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Anchor Checking Using ACI
318 Appendix D
Rob Abernathy
CASE Center
GTSUG
June, 2011 Delray Beach, FL
GTSTRUDL
What is “Anchoring to Concrete”
Appendix D, first added to 318 in 2002, “provides design
requirements for anchors in concrete used to transmit
structural loads…” This presentation is limited to the
provisions that are used in anchoring base plates to a
bearing surface, although Appendix D can be used in
some situations of anchoring to structural members.
This presentation is based on ACI 318-05, and includes
figures copied from the Appendix D commentary. Many of
the formulas and techniques found in Appendix D are
based on the paper “Concrete Capacity Design (CCD)
…”, ACI Structural Journal, 1995, which is reference D.9
in ACI 318-05 and -08.
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Anchoring to Concrete: Terms and Concepts
F is a reduction factor applied to calculated capacity.
y is a modification factor applied when determining
capacity. It may be greater than 1.0.
hef is the effective embedment depth of an anchor.
Anchor groups are sets of anchors with spacing ≤ 3hef
and having “approximately equal” hef.
Supplementary reinforcement is “reinforcement
proportioned to tie a potential concrete failure prism to
the structural member”, although the rules for
proportioning are not defined in Appendix D.
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Terms and Concepts: Breakout/Failure Cone
The major concern of Appendix D
is the failure of the concrete via a
“breakout” cone. Tension can
cause breakout from the top
surface of the concrete as shown
to the left or at an edge. Shear
can cause breakout on the
surface through “pryout” or at an
edge. Note that the area involved
extends 1.5hef from the anchor
center, hence the 3hef (1.5 + 1.5)
spacing definition of an anchor
group.
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What does Appendix D cover?
• Anchor + concrete capacity only – no
base plate provisions
• Limited to anchors 2” or less diameter
and hef (effective length) of 25” or less.
• f’c of 10,000 psi for cast-in anchors and
8,000 psi for post-installed anchors.
• “Regular” arrangement of similar
anchors. Not a formal requirement, but
only examples of such are given.
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What is not covered?
• Plate failures – overstressing of plate
material, weld failures, etc.
• Cyclic (fatigue) or impact loads
• Through bolts
• “Irregular” anchor arrangements.
• Shear lugs and embedded plates.
• Bearing surface crushing.
• Individual anchor capacity! Since anchors are
evaluated as ‘groups’, the failure of an
individual anchor is not necessarily detected.
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Capacity Criteria
• Seismic reduction (Section D.3.3)
• Check tension (N)
– FNn ≥ Nua
(D-1)
• Check shear (V)
– FVn ≥ Vua
(D-2)
• Check interaction if Nua > 0.2FNn and Vua >
0.2FVn:
Nua/FNn + Vua/FVn ≤ 1.2 (D-31)
• Spacing checks
– D.8 requirements unless supplemental
reinforcement exists.
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The checking process
• Get characteristics of anchors, base plate and
bearing surface concrete plus the location of
anchors and edges.
• Loadings: Section 9.2 or Appendix C load factors
• Check edge distance and spacing if
supplementary reinforcement does not exist.
• Create groups based on anchor geometry.
• Check anchor capacity for shear and tension –
reduce if seismic requirement
• Determine F factors based on governing sections
• Calculate interaction value
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Anchor characteristics
•
•
•
•
Cast-in or post-installed
Embedment length hef
Diameter do
Ductility – ductile or brittle, based on test
elongation or area reduction.
• Tensile strength futa
– The use of futa instead of fya is to match
with AISC LRFD design.
• Ase – effective cross-section area;
manufacturer’s value if not pdo2.
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Anchor Characteristics: Cast-in anchors
• Headed bolt
• Hooked bolt
• Headed stud
Optional data
Np pullout strength in cracked concrete
Abrg bearing area of head if Np not specified,
for headed bolts or studs.
eh
width of hook or L if Np not specified, for
hooked bolts
Washer – headed anchors, increases hef.
