Concrete Capacity Design (CCD) Approach for Fastening to Concrete

....
ACI STRUCTURAL JOURNAL
TECHNICAL PAPER
Title no. 92-S9
Code Background Paper:*
Concrete Capacity Design {CCD) Approach for
Fastening to Concrete
by Werner Fuchs, Rolf Eligehausen, and John E. Breen
A user-friendly, highly transparent model for the design of post-installed
steel anchors or cast-in-place headed studs or bolts, termed the concrete
capacity design (CCD) approach, is presented. This approach is compared
to the well-known provisions of ACI 349-85. The use of both methods to
predict the concrete failure load offastenings in uncracked concrete under
monotonic loading for important applications is compared. Variables
included single anchors away from and close to the edge, anchor groups,
tension loading, and shear loading. A data bank including approximately
1200 European and American tests was evaluated. The comparison shows
that the CCD method can accurately predict the concrete failure load of
fastenings for the full range of investigated applications. On the other
hand, depending on the application in question, the predictions of ACJ 349
are sometimes unconservative and sometimes conservative. The CCD
method is more user-friendly for design. Based on this, the CCD method is
recommended as the basis for the design offastenings.
Keywords: anchors (fasteners); concretes; failure; fasteners; loads
(forces); shear tests; structural design; studs; tension tests.
The demand for more flexibility in the planning, design,
and strengthening of concrete structures has resulted in an
increased use of metallic anchoring systems. Currently employed are cast-in situ anchors such as headed studs
[Fig. l(a)] or headed bolts and fastening systems to be installed in hardened concrete, such as torque-controlled expansion anchors [Fig. l(b)], deformation-controlled expansion anchors [Fig. l(c)], undercut anchors [Fig. l(d)], and
adhesive anchors [Fig. l(e)].
Cast-in situ elements are fastened to the formwork and
cast into the concrete. A common example is a plate with
welded-on headed studs [Fig. l(a)], which produces mechanical interlocking with the concrete.
Post-installed anchors can be fastened in almost any position desired in hardened concrete by installing them in a hole
drilled after concrete curing. A distinction is drawn between
metal expansion anchors, undercut anchors, and bonded anchors, according to their principles of operation.
Expansion anchors produce expansion forces and thereby
(frictional) holding forces in the concrete base material.
With torque-controlled expansion anchors [Fig. l(b)], a
ACI Structural Journal I January-February 1995
specified installation torque is applied. Thereby, one cone or
two cones, according to the type of anchor, is/are drawn into
the expanding sleeve or segments. Torque-controlled anchors should expand further under load. Deformation-controlled anchors [(Fig. l(c)] are expanded by driving the cone
into the sleeve [drop-in anchor, Fig. l(c 1)] or onto the cone
[Fig. l(c 2) (self-drilling anchor) and Fig. l(c 3) (steel anchor)] through a specified displacement. Deformation-controlled anchors cannot expand further under load.
Undercut anchors are anchors with parts that spread and
mechanically interlock with the concrete base material. After production of the cylindrical hole by drilling, the undercutting is produced in a second operation before installation
of the anchor [Fig. l(d 1) through l(d 3)] or during installation
of the anchor [Fig. l(d4 ) and l(d5)]. Much lower expansion
forces are produced during installation and loading than with
expansion anchors. In fact, certain undercut anchors can act
virtually identically to cast-in anchors if the angle and diameter at the undercut are within certain limits.
The operating principle of adhesive anchors [Fig. 1(e)] depends on gluing together a threaded rod and the wall of the
drilled hole with reacting resins. The load is transferred to
the concrete base material by chemical bonding. Adhesive
anchors are not covered in this paper.
BEHAVIOR UNDER TENSION LOADING
Under tension loading, fastening systems can experience
four different types of failures (Fig. 2), each with very different load-deformation patterns, as shown in Fig. 3. Fig. 3 is
valid for anchors with relatively low remaining prestressing
*ACI Committee 318 has endorsed early publication of this paper which serves as
background to upcoming code revisions.
ACI Structural Journal, V. 92, No. I, January-February 1995.
Received Feb. 2, 1994, and reviewed under Institute publication policies. Copyright
© 1995, American Concrete Institute. All rights reserved, including the making of
copies unless permission is obtained from the copyright proprietors. Pertinent discu~­
sion will be published in the November-December 1995 ACI Structural Journal1f
received by July I, 1995.
73
•
~cone
Werner Fuchs is Manager, Innovation of the Hilti Development Corp., Kaufering,
Germany. He received his diploma degree in civil engineering from the University of
Karlsruhe and PhD from the University of Stuttgart, Germany. After a postdoctoral
fellowship at the University of Texas at Austin, he joined Hilti. He has conducted
research and written extensively on topics related to techniques for fastening to concrete. He is a member of ACI 355, Anchorage to Concrete.
n-
expansiont
·
sleeve
[
e xpons ion
cutter
~sleeve
cone
ACI member Rolf Eligehausen is a Professor and Department Head for fastening
technique at the Institute for Building Materials, University of Stuttgart. He studied
at the University of Braunschweig and obtained his PhD from the University of Stuttgart in I979. After 2 years of research work at the University of California at Berkeley, he returned to the University of Stuttgart and was appointed to the rank of
Professor in I984. He is a member of several international committees on reinforced
concrete and fastening technique, and has published several papers in these fields.
He is a member of ACI Committee 355, Anchorage to Concrete.
I I
0
0
0
0
0
0
ACI honorary member John E. Breen holds the Nasser I. Al-Rashid Chair in Civil
Engineering at the University of Texas at Austin. He began research work in fastening to concrete in I963. He is a member and former chairman of ACI 318, Building
Code, and is former chairman of the ACJ Technical Activities Committee. He is an
associate member of ACI Committee 355, Anchorage to Concrete.
0
Fig. l(c)- Fastening systems: deformation-controlled
expansion anchor (upper sketches show assembled
anchors; lower sketches show anchor mechanism actions)
0
0
"'
Fig. l(a) -Fastening systems: headed studs
·u·. T.
: '""'
0
expansion
sleeve
cone
G
T
G
G
0
0
0
0
Q
0
0
0
0
.. 0
a o
.
...
Q
D
..
..
co
cutting
pin
d4
l
ds l
Fig. l(d) -Fastening systems: undercut anchors (left-side
sketches show hole shape; right-side sketches show
installed anchors)
T
fixture
0
0
0
0
0
..
..
<>
"0
anti
rot at ion
cone
0
0
0
0
0
0
0
0
0
Fig. l(b) -Fastening systems: torque-controlled expansion
anchor (upper sketches show assembled anchors; lower
sketches show anchor mechanism actions)
force after losses due to relaxation and other similar effects.
The magnitude of the prestressing force will influence the
behavior of the anchor at service load levels but has practically no influence at failure load levels.
Pullout or pullthrough failures are failure by sliding out of
the fastening device or parts of it from the concrete (pullout)
or by pulling the cone through the sleeve (pull through) without the breaking out of a fairly substantial portion of the surrounding concrete [Fig. 2(c)]. For deformation-controlled
fasteners, only the pullout failure mode is possible.
74
mortar
0
0
0
to
0
0
0
0
0
0
anchor
rod
0
Fig. l(e) -Fastening systems: bonded or adhesive anchors
(left-side sketches show hole shape; right-side sketches
show installed anchors)
For expansion anchors, the failure load depends on the design of the expansion mechanism, method of drilling the
hole, condition of the drilled hole, and deformability of the
concrete. Currently, there is no established procedure to determine theoretically the ultimate load to be expected of fastenings in the pullout or pullthrough type of failure. It must
be determined in comprehensive prequalification tests, such
ACI Structural Journal I January-February 1995
ductile steel
failure
~------~
a)
/
z
D
!...crete break out (brittle)
I
0
X
<(
1//
/
pull-through
b - - - - - - - - , o r pull-out
-
1
0
0
.,
0
00
c)
0
0
=
=o =
o.,::
•
<> 0""'
•
• 0
o""'
/7N!
I
!
!
d1)
dz)
v()
NNt
as those proposed in ASTM ZXXX. 1 In the case of a pullthrough failure, in general the load-displacement relationship continuously increases and failure occurs at relatively
large displacements (Line a 1 in Fig. 3). This anchor behavior
is mainly dependent on the quality of the anchor production,
and is acceptable in many applications.
In contrast, in the case of a pullout failure, the load-displacement curve may increase continuously until peak load
(Line a 1 in Fig. 3) or the anchor may slip significantly in the
hole at a load level larger than ·the remaining prestressing
force of the anchor (Lines a2 and a3 in Fig. 3) before expanding further and developing a higher load capacity. This behavior is influenced considerably by the installation
procedure and is highly undesirable. It must be prohibited by
performance requirements in prequalification testing of the
fastening device.
With expansion anchors, the depth of embedment can
control the type of failure. As shown in Fig. 4, there is a
critical embedment depth later termed hef the effective
embedment depth, at which the mode of failure changes
from concrete failure to pullout. This depends on the
expansion mechanism and hef is determined in
prequalification tests.
The concrete bearing area of undercut anchors and headed
studs is usually large enough to prevent pullout failure.
Ductile failures are failure by yielding of the fastening device or system fastened to the concrete before any breakout
of concrete occurs [Fig. 2(a)].
Under conditions that the steel material is sufficiently ductile and the length of the fastener or attachment over which
inelastic steel strains appear is large enough, and assuming
that the concrete base material does not fail, a ductile steel
failure will occur (Line c in Fig. 3).
ACI Structural Journal I January-February 1995
\az ;--:~:1
I
/'// _________ ...,;:,'
,.3
_./
Axial Deformation
d3)
Fig. 2-Failure modes for fastenings under tensile loading:
(a) steel failure; (b) concrete breakout; (c) pullout; (d) concrete splitting
/ ', '
//__ _',
11
'I
If
• N
' ',•1
Fig. 3-Idealized load-deformation curves for fasteners
under tension load
I
I
I
I
I
I
z
I
I
I
"0
0
I
0
I
_I
I
I
-0
I
X
<(
failure
pullout failure
he f
Embedment Depth
Fig. 4-Role of effective depth herfor expansion anchors
Brittle failures are failure by concrete breakout or splitting
of the structural concrete member before yielding of the fastener or fastened element [Fig. 2(b) and (d)] or by steel failure when the length over which inelastic steel strains appear
is rather small.
For nonductile fasteners and cases where the concrete capacity is less than the fastener device capacity, a brittle failure will occur (Line bin Fig. 3).
It is not yet possible to determine theoretically the failure
load to be expected in the "splitting" type of failure
75
0)
d'3
c)
Fig. 5-Failure modes for fastenings under shear loading:
(a) steel failure preceded by concrete spall; (b) concrete
breakout; (c) concrete pryout failure for fastenings far from
edge
[Fig. 2(d)]. This type of failure can be avoided by specifying
minimum values of center-to-center and edge spacings, as
well as component thickness. Again, prequalification testing
under ASTM ZXXX: 1 is designed to preclude such failures.
Concrete breakout failure [Fig. 2(b 1) through 2(b3)] is a
very important practical design case, because many fasteners
are made such that a concrete failure will occur before yielding of steel. In fasteners with deeper embedment but thinner
side cover, concrete blowout [Fig. 2(b4)] can govem. 2 This
latter case is not covered in this paper.
BEHAVIOR UNDER SHEAR LOADING
The failure modes of anchors loaded in shear are shown in
Fig. 5. In principle, the same behavior as that under tensile
loading can be observed. However, a pullout failure may theoretically occur only if the ratio of anchorage depth to anchor
diameter is very small and the tensile capacity is very low. In
contrast, in shear, a brittle concrete failure will occur for fastenings located close to the edge [Fig. 5(b)] and cannot be
avoided by increasing anchorage depth. Steel failure, often
proceeded by a local concrete spall in front of the anchor
[Fig. 5(a)], will be observed for fasteners sufficiently far
away from the edge. For that case, the load-displacement behavior will depend on ductility of the anchor steel. A concrete pryout-type failure of fastenings located quite far away
from the edge [Fig. 5(c)] may occur for single anchors and
especially for groups of anchors with a small ratio of embedment depth to anchor diameter and high tensile capacity. 3
The critical ratio depends on the anchor strength, concrete
strength, and number and spacing of fasteners. This failure
mode is not covered in this paper.
76
In practice, many fastenings or attachments are placed on
a grout bed. For this type of installation, a grout failure may
occur before any other type of failure. In this case, the shear
load must be transferred into the base by bending the anchors. This may reduce the load transfer capacity when cornpared to a fastening or attachment installed directly on the
base material. The effect of the grout bed on load transfer capacity is not discussed in this paper.
SCOPE
The relevant literature contains several approaches for the
calculation of concrete failure load in uncracked concrete.
The most important examples are design recommendations
of ACI Committee 349,4 PCI design procedures that are
somewhat similar to those of ACI 349, 5 and the concrete capacity design (CCD) method based on the so-called K -method developed at the University of Stuttgart. 6-8 The CCD
method provides a clear visual explanation of calculation of
the K -factors used in the K -method. It combines the transparency (ease of visualization of a physical model, making it
readily understood by designers for application) of the ACI
349 method, accuracy of the K -method, and a user-friendly
rectangular failure surface calculation procedure. A comparison of the CCD method with the K -method is given in Ref- .
erences 9 and 10. From this comparison, it is evident that the
CCD and K -methods predict almost identical failure loads.
In this paper, the provisions of ACI 349-85 and the CCD
method to predict the fastening capacity of brittle (concrete
breakout) failures in uncracked concrete are compared with
a large number of test results. To facilitate direct comparison, the capacity reduction factor <1> of ACI 349 and partial
material safety factor y m of the CCD method are both taken
as 1.0. The comparison is made for fastenings both under
tension load (single fasteners close to and far from the edge,
as well as anchor groups with up to 36 fasteners far from the
edge) and under shear load toward the edge (single fasteners
and double fastenings installed close to the edge in wide and
narrow as well as thick and thin members). Based on this
comparison, the accuracy of the two design approaches is determined.
RESEARCH SIGNIFICANCE
While ductility is highly desirable in applications where
there are substantial life safety concerns, a brittle failure
mode covered by a sufficient safety factor is often acceptable. In both cases, concrete capacity must be predicted as
accurately as possible to insure a ductile failure (ductile design) or sufficiently low probability of failure (brittle design), respectively. In many applications, the relevant design
methods (ACI 349-85 and CCD method) will predict rather
different concrete capacities. Therefore, screening of both
methods based on an extensive data base is needed. Comparable earlier studies 11 •12 are based on a small number of test
data and did not include the newly developed CCD method.
DESIGN PROCEDURES
Fig. 6 shows concrete breakout cones for single anchors
under tension or shear load, respectively, idealized according to ACI 349.4 From this figure, it is evident that the concrete cone failure load depends on tensile capacity of the
ACI Structural Journal I January-February 1995
ductile steel
failure
~-------....;
a)
/
z
D
1/
/.crete break out (brittle)
-c
I
0
0
_j
0
I
X
<(
•N
0
0
0
=
00
c)
0
0
=
= ==
•
<> D
• 0
•
Q
0
•
/7N!
I
I
I
d1)
dz)
0
I
v?J
NNt
/
as those proposed in ASTM ZXXX. 1 In the case of a pullthrough failure, in general the load-displacement relationship continuously increases and failure occurs at relatively
large displacements (Line a 1 in Fig. 3). This anchor behavior
is mainly dependent on the quality of the anchor production,
and is acceptable in many applications.
In contrast, in the case of a pullout failure, the load-displacement curve may increase continuously until peak load
(Line a 1 in Fig. 3) or the anchor may slip significantly in the
hole at a load level larger than the remaining prestressing
force of the anchor (Lines a2 and a3 in Fig. 3) before expanding further and developing a higher load capacity. This behavior is influenced considerably by the installation
procedure and is highly undesirable. It must be prohibited by
performance requirements in prequalification testing of the
fastening device.
With expansion anchors, the depth of embedment can
control the type of failure. As shown in Fig. 4, there is a
critical embedment depth later termed hef• the effective
embedment depth, at which the mode of failure changes
from concrete failure to pullout. This depends on the
expansion mechanism and hef is determined in
prequalification tests.
The concrete bearing area of undercut anchors and headed
studs is usually large enough to prevent pullout failure.
Ductile failures are failure by yielding of the fastening device or system fastened to the concrete before any breakout
of concrete occurs [Fig. 2(a)].
Under conditions that the steel material is sufficiently ductile and the length of the fastener or attachment over which
inelastic steel strains appear is large enough, and assuming
that the concrete base material does not fail, a ductile steel
failure will occur (Line c in Fig. 3).
ACI Structural Journal I January-February 1995
-
'
'.~
1/ ' \ \
//~~-
#
///
--------'
1°2
,_ pu II
r out
', ,.3
Axial Deformation
d3)
Fig. 2-Failure modes for fastenings under tensile loading:
(a) steel failure; (b) concrete breakout; (c) pullout; (d) concrete splitting
~
/
/
pull-through
b - - - - - - - - ......or pull-out
Fig. 3-/dealized load-deformation curves for fasteners
under tension load
I
I
I
I
I
I
z
I
I
-c
I
0
,
0
_j
I
I
I
I
0
X
<(
failure
pullout
failure
he f
Embedment Depth
Fig. 4-Role of effective depth hetfor expansion anchors
Brittle failures are failure by concrete breakout or splitting
of the structural concrete member before yielding of the fastener or fastened element [Fig. 2(b) and (d)] or by steel failure when the length over which inelastic steel strains appear
is rather small.
