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COMPREHENSIVE ANALYTICAL MODEL FOR ANCHORAGES
WITH SUPPLEMENTARY REINFORCEMENT
Akanshu Sharma1*, Rolf Eligehausen1,2, Jörg Asmus2
1 Institute of Construction Materials, University of Stuttgart, 70569 Stuttgart, Germany
2 IEA, Engineering Office, Eligehausen-Asmus-Hofmann, 70563 Stuttgart
*Corresponding Author Email: akanshu.sharma@iwb.uni-stuttgart.de
ABSTRACT
The models included in the current standards and guidelines1,2,3 to evaluate the failure loads for
anchorages with supplementary reinforcement subjected to either tension or shear forces are very
conservative. The existing models do not explicitly consider all three major components that provide
resistance to applied forces for anchorages with supplementary reinforcement namely the concrete
struts, the tension ties and the nodes. The models in EN1992-41 and fib Bulletin 583 consider the
failure of tension tie (stirrups) due to bond or yielding while giving an indirect and very conservative
consideration to the node (hooks) and ignore the possibility of strut failure. ACI 3182 considers only
yielding of the stirrups provided sufficient anchorage length is available within and outside the
breakout body, while not considering strut failure. For anchorages under shear forces, the model in
EN1992-4 considers the failure crack to originate from the front row of the anchors, which leads to a
small reinforcement resistance making the model very conservative. The model in ACI and fib
consider the failure crack to originate from the back anchor row however in that case the anchor steel
failure (as well as the pryout failure) is calculated considering that the shear load is taken up by only
the anchors in the back anchor row as well. Nevertheless, in all the models, the resistance for the
concrete breakout and the reinforcement are not combined but only the higher of the two resistances
is considered as the failure load of the anchorage. These assumptions make the existing models quite
conservative for many cases. However, on the other hand, due to the fact that the possibility of the
strut failure is not explicitly considered, for the cases of anchorages with high amounts of
supplementary reinforcement, the existing models tend to get unconservative.
In this work, a new analytical model is developed based on detailed experimental investigations
performed on anchorages with supplementary reinforcement to take up tension forces subjected to
tension loads and anchorages with supplementary reinforcement to take up shear forces close to an
edge loaded in shear perpendicular and towards the edge. The model gives due consideration to and
explicitly considers all three components of resistance provided by the anchorage with
supplementary reinforcement. The model combines and synergizes the strength of the models
proposed based on research performed at the University of Stuttgart4,5. The mean failure loads
calculated by the new model are shown to be in very good agreement with the experimentally
obtained mean failure loads. The model is objective and is applicable equally well for anchorages
with supplementary reinforcement under either tension or shear forces.
3rd International Symposium on
Connections between Steel and Concrete
Stuttgart, Germany, September 27th -29th , 2017
Akanshu Sharma, Rolf Eligehausen and Jörg Asmus
1 Introduction
In an accompanying paper6, systematic investigations made on quadruple anchorages (2x2 anchor
groups), in the form of WELDA® anchor plates from Peikko Group Corporation, without and with
supplementary reinforcement under tension loads and under shear loads close and towards the edge
are presented. Different amounts of supplementary reinforcement were used in the tests targeting the
reinforcement and concrete failure modes. It was shown that the failure load for anchorages under
tension or shear close and towards the edge can be significantly increased by using supplementary
reinforcement. In case of anchor groups with supplementary reinforcement, once the concrete cracks,
the stirrups get activated and provide resistance to the applied tension (or shear) loads until
reinforcement yielding or bond failure occurs. Thus, the tension or shear strength of the anchorage
can be increased by increasing the amount of supplementary reinforcement. However, this increase is
limited by concrete based failure modes such as strut failure or pryout failure in case of anchorages
provided with high amount of supplementary reinforcement.
In the current standards, such as EN1992-41, ACI 3182 and fib bulletin 583, a very conservative
approach is given to consider the influence of the supplementary reinforcement on failure loads of
the anchorages. In this paper, the test results are compared with the existing models as given in
EN1992-41 for anchorages with supplementary reinforcement loaded in tension or shear towards the
edge. Further, a new model is proposed for predicting the failure loads for anchorages with
supplementary reinforcement undergoing reinforcement failure by modifying the model proposed by
Schmid4 for anchorages with supplementary reinforcement loaded in shear towards the edge and the
model proposed by Berger5 to consider the possible strut failure in case of anchorages with high
amount of supplementary reinforcement. Additionally, a new approach is presented to calculate
pryout failure loads for anchor groups with more than one anchor row when the failure crack for
concrete edge failure is assumed from the back anchor row. It is shown that with the proposed
model, the failure loads for the low to high amount of reinforcement (where reinforcement failure
dominates) can be predicted very well.