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Anchor Characteristics: Post-installed anchors
• Type: UC (undercut), TC (torquecontrolled), DC (displacementcontrolled)
• Pullout strength Np
• Category: 1, 2 or 3 – low to high
sensitivity.
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Anchor Characteristics: Post-installed anchors
Optional data
• cac: Manufacturer’s critical edge
distance or taken from D.8.3.
• Vsa: Shear strength in lieu of D-20
• kc and yc,N – Concrete breakout strength
coefficient + cracked concrete
modification factor. If kc from the
manufacturer is used, the specified yc,N
must also be used.
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Anchor Configuration and
Base Plate Conditions
• Anchor and edge locations
– In general, edges > 1.5*hef may be ignored
– Without supplement reinforcement, other
criteria should be checked and may be up to
4.0*hef for post-installed anchors.
• Grout pad under plate – affects y factors
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Concrete Characteristics
• f’c
• Cracked/Uncracked
• Supplementary reinforcement
– Outside the scope of Appendix D in ’05.
Note: ’08 adds “Anchor reinforcement” with
specific design guides.
• Thickness
– In general, > hef*1.333 or hef+4” for postinstalled without supplemental
reinforcement.
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Tension capacity: Section D.5
Tension capacity is determined using “Section D.5 –
Design requirements for tensile loading”, with four types
of strength measures specified in sections D.5.1 to
D.5.4. The lowest value of Nn calculated is used in
equation D-1 and its type will be used when determining
F for tension.
Processing must be done on a load-by-load basis, since
not all anchors will be in tension for all loads and this will
affect capacity calculations, especially yec,N, the
modification factor for loading eccentricity.
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D.5.1 Steel Strength of Anchor
The simplest check!
For all loaded anchors in each load case:
Nsa = n*Ase*futa (D-3)
n
Ase
= number of loaded anchors
= cross-section area
from do or manufacturer specified
Note that the calculated value is for the sum
of all loaded anchors, without a specified
check on individual anchors.
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D.5.2 Concrete Breakout
Ncb = (ANc/ANco)*yec,N*yed,N*yc,N*ycp,N*Nb
yec,N: Eccentricity factor from D-9 (single anchor = 1.0)
yed,N: Edge proximity factor
yc,N: Cracked concrete factor
ycp,N: Post-installed cac reinforcement factor (cast-in = 1.0)
Nb = Concrete breakout for a single anchor, no edges
From D-7, D-8 or manufacturer’s specs
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D.5.2 Concrete Breakout: (ANc/ANco)
ANc , the total projected
concrete failure area of an
anchor group, is affected by
anchor spacing and edge
distance.
ANco
= Maximum area of single breakout cone
= 9.0*hef2
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D.5.2 Concrete Breakout: yec,N
If eccentricity exists in both X and
Y, yec,N is the product of yec,N_X
and yec,N_Y.
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D.5.3 Pullout Strength
For each anchor in tension – no grouping:
Npn = yc,P*Np
Cast-in anchors: Np from D-15 or D-16
Np = 8*Abrg*f’c
(D-15)
Np = 0.9*f’c*eh*do
(D-16)
Post-installed anchors: Np specified
yc,P
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= 1.0 for cracked concrete
= 1.4 for uncracked concrete
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D.5.4 Concrete side-face blowout
Only cast-in, headed anchors with ca1 < 0.4*hef:
Nsb = 160*ca1*sqrt(Abrg)*sqrt(f’c)
If there are multiple anchors, Nsb is modified by:
1.0 + s/(6*ca1)
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Shear capacity: Section D.6
Shear capacity is determined using “Section D.6 – Design
requirements for shear loading”, with three types of strength
measures specified in sections D.6.1 to D.6.3. The lowest value of
Vua calculated is used in equation D-2 and its section will be used
when determining F.
Processing must be done on a load-by-load basis, even
though all anchors tend to share the shear load, since yec,N, the
modification factor for loading eccentricity, will vary.
If edges are present, processing for shear becomes very
complicated, since ca1, the minimum edge distance, is measured
“in the direction of the applied shear”, and may in fact be different
for every anchor if in-plane rotation exists. One solution is to
separate the shear into (X, Y) components and process separately,
but ACI does not address this issue directly. Non-orthogonal edges
would complicate the problem even more.