For nonductile fasteners and cases where the concrete capacity is less than the fastener device capacity, a brittle failure will occur (Line bin Fig. 3).
It is not yet possible to determine theoretically the failure
load to be expected in the "splitting" type of failure
75
2h
+ d
0
J
AN = (211:-_!_11: ...
180
e=
sine)( h., .~) 2
l
2
•
,!d2
2 "
5- '-
2·cos· 1 -
2·h 8 r + du
St :s; 2 h.r + du:
:&x . . 4·sina)(h"' + ~r. i-d~
AN= ( 41t-
a) tension
e = 2 cos· 1
S 1 S:
- ' - •-
2·h., + du
../2 · (h"'
AN = ( 3n:-
(n., + ~
+
du/2):
i>l't + 2·sin9. 2 cos&+ 2}
r.~ d~
e = 2 cos· 1 - ' - •-
2·h 11 + du
bz)
b) shear
Fig. 6-Concrete breakout bodies idealized according to
ACI 349: (a) tensile loading; (b) shear loading
concrete, considered throughout this paper to be proportional to
or![; . Both design procedures predict average
or mean failure loads; Nn or Vn- In subsequent codification of
the CCD procedure for consideration by ACI
Committee 318, 13 equations are based on the 5 percent fractile to provide part of the safety requirement. In addition, the
codification proposal bases the equations on the strength of
anchors in cracked concrete, with a multiplier that increases
the capacity when used in uncracked concrete. This paper
presents the results for uncracked concrete only and should
be compared with design expressions for uncracked concrete. The behavior of anchor groups is infuenced by stiffness of the base plate. In this paper, a rigid base plate is
presumed and no plastic action of the anchor group is considered.
Fig. 7-Projected areas for multiple fastenings under tensile loading according to ACI 349: (a) double fastening; (b)
quadruple fastening
(1)
JJ:
ACI 349-85 tension loads
ACI Committee 349 is concerned with nuclear-related
structures. Because of concern with nuclear safety, the philosophy of ACI 349 is to design ductile fastenings. To obtain
a limit to guard against brittle concrete failure, the cone model was developed. 4 •14•15
Under tension loading, the concrete capacity of an arbitrary fastening is calculated assuming a constant tensile
acting on the projected area of the
stress equal to <j> · 4 ·
failure cone, taking the inclination between the failure surface and concrete surface as 45 deg
JJ:
ACI Structural Journal I January-February 1995
with
=
=
<1>
AN =
fer
capacity reduction factor, here taken as 1.0
actual projected area of stress cones radiating
toward attachment from bearing edge of anchors.
Effective area shall be limited by overlapping
stress cones, intersection of cones with concrete
surfaces, bearing area of anchor heads, and overall
thickness of concrete member
In the following, it is assumed that member thickness is
sufficiently large to avoid any reduction of the concrete cone
failure load.
For a single anchor unlimited by edge influences or overlapping cones [Fig. 6(a)]
(2)
with
ANa=
projected area of a single anchor
=
The SI equivalent ofEq. (2) was detern;1ined assuming that
77
...
/-~
~
a)
Av
0
= ~c2
2
1
bl
Av
= ( 7t
7t·S
- 180 +sine)
c
·t
2
e = 2cos·1 (~)
Av
cl
9
= ( 1t
1t I 2·9
- ---
180
. ) .c 2
+ sm9
1
= 2cos· 1 (~)
2c
1
Fig. 8-Projected areas for fastenings under shear loading according to ACI 349: (a) single
fastening installed in thick concrete member; (b) single fastening installed in thin concrete
member (h ~ c 1); (b) doublefastening installed in thick concrete member (s 1 < 2c1)
1 in.
and
=25.4 mm, 1 psi = 0.006895 N/mm2, 1 1b =4.448 N,
JJ:: = 1.18 Jl:
{i"l
2
Nno=0.96·,.,;Jcc'hef'
(
du)
1+h' N
(3)
ef
For fastenings with edge effects (c < hef) and/or affected
by other concrete breakout cones (s < 2 · he1), the average
failure load follows from Eq. (4)
78
(4a)
AN
=A. Nno[Eq(2)]
'lb
(4b)
No
To obtain the failure load in SI units (N), Eq. (3) may be
used in place ofEq. (2) in Eq. (4b).
ACI Structural Journal I January-February 1995
Fig. 7 shows the determination of the projected areas AN
for double and quadruple fastenings. Note the computational
complexity of determining e and AN.
ACI 349-85 shear loads
The shear capacity of an individual anchor failing the concrete (Fig. 8), provided that the concrete half-cone is fully
developed, is
(5)
a)
= 1 and the conversion factors given, the
Again, with <1>
SI equivalent is
=
Vno
l
(0.48 ·
JJ::')c~),
N
(6)
If the depth of the concrete member is small (h < c 1) and/
or the spacing is close (s < 2 · c 1 ) and/or the edge distance
perpendicular to the load direction is small (c2 < c 1), then the
load has to be reduced with the aid of the projected areas on
the side of the concrete member
( 7a)
Av
= AVo . vno, [Eq. (5)] '
where
Av =
Avo
lb
( 7b)
actual projected area
=
projected area of one fastener unlimited by edge
influences, cone overlapping, or member thickness
[Fig. 8(a)]
=
n/2 · c 1
2
To obtain the failure load in SI units (N), Eq. (6) may be
used in place ofEq. (5) in Eq. 7(b).
Fig. 8 shows the determination of the projected areas Av
for shear loading using the cone concept of ACI 349. Again,
the computations are complex for the examples shown in
Fig. 8(b) and 8(c).
ceo method tension loads
The concrete capacity of arbitrary fastenings under tension
or shear load can be calculated with the CCD method. To
predict the steel capacity, additional design models are necessary, such as the one proposed in Reference 8 for elastic
design of ductile and nonductile fasteners, or in
Reference 16 for plastic design of ductile multiple fastenings. Note that failure load of anchors by pullout is lower
than the concrete breakout capacity. Equations for calculation of pullout capacity are available but are not sufficiently
accurate or general. Therefore, the pullout failure loads must
be evaluated and regulated by prequalification testing.
ACI Structural Journal I January-February 1995
Fig. 9-Idealized concrete cone for individual fastening
under tensile loading after CCD method
Under tension loading, the concrete capacity of a single
fastening is calculated assuming an inclination between the
failure surface and surface of the concrete member of about
35 de g. This corresponds to widespread observations that the
horizontal extent of the failure surface is about three times
the effective embedment (Fig. 9).
The concrete cone failure load Nno of a single anchor in
uncracked concrete unaffected by edge influences or overlapping cones of neighboring anchors loaded in tension is
given by Eq. (8)
(8)
where k 1, k 2 , k 3 are calibration factors, with
(9a)
where
35, post-installed fasteners
40, cast-in situ headed studs and headed anchor
bolts
79
Fig. 10-Definition of effective anchorage depth hedor different fastening systems
JJ: =
hef
=
concrete compression strength measured on 6 by
12-in. cylinders, psi
effective embedment depth, in. (Fig. 10)
In SI units, Eq. (9a) becomes
(9b)
where
knc =
knc =
JT::=
hef
=
head is:::;; 13 Jfc' at failure. 8 Because the concrete pressure
under the head of most currently available post-installed undercut anchors exceeds 13[/ at failure, knc = 35 or 13.5 (SI)
is recommended for use with this and other post-installed anchors.
In certain cases, when deeper embedments are used with
relatively thin edge cover, there is a chance of a side-face
blowout failure at a significantly reduced load. Such cases
are not covered in this paper.
If fastenings are located so close to an edge that there is not
enough space for a complete concrete cone to develop, the
load-bearing capacity of the anchorage is also reduced. This
is also true for fasteners spaced so closely that the breakout
cones overlap. One of the principal advantages of the CCD
method is that calculation of the changes in capacity due to
factors such as edge distance, spacing, geometric arrangement of groupings, and similar .variations can be readily determined through use of relatively simple geometrical
relationships based on rectangular prisms. The concrete capacity can be easily calculated according to Eq. (10)
(lOa)
13.5, post-installed fasteners
15.5, cast-in situ headed studs and headed anchor
bolts
(lOb)
concrete compression strength measured on cubes
with side length equal to 200 mm, N!mm 2
effective embedment depth, mm (Fig. 10)
In Eq. (8), the factor k,. JJ: represents the nominal concrete tensile stress at failure over the failure area, given by
k 2 · h~1 , and the factor k 3!
gives the so-called size effect. Note that, by basing the tensile failure load on the effective embedment depth heft the computed load will always be
conservative, even for an anchor that might experience pullout, as shown in Fig. 4.
Fracture mechanics theory 17 indicates that in the case of
concrete tensile failure with increasing member size, the failure load increases less than the available failure surface; that
means the nominal stress at failure (peak load divided by
failure area) decreases. This size effect is not unique to fastenings but has been observed for all concrete members with
a strain gradient. For instance, it is well known that the bending strength of unreinforced concrete beams and shear
strength of beams and slabs without shear reinforcement decrease with increasing member depth. Size effect has been
verified for fastenings by experimental and theoretical investigations.8·18-20 A more detailed explanation of the application of Bazant's theory to fastenings is given in Reference
21. Since the aggregate size in the test specimens is not specifically introduced into the CCD method, an approximation
is used. Since strain gradient in concrete for fastenings is
very large, size effect is maximum and very close to the linear elastic fracture mechanics solution. Therefore, the nominal stress at failure decreases in proportion to 11
and the
failure load increases with
Higher coefficients for headed studs and headed anchor
bolts in Eq. (9) are valid only if the bearing area of headed
studs and anchors is so large that concrete pressure under the
where
projected area of one anchor at the concrete surface unlimited by edge influences or neighboring
anchors, idealizing the failure cone as a pyramid
with a base length scr = 3hef [Fig. ll(a)]
ANa=
Jh:.r
h!).
80
Jh:.r
2
9. hef
actual projected area at the concrete surface,
assuming the failure surface of the individual
anchors as a pyramid with a base length scr =3hetFor examples, see Fig. ll(b) through (d)
tuning factor to consider disturbance of the radial
=
symmetric stress distribution caused by an edge,
valid for anchors located away from edges
(lOc)
(lOd)
where
c 1=
edge distance to the closest edge. (Note that
knc
Nno
=
=
symbols for 'lf 1, \jl 2, \jl 4, and \jl 5 and the order
in which they appear in this text were selected
to agree with Reference 13.)
see Eq. (9)
concrete cone failure load of one anchor unaffected
by edge or overlapping stress cones acording to Eq.
(9)
ACI Structural Journal I January-February 1995
hef
=
effective anchorage depth (Fig. 10). For fastenings
with three or four edges and cmax :5: 1.5hefCcmax =
largest edge distance), the embedment depth to be
inserted in Eq. (lOa) and (lOb) is limited to hef=
cma/1.5. This gives a constant failure load for deep
embedments22
Examples for calculation of projected areas are given in .
Fig. 11. Note the relatively simple calculation for the CCD
method compared to Fig. 7 illustrating the ACI 349 method.
In Eq. (10), it is assumed that the failure load is linearly
proportional to the projected area. This is taken into account
by the factor A!lA-,.~. For fastenings close to an edge, the axisymmetric state of stress, which exists in concrete in the
case of fastenings located far from the edge, will be disturbed by the edge. Due to this disturbance, the concrete
cone failure load will be reduced. (This also occurs in
cracked concrete. 8•23 ) This is taken into account by the tuning factor 'I' 2• A linear reduction from 'I' 2 = 1.0 for c 1 ;;:;
1.5he1 (no edge influence) to 'Jf 2 =0.7 for the theoretical case
c 1 =0 has been assumed.
·
Up to this point, it has been assumed that anchor groups
are loaded concentrically in tension. However, if the load
acts eccentrically on the anchor plate; it is not shared equally
by all fasteners. Based on a proposal in Reference 24, this effect can be taken into account by an additional factor 'I' 1
[Eq. (11)]
--:~
A, = A"
{single fastening)
= {2·1.5h.){2·1.5h.)
= {3h. )2 = 9h!
A, = (c, + tsh.){2·t5h.)
if: c, s: 1.5haf
b)
A, = {2·1.5h• + s,){2·1.5h•)
its, s a.oh..
c)
A, = {c, + s, + tsh.)(c, + s, + tsh.J
it:
c,, c 2 s tsh ..
$ 11
S:z S 3.Qhet
d)
Fig. ]]-Projected areas for different fastenings under tensile loading according to CCD method
(lla)
with AN, A No• 'I' 2, and Nno as defined in Eq. (1 0).
'Jf 1 = factor taking into account the eccentricity of the
resultant tensile force on tensioned fasteners. In the
case where eccentric loading exists about two axes
(Fig. 11), the modification factor 'I' 1 shall be computed for each axis individually and the product of
the factors used as 'I' 1 in Eq. (lla)
=
(llb)
relationship of the concrete capacity is proposed between
these limiting cases (Fig. 14).
ceo method shear loads
The concrete capacity of an individual anchor in a thick
uncracked structural member under shear loading toward the
free edge (Fig. 15) is
where
outside diameter of fastener, in.
eN'
=
distance between the resultant tensile force of ten-
sioned fasteners of a group and centroid of tensioned fasteners (Fig. 12)
Fig. 12 shows examples of an eccentricaly loaded
quadruple fastening under tensile loading located close to a
comer. In Fig. 13, Eq. (lla) is applied for the case of a
double fastening. In this figure (as in Fig. 12), it is assumed
that the eccentricity eN' of the resultant tension force on the
fasteners is equal to eccentricity eN of the applied load. This
is valid for eN :5: s1 16 and for eN > s1 16 if the fastener
displacements are neglected. If the load acts concentrically
on the anchor plate, Eq. (10) is valid ('I' 1 = 1) [Fig. 13(a)]. If
only one fastener is loaded [Fig. 13(c)], the failure load of
the group is equal to the concrete capacity of one fastener
without spacing effects. For 0 :5: eN' :5: 0.5s1, a nonlinear
ACI Structural Journal I January-February 1995
activated load-bearing length of fastener, in., :5: 8d0
(Reference 25)
= hef for fasteners with a constant overall stiffness,
such as headed studs, undercut anchors, and torquecontrolled expansion anchors, where there is no
distance sleeve or the expansion sleeve also has
the function of the distance sleeve
= 2d0 for torque-controlled expansion anchors with
distance sleeve separated from the expansion sleeve
c 1 = edge distance in loading direction, in.
In SI units with length quantities in mm and stress in N/
mm2, this equation becomes
(12b)
81
C2
S I ,2
Fig. 12-Examples of eccentrically loaded quadruple fastening under tensile loading
located close to corner
N
s,
' '
N
n
-
An ·N
A
no
Nn
=
AN
. "'1 . Nn 0
AN 0
'1'1
=
1
1 + 2e'N I (3h 61 )
no
0)
b)
c)
Fig. 13-Effect of eccentricity of tensile force on failure load of double fastening 24
82
ACI Structural Journal I January-February 1995
a)
2
0
c::
:z
..........
c::
:z
1
b)
Fig. 15-Concrete failure cone for individual fastener in
thick concrete member under shear loading toward edge:
(a) from test results; (b) simplified design model according
to CCD method
0
0
0,25s,
e'n
Fig. 14-lnjiuence of eccentricity of tensile force on failure
load of double fastening 24
According to Eq. (12), the shear failure load does not
increase with the failure surface area, which is proportional
to c~. Rather, it is proportional to c:·s. This is again due to
size effect. Furthermore, the failure load is influenced by the
anchor stiffness and diameter. The size effect on the shear
failure load has been verified theoretically and
experimentally. 26
The shear load capacity of single anchors and anchor
groups loaded toward the edge can be evaluated from Eq.
(13a) in the same general manner as for tension loading by
taking into account that the size of the failure cone is dependent on the edge distance in the loading direction, while in
tension loading it is dependent on the anchorage depth (Fig.
a)
16)
(13a)
where
Av =
b)
actual projected area at side of concrete member,
idealizing the shape of the fracture area of individ-
ACI Structural Journal I January-February 1995
Fig. 16-Comparison of tension and shear loading for CCD
method
83
Av = Av,
(single fastening)
= 1.5c, (2 ·1.5c 1 )
= 4.5·c~
3c,
Av = 1.5c,(1.5c, + c 2 )
if:
c 2 :s; 1.5c 1
Av = 2·1.5C 1 ·h
if: h :s; 1.5c 1
1,5c, 1,5c,
Av = (2·1.5c 1 + s,)·h
if: h :s; 1.5c1
s, :s; 1.5c,
1,5c 1 s, 1,5c,
Fig. 17-Projected areas for different fastenings under shear loading according to CCD
method
Avo =
\jl 4
stress distribution caused by a comer
ual anchors as a half-pyramid with side length
1.5c1 and 3cdFig. 17)
projected area of one fastener unlimited by comer
influences, spacing, or member thickness, idealizing the shape of the fracture area as a half-pyramid
with side length 1.5c 1 and 3c 1 [Fig. 15(b) and
17(a)]
=
(13c)
effect of eccentricity of shear load
c1 =
=
1
(13b)
distance between resultant shear force of fasteners
of group resisting shear and centroid of sheared fasteners (Fig. 18)
'l's=
84
tuning factor considering disturbance of symmetric
edge distance in loading direction, in. (Fig. 17); for
fastenings in a narrow, thin member with c2,max <
1.5c 1 (c2,max =maximum value of edge distances
perpendicular to the loading direction) and h <
1.5ct. the edge distance to be inserted in Eq. (13a),
(13b), and (13c) is limited to c 1 =max (c2,maJ1.5;
h/1.5). This gives a constant failure load independent of the edge distance c 1 (Reference 21)
ACI Structural Journal I January-February 1995
-
I
F
I
~~~-
I
v
-·
Vn•.L
I
-
J
~
u
a)
sS3c,
-
s
s
St
Fig. 18-Example of multiple fastening with cast-in situ
headed studs close to edge under eccentric shear loading
tV n,11
=
edge distance perpendicular to load direction (Fig.
