Civ Eng 771

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Nov 26, 2013 (3 years and 11 months ago)

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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
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Civ
Eng 771 Advanced Concrete Design
Spring 2010
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Civ Eng 771 Advanced Concrete Design
Concrete Anchors
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Civ Eng 771 Advanced Concrete Design
Concrete Anchor Failures
Demonstrations of anchor connections
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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.
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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
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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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Failure Modes
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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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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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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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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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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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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
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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)
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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
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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
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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
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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
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Eng 771 Advanced Concrete Design
Anchors in Shear
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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
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Eng 771 Advanced Concrete Design
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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
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Civ
Eng 771 Advanced Concrete Design
Concrete Breakout In
Shear

D.6.2
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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
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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
Vco

maximum
projected concrete failure
area of a single anchor
Concrete Breakout In
Shear

D.6.2
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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
ec,V

Modification for eccentric load
(
Eq.
D
-
26)
Concrete Breakout In
Shear

D.6.2
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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
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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
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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
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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
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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)
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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
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Eng 771 Advanced Concrete Design
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Civ Eng 771 Advanced Concrete Design
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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
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Civ
Eng 771 Advanced Concrete Design
Phi (Φ)
factors D.4.4
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Civ
Eng 771 Advanced Concrete Design
Phi (Φ)
factors D.4.4
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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
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Civ
Eng 771 Advanced Concrete Design
Seismic Provisions
Spring
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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
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Civ Eng 771 Advanced Concrete Design