2 Model given in EN1992-4
According to EN1992-41, for anchorages with supplementary reinforcement, the load corresponding
to failure of reinforcement in the concrete breakout body can be obtained on the basis of the strut-
and-tie model (Figure 1). In EN1992-4, only bars with a distance ≤ 0.75 times the embedment depth
(for tension loads, see Figure 1a) or the edge distance (for shear loads, see Figure 1b) from the
fastener are assumed as effective.
(a) Tension loads (b) Shear loads
Figure 1: Strut-and-tie Model in EN1992-41 for anchorages with supplementary reinforcement
Akanshu Sharma, Rolf Eligehausen and Jörg Asmus
The stirrups are considered effective provided the anchorage length l1 (Figure 1) in the concrete
breakout body is at least equal to 10 times the rebar diameter (straight bars) or at least equal to 4
times the rebar diameter (bars with a hook, bend or loop).
As per EN1992-4 (2015), the characteristic resistance, NRk,re of the supplementary reinforcement
provided for one fastener associated with anchorage failure in the concrete breakout body is given
by:
,
0
,
Rk re
Rk re n
NN
(1)
With, n = number of legs of the anchor reinforcement effective for one fastener
1,
0, , ,
12
s re bk
Rk re yk re s re
l d f
N f A
(2)
Where,
l1 = anchorage length = distance from the intersection of theoretical crack and the rebar to the stirrup
end (Figure 1)
ds,re = diameter of the stirrup
fbk = characteristic bond strength = 1.5 fbd
fbd = design bond strength according to EN1992-1-17
fyk = characteristic yield strength of reinforcing bars
As,re = Area of reinforcing bar used as stirrup
α1 = influencing factor that assumes a value of 0.7 for hooked rebar if cd < 3dsre or 1.0 if cd ≥ 3dsre
and 1.0 for straight rebar7
α2 = factor to consider the influence of cover on the bond strength defined for hooked bars as7
2 , , 2
1 0.15 3 ; with 0.7 1.0
d s re s re
c d d
cd = clear cover to the reinforcing bar in any direction or half the clear distance to the adjacent rebar,
whichever is smaller
For tension loads, Eq (1) gives the load corresponding to supplementary reinforcement failure. For
shear loads, this load is converted to shear loads considering the eccentricity between the applied
shear force and stirrups as
,
,
Rk re
Rk re N
Vx
(3)
Where, x is the factor to consider for the eccentricity between the reinforcement and the applied
shear load (compare Figure 1b)
1s
e
xz
es = distance between reinforcement and shear force acting on a fixture
z = internal lever arm of the concrete member that is approx. equal to 0,85d
d = min(depth of concrete member, 2hef, 2c1)
Akanshu Sharma, Rolf Eligehausen and Jörg Asmus
The characteristic failure load for the anchorage with supplementary reinforcement under tension (or
shear) loads, is given as
,,
max ;
Rk Rk c Rk re
N N N
;
,,
max ;
Rk Rk c Rk re
V V V
Where,
NRk,c = Characteristic resistance corresponding to concrete cone failure (under tension) of an
anchorage without supplementary reinforcement
VRk,c = Characteristic resistance corresponding to concrete edge failure (under shear) of an anchorage
without supplementary reinforcement
The mean resistances can be obtained by multiplying Eq. (2) by 1.338.
From Eq. (2), it implies that if sufficient cover is available, the hook resistance is considered as
around 40% of the bond resistance of the stirrups. Thus, longer the bond length, higher is the hook
resistance as well, which does not seem logical intuitively. This aspect was highlighted and targeted
in the model by Schmid4 as will be discussed later.
3 Comparison of test results with the model of EN1992-4
3.1 Tension tests
The comparison of the mean failure loads obtained from the experiments with the mean failure loads
calculated as per the model of EN1992-41 for the tension tests are given in Table 1. As described in
the accompanying paper6, two different configurations of supplementary reinforcement against
tension forces were tested, with 2 stirrups only outside the anchorage (4 stirrup legs in total) and with
2 stirrups outside and two within the anchorage (8 stirrup legs in total). These configurations were
named as Type 1 and Type 2 reinforcement configuration respectively.