17)
Examples for calculation of projected areas are shown in
Fig. 17. Note the relatively simple calculation compared to
the more complex geometry of the ACI 349 procedures illustrated in Fig. 8.
The considerations just presented relate to shear loads acting perpendicular to and toward the free edge [Fig. 19(a)]. If
the load acts in a direction parallel to the edge [Fig. 19(b)],
the test performed at TNO Delft27 indicates that the shear
load capable of being resisted is about twice as large as the
load that can be resisted in the direction perpendicular to and
toward the edge (Fig. 19). A similar value can be conservatively used for resistance to loads in the direction perpendicular to but away from the edge. 26
Cz
b)
~
Vn)t
= 2·Vn.l-
Vn,l. according to Eq. (13)
Fig. 19-Doublefastening: (a) shear load perpendicular to
edge; (b) shear load parallel to edge
2. The assumption of slope of the failure cone surface.
This leads to different minimum spacings and edge distances
to develop full anchor capacity.
3. The assumption about the shape of the fracture area
(ACI 349: cone, CCD method: pyramid approximating an
idealized cone). In both methods, the influence of edges and
overlapping cones is taken into account by projected areas,
based on circles (ACI 349) or rectangles (CCD method), respectively. Due to this, calculation of the projected area is
rather simple in the case of the CCD method and often rather
complicated in the case of ACI 349.
4. The CCD method takes into account disturbance of the
stresses in concrete caused by edges and influence of load
Comparison of ACI 349 and CCO methods
The main differences between these design approaches are
summarized in Table 1. They are as follows:
1. The way in which they consider influence of anchorage
depth hef (tensile loading) and edge distance c 1 (shear loading).
Table 1-Comparison of the influence of main parameters on maximum load
predicted by ACI 349 and CCO methods
Anchorage depth, tension
Edge distance, shear
ACI 349-85
CCDmethod
h;,
hL5
2
c,
'!
1.5
ci
Slope of failure cone
a= 45 deg
a= 35 deg
Required spacing to develop full
anchor capacity
2 h4 , tension
3 h,1 , tension
2c 1 ,shear
3 c 1 , shear
I h,1 , tension
1.5 h,1 , tension
Required edge distance to develop
full anchor capacity
I
Small spacing or
close to edge
1
I direction
2 directions
Eccentricity of load
ACI Structural Journal I January-February 1995
I c 1 , shear
1.5 c 1 , shear
Nonlinear (area-proportional)
reduction
Linear reduction
Nonlinear reduction
-
Taken into account
85
...
Table 2-Single fastenings with post-installed fasteners far from edge, test series-Tensile loading
Edge
spacing
Country
of test
GB
F
s
CJ
1.5hef
D
EUR
USA
~
GB
F
s
CJ
l.Ohef
D
EUR
USA
~
fc~200 • N/mm 2
hepmm
n
55
79
28
360
522
88
610
Minimum
Average
Maximum
Minimum
Average
Maximum
23.0
13.6
16.3
8.8
8.8
15.3
8.8
27.5
28.9
29.8
31.7
30.8
33.1
31.1
34.0
54.9
43.7
75.4
75.4
52.0
75.4
22.0
42.0
32.0
17.6
59.2
89.0
55.9
62.7
136.0
156.0
125.0
220.0
17.6
24.5
17.6
65.9
69.0
66.3
220.0
275.0
275.0
58
81
28
400
567
23.0
92
659
15.3
8.8
27.1
28.0
29.8
31.6
30.7
32.6
34.0
54.9
43.7
75.4
75.4
52.0
63.2
87.0
55.9
62.6
65.1
67.6
31.0
75.4
22.0
42.0
32.0
17.6
17.6
24.5
17.6
136.0
156.0
125.0
220.0
220.0
275.0
275.0
13.6
16.3
8.8
8.8
65.5
Table 3-Single fastenings with cast-in situ headed studs far from edge, single tests-Tensile loading
Edge
spacing
Country
of test
s
cs
CJ
1.5hef
D
EUR
USA
~
s
cs
CJ
l.Ohef
D
EUR
USA
~
fc~200 • N/mm 2
n
3
26
192
221
27
248
Average
Maximum
Minimum
Average
Maximum
30.9
28.3
11.4
11.4
24.3
11.4
39.5
31.2
28.5
28.9
28.9
28.9
56.7
34.4
71.9
71.9
43.1
71.9
130.0
50.0
42.9
137.3
177.0
156.4
42.9
63.5
42.9
158.5
109.7
152.6
142.0
450.0
525.0
525.0
251.4
525.0
6
26
220
252
28
280
30.9
28.3
11.4
11.4
24.3
11.4
38.6
31.2
28.3
28.8
29.3
28.6
56.7
34.4
71.9
71.9
43.1
71.9
112.0
50.0
42.9
42.9
63.5
42.9
133.3
177.0
145.0
147.0
107.9
141.7
eccentricities. These influencing factors are neglected by
ACI 349.
TEST DATA
In the following sections, some extracts of the data base
are reproduced to give the reader a sense of the large number
of test series, individual tests, and range of variables considered. The original summary of test results is given in
Reference 10. Only tests where a concrete breakout failure
occurred were taken into account. In response to review
comments after submission of this paper for publication,
data from the Prague tests reported by Eligehausen et al. 21
and the Arkansas Nuclear One tests 28 were added.
Tensile loading
Tables 2 through 5 give an overview of the number of tensile tests and range of the varied parameters. No difference
in the procedure of performing tests with anchors under tensile loading between Europe and the U.S. could be discovered.
86
he!• mm
Minimum
142.0
450.0
525.0
525.0
251.4
525.0
Shear loading
Tables 6 through 8 give an overview of the number of
shear tests and range of the varied parameters.
In European tests with anchors under shear loading, a fluoropolymer sheet was always inserted between the concrete
surface and steel plate. This is to simulate reduction in friction between the steel plate and concrete surface caused by
reduction of the prestressing force with time 9 and by use of
a plate with a relatively smooth surface (e.g., a painted, colddrawn, or greased plate). In the U.S., tests are usually performed with an unpainted steel plate attached directly on the
concrete surface with no fluoropolymer sheet in between.
This increases friction resistance and causes the U.S. test
values to be higher.
COMPARISON OF DESIGN METHODS
WITH TEST DATA
In this section, test data from the wide range of tests shown
in the previous section will be compared with the CCD and
ACI design procedures.
ACI Structural Journal I January-February 1995
Table 4-Single fastenings with post-installed fasteners close to edge, test series-Tensile loading
Edge
spacing
fc~200 , Nlmm 2
Country
of test
GB
F
D
EUR
USA
CJ ~ 1.5 hef
:E
CJ ~ 1.0 hef
D
USA
:E
c 1,mm
hef• mm
n
3
2
36
41
42
83
Minimum
Average
Maximum
Minimum
Average
Maximum
Minimum
Average
Maximum
23.0
18.4
24.0
18.4
17.2
17.2
23.8
18.4
28.7
27.9
27.1
27.5
25.5
18.4
59.0
59.0
34.1
59.0
37.0
63.5
30.0
30.0
34.2
30.0
67.3
63.5
81.5
79.6
118.0
99.0
100.0
63.5
220.0
220.0
222.3
223.3
50.0
63.5
30.0
30.0
31.8
30.0
83.3
63.5
95.6
93.1
96.0
94.6
120.0
63.5
330.0
330.0
177.8
330.0
10
30
40
24.0
18.6
18.6
26.3
27.7
27.3
37.7
34.1
37.7
53.0
34.2
34.2
100.9
137.8
128.6
220.0
222.3
222.3
30.0
31.8
30.0
93.5
100.8
98.9
220.0
158.8
220.0
Table 5-Quadruple fastenings with cast-in situ headed studs, single tests-Tensile loading
fc~200 ' N/mm2
Edge
Country
spacing
of test
QuadUSA
rup1e
D
fastening
:E
n
3
32
35
32.5
17.9
17.9
33.6
27.5
28.1
161.9
67.3
67.3
35.8
38.9
38.9
161.9
179.4
177.9
s,mm
c 1,mm
hef• mm
Minimum Average ~aximum Minimum Average Maximum Minimum Average
-
161.9
360.3
360.3
~aximurr
-
-
-
-
-
-
Minimum Average !Maximum
76.2
125.5
146.0
50.8
80.0
50.8
101.6
400.0
400.0
Table 6-Single fastenings with post-installed fasteners and fully developed concrete breakout, test
series-Shear loading
fc~200 ' N/mm2
Country
of test
USA
D
Minimum Average Maximum Minimum Average Maximum Minimum Average Maximum Minimum Average Maximum
n
60
84
144
:E
c 1,mm
d,mm
hef• mm
31.7
25.7
28.2
21.3
16.1
16.1
53.9
48.4
53.9
94.5
70.3
80.4
25.0
27.4
25.0
220.0
167.6
220.0
8.0
6.4
6.4
20.9
14.6
17.2
32.0
25.4
32.0
40.0
38.1
38.1
128.3
98.0
110.6
300.0
203.2
300.0
Table 7-Single fastenings with post-installed fasteners in concrete members with limited thickness,
single tests-Shear loading
Country
of test
D
n
38
MaxiAverage mum
35.2
42.8
46.4
c 1,mm
hef• mm
d,mm
MiniMaximum Average mum
MiniMaximum Average mum
fc~200 , N/mm2
Minimum
155.0
250.8
306.0
20.0
27.5
40.0
Minimum
63.0
c 2,mm
MaxiAverage mum
140.2
220.0
Minimum
62.5
Average Maximum
184.1
300.0
Table a-Double fastenings in thick concrete members, single tests
Anchorage Country
device oftest
n
Expansion
anchor
D
36
fc~200 ' Nlmm 2
hef• mm
d,mm
c 1,mm
c 2,mm
MiniMaximum Average mum
MaxiMinimum Average mum
MiniMaximum Average mum
MiniMaximum Average mum
Mini- Average Maximum
mum
20.5
24.8
27.2
80.0
81.7
100.0
Tensile loading
In Fig. 20 and 21, measured failure loads of individual anchors are plotted as a function of embedment depth. The tests
were performed on concrete with different compression
strengths. Therefore, the measured failure loads were normalized to fc: = 25 N/mm2 lfc' = 3070 psi) by multiplying
them with the factor (25/fcc, tes 1) 0 ·5 . In addition, predicted failure loads according to ACI and the CCD methods are plot-
ACI Structural Journal I January-February 1995
18.0
20.7
24.0
80.0
172.1
200.0
80.0
190.0
400.0
ted. As can be seen, the tension failure loads predicted by the
CCD method compare rather well with the mean test results
over the total range of embedment depths, with the exception
of the two post-installed fasteners at the deepest embedment.
In contrast, anchor strengths predicted by ACI 349 can be
considered as a lower bound for shallow embedments and
give quite unconservative results for the deepest embedded
headed studs. This is probably due to the fact that size effect
87
h~
het [in]
500.0
2
I
4
6
8
UnJ
1200.0
10
5
10
15
20
I
100
ac~""J
1000.0
90
400.0
/x
800.0
80
200
I
350.0
z=:.
70
z
=:.
250
X/
450.0
300.0
"iii
Q.
60
z
I
I
600.0
150
"iii
- CCD-Method
.Q.
=:.
z
I
z
I
~
z
100
400.0
250.0
50
200.0
tN
200.0
50
40
X
CCD-Method~x
150.0
:
•
X
~
X
~~
100.0
X/
X
l
X
30
.
X
50.0
h. [mm]
- 20
tN
10
h~
0
0
50.0
100.0 150.0 200.0 250.0 300.0
het [mm]
Fig. 20-Concrete breakout load for post-installed fasteners, unaffected by edges or spacing effects-Tensile test
results and predictions
is neglected by ACI 349. Substantial scatter exists with the
deep embedment data, justifying a conservative approach in
this region.
Fig. 22 shows the results of all evaluations for tensile loading with post-installed fasteners far from the edge. Average
values of the ratios Nu,test to Nn,predicted and corresponding coefficients of variation for both methods are plotted. The average and coefficient of variation are substantially better for
the CCD method than for ACI 349. This is also true when the
data are subdivided into five different anchor types (Fig. 23)
and for headed studs without edge or spacing influences
(Fig. 24). Eq. (9) uses the same coefficient knc for undercut
anchors as for other post-installed anchors. The results
shown in Fig. 23 support this procedure. These undercut anchor tests were typically for undercut anchors with head
bearing pressures greater than 13fc'- Better values would be
expected if the undercuts were proportioned for lower bearing pressures.
The coefficient of variation of the ratios of measured failure load to the value predicted by the CCD method is about
15 percent for headed studs and undercut anchors, which
agrees with the coefficient of variation of the concrete tensile
88
Fig. 21-Concrete breakout load for cast-in situ headed
studs, unaffected by edges or spacing effects-Tensile test
results and predictions
capacity when tests include many different concrete mixes.
The coefficient of variation of expansion anchors is slightly
larger, which might be a result of the different load transfer
mechanisms.
Note that in Fig. 22 through 24, the average of the ratio
Nu,tes!Nu,predicted is higher for the ACI 349 method than for
the CCD method. This is due to the fact that the majority of
the evaluated data has an effective embedment depth hef
smaller than 150 mm (6 in.). For headed studs with embedments greater than 300 mm (12 in.), ACI 349 predictions become unconservative (Fig. 21). Thus, the average values do
not indicate local unconservative cases.
In Fig. 25, results of tests with quadruple fastenings with
headed studs are evaluated in the same way as in Fig. 22. The
figure indicates that spacing influence is more easily and accurately taken into account by the CCD method than by ACI
349. While the average failure load is predicted correctly by
the CCD method, it is significantly overestimated by ACI
349. This can also be seen from Fig. 26, which shows failure
loads of groups as a function of the distance s1 between the
outermost anchors. Groups with 4 to 36 anchors were installed in very thick concrete specimens loaded concentrically in tension through a rigid load frame to assure an almost
equal load distribution to the anchors. Light skin reinforcement was present near the top and bottom surfaces of the
specimens and light stirrups were present near the edges in
some specimens for handling. The stirrups did not intersect
the concrete cone. No reinforcement was present near the
fastening heads. These specimens represent the capacity of
groups of fasteners installed in plain concrete. Embedment
depth and concrete strength were kept constant. In all tests a
ACI Structural Journal I January-February 1995
2.00
-.....,
_...,..
u
.."'0
2.50
.
.
....
1.50
0..
'-Z
;: ......
<-=.."'
G
u
....
...
.. c
C'>
-~
0~
.."'"
oz
;
. -,.
1.00
...:-
.so
z"
::>
.00
1.50
ACI 349
CC-Method
610
610
>
.
10.0
r:::
~
.50
%
v:~
268
~
"
>"
20.0
..
~
r:::
V::
~
%
r:::
48
~
~
~
98
~
~
~
~
~
~
~
~
~
20.0
0
-~
%
~
-
r:::
-~
~
r:::
10.0
~
~
~
~
~
~
~
~
~
7~
-
~
~
%
~
%
~
110
~
%
~
~
r:::
%
~
1--
~
~
r.:::
~
~
u
c
-..
~
.0
0
0
u
-~
1.00
.00
c
0
.
=
~
N
;:..:
<
0
u
.0
-......
-
....
:
z
c
,...,
•
2.00
30.0
-;
30.0
0
u
~0.0
0
u
40.0
Fig. 22-Comparison of design procedures for postinstalled fasteners, unaffected by edges or spacing effectsTensile loading
common cone failure was observed. For comparison, single
anchors were also tested. For the chosen embedment depth
[het= 185 mm (7.3 in.)], the capacity of single anchors is predicted almost equally by both methods. However, with increasing spacing of the outermost anchors, the failure load is
significantly overestimated by ACI 349 and correctly predicted by the CCD method. This is due to the fact that the
critical spacing scr = 2hef assumed by ACI 349, which follows from the assumption of a 45-deg cone, is too small. Obviously, provision of special reinforcement designed to
engage the failure cones and anchor fastenings back into the
block could provide substantial increase in load. This was
not investigated in these tests and such increases are not
treated in this paper.
In Fig. 27, results of tests with single post-installed fasteners close to the edge are evaluated. The average ratio Nu,test
to Nn,predicted is approximately the same for both methods.