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D.6.1 Steel shear strength
For all loaded anchors in each load case,
For cast-in headed studs:
Vsa = n*Ase*futa (D-19)
For cast-in headed and hooked bolts, plus
post-installed anchors without sleeves in
the shear plane:
Vsa = n*0.6*Ase*futa (D-20)
Else: Manufacturer’s specified value
Use resultant
shear for 6.1
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n
Ase
= number of loaded anchors
= cross-section area
from do or manufacturer specified
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D.6.2 Concrete breakout in shear
This is the most complicated provision,
but only applies to anchors “near” an
edge, such that 4.5*ca13.5*sqrt(f’c)
approaches Ase*futa (D-19).
Vcb = (AVc/AVco) *yec,V*yed,V*yc,V*Vb (D-22)
yec,V = Eccentricity factor, = 1.0 for single anchors
yed,V = Edge proximity factor
yc,V = Cracked concrete factor
Vb = Single anchor breakout strength in cracked concrete
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D.6.2 (con’t)
AVco
= max. single anchor shear breakout area
= 4.5*ca12
(D-23)
(D-24)
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D.6.3 Concrete pryout
Vcp = kcp*Ncb
Vcp = kcp*Ncbg
kcp =
(D-29)
(D-30)
1.0 if hef < 2.5 inches
2.0 if hef ≥ 2.5 inches
Note the back-reference to Ncb – hopefully
D.5.2.1 (concrete breakout strength) was not
limited by nN*ANco (nN = # of loaded anchors
in tension), or D.5.2.1 will need to be recalculated for the shear group.
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Determining F values:
Section D.4.4, loads from Section 9.2
Determine governing failure mode:
If steel element governs,
Ductile: F = 0.75 for tension, 0.65 for shear
Brittle: F = 0.65 for tension, 0.60 for shear
If concrete governs, but not D.5.3 or D.6.3, and supplementary
reinforcement exists,
F = 0.75 for shear, all anchors
F = 0.75 for tension, cast-in & post-installed Cat 1
-0.10 for Category 2, -0.20 for Category 3
If concrete governs but not the above conditions
F = 0.70 for shear, all anchors
F = 0.70 for tension, cast-in
F = 0.65 for tension, post-installed Category 1
-0.10 for Category 2, -0.20 for Category 3
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Determining F values:
Section D.4.5, loads from Appendix C
Determine governing failure mode:
If steel element governs,
Ductile: F = 0.80 for tension, 0.75 for shear
Brittle: F = 0.70 for tension, 0.65 for shear
If concrete governs, but not D.5.3 or D.6.3, and supplementary
reinforcement exists,
F = 0.85 for shear, all anchors
F = 0.85 for tension, cast-in & post-installed Cat 1
-0.10 for Category 2, -0.20 for Category 3
If concrete governs and no supplementary reinforcement,
F = 0.75 for shear, all anchors
F = 0.75 for tension, cast-in & post-installed Cat 1
-0.10 for Category 2, -0.20 for Category 3
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Seismic Loads, Section D.3.3
D.3.3.3
If seismic loads are used and in regions of moderate to high
seismic risk, an additional reduction factor of 0.75 must be
applied to FNn and FVn.
0.75FNn ≥ Nua
0.75FNn ≥ Nua
D.3.3.4
Nn and Vn must be governed by ductile steel elements or
D.3.3.5
The “attachment” must undergo ductile yielding at loads
below failure of the anchors. No guidance is offered as to
making this determination.
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Section D.8 – Edge distances, spacings and thickness
If no supplementary reinforcement exists:
Min c-to-c spacing:
4*do for cast-in, untorqued anchors
6*do for all other anchors
Minimum edge distance:
Cover requirements for cast-in, untorqued
6*do (or cover) for cast-in, torqued
6*do for post-installed UC
8*do for post-installed TC
10*do for post-installed DC
Minimum concrete thickness for post-installed anchors
t ≥ 1.5*hef
t ≥ hef+4”
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