Table 1: Comparison of mean failure loads for tension tests
Diameter of
supplementary
reinforcement
Type of
reinforcement
Total c.s. area of
stirrup legs [mm2]
Mean failure loads [kN]
Experiment
EN1992-4
Ratio Nu,exp/Nu,calc
0 (Unreinforced)
NA
0
256.9
295.2
0.87
10 mm
Type 1
314
361.2
295.2
1.22
Type 2
628
460.0
295.2
1.56
16 mm
Type 1
804
447.6
295.2
1.52
Type 2
1608
589.6
295.2
2.00
The mean tension failure predicted by the model of EN1992-41 for the anchorage in unreinforced
concrete is slightly on the unconservative side, which can be attributed to the scatter of the failure
loads. However, for the cases with supplementary reinforcement, while the tests show a clear
increase in the failure loads but the model in EN1992-41 predicts no increase in the failure loads.
This is due to the fact that the reinforcement resistance never exceeds the concrete cone resistance in
unreinforced concrete for the tested cases. The results clearly bring out the conservatism in the
existing model of EN1992-41.
Akanshu Sharma, Rolf Eligehausen and Jörg Asmus
3.2 Shear tests
Table 2 presents the comparison of the mean failure loads obtained from the experiments with the
mean failure loads calculated as per the model of EN1992-41 for the shear tests. It can be seen that
the model for concrete edge failure under shear loads is even more conservative than the model for
concrete cone failure under tension loads. This is due to the fact that EN1992-4 considers the failure
load to be evaluating considering the failure crack from front anchors. Even for the case of
anchorage without supplementary reinforcement, the model given in EN1992-4 is quite conservative.
Again, as per the model the reinforcement resistance does not exceed the concrete edge resistance in
unreinforced concrete for the tested cases.
Table 2: Comparison of mean failure loads for shear tests
Diameter of
supplementary
reinforcement
C.S. area of one
stirrup leg [mm2]
Mean shear failure loads [kN]
Experiment
EN1992-4
Ratio Vu,exp/Vu,calc
0 (Unreinforced)
0
161.7
60.2
2.69
12 mm
113
263.4
60.2
4.38
20 mm
314
328.8
60.2
5.46
4 New model
4.1 Reinforcement failure
The model for reinforcement failure proposed here is a modified version on the model developed by
Schmid4 for anchorages with supplementary reinforcement loaded under shear loads. Schmid4
proposed that the anchorage capacity of the stirrup leg is given by the sum of the hook capacity and
the bond capacity. As per Schmid4, the hook capacity is relatively independent of the bond length of
the stirrup in the breakout body. The original model by Schmid4 has been modified considering the
observations made in the tests as well as to make the model suitable for tension loads as well.
For anchorages in unreinforced concrete, in general, the new model uses the same formulations as
given in EN1992-4 to calculate the failure loads. However, under shear loads close and towards the
edge, it is assumed in the proposed model that the failure loads are always calculated from the back
anchor row both in case of anchorage without and with supplementary reinforcement. Further, the
load carrying capacity of the anchor reinforcement consists of two parts: the contribution of hook
and the contribution of bond.
The mean anchorage capacity of one stirrup leg,
0,
Rm re
N
is given as
0 0 0
, , , ,
Rm re Rm hook Rm bond s re ym
N N N A f
(4)
Where, As,re = area of one stirrup leg and fym = mean yield strength of stirrup
The stirrups that enclose the surface reinforcement (for tension loads) or the edge reinforcement (for
shear loads) are considered as effective provided they have a bond length of at least 4ds within the
breakout body. The mean value of hook contribution for a particular stirrup leg,
0,
Rm hook
N
is given as
Akanshu Sharma, Rolf Eligehausen and Jörg Asmus
0.1
,
0, 1 2 3
30
cm cube
um hook s ym f
N A f
(5)
Where, the factor
1
considers the influence of the position of the stirrup. A value of
10.95
is
assumed for stirrups that either lie between the outermost anchors or, if they lie outside the
anchorage, are first intercepted by the crack. If yielding of the stirrups first intercepted by the crack
takes place, the next stirrup is assigned a value of effectiveness factor,
1,2 0.95
else,
1,2 0.16
.
The factor
2
considers the influence of the diameter of the surface reinforcement (for tension) or
edge reinforcement (for shear), ds,L with respect to the diameter of the stirrup, ds,re:
23
,
2,
1.2
sL
s re
d
d
(6)
The factor
3
considers the influence of the bond length, l1, of the stirrup in the breakout body and
its diameter given as:
0.4 0.25
1
3,
10
ef s re
l
hd
(for tension loads) (7)
0.4 0.25
1
31, ,
10
n s re
l
cd
(for shear loads) (8)
Where, hef is the effective embedment depth of the anchors (in case of tension loads) and c1,n is the
edge distance of the back anchor row (in case of shear loads).