However, the coefficient of variation is much smaller for the
CCD method and amounts to about the same value as for single fasteners away from edges. This shows that assumptions
about the critical edge distance ccr =1.5hef• and the stress disturbance factor 'If 2, are correct. Note that most of the tests
were done with rather shallow anchors (Table 4). For deeper
anchors, it would be expected that the CCD method would
predict more accurate capacities due to its consideration of
ACI Structural Journal I January-February 1995
+)
A1
A3
B
C
D
torque controlled expansion anchor with one cone
torque controlled expansion anchor. bolt type
drop-in anchor
self-drilling anchor
undercut anchor
Fig. 23-Comparison of design procedures for postinstalled fasteners, unaffected by edges or spacing effects,
divided into different fastening systems-Tensile loading
size effect and effect of stress disturbance, as well as its assumption of a characteristic edge distance ccr = 1.5 hef·
Influence of load eccentricity on the failure load of anchor
groups is shown in Fig. 28. The eccentricity en' is calculated
using the general assumptions of the theory of elasticity, i.e.,
stiff anchor plate, anchor displacement equal to steel elongation, and linear elastic behavior of concrete. It can be seen
that the CCD method yields conservative results. This effect
is also neglected by ACI 349.
Shear loading
Fig. 29 shows a comparison of results of U.S. and European shear tests performed with single post-installed anchor
fastenings in thick concrete members with the design procedure of the CCD method and ACI 349. The tests \vere performed on concrete with different concrete strengths,
different anchor diameters, and different ratios of embedment depth to anchor diameter. Therefore, the measured failure loads were transformed to a concrete strength fcc' =25
N/mm2 Cf/ = 3070 psi), anchor diameter d0 = 18 mm (0.71
in.), and a ratio lld0 =8 by multiplying them with the factor
(25/fcc',test) 05 . (18/ do,test) o.s .. [ 8/ (ll d)]~~~~· On the average, the concrete breakout loads of the U.S. tests are higher
than those of the European tests, especia~ly at smaller edge
89
2.00 . - - - - - - - - - - - - -
2.00
.,
"'
_.,.,
0
.
0
1. 50
(,.) 1.50
.._
a..
~'­
oO.
~
o:n
0
.
-o
c
'-Z
1. 00
~ ......
<-:='
.
"'
.50
::>
z
.00
ACI 349
CC-Method
248
248
ACI 349
CC-Method
32
35
.0
.0
N
;:-.:
c
0
10.0
c:
"';;
0
·"';;
...
0
>
~
.
...0
20.0
>
0
c
·0
..
10.0
20.0
..
30.0
c:
0
..
0
u
40.0
30.0
0
u
40.0
Fig. 24-Comparison of design procedures for cast-in situ
headed studes, unaffected by edges or spacing effects-Tensile loading
Fig. 25-Comparison of design procedures for quadruple
fastenings with cast-in situ headed studes--Tensile loading
675
3000
n
25 N/mm 2 (3,6 ksi)
=185 mm
(7,3 in)
fcc :
he
n
f
1
4
16
=1-36 headed studs
06.
+D Mean value of a series
2000
36
Symbol
+
b
~-~--
0
6.
0
-
~'0. --
~~\--
~--~5~,----~----------~----------~----------~~--------~
'
450
,. - - - - . n=9
:
-:.
:M
.......
z
225
-·...
,., :'
~:
'
200
400
600
800
1000[mm]
7,9
15,7
23,6
31,5
39,4 [in]
Fig. 26-Actual and predicted loads for groups of cast-in situ headed studs as function of distance between outermost
anchors-Tensile loading
90
ACI Structural Journal I January-February 1995
2.00
.
_...,....
...,
v
..
0
1. so
0~
O>C:
o:z
1. 00
:;;-....
."'
>~
<-
'
N2 :
'
'
~
.so
N4e~JO
N3
H
it
'
::>
I
~1~100 ;,~ 1~.Smm
:z
!4----4'~ 4'!......+toll--4~in
.00
ACI 349
CC-Method
30
83
s,
s,
=300
= 12"
mm
in
.0
X
10.0
c:
0
~
...
"
20.0
>
c:
.,
.v,-----0.8
~
-.
.2
-...
0
~
30.0
8
~
r--
0 .6
40.0
so.o
0. 4
0. 2
0.0
Test results
CCD-Method
§
v
u
0
-
0.2
0.4
0.6
I
--
0.8
1.0
Fig. 27-Comparison of design procedures for single fastenings with post-installed fasteners close to edge-Tensile
loading
Fig. 28-Comparison of test results on eccentrically loaded
line fastenings composed offour cast-in situ headed studs
with load predicted by CCD method-Tensile loadinl
distances. This can be attributed to the absence of a ·fluoropolymer sheet in the U.S. tests and resulting friction contribution leading to higher shear capacity. The friction
contribution relative to the failure load is large for small edge
distances.
Failure loads predicted by the CCD method agree well
with the average failure loads measured in European tests.
On the contrary, ACI 349 is conservative for small edge distances and unconservative for large edge distances. This is,
again, probably due to the neglect of size effect by ACI 349.
Due to the friction contribution just mentioned, the U.S. test
data are predicted more conservatively by both methods.
In Fig. 30 and 31, average values of the ratios Vu,tes!Vn,prediction and corresponding coefficients of variation for post-installed fasteners are given for European and U.S. test data,
respectively. The ACI 349 averages are more conservative.
This is due to the fact that most tests were done with small
edge distances. However, the ACI 349 coefficients of variation are larger. A similar result was found for headed studs. 10
The results of European tests with double fastenings parallel to the edge and loaded toward the edge (Fig. 32) and
tests with single fastenings in thin concrete members
(Fig. 33) are similarly evaluated. As can be seen, the CCD
method compares more favorably with the test data. For both
applications, average failure loads predicted by ACI 349 are
unconservative and coefficients of variation are much larger.
ACI Structural Journal I January-February 1995
CONCLUSIONS
In this study, the concrete capacity of fastenings with castin situ headed studs and post-installed anchors in uncracked
plain concrete predicted by ACI 349 and the CCD method
has been compared with the results of a large number of tests
(see Tables 2 through 8). Based on this comparison, the following conclusions can be drawn:
1. The average capacities of single anchors without edge
and spacing effects loaded in tension are predicted accurately by the CCD method over a wide range of embedment
depths [20 mm (0.8 in.)< hef$. 525 mm (20.7 in.)]. For a few
post-installed anchors with embedment depths in the 250mm (10-in.) range, the CCD method was quite conservative.
Conversely, ACI 349 underestimates the strength of shallow
anchors and is unconservative for quite a number of deep
embedments. The same result was found for the predicted
capacities of single anchors loaded in shear toward the edge
with small or large edge distances, respectively.
This result is due to the fact that ACI 349 assumes the failure load to be proportional to a failure area that increases
with the square of the embedment depth. On the other hand,
the CCD method takes size effect into account and assumes
91
c, [In]
c ,[in]
200.0 , - - - , - - - - , - - - , - - - , - - -.......- - c - - - .
2
4
10
12
175.0
200.0 .--...,----....,-----,-- --,--...,.-----.----,
4
10
6
40
I
I
I
I
150.0
30
I
I
+
•
I
100.0
20
CCD-Method
i"
•I •
y ,
• ;j
I>
ACI349-/
~
/ + - CCD-Method
75.0
-30
I
125.0
ACI349-(
100.0
I
150.0
I
125.0
40
I
175.0
20
75.0
•
50.0
10
50.0
10
25.0
25.0
100.0
150.0
200.0
250.0
300.0
150.0
c, [mm]
200.0
250.0
300.0
c, [mm]
(a)
(b)
Fig. 29-Comparison of shear test results with ACI 349 and CCD method for single post-installed fasteners in thick concrete
members: (a) European tests; (b) U.S. tests
2.00
2.00
.
.,.
...
.,
.,
u
.
.
1. 50
.,u
oz
.
0~
-----
1.00
:;; .....
a>C
oz
:;; .....
.
<</)
<-
.50
z
.00
.00
ACI 349
CC-Method
55
55
.0
10.0
0
84
10.0
"
>
"
>
'";;
'";;
20.0
.
20.0
c
c
u
u
-..
84
.0
~
~
..
CC-Method
0
0
30.0
..
30.0
0
0
(..)
(..)
40.0
Fig. 3D-Comparison of design procedures for European
tests with single post-installed fasteners in thick concrete
members-Shear loading toward edge
92
X
ACI 349
c
c
"
.50
z"
=>
X
1.00
>~
>~
."'
1. 50
-~
~~
a>C
..
40.0
Fig. 3/-Comparison of design procedures for U.S. tests
with single post-installedfasteners in thick concrete members-Shear loading toward edge
ACI Structural Journal I January-February 1995
2.00
....
"'u
...,
..."'
oD.
1. 50
"'o:z
1. 00
-
O>C
2.00 , - - - - - - - - - - - - - - - ,
!
- ...
-----
0~
:;;-.....
.."'
""c
"'
o:z
>~
...:-
1.50
1.00
-----
:;;-.....
>-
..
<-;;;
.50
:::>
:z
.50
:>
:z
.00
:-<:
ACI 349
CC-Me I hod
36
36
.0
ACI 349
CC-Method
99
99
c
0
;;
...
10.0
c
20.0
>
0
10.0
0
...
>
~
.
0
20.0
c
u
"'
.
c
30.0
0
w
u
..
30.0
0
w
Fig. 32-Comparison of design procedures for double fastenings with post-installed fasteners in thick concrete members (European tests)-Shear loading toward edge
Fig. 33-Comparison of design procedures for European
tests with single post-installed fasteners in thin concrete
members-Shear loading toward edge
failure load to be proportional to the embedment depth to the
1.5 power.
2. In many applications (for example, anchor groups away
from edges loaded in tension, single anchors in thin concrete
members loaded in shear, double fastenings in thick concrete
members loaded in shear), the capacity is predicted more accurately by the CCD method. Failure loads predicted by ACI
349 for these cases are significantly unconservative. This is
mainly due to the fact that ACI 349 assumes a 45-deg failure
cone. The CCD method is based on an assumed inclination
of the failure surface of about 35 deg, which produces better
agreement with test results.
3. In some applications, such as single anchors at the edge
loaded in tension, the mean capacity is predicted accurately
by both methods. However, the coefficient of variation of the
ratio of measured failure load to the value predicted by ACI
349 is rather large (V"' 45 percent).
4. In all applications investigated, concrete capacity is predicted with consistent accuracy by the CCD method. The coefficient of variation of the ratios between measured and
predicted capacities is about 15 to 20 percent. This coefficient of variation is equal to or not much larger than the value
expected for concrete tensile strength when the test specimens are produced from many different concrete mixes.
5. Calculation of the projected areas is simpler with the
ectangular areas of the CCD method, making it user-friend-
ly. In contrast, the circular areas of ACI 349 result in considerable computational complexity.
Summarizing, the CCD method is a relatively simple,
transparent, user-friendly, and accurate method for efficient
calculation of concrete failure loads for fastenings in uncracked concrete. It is based on a physical model to assist designers in extrapolating the empirical results to other
applications. Therefore, this method is recommended for the
design of fastenings. It is not incorrect to use the ACI 349
method for many fastening applications. However, since it
does not seem universally advantageous and in some applications produces unconservative values, the authors strongly
recommend use of the CCD procedures.
,~J
Structural Journal I January-February 1995
CAUTION
It is known that the presence of tensile cracks can substantially reduce the concrete capacity of fasteners.* Some fasteners are not suitable for use in cracked concrete. For those
fasteners suitable for use in cracked concrete, it is possible to
adjust the uncracked concrete failure loads predicted by the
CCD method by using an additional multiplicative factor.
This factor results in cracked concrete capacities around 70
percent of uncracked concrete capacities.t Similarly, it is
*'tEligehausen, R., and Balogh, T., "Behavior of Fasteners Loaded in Tension in
Cracked Concrete," accepted for publication in ACI Structural Journal.
93
known that the concrete capacity of fasteners can be enhanced by properly detailed local reinforcement. Such enhancement can be included in design provisions but is
outside the scope of this paper.
NOTATION*
c
distance from center of a fastener to edge of concrete
distance from center of a fastener to edge of concrete in one
CJ
direction. Where shear is present, CJ is in the direction of the
shear force
distance from center of a fastener to edge of concrete in direction orthogonal to CJ· Where shear is present, cz is in the direction perpendicular to shear force
outside diameter of fastener or shaft diameter of headed stud or
headed anchor bolt
head diameter of headed studs or headed anchors
concrete compressive strength, measured on 6 by 12-in. cylinders
fcc 1
concrete compressive strength, measured on 200-mm cubes
fct
h
hef
concrete tensile strength
• thickness of concrete member in which a fastener is anchored
effective embedment depth
n
s
number of test results
distance between fasteners, spacing
distance between outermost fasteners of a group
St
v
coefficient of variation
ratio of actual to predicted load
mean value of x
projected area, tension
X
X
AN
Av
projected area, shear
CEB
cs
D
EUR
F
GB
N
S
USA
V
=
Euro-Intemational Concrete Committee
Czechoslovakia
Germany
Europe
France
Great Britain
tensile load
Sweden
United States of America
shear load
a.
slope of concrete breakout cone
<P
capacity reduction factor for safety considerations
REFERENCES
I. ASTM ZXXX, "Standard Specification for Performance of Anchors
in Cracked and Non-Cracked Concrete Elements," Draft 1, Mar. 22, 1993.
2. Furche, J., and Eligehausen, R., "Lateral Blowout Failure of Headed
Studs near a Free Edge," Anchors in Concrete-Design and Behavior, SP130, American Concrete Institute, Detroit, 1991, pp. 235-252.
3. Zhao, G., "Befestigungen mit Kopfbolzen im ungerissenen Beton
(Fastenings with Headed Studs in Uncracked Concrete)," PhD thesis, University of Stuttgart, 1993.
4. ACI Committee 349, "Code Requirements for Nuclear Safety Related
Concrete Structures (ACI 349-85)," American Concrete Institute, Detroit,
1985.
5. PC/ Design Handbook, 4th Edition, Precast/Prestressed Concrete
Institute, Chicago, 1992.
6. Eligehausen, R.; Fuchs, W.; and Mayer, B., "Loadbearing Behaviour
of Anchor Fastenings in Tension," Betonwerk & Fertigteil-Technik (Wiesbaden), No. 12, 1987, pp. 826-832; and No. I, 19~8, pp. 29-35.
7. Eligehausen, R., and Fuchs, W., "Loadbearing Behaviour of Anchor
Fastenings under Shear, Combined Tension and Shear or Flexural Loading," Betonwerk & Fertigteil-Technik (Wiesbaden), No.2, 1988, pp. 48-56.
8. Rehm, G.; Eligehausen, R.; and Mallee, R., "Befestigungstechnik
*Notations for specific design procedures are defined in sections related to that procedure.
·
94
(Fastening Technique)," Betonkalender 1992, V. II, Ernst & Sohn, Berlin,
1992, pp. 597-715. (in German)
9. Eligehausen, R., "Vergleich des
(Comparison of the
K
K- Verfahrens
mit der CC-Methode
-Method with the CC-Method)," Report No. 12/16-
9217, Institut fiir Werkstoffe im Bauwesen, Universitlit Stuttgart, 1992. (in
German)
10. Fuchs, W., "Entwicklung eines Vorschlags fiir die Bemessung von
Befestigungen (Development of a Proposal for the Design of Fastenings to
Concrete)," Report to the Deutsche Forschungsgemeinschaft, Feb. 1991.
(in German)
11. Klingner, R. E., and Mendonca, J. A., "Tensile Capacity of Short
Anchor Bolts and Welded Studs: A Literature Review," ACI JOURNAL, Proceedings V. 79, No.4, July-Aug. 1982, pp. 270-279.
12. Klingner, R. E., and Mendonca, J. A., "Shear Capacity of Short
Anchor Bolts and Welded Studs: A Literature Review," ACI JoURNAL, ProceedingsV. 79, No.5, Sept.-Oct. 1982, pp. 339-349.
13. ACI Committee 318, Letter Ballot LB 93-5, CB-30, Proposed
Chapter 22, Fastening to Concrete, 1993.
14. ACI Committee 349, "Code Requirements for Nuclear Safety
Related Concrete Structures (ACI 349-76)," American Concrete Institute,
Detroit, 1976.
15. ACI Committee 349, "Design Guide to ACI 349-85," American
Concrete Institute, Detroit, 1988.
16. Cook, R. A., and Klingner, R. E., "Behavior and Design of Ductile
Multiple-Anchor-To-Steel-Connections," Research Report No. 1126-3,
Center for Transportation Research, University of Texas at Austin, 1989.
17. Bazant, Z. P., "Size Effect in Blunt Fracture, Concrete, Rock, Metal,"
Journal of Engineering Mechanics, ASCE, V. 110 No.4, 1984, pp. 518535.
18. Bode, H., and Roik, K., "Headed Studs-Embedded in Concrete and
Loaded in Tension," Anchorage to Concrete, SP-103, G. B. Hasselwander,
ed., American Concrete Institute, Detroit, 1987, pp. 61-88.
19. Eligehausen, R., and Sawade, G., "Fracture Mechanics Based
Description of the Pull-Out Behaviour of Headed Studs Embedded in Concrete," Fracture Mechanics of Concrete Structures. From Theory to Applications, L. Elfgren, ed., Chapman & Hall, London, 1989, pp. 263-281.
20. Eligehausen, R., and Ozbolt, J., "Size Effect in Anchorage Behaviour," Proceedings, European Conference on Fracture Mechanics, Fracture Behaviour and Design of Materials and Structures, Turin, Oct. 1991,
pp. 17-44.
