Shear
Spring 2011
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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
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Civ
Eng 771 Advanced Concrete Design
Spring 2011
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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
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Civ
Eng 771 Advanced Concrete Design
Concrete Breakout In
Shear
–
D.6.2
Spring
2011
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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
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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
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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
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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
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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
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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
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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
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Civ
Eng 771 Advanced Concrete Design
Spring 2011
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Civ Eng 771 Advanced Concrete Design
Spring 2011
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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
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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
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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
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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
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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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