The contribution of the bond of one stirrup leg is given as:
0, , 1 1,min 2
( ) /
Rm bond s re bm
N d l l f
(9)
Where, l1,min is the minimum anchorage length required (=4ds,re), fbm is the mean bond strength
(=1.33fbk)
α2 = factor to consider the influence of cover on bond strength defined as
2 , ,
1 0.15( ) /
d s re s re
c d d
cd = clear cover to the stirrup leg in any direction or half the clear distance to the adjacent stirrup,
whichever is smaller
The total capacity of the anchor reinforcement is calculated by summing up the capacities of all
effective stirrup legs
0
,,
Rm re Rm re
n
NN
(10)
Akanshu Sharma, Rolf Eligehausen and Jörg Asmus
n = number of effective stirrup legs of the anchorage. Effective are stirrups with an anchorage length,
l1 ≥ 4ds,re in the theoretical breakout body
Under tension, Eq. (10) gives the contribution of the supplementary reinforcement under tension
loads. However, to obtain the contribution of the supplementary reinforcement towards the shear
loads, Eq. (3) is used to convert the tension resistance of the reinforcement to the shear resistance.
The evaluation of the test results6 highlighted that the concrete carries a significant percentage of the
failure load corresponding to concrete cone (or edge) failure in unreinforced concrete when the peak
load of the anchorage is reached. Based on the evaluation of the test results and to keep the model
simple, it seems reasonable to assume that at peak load, the load taken up by the concrete is approx.
50% of the concrete cone (or edge) failure load of the anchorage without supplementary
reinforcement. Therefore, it is proposed that the peak failure load of an anchorage with supplemental
reinforcement is given as the failure load corresponding to 50% of the concrete cone (or edge) failure
load in unreinforced concrete plus the load corresponding to reinforcement failure calculated in
accordance with the new model. Thus the mean tension resistance of an anchorage with
supplementary reinforcement is given by
Rm, Rm, ,
0.5
Rm c re Rm c
N N N N
(11)
Similarly, the mean shear resistance of an anchorage loaded towards the edge with supplementary
reinforcement is given by
Rm, Rm, ,
0.5
Rm c re Rm c
V V V V
(12)
4.2 Strut failure
An upper limit to the tension failure load of the anchorage with supplementary reinforcement applies
due to a possible strut failure. This failure mode was investigated by Berger5 by performing
equivalent tests on anchorages in unreinforced concrete with varying the position of the supports.
According to the model by Berger5, the maximum possible failure load of an anchorage with anchor
reinforcement compared to the same anchorage in unreinforced concrete is given by Eq. (13).
,max ,
um strut Rm c
NN
(13)
where,
strut
is the strut factor which depends on the anchorage and stirrup configuration.
The basic strut factor is defined as
02.75 1.17 1.0
strut ef
x
h
(14)
x = distance between the secondary failure cone on the concrete surface and the anchor axis (see
Figure 2). Eq. (14) is valid for stirrups that enclose the surface reinforcement.
Akanshu Sharma, Rolf Eligehausen and Jörg Asmus
Figure 2: Strut-and-tie Model according to Berger5 for anchorage with supplementary reinforcement
For single anchor with one stirrup each at both sides of the anchor, the strut factor,
strut
is equal to
the basic strut factor,
0
strut
. For the case of anchor groups with supplementary reinforcement,
Berger5 proposes that the factor for strut failure should be calculated considering the contributory
area of the anchorages.
(a) Type 1 (b) Type 2
Figure 3: Consideration of strut formation in case of anchor groups with supplementary
reinforcement under tension forces
For anchorages with stirrup legs arranged symmetrically outside the anchorage (Type 1), the
maximum failure load considering strut failure is given as
, ,1 , ,2 , ,3
00
, , ,
( ) ( )
c N c N c N
strut strut strut
c N c N c N
A A A
xx
A A A
(15)
Struts
Secondary failure cone
Primary failure cone
x
Akanshu Sharma, Rolf Eligehausen and Jörg Asmus
For the case of anchorages with supplementary reinforcement also lying within the outermost anchor
rows and arranged symmetrically to the anchors (Type 2), the factor ψstrut is given as:
)()()()(
,
3,,2,,
2
0
,
41,,
1
0
Nc
NcNc
strut
Nc
Nc
strutstrut A
AA
x
A
AA
x
(16)
A model analogous to the model shown here is also applicable for anchorages with supplementary
reinforcement under shear loads. However, due to the space limitations and the fact that in the tests
under shear loads, strut failure did not occur due to the precedence by pryout failure, it is not
discussed here.