21. Eligehausen, R.; Bouska, P.; Cervenka, V.; and Pukl, R., "Size Effect
on the Concrete Failure Load of Anchor Bolts," Fracture Mechanics of
Concrete Structures, Elsevier Applied Science, 1992, pp. 517-525.
22. Eligehausen, R., and Balogh, T., 'CC-Method (Concrete Capacity
Method)," Report No. 12115-92/1, Institut fiir Werkstoffe im Bauwesen,
Universitlit Stuttgart, 1992.
23. Eligehausen, R.; Fuchs, W.; Lotze, D.; and Reuter, M., "Befestigungen in der Betonzugzone (Fastenings in the Concrete Tensile Zone)," Beton
und Stahlbetonbau (Berlin), No.1, 1989, pp. 27-32; and No.2, pp. 71-74.
(in German)
24. Riemann, H., " 'Extended
K
-Method' for the Design of Fixing
Devices as Exemplified by Headed Stud Anchorages," Betonwerk & Fertigteil-Technik (Wiesbaden), No. 12, 1985, pp. 808-815.
25. Paschen, H., and Schonhoff, T., "Untersuchungen iiber in Beton
einge1assene Scherbolzen aus Beton (Investigations about Shear Bolts
Made from Reinforcing Bars in Concrete)," Deutscher Ausschuss for
Stahlbeton (Berlin), No. 346, 1983.
26. Fuchs, W., "Tragverhalten von Befestigungen unter Querlast im ungerissenen Beton (Behaviour of Fastenings under Shear Load in Uncracked
Concrete)," Mitteilungen No. 1990/2, Institut fiir Werkstoffe im Bauwesen,
Universitlit Stuttgart, 1990.
27. Stichting Bouwresearch, "Uit beton stekende ankers (Anchors Sticking Out of Concrete)," Report of the Study Commission B7, V. 27, 1971.
28. Maxi-Bolt Load Test Program, Arkansas Nuclear One, Engineering
Report 92-R-0001-01.
29. Burdette, E. G.; Perry, T. C.; and Funk, R. R., "Load Relaxation
Tests of Anchors in Concrete," Anchorage in Concrete, SP-103, G. B. Hasse1wander, ed., American Concrete Institute, Detroit, 1982, pp. 133-152.
ACI Structural Journal I January-February 19f
Disc. 92-S9/From the January-February 1995 AC/ Structural Journal, p. 73
Concrete Capacity Design (CCD) Approach for Fastening to Concrete. Paper by .Werner Fuchs, Rolf Eligehausen, and John E. Breen
Discussion by Robert W. Cannon, Phillip J. Iverson, LeRoy A. Lutz, RichardS. Orr, and Authors
By ROBERT W. CANNON
MemberACJ, Consulting Engineer, Maryville, TN
The authors of the CCD approach have been very eloquent
in their efforts to persuade the reader of the benefits of the
CCD approach. Unfmtunately, the approach is limi ted with
respect to applicability and departs from time-honored approaches to the development of design criteria based on lower-bound test results. The so-called "five percent fractile" is
completely misleadi ng, with respect to the approach's ability
to predict group pullout and edge effects on concrete capacities or provide meaningful explanations for significantly
higher test results than those achieved at Stuttgart, which
constitutes the principal database for the CCD approach.
The ACI 349 equation for determining the pullout capacity of the concrete is basically a lower-bound equation used
for determining the embedment requirements of ductile anchorage systems to increase design reliability by limiting the
mode of failu re to the tensile strength of steel rather than ,
concrete. To assure yielding of the steel and full load transfer
at th e anchor head, the code requires development of the
minimum specified tensile strengths of all tensile stressed
anchors by application of appropriate strength reduction factors in detennining the tensile pullout capacity of the concrete (when all of the tensile anchors must be fully
developed, there is no need to calculate the eccentricity of
the load as required in the CCD approach). The only exceptio n to these requirements in the present code relates to expansion anchors, whose design is restricted to tests that are
representative of the anchor spacing and load application,
along with the application of significantly lower strength adjustment factors for design loading.
ACI Structural Journal I November-December 1995
ACT 349 made no provisions for the design of nonductile,
cast-in-place anchorages. When you consider the reduced~
factors that must be applied for the less reliable brittle failure, and the relatively minor differences in embedments required for a ductile anchorage to develop a given load
requirement, there appears to be no justification for such provisions.
The paper makes quite a point about the simplici ty of the
CCD procedure for quadruple anchorages in comparison
witb the complicated calculations of ACT 349. Most people
today use computers; however, there are design charts
available 30 for hand calculations. There are eq ualizing simplifications that can be used to overcome the complications
of calculating overlaps. In add ition, the reduced area requ irements for anchor heads were inserted in the code primarily
to discourage designers from complicatin g designs by add ing plates and washers at the anchor head and is relatively insignificant when applied to the calculated pullout capacity of
standard bolts and studs.
By eliminating the bead size from the formula, the following equation can be used for a group-projected area
where Sx and Sy are the out-to-out dimensions in the x- and
y-directions.
The major thrust of the paper follows the continuing efforts over the past 10 years of the authors to discredi t the 349
Code and to promote their theoretical " best fit" formula
based on the results of tests whose details were largely withheld from the review of Committees 349 and 355 on clai ms
of proprietary information. This test data did not become
available to the committees until Dr. Fuchs brought the data
787
CC METHOD PREDICTIONS VS CAPACITY
(German Testing of Four Stud Anchors)
II)
.Q
1.4.-----.,--x--·
:----~------,----~,----~-----.------,----~
:§
-o
13
I
.
!
l
l
+
;
;
!
... -~··········· ....,
i
r: . . . . L. . . . . .
ct-o 1:2· :::::·::::::::::·::L.::·::.:::::::::r::::::::·::::: :r::::::::.:.::::·:.l::·:::::::::::
..:.:.::::.: :::: ......
I
I
_g
~
\
1.1
0
~
~
~
I
j
'
X
iX
AVG = 0.98
I
0.8
!
· ·················(··········· ····! ........ ... ................f..
I
!
!
l
i
· · · · · j· · t~ . i
0
50
~
l ·•
l •
-~
~
100
150
200
250
300
350
Out-to-out Distance of Anchors in mm
= 185 mm
he
I •
I
... .. ... j... ........)............... .... j,.,.........:.
' • ,
i
~ 0 .7 +---+-- ---=i;::__- +----+---tr-
I
.!..... ....
· · · · · · · · ···~ :t··· · ·!·· · · · · · ·~·· · · · ··./ STD: .01~ ....J••···········f ··············
I
0.9
I
•
he = 360 m·m x
t
·· j······
l
'
400
!
m
450
he = 67 mm
Fig. A - CC method predictions versus capacity (German testing offour stud anchors)
RATIO OF AVERAGE ANCHOR STRESS TO YIELD
(German Testing of Four Stud Anchors)
1 . 6 ,.----.---~----,---,---
'0
(j)
;
i
>=
1.4 ······ ··- ~-·--·---+ ................. jj.................!I ...........
g_
1.2
-o
(1)
·-·--t- ........
j
cr:
....
0.8
0.6
<(
0.4
~
i
.... . ........ 1 .................... ,.....•..........
--t- .......... ... t......... ......,..... :
. t ;~': JIL
(1)
(1)
YIELDt,.
•
_g
u
c:
~
i
!
.. ······ ·······j '"''' ....... ···t
i
i
1
;
. ·---·-·
····r············ ...•................ · ~.................
.'
L... ·········+·· ~··· ·+·· ········· ····!· ·
1
(/)
~
--··· ·-~·-··· .......... ....t··········;
!!
........ i. ... .
l:
················-~---····
l
i
(1)
I
I
!
•
i
.
·j
'
~
i
········+········ ·······i·············· ·i
+····
!
~~~; ~.;~
'-------.! - - - ----.-- '
......... +................... ,................... +...................,....................L ................. +..................!..................................... .
0.2
i(
0+---~--·---r----r----+----.---_,-----r----~--~
0
50
100
150
200
250
300
350
Out-to-out Distance of Anchors in mm
400
450
Fig. B-Ratio of average anchor stress to yield (German testing offour stud anchors)
with him when he joined the staff of the University of Texas
at Austin for a postdoctoral fellowship.
Relevant information conceming the applicability of tests
to accepted standards was not revealed along with the data,
nor discussed in the paper. For example, European
standards31 clearly state that the minimum stmctural thickness for testing anchms should be twice the embedment
depth of the anchor. Yet, the thickness of the slab used to test
the individual 525-mm embedments, shown in Fig. 21 , was
only 600 mm and so lightly reinforced that it was totally in-
788
capable of developing the cracking strength of the slab.
While the au thors admit the cracking of these slabs, they
continue to show these test results as "uncracked" concrete
and use them as a maj or point of argument agai nst the reliability of the 45 deg stress cone equation of ACI 349 for deep
embedments.
There is an old saying that "figures don't lie," that also applies to statistics. Statistical comparisons of apples and oranges are meaningless and statistical comparisons of lower-bound equation predictions with "best fit" data equations are
ACI Structural Journal I November-December 1995
CAPACITY OF 2 & 4 ANCHORS vs EMBEDMENT
ACITEMP2 MISCELLANEOUS TEST DATA
(/)
.0
c
0
u_
h:a
C/)
---
5
6
7
8
10 11
EMBEDMENT DEPTH in inches
c-=
4 ANCHORS
o
2 ANCHORS]
Fig. C-Capacity of two andfour anchors versus embedm.enJ (ACTJem2 miscellaneous test data)
meaningless as well. It should be obvious that such comparisons will always show the inability of the lower-bound
equation to predict the mean and correspondingly show increased variability with respect to the predicted mean. In addition, the reliability of statistical comparisons of anchor
tests is not dependent on the total number of comparisons
nearly as much as it is dependent on weighted numbers with
respect to embedment depths. The inclusion of Fig. 22
through Fig. 27 to graphically show these meaningless statistical comparisons can only be intended to mislead the reader.
The authors attempt to support their theory of "size effect"
by referencing fracture mechanics theory based on "in the
case of concrete tensile failure with increasing member size,
the failure load increases less than the available failure surface." There is definitely a "size effect" related to the pullout
capacity of headed anchors, but it is totally unrelated to any
decreasing ability of concrete, with embedment depth, to
transfer loads from the head of the anchor into the concrete,
as claimed by the authors. The size effect has to do with the
oversizing of anchors to assure a concrete failure, and its effect on the manner of load transfer from anchor to concrete.
Tests performed by TV A32 on mechanically anchored 1•/.-in.
grade 60 reinforcing b.ars under varying methods of surface
treatment clearly demonstrated that full-load transfer to the
head of the anchor only occurred at yielding of the steel. Prio r to yielding, patt of the cast-in-place headed anchor's load
was transfetTed through bond, with the amount depending on
load, ancho r size, and depth of embedment. The effect of
partial, rather than full , load transfer at the anchor head is a
reduction in the effective embedment resisting pullout and a
reduced capacity for given embedment.
The Prague test data, shown in Fig. 2 1, at embedment
depths of 150 and 450 mm (6 and 18 in.) had average anchor
stresses at pullout failure of the concrete of345 and 262 MPa
ACI Structural Journal/ November-December 1995
(50 and 38 ksi), respectively. The stress level of the 150-mm
embedment corresponds to yield, assuming the anchors were
composed of typical welded stud material. Please note that
the ACI 349 curve in Fig. 21 corresponds to the lower-bound
of the 150-mm embedment data and the center of the 450mm embedment data. These tests were performed with test
span and block size correlated to anchor size to preclude any
effects of the size of structure on pullout. From the previous
information, it is reasonable to expect that yielding of the
steel, prior to failure, would increase capacities of the 450mm embedments if sized for ductility.
Fig. 25 through 27 are clearly misleading and were intended to show the 349 Code as being unconservative. I do not
understand why there would be a different number of castin-place tests of headed anchors for the ACI 349 and CC
method comparisons in Fig. 25. I have all of the test data.
Apparently, the 32 quadruple anchor tests for the CC method
are those listed in the ACI data bank as Tests GER7-0l
through GER7-32. Fig. A is a plot of that data as a function
of distance between outermost anchors with the differences
in embedment indicated by symbols. Fig. B is a plot of the
same data as a function of average anchor stress divided by
the reported yield. Again, note that the average stress level is
substantially below yield at pullout failure of the concrete.
Fig. C is a comparison of all two- and four-anchor test data,
with respect to embedment depth for both headed and undercut
anchors, with anchor spacing sorted from the largest to the
smallest for the prediction graph of equations to proceed from
the smallest to the largest from one embedment to another. It basically shows the increasing conservatism of the CC method
with embedments greater then 6 in. Of special interest is the 14in. embedment test that falls below CCD predictions. These are
the same 360 mm tests shown in Fig. A. I assume the explanation must be structural, rather than the spacing of anchors, since
789
Table A- Comparison of
Spacing,
mm
No. of
studs
ceo with ACI349 and Section 11.11.2
ceo
Cap, kN
Design, kN*
ACI 349
Design, kN ·r
Cap, kN
Section 1 Lll.2
Design,
Cap, kN
kN'~'
-
-
2 19
-
-
346
-
-
385
-
-
-
-
734
440
-
-
863
518
822
-
-
1056
634
821
782
-
-
1055
633
-
-
994
1274
956
-
-
1178
596
' 707
1349
1012
-
-
1227
736
100
4
267
200
290
150
4
4
309
23 1
365
270
423
317
400
4
567
425
577
642
450
16
690
518
555
16
842
632
711
16
1096
711
740
36
1094
9
1043
810
16
850
36
174
'¢> = 0. 75 m accordance w1lh ACI 3 J8. Chapter 22 recomrnendat10ns.
t¢> =0.60 in accordance with author'; recommendations to ACl 349.
Table 8-Embedment requirements for ductile anchors in 3000 psi concrete
Cracked, in.
One anchor
8.00
9.00
7 00
8.00
7.00
800
Two anchors
!US
10.25
8.00
10.00
9.00
J LOO
Four anchors
10.25
12.50
10.00
13.00
12.00
20.00
1wo 16-m. edges
One anchor
Two anchors
Four anchors
.. .
8.00
9.00
7.00
8.00
7.00
8.00
8.75
10.25
10.25
8.00
10.00
10.00
9.00
14.00
13.00
22.00
37 .00
12.50
One
8-111.
and one 24-ln. edge
One anchor
8.00
9.00
7.00
9.00
8.00
11.00
Two anchors
11.00
11.25
8.00
12.00
13.00
20 .00
Four anchors
11.00
14.25
10.00
19.00
26.00
40.00
One 4-tn. and one 24-m. edge
10.00
12.75
12.00
16.00
9.00
12.00
12.00
17.00
11.00
16.00
25 .00
Four anchors
12.75
16.00
17.00
23.00
30.00
44.00
the significantly higher undercut anchor tests at the 11.25-in.
embedment had identical spacing.
The described data plots of Fig. 26 as "mean value of a series" also appear to be misleading. Most of the plots appear
to be that of individual tests, and the mean value of the 4-anchor plot does not appear to come from the data of Fig. A In
my search of the ACT data bank, I could not find any 36-anchor tests listed, and I could only find three 16-anchor tests
at 561-, 711-, and 810-mm spacings. The 711 -mm spacing
conesponds closel y with the plotted 36-anchor tests, and
CCD method predictions are not affected by the number of
anchors. The data bank indicates 22-mm (7/,-in.) diameter
studs. If so, the average anchor stress of tJ1ese thre e tes ts are
29.5, 36, and 54.5 ksi, increasi ng, respectively, with the outermost spacing. Note the significantly higher pullout capacity of the higher stressed anchors witb respect to predictions.
The same size anchors at the lower 400-mm spacing will
have yet a lower average stress.
The incorporation of multiple rows of interior studs into an
anchorage transforms the stiffness of the concrete within the
790
14.00
One anchor
Two anchors
zone of the anchorage in much the same way as an embedded
plate attached to the anchor heads. Under these conditions,
the anchorage is more prone to act in a manner similar to that
of an embedded plate and should be designed for the shew:
strength of the periphery by using he as d under the special
provisions for slabs and footings, Section 11.11 .2. This has
the effect of subtracting w·ea S, • Sy from Eq. ( 1) in determining pullout capacity.
Table A provides a comparison of Section 11.11 .2 with the
CC method for the test data of Fig. 26. Please note the close
comparisons of the capacities for the multiple rows of studs
between the CCD and Section 11.11.2 predictions. Based on
the number of low tests in Fig. A, the design c)> for nonductile
headed anchors should probably not be more than 0.5.
1 believe 1 have spent enough time defending ACI 349-85
for now. Upon receipt of ACI 318's proposed Chapter 22, I
wrote a two-part paper32 entjtJed "Straight Talk about Anchorage to Concrete," which was recently published in the
September-October 1995 ACI Structural Journal , and I have
created a computer prog ram . Both U.S. and metric versions
ACI Structural Journal I November-December 1995
are identical and are supplied as a unit. The program's default
option is the 349 Code and it contains all of the proposed
/changes that I have made to Committee 349 to correct existing problems for incorporating the design of different types
of expansion anchors and other nonductile designs into the
code. For comparisons, the program contains the CCD .option, a variable stress cone option based on a "best fit" equation varying individual capacities on the basis of embedment
to the 1.7 power, a CCD approach using the same equation,
and a CCD option in which all of the components of the basic
equation can be changed.
The basic problem with the CCD approach for practical
design is that it is mostly limited to nonductile fixed depth
embedments generally less than 10 in. For the design of ductile anchorages, there is nothing simple about the procedure,
primarily because every aspect of the calculated capacity
changes with embedment depth.
The CCD option is clearly not suitable for the design of
ductile anchor systems. Under certain relationships of anchor size, cracke,d condition of the concrete, spacing of anchors, and edge distances, the embedment requirements
become excessive. This does not necessarily involve large
high-strength anchors. For example, this is shown in Table B
for l-in. bolts spaced 9 in. on center. It is clear from Table B
that with decreasing edge distances, the two- and four-anchor grouping of CCD becomes more and more conservative
with respect to Appendix B; to a lesser degree so does CCMV AR. While there is no substantiating test data to prove or
disprove the edge effects on groups, there is plenty of test
data to substantiate the correlation of the original Eligehausen equation (with modifications for determining the 349-85
embedments) on the effects of edge distance on individual
anchors. I have also studied the ACI data bank on shear and
repm1ed my findings to the working group of Committee
349. I found that the vast majority of tests, pelformed on
shear in Europe, were pelformed on relatively shallow embedments of nonductile tensile anchorages and that breakout
shear capacities were basically controlled by the tensile
strength of the anchors against pullout. For cast-in-place anchors, it makes very little sense to use nonductile anchors to
transmit shear.
REFERENCES
30. Beseler, Jan W., and Siddlqui, Faruq M. A., "Computer Concrete Pullont Strength ," Concrete Jncernationol , V. I 1, No.2, Feb. 1989, pp. 62-64.
31. UEAtc, "Directives for Assessment of Anchor Bolts," M.O.A.T. No.
42, European Union of Agreement, British Board of Agreement, Watford,
UK, Dec. 1986.
32. Cannon , Robert W., "Straight Talk about Anchorage to ConcreteParts I and II," ACJ Structural Journal, V. 92, No. 5, Sept. -Oet. 1995, pp.
580-586. Also, ACJ Struci/JraJ Journal, V. 92, No.6, Nov.-Dec. 1995, pp.
724-734.
By LEROY A. LUTZ
FAC!. Milwaukee, WI
This is a very informative article on anchorage behavior
and on explanation of an analytical procedure to predict tensile and shear capacity for anchors. I had previously examined the proposed ACI Code provisions developed earlier
based on using the CCD method. I found that several of my
ACI Structural Journal I Novem ber-December 1995
questions developed from that examination of the CCD
method have been answered in this ar1icle.
My initial concern related to the fact that the original equation for tensile capacity of a section of limited size indicated
that a lesser capacity was calculated for a deep anchor as
compared to a shallow anchor. This occurred because the
while the
nominal stress decreased in propor1ion to 1/
area of the failure cone was constant when it encompassed
the entire concrete cross section. This concern was addressed
by the expansion of the definition of her used in Eq. (1 0) so
that the value of h 4 used in the equation was limited by the
maximum edge distance. To be more con-ect, the reference
for use of the newly defined h~r should include Eq. (9), as
well as Eq. (lOb) and Eq. (lOa) to assure that the same heris
used in evaluating N,., in Eq. (9).
. A similar concern with the calculated shear capacity of anchors with large edge distances in the direction of the shear
force was addressed by the expansion of the definition for c 1.
However, this definition is complex. It took some effor1 to
understand this definition when it was first encountered.
I believe that a more straightforward approach to handle
this situation would be to create a new variable c that differs
from c 1. c 1 would be the actual edge distance; c would be defined as max(c2max•h) :S: 1.5c 1, the governing perpendicular
edge distance.
Jh:;,
Then
1jf5
= 0.7 + 0.3c2mu,lc;
1jf4
c2
is actually c2min
= 11(1 + e //c)
and
since the defined c was indicated as being applied to all components of Eq. (13a). Since variable c represents the dimension perpendicular to the anchor, the 1jf4 and 1jf5 expressions
become simpler without a 1.5 factor. As noted in the definition, the shear failure load may be independent of the actual
edge distance c 1•
This approach of defining the governing effective distance
with a different variable name could also be used for the anchor in tension. For example, the actual anchor depth could
be identified as h0 , while hercould be retained as the effective
·
anchorage depth.
Even with this change, the use of Eq. (10) and (13) would
be easier to apply and visualize conceptionally if the expressions were rewritten simply in terms of a stress times an area.
This is done in ACI 318-89, Chapter 11 in the evaluation of
the various shear force limits and in the evaluation of anchors using ACI 349. If the user is performing a hand calculation using Eq. ( 10) and (13), less computation is necessary
if NnJAno are combined into a simple axial stress term, and
Vn)Avo are combined into a simple shear stress term. The
present format is of little benefit to the designer.
On another matter, I was glad to see that a specific provision for shear capacity parallel to an edge was presented.
This allows the designer to take advantage of the extra ca-
791
pacity as compared with load toward an edge. It appears that
one must simply calculate V,.l and then multiply by 2 to obtain V11 11· However, one should be aware that one can calculate Vn using Eq. (13a) for a single anchor near a corner for
shear toward each of the two faces. By doing this and varying the relative distance to the two faces, one will find that
the relative capacity in the two perpendicular directions continues to increase as the ratio of the two edge distances increases. These results indicate that the factor of 2 previously
noted cannot be substantiated by the Vn calculations. Maybe
a limit needs to be applied to the shear calculation for the
corner condition, perhaps by using a further redefinition of
Ct.
One item of importance to designers that was not addressed by the authors is a recommendation on evaluating
the shear capacity of anchor groups where aU anchors do not
have the same edge distance. The commentary to the proposed ACI Code provisions developed earlier suggested that
all anchors share the total Load equally. This was identified
as the "elastic distribution," where the capacity of the weakest anchor controls the group's capacity.
This approach does not necessarily give the "strength" of
the group, but may be just the load where initial failure occurs and load redistribution begins. The current procedure
for anchor groups in the PC! Design Handhoo/2 or in Section 1925.3.3 of the UBC Code, 33 where the capacity of the
anchors away from the edge is considered, is a definite improvement for group capacity evaluation.
Admittedly, one anchor's failure may influence the capacity of an adjacent anchor, but the designer needs a procedure
that will give a reasonable strength value for all situations. A
very common situation, that of four anchors in a 2 x 2 pattern
in the top of a rectangular pier, should be addressed properly,
not in an overly conservative manner.
REFERENCES
33. Unrform Budding Code , V. 2, Intemalional Conference of Building
Officials , Whittier. CA, 1994.
By RICHARD S. ORR
Member ACI. Advisol )' Eng ineer. Westinghouse ElecJric Corpora1io11
The paper on fastening to concrete provides an excellent
background for the consideration of code requirements for
fasteners. As chairman of the ACI 349 subcommittee responsible for the steel embedment requirements, I would like
to share the results of some of our subcommittee activities in
this area. A task group of Committee 349 bas been reviewing
the test data that is the basis for the recommendabons given
in the paper. It includes a large amount of data that was not
available when ACI 349, Appendix B was first developed in
·the mid 1970s. The task group has not yet finalized their recommendations, but a number of issues have been discussed.
Single anchor capacity away from free edge
A key difference of the concrete capacity method relative
Lo ACI 349, Appendix B and other industry standards is the
variation of capacity with depth. Our review of the test data
shows that a variabon to the power of 1.6 or l.7 provides a
good fit to the test data. This power is important to the design
capacity of deep anchors. Tes ting of deep anchors is expen792
sive and, therefore, the majority of the test data is for relatively shallow anchors. Both the concrete capacity method
and Appendix B are adequate for embedments up to about 10
in. However, th~ design capacity equations also need to be
reasonable when used for very deep embedments.
Extrapolation of the equations to 3-ft-deep anchor bolts results in the concrete capacity method giving a capacity about
one-half of that predicted by Appendix B. Such a deep embedment should also have a capacity that is reasonably consistent with the capacity calculated as if it were a column
load on a slab. The requirements of ACI 349 Appendix B
parallel the requirements of ACI 318 Paragraph 11. 12.2.1 for
shear in slabs and footings. The shear strength is based on an
effective shear stress in the concrete of 4
acting on an
area b 0 d. This area is based on the shear periphery at a distance from the face of the column proportional to the depth
of the slab; thus, the shear capacity of a slab increases as the
square of the depth of the slab for a small bearing area. The
paper argues that the difference in predicted capacities is due
to a size effect that bas also been observed in shear tests on
beams. Committee 349 is hesitant to make changes to the basic principle of the 45-deg cone that is also the basis for other
provisions of the code unless the test data fully supports that
such revisions are necessary.
JJ:',
Single anchor close to free edge
The provisions in ACI 349 were based on very limited
testing available at the time that ACI 349 was published. Our
review of the recent test data confirms the findings of the authors of the paper. Proposed revisions are being developed
for ACI 349 for anchors close to a free edge.
Group of anchors
The paper recommends that the spacing between anchor
bolts should be 3hef to assure full capacity of each bolt. This
constant value of 3he; has been selected for simplicity. Test
data suggests that the spacing may be higher for shallow anchor bolts but may reduce to 2 for deeper anchor bolts. This
spacing of 2hef for deep anchor bolts .would be consistent
with the 45-deg cone that is the basis of ACI 349. Use of the
3he; spacing is another severe penalty for design of deep anchor bolts.
The paper proposes an approach for small eccentricities of
load. This should be treated as a special case of axial pius
.flexural loading. An ACI 349 committee report has been
published with design examples showing a method similar to
that used for reinforced concrete cross sections to calculate
the anchor bolt loads for a group of anchors under combined
loads. It is believed that this approach is more rational than
that proposed in the paper. However, it needs to be expanded
by additjonal testing to show the increase in capacity of the
concrete due to the compression reaction from the flexural
loads.
The paper proposes that edge effects for groups are considered by reducing the capacity of the full group in proportion to the reduction in capacity of the anchor closest to the
edge. This proposal appears overly conservative. Unfortunately , there is little published test data to improve on this'
recommendation.
ACI Structural Journal I November-December 1995
Design friendliness
., The paper argues that the Concrete Capacity method is user
'friendly and highly transparent. This may be true for the textbook examples sho wn in the paper but it is less true for real design situations, such as cases of adjacent embedments with
different depths of anchor bolts, or nonrectangular gro ups of
anchors. It is essential that any design method be sufficiently
close to the expected physical behavior so that the design engineer may make design interpretations for the unusual cases.
The 45-deg cone has been the basis for many successful past
designs and should not be eliminated too hastily.
Miscellaneous
The paper treats undercut anchors the same as other expansion anchors. The U.S. data fo r undercuts shows that
these anchors have capacities more similar to headed studs.
The difference between the U.S. data and the European data
is still being evaluated but may be dependent on design details of the proprietary anchors.
Fig. 21 shows the ACI 349 prediction of concrete breakout
data superimposed on the test data. This requires an assumption on the head diameters. This assumption should be
spelled out.
By PHILLIP J. IVERSON
Technical Director; P recast/Prl!.sr.ressed Couctt'lC brslitufe
The authors have presented an important contribution to
the development of "code rules" for the design of anchorages
to concrete. The development of the Concrete Capacity Design (CCD) approach is fundamentally based on the extensive research conducted at the University of Stuttgart under
the direction of Dr. Eligehausen. The European equivalent of
the CCD method i,s the Kappa method.
Because this paper is a code background paper, it concentrates on the behavior of anchors. All types of anchors are included in this discussion, including headed studs, embedded
bolts, coil loops, undercut anchors~ and a variety of other
post-installed torque and displacement controlled anchors.
In other words, the empirically developed (althoug h now
verified analytically) formulas are best fit equations of m any
data sn bsets. These formul as also apply to anchors over a
broad range of concrete compressive strengths and embedment depths. It is encouraging that the many different anchor
types, compressive strengths of concrete, and embedment
depths can all be generally g rouped together under one behavior model for failure of concrete.
The Precast/Prestressed Concrete Institute is also pleased
that the CCD model is pictorially very similar to the current
PCI design approach for groups of headed studs. The authors
have taken this user-friendly picture and developed it into a
highly transparent behavior model for anchorage to concrete. At PCI , there is an ad hoc task gro up reviewing the database used fo r the author's paper. The task group's prim ary
interest is in anchors used most often in the precast concrete
industry, that is, the behavior performance of welded, -headed studs that have embedment depths Jess than 8 in. (200
mm). Thro ugh the ad hoc task group's studies, some observations and several opinio ns have been formed regarding the
behavioral equations. The issue of capacity reduction factors
ACI Structural Journal I November-December 1995
for design is reserved for the code committee discussion;
PCI would like to express irs opinions on "design" equations
based on its experience during the last 25 years of using information available in the PC! Design Handbook. Following
are opinions the ad hoc group believes are appropriate to
share with the discussion readers and authors:
I. As described, the data from which the CCD method was
derived is a collection from various tests on a variety of different anchorage conditions, many of which have their own
unique failure mode but which can be generally characterized by a concrete cone-type failure. Each famil y of data
does have its own statistical characteristics that may be diffe rent from those of the entire database. Specific interest
gro ups, like PCI, should look at the data applicable to their
situation and analyze the results for comparison to the generalized CCD method and to existing recommendati ons.
2. Based on o ur limited anal ysis of the database, it seems
that for single-headed studs with effective embedment
depths of 3 to 8 in., the PCI Design Handbook recommendations, the ACI 349 method, and the CCD method all can predict performance with acceptable accuracy. What this
implies is that the calculation model used for this situation is
not very sensitive to the assumption of the slope of the concrete failure cone. The authors' Fig. 21 with htrbetween 100
and 200 mm illustrates this point.
·
3. The autho rs' desire to have a behavior model that covers
the very short effective embedment case through the very
long effective embedment case is ambitious and, fo r many
practical design cases, unnecessary. Headed studs of 500
mm (20 in.) in length are rarely, if ever, used in our industry.
Our producers would most likely use a bent or hooked deformed bar anchor to achieve the higher capacities necessitated by large embedments.
4. For headed studs, the difference between the 35- and 45deg slope of the fa ilure cone has the most impact on the edge
and spacing effect situations. Anchorages close to edges are
a common application in our industry. The amo unt of test
data available on headed stud anchorages to evaluate edge
distance effec ts, however, is minimal. For single studs in tension, there are 25 data points closer than hef to an edge. For
group studs in tension, there are 8 data points closer than hef
to an edge. We believe further research and study into the often used "edge effect" situation is needed before we can develop design confidence in the CCD method.
Another very common application in the precast industry is
grouped headed studs in tension and in shear or their combined
effects. From Table 5 we find that only 35 tests points are available for the tension situation. We have not been able to access
anchorage group data for headed studs in shear. Our need for
further study or research into this application is also clear.
5. Although an effort has been made to no rmalize the failure loads to f/ =25N/mm2 (f/ = 3070 psi), our study of the
data provided indicates that a majority of the headed stud
tests were conducted in concrete wi th compressive strengths
of less than 3000 psi and many were less than 2500 psi. In
the precast concrete i ndustry, this would be considered very
low-strength and not very typical of the strength when our
anchorages must perform. The more typical and consistently
available strength would be 5000 psi. A research program is
793
underway at the Graduate School of Florida Institute of
Technology entitled "Tensile Behavior of Embedment Anchors in High-Strength Concre te" by Eric Primavera. The results of that program should provide us with more insight on
the effect that higher strength concrete has on headed stud
anchorages.
6. There are many discussions that need to take place prior
to the application of the CCD method's "design recommendations," as alluded to earlier. Some of the points PCI would
have comments on are listed below:
a. Cast-in anchorages have more consistency and reliability than post-installed anchorages. Appropriate recognition
of this fact should be acknowledged.
b. Is it proper to assume no plastic action for an anchor
group?
c. Is the 5-percent fractile of the complete database appropriate for a special anchor like the headed stud? The code
commi ttee has tended to take the lower-bound value for design. Is the 5-percent fractile low enough?
d. Were all of the tests in the database pelformed in the
same manner so that they can all be considered a set? There
are many test variables that can affect pullout capacity, such
as rate of pull, and it would be interesting to review the test
setup information for each group of data.
e. We understand that a design code would want to have
generalized equations applicable to any situation. We question whether the design community would really want one
equation to apply to aU of the design situations described. In
the future, won't each of the indnstries, manufacturers, and
users of the wide range of applications covered be constantly
trying to infJuence this general procedure with new test results and special considerations for capacity reduction factors? The allowable stress method using manufacturers' data
has worked reasonably well , although the aUowable stress
approach is not consistent with current code philosophy.
f. Most real-world applications result in some combination
of shear and tension; for example, a simple shelf angle
bracket. This paper makes no recommendations for this interaction situation, although we believe information is available fo r that equation.
g. Are there other privately held data that can contribnte to
the database?
7 . Is the conversion factor for cube tensile strength and
cylinder tensile strength printed immediately before Eq. (3)
correct? We would have assumed the 1.1 8 factor to be inside
the radical.
This contribution by the auth ors adds significantly to the
knowledge available on the subject of anchorage to concrete.
The predictability of the single cone tension fail ure should
greatly add to the designer 's confidence. However, the paper
and the research seem to clearly point to the need to better
understand both edge effects and gronps of welded-headedstuds, as well as groups of other types of anchorages.
In an effort to answer some of the questions that the University of Stuttgart research and the publication of "Concrete
Capacity Desig n (CCD) Approach for Fastening to Concrete" by Werner Fuchs, Rolf Eligehansen, and John E.
Breen have brought to the forefront, PCI has initiated two research programs on the subject of anchorage to concrete. The
first will be a small pilot program on groups of headed studs
794
that we hope will give qmck insight and direction to a more
extensive program administered by our Research and Development Committee.
AUTHORS' CLOSURE
The authors were pleased that their article received the considerable interest evidenced by the fairly lengthy discussion.
Since several of the discussers referred to conflicts with the anchorage requirements of Appendix B of ACI 349, "Code Requirements for Nuclear Safety-Related Concrete Structures,"
and since the authors compared the CCD approach with the ACI
349 provision in the article, it is important to recognize that the
authors' proposal for the. CCD approach is as a prutial basis for
..a code proposal for ACI 318 "Building Code Requirements for
Structural Concrete."
It would seem to the authors that these general building
code requirements should generally be less conservative
than the requirements for nuclear-re lated stru ctures that
would have higher consequences of failure. It is not the authors' intent to ask ACI 349 to abandon a philosophy of precluding brittle failure modes in sttuctures that are of
importance for nuclear safety. Nor is it the authors' intent to
tell experienced nuclear designers and the nuclear regu lators
what the proper safety level is for nuclear-related fastenings.
In fact, in many applications in general buildings, the designer m ay wish to design ductile fastenings. The improved accuracy of the CCD approach, illustrated in the comparisons
in the paper, allow a designer to assess more accurately the
concrete capacity of the fasteners. If the designer so chooses,
the fasteners or, more logically, the attachment can then be
designed as a "dnc tile fuse" to govern the failnre and impart
the desired ductility to the systems.
In several of the discussions, fairly lengthy comments are
provided regarding material contained in the 318 proposal, 13
but they are not actually addressed in the paper being discussed. For the benefit of jo urnal readers not having access
to that committee document, we wonld point out that the
code proposal first presented a general performance requirement fo r fas tening to concrete and indicated that any procedure that showed acceptable agreement with.comprehensive
tests could be utilized. The specific code language was patterned after the existing provisions that allow the designer to
use any acceptable stress block in flexural analysis that gives
agreement with comprehensive test results. The well-known
rectangular stress block is only a "deemed to satisfy" approach. The Code proposal then indicated that a specific approach based on the CCD procedure of this article, modified
by inclusion of fac tors for concrete cracking and for adjusting the basic eqnations of the present article to a five percent
frac tile, would be " deemed to satisfy" the general requirements. This procedure has not yet been adopted by ACI
Committee 318. The current discussion will be useful in future revisions and in the debate of that proposal. Proponents
of existing design procedures, like the ACI 349 procedure4
and the PCI procedure,5 should recognize that those procedures would be admissible for use in any range where comprehensive tests show that they meet the general
requirements.
ACI Structural Journ al I Nove mber-December 1995
RESPONSE TO ROBERT W. CANNON
In the authors' paper, the provisions of ACJ 349-85 and the
dtD method for predicting the fastening ,capacity of concrete breakout failures in uncracked concrete are compared
with a large number of test results. To facilitate direct comparison with test results, the capacity reduction factor <l> of
ACI 349 and partial material safety factor Ym of the CCD
method are both taken as 1.0.
Mr. Cannon apparently misunderstood the authors' mention of the 5-percent fractile under "Design Procedures." As
clearly indicated in the text of the article, CCD equations
representing the average.or mean of the behavior, as given in
this article, were subsequently reformulated with changed
coefficients to represent five percent fractiles for consideration by ACI Conunittee 318. His objection to the 5-pen.:ent
fractile is really not germane to the present article. However,
his insistence on a design philosophy based upon " time honored ... lower-bound test results" is neither practical nor
consistent with the ACI 318 Building Code, where concrete
and steel properties and nominal resistance expressions do
not represent absolute lower-bounds.
Mr. Cannon claims that the ACl 349 equation is basically a
lower-bound equation for the concrete cone failure load. If this
is correct, then the ACI 349 related ratios Nu tes/N, predicred or
Vu tes! Vnpredicted• respectively, should be~ 1.0 for all test results and certainly ~ 1.0 for averages. As can be seen from Fig.
2 1, 25, 26, 29, 32, and 33, this is not the case. To show this in
more detail, in Fig. D , the ratios Nu cest to Nn predicted for single
fastenings with headed studs embedded away from a free edge
are plotted as a function of the embedment depth. Fig. D(a) is
valid for ACI 349 predictions and Fig. D(b) is valid for the
CCD method. Note, while in Fig. 21 the prediction by ACI
349 had been plotted with the assumption d,/h~r = 0 [compare
Eq. (2)], in Fig. D(a), the actual size o f the head has been taken
into account for calculation of the failure loads predicted by
ACI 349.
Fig. D(a) clearly demonstrates that the ACl 349 equation
is a lower-bound of the test results for only the smallest embedment depths. Even with he/around 75 mm (3 in.), some
test results are well below this "lower-bound." The expression has become a fractile, statistically. For larger embedment depths, even the average capaci ties are significantly
lower than the predicted values. In contrast, Fig. D(b) shows
that the CCD method is much more of an average capacity
predictor for the total ran ge of embedment depths with good
accuracy. By using the 5-percent fractile (Nu, 5 % "" 0.75 N,.)
in design, one does, in fact, get a practical lower-bound of
the test results (see Fig. E). However, th.is bound is based on
·
a clear statistical meaning.
In the CCD metbod, the projected areas of any fastening
loaded in tension or shear ca n be easily calculated with rectangular areas. In contrast, the calculation of the projected areas
in the ACl 349 approach is rather complicated (compare Fig.
7 and 8 to Fig. 11 and 17).
To overcome this problem, Mr. Cannon proposes a simplified equation [Eq. (A)] to calculate the proj ected areas of anchor g roups loaded in tension. T he derivation of this
eqvation is unclear to the authors. It certainly is not a transparent model. It can only be a rough approach when compared to the many possible applications occurring in practice
ACI Structural Journal I November-December 1995
(see Fig. 7). His suggestion that designers should rely on
computer programs and design chm1s seems to be a poor
substitute for clarity and transparency.
Mr. Cannon claims that in the Stuttgart tests, with deep
headed studs [h~r = 525 mm (20.6 in.)], the member depth
was too small and the reinforcement was insufficient to precllude a structural failure of the concrete member. He suppot1s his opinion hy referring to European test standards. 31 It
should he pointed out that the UEAtc directive referenced is
only valid for expansion anchors that create rather high expansion and splitting forces. Therefore. a minimum member
depth h- 2 hef is required to preclude a splitting failure . Because the splitting forces o f headed studs are approximately
only one-third of the value valid for expansion anchors for
the same magnitude tensile loads, the member depth for
headed stud tests can be much smaller than 2 her ln some of
the Stuttgart tests, radial cracks appeared at the surface of the
test member just before reaching peak load. The radial
cracks were kept very small by the existi ng stmctural surface
reinforcement. Because o f the state of stress in the concrete
member, the cracks did not penetrate very far into the slab.
Therefore, they did not significantly influence the stresses in
the load transfer zone of the anchor and, thus, the concrete
cone failure load. In contrast, when tests are performed in
cracked concrete. the anchors are located in a crack with a
defined width over the complete embedment depth from the
start of the anchor location.34 This effect of such cracked
concrete was specificall y addressed in the proposal submitted to ACl Committee 3 I 8. 13
Mr. Cannon claims that Fig. 22 through 27 can only be intended to mislead a reader because he states that a comparison of the test results with the ACT 349 prediction will
always show the inability of the (claimed) lowest-bound
equation to predict the mean and will show increased variability with respect to predictions. This statement is incorrect
with respect to the ·variability if the prediction equation correctly takes into account all influencing parameters. This can
be seen from Fig. E , in which the same test results were used
as in Fig. D. However, the measured failure loads are compared not with the mean, but rather, with the five percent
fracti le of N,, predicted by the CCD method [Nu, 5 % = 0.75
N., Eq. (9a)]. The variation coefficient of the ratios Nu 1es/N"
prediction is the same as in Fig. D (b).
Mr. Cannon attacks the authors' introduction of a size effect
utilizing fracture mechanics theory by an extraneous discussion
of the decreasing ability of concrete to transfer loads from the
head of the anchor into the concrete. T he statements regarding
the limits on head bearing stress are in a separate paragraph in
tl1e original paper following the two paragraphs regarding size
effect. He apparently misinterpreted the statement.
Numerous experimental and numerical investigations
(e.g., References 35 through 37] have shown that concrete
structures in the size range encountered in practice are subjected to a size effect if there is a strain gradient and the failure is caused by overcoming tJ1e concrete tensile' capacity.
Since tl1e strain gradient for fastenin gs in concrete is very
large, the size effect is max imum.
Generally speaking, in the Stuttgart and Prague tests, 21 the
anchors were designed not to yield at peak load to prevent a
steel failure so that the concrete capacity could be deter795
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mined. To insure a full load transfer to the anchor head, the
anchor shank was thoroughly oiled. Therefore, the effect of
bond between anchor shaft and concrete on the test results
was negligible. This is a distinct contrast to his reported test
of mechanically anchored deformed reinforcing bars.
Mr. Cannon indicated in the discussion of this article
which he originally submitted that there was a discrepancy
between the data reported in the article and the data on aversion of the authors' database, which he had obtained from a
source other than the authors. The authors then immediately
sent directly to Mr. Cannon a new diskette with the complete
database. This database includes 35 German and US group
tests with quadruple fastenings. He then revised his original
discussion but still indicates he found only n = 32. The authors do not understand why he did not find n = 35. Then =
35 points were used in the comparisons in Fig. 25. Unfortunately, this figure contained a typographical error in the legend for the ACI 349 comparisons It indicated n = 32, but
should have indicated n = 35 as was shown for the CCD
method.
Mr. Cannon's revised Fig. A is con·ect for n =32 but not n
=35. However, even for the subset n = 32, his Fig. A shows
that the CCD method is a reasonable predictor of the mean
behavior with quite acceptable scatter around that mean. In
Fig. F, the ratios of measured failure loads of quadruple fastenings (n = 35) to the failure load of a single fastening, as
predicted according to Eq. (9), are plotted as a function of the
ratio of spacing to embedment depth. The test resultS scatter
around the solid line and give the capacity predicted by the
CCD method. As shown, maximum group capacity is
reached for s 3hep In Fig. G, the ratios of measured failure
loads to values predicted by the CCD method are plotted in
a histogram. The average value is X= 0.99, with a coefficient of variation V = 13 percent. In Fig. H, the same test data
are compared with the ACI 349 prediction. These figures
clearly demonstrate that ACI 349 is unconservative, especially for spacing s/h~r> 1.5.
ln Fig. B, Mr. Cannon shows that in most of the tests, the
stress in the anchors at failure was below yield. As previously discussed, this was purposely intended to reach a concrete
cone failure. Again, the shanks were thoroughly oiled to insure the load transfer to the anchor head. Tests that yield before concrete capacity is developed are not useful in
developing theories for concrete failure.
Cannon's Fig. C is a comparison of all two- and four-anchor test data with headed studs and undercut anchors. He indicates that it demonstrates the increasing conservatism of
the CCD method for embedment depth h,r> 150 mm (6 in.).
That statement is indefensible when one compares the relatively close agreement in Fig. C with the lower point at the
ll-in. embedment depth and all of the points with embedment depth above ll in. For the points with the greatest embedment, even the CCD predictions are unconservative and
the four (Ae) predictions of Mr. Cannon are greatly unconservative.
Most of the tests with large embedment depths were performed with undercut anchors at a single construction site of
a nuclear power plant and were described in Reference 28.
Concrete for the test specimens was made from crushed, ,
hard aggregate, with a maximum aggregate size of 30 mm
796
=
ACI Structural Journal I November-December 1995
(1•/, in.). O n the contrary, in most of the other tests, natural
·, round aggregates with a maximum size of 16 mm (s/s in.)
· were nsed. It is well known that the concrete tensile capacity
significantly increases with increasing maximum aggregate
size and is mnch higher for cmshed, hard aggregates than for
natural round aggregates.38•39 "Therefore, these test results
cannot be taken as representati ve for the ordinary concrete
often used in the building construction industry. If the influence of special concretes is to be considered in design, it
seems more reasonable to increase the basic computed concrete cone capacity by use of a correction factor. Corresponding research to determine such factors is underway.
All of the test res ults used in Fig. 26 have been reported to
ACI 349, Subcommittee 3. For reasons unknown to the authors, all of the results with groups of more than four anchors
are no t contained in their database. As explained, the anchor
shanks were thoroughly oiled to minimize bond between anchor shaft and concrete.
As shown in Fig. 26, the CCD method reasonably predicts
the concrete con'e failure loads of large anchor groups independent of the number of anchors and the spacing between
the outermost anchors. Mr. Cannon proposes the use of two
different models : 1) the cone model for quadmple fasten"
ings; and 2) the punching shear model for groups with more
than fonr anchors. Fundamentally, punching shear behavior,
shown in Fig. l(a), is completely different from the cone
pullout failure shown in Fig. I(b). With flat slabs, the punching shear failu re load depends significantly on the strength of
the compression ring around the column.40 The use of two
different models for calculating the failure load for a concrete cone failure mode is very confusi ng.
In the punching shear model, the height of the compression
ring is governed by the reinfo rcement ratio of the bending reinforcement. In contrast, the concrete cone capacity for fastenings depends on the concrete tensile capacity and is not
influenced ve1y much by the area of the bending reinforcement.8 For these reasons, the punching shear equations of ACT
3 18 or ACI 349, respectively, should not be generally used for
the calculation of the concrete cone capacity of fastenings.
The satisfactory agreement between the values calculated according to the CCD method and ACT349, Section 11.11 , presented in Cannon's Table A, are a mere confirmation of the
general usefulness of the CCD method. However, the punching shear values should not be relied on because they could be
affected by changes in the fl exural reinforcement.
The CCD method predicts the concrete cone capacity with
sufficient accuracy for practical purposes, as shown in the
paper. Mr. Cannon complains that the CCD method is
"clearly no t suitable for the desig n of ductile anchor systems." When desig ning for ductile fas tenings, the concrete
cone capacity mnst be larger than the steel capacity. The resulting required embedment depths are given in Mr. Cannon's Table B. Because of the different assumptions in the
models, the required embedment depths calculated according to the CCD method certainly may be larger than those
calculated according to ACT349. T his is especially valid for
quadruple fastenings. Note, however, that ACl 349 is often
unconservati ve for large embedment depths and for anchor
groups (see Fig. 2 1, 25, 26, 29, and 32). T herefore, the com-
ACI Structural Journal I November-December 1995
15
n = 35
X= .99
v = 13.0 %
10
..----
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"--'
1::
5
0
0,4
0,0
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·~ · I
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sl lhef
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a)
b)
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~f
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Fig. I
797
parison in Table B does not show that the CCD method is not
suitable for tbe design of ducti le anchor systems. In reality,
it demonstrates that anchor groups designed according to an
unconservative ACI 349 may not fail in the ductile manner
anticipated, but by a brittle rupture of a concrete cone. Note
that, in practice, tJ1e concrete cone capacity may be favorably
influenced by factors not yet taken into account in the CCD
method, such as localized hanger reinforcement or the compression force on a fastening loaded by a bending moment.
In Europe, most shear tests towards the edge were perfanned with post-installed anchors. Contrary to the opinion
of Mr. Cannon, the failure loads were not governed by the
anchor pull out capacity because, in many tests, due to the
small edge distance, the measured shear failure load was
a)
smaller tban the pullout failure load. Mr. Cannon proposes to
use ductile cast-in-place anchors to transmit shear foi·ces.
However , according to Reference 41 , ductile anchors are not
needed to insure the concrete edge failure load. This agrees
with the findings of the authors.
The authors have tried to respond to all of tbe technical
points raised by Mr. Cannon in a professio nal manner. They
greatly regret his incorrect characterization of their motives
for writing the original paper.
RESPONSE TO LEROY A. LUTZ
The authors appreciat~ the positive and helpful discussion
by Mr. Lutz.
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798
ACI Structural Journal I November-December 1995
tv
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Fig. K
As indicated in the original paper, for fastenings with three
or four edges and Cma.x $ 1.5 hef[crruu =largest edge distance;
for examples, see Fig. J(a) and (b)], the embedment depth
should be limited toh,j = c,ax I 1.5. This gives a constant
failure load for deep embedments. Mr. Lutz. is correct that for
these cases, the newly defined he/ should be used in Eq. (9),
(lOd), and (llb) and for the calculation of AN and ANo (see
Fig. 11). Similarly, for fastenings in a narrow, thin member
with c 2, max$ 1.5 c 1 (for example, see Fig. K), the edge distance should be limited to c 1 = ma.x (c2 , max/1 .5; hi 1.5). This
gives a constant failure load independent of the edge distance c 1. The newly defined c 1 should be used in Eq. ( 12),
(13b), and (13c) and for the calculation of Av and Avo (see
Fig. 17). The use of this proposal is demonstrated in Fig. J
and K. Apparently, these more precise definitions are needed
to clarify the application raised by Mr. Lutz. The corrected
equations should read
e )o.2
1.s
vm =( do JdoJJ::: c/ ' lb
'II4
= ----:-----:1 + (2/ /3c;')
minc 2
'lis = 0.7 + 0.3 l. 5 c .'
I
(l4a)
(14b)
(14c)
Mr. Lutz also suggests the combination of the quotient
N 11 jA11 0 to ~ shear stress 1:0 . In principal, this could be done.
However, the authors do not propose to do so because the
stresses a 0 and '!0 are not constant. Instead , they decrease
with increasing embedment depth or increasing edge distance, respectively. They believe this would be an annoyance
to the designers.
Mr. Lutz discusses the case of a single anchor near the corner. In this case, the capacity V,.L and V11 11 must be calculated for both edge distances, and the smaller value governs the
ACI Structural Journal I November-December 1995
design (see Fig. L). The ratio V,d/Vall varies with varying
ratio c/c 2.
It is a= 2.0 for c 1 = c2 , ex> 2 for c 1 < c2 and ex< 2 for c 1
> c2 . This tendency seems correct. However, it should be
noted that up to the present time, only the case of a single anchor in a corner with equal edge distances in the two directions has been tested.
Lastly, Mr. Lutz asks for a procedure to calculate the shear
resistance of anchor groups where all anchors do not have
the same edge distance (e.g., double-fastening perpendicular
to the edge or quadruple fastenings) situated at the edge or in
a corner and loaded by a shear force with an arbitrary angle
between shear force and edge. This application has not been
covered in the paper because of reasons of space. Engineering models based on the CCD method for calculating the
shear resistance in this case have been proposed in References 8 and 42. This proposal has also been incorporated in the
draft CEB Design Guide.43 However, it should be pointed
out that only limited test data is available to check the accuracy of the proposed equations. Hopefully, it will be discussed in ACI Corrunittee 3 18 whether this proposal should
be incorporated in the proposed Fastening to Concrete Chapter of ACI 318.
RESPONSE TO RICHARD S. ORR
Mr. Orr is properly concerned with the behavior of very
deep embedments and claims that a variation of the embedment depth to the power of 1.6 or 1. 7 provides a good fit to
the test data for single anchors without edge and spacing effects. Four major test series have been performed with the
main aim to check the int1uence of the embedment depth on
the concrete cone failure load. 18, 21,28.47 In References 18, 2 1,
and 47, headed studs were tested. The size range was 50 to
175 rom (2 to 6.9 in.), 18 50 to 450 mm (2 to 17.7 in.),21 and
130 to 525 rom (5. 1 to 20.7 in.)47 . In Reference 28, undercut
anchors were used in a size range of 38. 1 to 304.8 mm (1.5
to 12 in.). The test results are included in the database in the
article.
799
h.r [in)
20
40
15.0
60
80
100
I
/ . {),. _..-···
/
12.5
I
1
~.
z
Yn,J.
I
Nu - her2
10.0
I
I
1
/
7.5
I
/
5.0
I
2.5
/
1
.
}
17
/.l
/
1.6 •
lcr Iller
I ' _/
/ ·/<-----··
•
.·
,/
.·
/
/
•. ··
.. --
3
25
hcrI s
2
0
f'.~ = 33 Nlmm'
I
./ ;...--
z
(4786 psi)
6. Numerical analysis
L/,:./ ·
c.
1.5 :::::.,
/ / ___/
' 6, ......
/./.-···
/..···
~
:.;;:
0.5
o Tests
0.0
0.5
0.0
l.O
1.5
h.r [m]
2.0
2.5
3.0
Fig. M
h.r[in]
4
50
16
40~n = ll ~----~-----+-----+----_,
n
n=6
Yn,u = 2V~,.L
---~n=9
-n
-~~-+----4-----t-~
~
30 ~---1-----+-----r----~--~
~20~~,~~~
Ynu
,
10 f-
o
Fig. L
her
"-'::
100
- - 1 -- -- --1
(l
L __ ____j_l_ __ ___,______
0
I._______._____
200
300
h.r[mm]
___J
400
500
Fig. N
While in the tests of References 18 and 47the failure loads
basically increased with
In the tests of Reference 28,
they increased in proportion to h~). Because, in general, not
all dimensions were scaled in proportion to the embedment
depth and the amount of the data for hef > 200 mm (8 in.) is
rather limited in the tests, a numerical investigation was carried out in Reference 45 using a nonlinear finite element
model. For the material model for concrete, a very advanced
nonload microplane model was used that takes into account
nonlinear fracture mechanics.
The matetial model parameters were calibrated to match
the average test result of the Prague tests21 or h(f = 150 mm,
and thus, kept constant for all calculations. In the numetical
study, all dimensions were scaled in proportion to the embedment depth [he! = 50, 150,450, 1350, and 2700 mm (2,
5, 9, 17.7, 53.1, and 106.2 in.)]. The calculated concrete cone
failure loads were plotted in Fig. Mas a function of the embedment depth. For comparison, the test data are shown as
welL Furthen~ore, failure_ cur~es are plotted for theL~ssurr~­
tion that N 11 mcreases wtth hcf (ACI 349-85), hef , hef ,
andh~/ (CCD method), respectively, taking N, == constant
for he!= 200 mm. Fig. M demonstrates that in this large scale
range, the failure loads of deep anchors are significantly
overestimated by ACI 349-85 and slightly underestimated
h!} .
800
12
8
by the proposed Eq. (9). This was to be expected because Eq.
(9) is based on linear fracture mechanics that yield the larges t
size effect
Because only a limited amount of test data is available for
anchors with h~r = 500 mm (19.7 in.) and none for deeper
anchors, a design equation sho uld be a conservative fractile
and in agreement with theoretical considerations. The authors believe that the proposed Eq. (9) satisfies these conditjons. Needless to say, if further tests of very deep bolts
indicate hl.6, or even hu, are appropriate and safe for massive nuclear-related structures, Committee 349 could change
their very unconservative h2 values to one of these values.
Committee 318 could consider such a change a special case
for extremely deep embedments.
Mr. Orr argues that the failure load of deep anchors should
be reasonably consistent with the capacity calculated as if it
were a column load on a slab. As discussed in connection
with the Cannon discussion, the behavior of fastener pullout
and slabs failing in punching shear is quite different Furthermore, in recently drafted codes, such as Eurocode 2,46 the perime ter for calculating the shear stress is taken at a distance
1.5d from the column face, and the design shear stl'ength decreases with increasing slab thickness because of a size effect found in experimenta!40 and numerical47 investigations.
ACI Structural Journal I November-December 1995
According to Mr. Orr, the test data suggest that the spacing
scr for full anchor capacity could be higher than 3herfor shal-
low anchors, and may be reduced to 2her for deeper anchor
bolts. According to the evaluation of the authors, the influence of the.embedment on the spacing scr is small and was,
therefore, neglected for reasons of simplicity. Because anchor groups with deep anchors [hef> 350 mm (16.6 in.)] have
not yet been tested, the shape of the failure cone of single anchors may be taken as a first indication of the spacing scr In
the Prague tests, 21 the shape of the failure cone has been
measured very carefully. The average angle of the failure
cone for tests with an almost constant pressure under the
head at shear load is plotted in Fig. Nasa function of the embedment depth. It can be seen that the shape of the failure
cone is not much influenced by the embedment depth. On an
average, the angle amounts to about 33 deg, which gives scr
3 hefi and agrees with the proposed value of the CCD method. Therefore, the authors believe that the proposal for scr =
3 hef is reasonably accurate for the ordinary embedment
depths used in practice.
If normal forces and bending moments are acting on the
base plate, Mr. Orr proposes to calculate the loads on the anchor bolts with a method similar to that used for reinforced
concrete cross sections. The authors generally agree with
this proposal. Note that the paper does not discuss the method of calculation of the loads on the anchors, but only thecapacity (resistance) of the anchorage in case of concrete cone
failure. The proposed factor 'I' I takes into account the influence of an eccentric tension load on the concrete cone failure
load in a rational way (see Fig. 14). It agrees reasonably well
with test results (see Fig. 28).
The authors agree that the concrete cone capacity might be
influenced by a compression reaction from flexural loads.
That case is currently under study at the University of Stuttgart and a design proposal will be presented in due time.
Mr. Orr also suggests that some data show undercut anchors
to be superior to other expansion anchors and feels that they
should be treated more like headed studs. Until complete information is available concerning the effect of bolt prestressing and other variables on the behavior of these anchors, the
authors would prefer to keep all of the post-installed anchors
in a classification separate from cast-in-situ anchors.
The authors disagree that in the proposed method the edge
effects of groups are considered by reducing the capacity of
the full group in proportion to the reduction in capacity of the
anchors closest to the edge. Because the projected area AN is
· calculated for the full group [see Fig. 11 (d)] , the capacity of
the anchor(s) closest to the edge anJ. further away from the
edge is averaged. This might be unconservative for very
small edge distances. However, in general, for these edge
distances, other failure modes will govern the design (e.g.,
splitting or blowout failure).
The authors cannot see why the CCD method cannot be
applied to unusual design cases in a similar but simpler way
than has been perf01med with the 45-deg cone in the past.
=
RESPONSE TO PHILLIP J. IVERSON
The authors appreciate the constructive criticism by Mr.
Iverson and the careful review of the CCD proposal by the
PCI ad hoc group. Many of the limitations of data cited by
ACI Structural Journal I November-December 1995
Mr. Iverson are also shortcomings that apply to the present
PC/ Design Handbook procedures. It behooves all of us interested in fastening to concrete to see continued research
and development in this important area. The authors agree
that more data on fastenings close to an edge are needed and
that there should be a reduction in capacity for fasteners that
must be installed in the edge zone, as is often required in repair and strengthening situations. Fig. 26 shows considerable
data on groups of headed studs. The authors did not understand Mr. Iverson's concern in that area.
Mr. Iverson indicates that producers would most likely use a
bent or hooked defoLmed bar anchor to achieve the higher capacities necessitated by large embedments. By designing in
this manner, a very limited increase of the concrete breakout
compared to headed studs or post-installed anchors can be expected. A hook can be compared to an idealized head of a headed stud. it may mobilize a wider base of cone but, in reality,
often no significant increase in the failure load can be realized.
The CCD method only covers the failure mode of the concrete cone type breakout. For very small edge distances c <
0.5 hef; a lateral blowout failure will occur; this has been
shown in many U.S. and European tests. Design equations
for applications very close to the edge are given in Reference
2, and provisions of this type will be added to the ACI 318
proposal.
Fastenings failing by concrete breakout systematically are
governed by the concrete tensile capacity. Investigations
have been conducted into the applicability of the 0.5 power
relationship between the concrete compressive and tensile
strength for high-strength concrete.48 They have shown that
the load-bearing capacity of anchors increases in the practical range of concrete strength, including normal highstrength concrete with
The limited data for fasteners in
high-strength concrete have not precluded the extensive section on fasteners in PC! practice. 5
Cast-in-situ anchorages and well-designed, tested, and approved post-installed anchors have the san1e level of installation
safety and reliability. The ad vantages of the flexibility in application of post-installed anchoring techniques cannot be denied.
These facts should be acknowledged in the precast industry.
Several concerns raised by Mr. Iverson are certainly at the
cutting edge of current technology. It is useful to view them
from the perspective that at the present time, ACI 318 simply
does not address fastening to concrete, the PC/ Design
Handbook implicitly contains many of the same limitations
that he raises, and technical committees, like ACI 355 and
the CEB Committee on Fasteners, are actively studying
these questions. Certainly one of the most important questions is whether a fastener group should be analyzed for lo~d
distribution using elastic or plastic theory. Investigation of
this question has been underway and tests have been run.
However, at the moment, this question is still hotly debated.
Similarly, he questions the interaction of tension and shear
on fasteners. While length limitations precluded treatment of
that subject in the original paper, the 318 proposal 13 and the
CEB Design Guide43 both treat that interaction.
Mr. Iverson also asks whether all of the tests in the database were performed in the same manner, at the same loading rate, etc. Obviously, a world data bank with no world
JJ:.
801
testing standard will include vast testing differences. This is
a distinct advantage, as the procedure is envisioned to apply
to a wide range of applications. All the tests in the database
are reproducible and were performed in ways so that they
can be considered a set. A very extensive and detailed response to this question was given to ACJ 349, Subcommittee
3, in September 1993; the database was accepted and evaluated at that time.
Finally, Mr. Iverson asks if the 5-percent fractile is appropriate for a special anchor like the headed stud. He indicates
a concern over whether a 5-percent fractile is a sufficiently
low lower-bound. As mentioned previously, examination of
test data will indicate most code provisions for shear, development length, axial load, flexure, etc. are not absolute lower
bounds. The 5-percent fractile is only a statistical tool for
drawing a line th at encompasses most of the data. Comparison ofthe test data and the 5-percent fractile are given in Fig.
E. Only one outlier test falls more than 10 percent below the
5-percent fractile. We doubt that any segment of the industry
would accept design provisions with a lower-bound based on
that single outlier. In addition, the ACJ 318 proposal, 13 with
which PC! is extremely familiar, includes both the usual load
factors and conservative <j> failures and, in addition, is based
on fastener prequalification under Reference 1 to provide appropriate safety.
The authors believe that the conversion factor for cube
tensile strength and cylinder tensile strength is correct. They
appreciate the interest and support of PC! in advancing fastener technology.
CONCLUDING REMARKS
According to the authors' opinions, the CCD method is userfriendly, sufficiently accurate for practical applications, and can
be easily extended to cases not covered in this paper. Some factors favorably influencing the concrete cone failure load (e.g.
compression reaction due to flexural loads and hanger reinforcement) should be taken into account in the future
REFERENCES
34. Eligehausen, R. and Balogh, T. , " Behavior of Fasteners Loaded in
Tension in Cracked Concrete," ACJ Structural Joumal, V. 92, No.3, MayJune, 1995,pp.365-379.
35. Fracture Mechanics of Concrete Structures, Z. P. Bazant, ed ..
Elsevier Applied Science, London and New York, 1992, pp. 1-996.
802
36. Size Effect in Concrete Structures, H:. A. Mihushi, H:. Okamura, and
z. P. Bazant, eds., E & FN Spon, London, 1994 . pp. 1-564.
37. Fracture Mechanics of Concrete Stmcwres, F. H. Wittmann, ed.,
Aedification Publishers, Freiburg, 1995 , pp. 1-1 594.
38. Comite Euro-International du Beton: CEB-FIP Model Code 1990,
Thomas Telford, London, 1993.
39. Neville, A.M., Properties of Concrete, Pillman Books Ltd., London,
1991.
40. Kord ina, K., and Nolting, P., "Tragfaihigkeit durehstanzgefli.hrdeter
Stahlbeton-platten-Entwicklung von Bemessungsvorschlagen (Capacity
of Reinforced Concrete, (Slabs Falling in Punching Shear- Evalnation of
Design Proposals)," DAfStb, V. 37 I , W. Ernst & Sohn, Berlin, 1986.
4 1. Shaikb, A. F., and Whagong, Y., "In-Place Strength of Welded
Headed Studs, " Joumal of the Pr(!stressed Concrete Institute, Mar.-Apr.
1985, pp. 56-81.
42. Fuchs, W. and Eligehausen, R., "CC Verfahren ftir die Berechnung
der Betonausbruchlast von Verankerungen (CC Design Method to Determine the Concrete Breakout Load of Fasteners), Beton-und Stahiberonbau,
V. I , 2, 3, Wilhelm Emst & Sohn, Berlin, 1995.
43. Comite Euro-Intemational du Beton. CEB Design Guide, "Design o f
Fastenings in Concrete, Draft CEB Guide-Part. 1-3, " B~tlletin d'biformation No. 226, Lausanne, Aug., 1995.
44. Eligehausen, R.; Fuchs, W.; Ick. U.; Mallie, R. ; Reuter, M.; Schimmelpfennig, K.; and Schmal, B., "Tragverhalten von Kopfbolzenverankerungen bei zenlrischer Zugbeanspruchung (Load-Bearing Behavior of
Fastenings with Headed Studs under Tension Loading), " Bauingenieur 67
(1192), H. Y., pp. 183-196.
45. Ozbolt, J., "Mallstabseffekt nnd Duktiltiit. von Bcton-und Stahlbetonkonsuuktionen (Size Effect and Ductility of Concrete and Reinforced Concrete Structures)," Habilitation thesis, University of Stuttgan, 1995.
46. Design of Concrete Structures-Part I: General Rules and Rules for
Structnres, ENV 1992-1-1 (Eurocode 2), 1992.
47. Menefrey, Ph., Simulation ofP•mching Failure- Failure Mechanism
and Size-Effect; Fracture Mechanics of Concrete Structures, F. H. Wittmann, ed., Aedification Publishers, Freiburg, 1995.
.
48. Ahmad, S. D., and Shah, S. P., "S tructural Properties of HighStrength Concrete and Its Implications for Precast Prcs!Tessed Conerete, "
PC Journal, V. 30, No.6, Nov.-Dec. 1985, pp. 92-119.
ERRATA
p. 81 , Eq. (12a)-For clarity, replace 1 with e in term (e/d0 ) 0·2·
p. 81, below Eq. (12a)-In definitions, replace 1 with an e
to read: e=activated load-bearing ....
p. 81, Eq. (l2b)- For clarity in first term, replace l with t
p. 84, Eq. (13b)-Rewrite final term of denoQ'linator as (3C1)
p. 84, Definition of C 1-Reference should be to Reference 22
p. 91, Fig. 28-Heading for abscissa should be 2 e; Is 1
ACI Structural Journal I November-December 1995