4.3 Pryout failure
As described in the accompanying paper6, in case of tests with high amount of supplementary
reinforcement under shear loads, the reinforcement failure was preceded by the pryout failure. Please
note that this failure could be avoided by using a restraint against uplift of the base plate as was used
in another similar test program by the authors9. In such cases the concrete contribution is not 50% of
its capacity in unreinforced concrete as used in Eq. (12) but 100%, even at the point of reinforcement
yielding. Nevertheless, it is impractical or unreliable to have such a constraint in reality, therefore in
this test program, the uplift restraint was not used.
The current approach to evaluate the failure load of an anchorage corresponding to pryout failure,
VRm,cp involves multiplying the tension failure load of the anchorage by a factor, k3. This model
considers the resistance associated with concrete breakout as well as the ratio between the tension
force in the anchor and the applied shear force8.
, 3 ,
Rm cp Rm c
V k N
(17)
Where,
VRm,cp is the mean pryout failure load for the anchorage
NRm,c is the mean tension failure load for the anchorage
k3 is the factor that assumes the value
3
3
1.0 for 60mm
2.0 for 60mm
ef
ef
kh
kh
As per the current standards1,3, for the anchorages close to an edge and loaded in shear towards the
edge, if the concrete edge failure load is evaluated assuming the failure crack from the front anchor
row, all anchors are considered to evaluate the pryout failure load (approach given in EN1992-41).
However, if the load corresponding to concrete edge failure is evaluated assuming the failure crack
from back anchor row then only the back anchors are considered to evaluate the pryout failure load
(approach given in fib3).
Akanshu Sharma, Rolf Eligehausen and Jörg Asmus
In the new model, the concrete edge failure loads are calculated assuming the failure crack from back
anchor row. However, if only the back anchor row is considered to calculate pryout failure load, the
failure loads of the anchorages with two or four anchor rows would be essentially equal. This
concept is explained in Figure 4a. However, the results of a few tests additionally performed on
anchorages with four anchor rows (not presented here) clearly show that the failure loads for
anchorages with four anchor rows could reach much higher values than the loads which induced
pryout failure in anchorages with two anchor rows with supplementary reinforcement. Therefore, the
approach of considering only the anchors in the back row to calculate pryout failure loads is
unobjective.
(a) Current approach (b) Proposed approach
Figure 4: Approach to evaluate pryout failure loads of anchorage
The test results6 displayed that in the cases where pryout failure occurred, a major crack appeared
from the front anchor row. Therefore, this anchor could not take up major shear load. Therefore, it is
proposed that the pryout failure load for an anchorage with supplementary reinforcement is evaluated
considering the anchor group formed by all anchor rows except the front anchor row and considering
a free edge at the line of the front anchor row. This method is explained in Figure 4b.
Akanshu Sharma, Rolf Eligehausen and Jörg Asmus
5 Comparison of test results with the new model
Using the formulations given above, the mean failure loads for the anchorages as obtained following
the new model were compared with the experimentally obtained mean failure loads for the
anchorages tested.
5.1 Tension loads
The comparison of the mean failure loads obtained from the experiments with the mean failure loads
calculated as per the new model for the tension tests are given in Table 3. For comparison, the failure
loads calculated as per the model of EN1992-41 are also included in Table 3.
Table 3: Comparison of mean failure loads for tension tests with new model
Diameter of
supplementary
reinforcement
Type of
reinforcement
Total c.s. area
of stirrup legs
[mm2]
Mean tension failure loads [kN]
Experiment
EN1992-4
New
model
Ratio
Nu,exp/Nu,calc,EN1992-4
Ratio
Nu,exp/Nu,calc,NewModel
0 (Unreinforced)
NA
0
256.9
295.2
295.2
0.87
0.87
10 mm
Type 1
314
361.2
295.2
317.2*
1.22
1.14
Type 2
628
460.0
295.2
486.9*
1.56
0.94
16 mm
Type 1
804
447.6
295.2
500.4#
1.52
0.89
Type 2
1608
589.6
295.2
566.6#
2.00
1.04
* The failure load is controlled by reinforcement failure. # The failure load is controlled by strut failure
It can be seen that for the cases with supplementary reinforcement, the new model gives much better
predictions compared to the model in EN1992-41. The new model predicts an increase in the failure
loads even with relatively low amounts of supplementary reinforcement, same as in the experiments.
Furthermore, due to the consideration of strut failure, the failure loads calculated by the new model
are in close agreement with the experiments also for high amounts of supplementary reinforcement.
The failure modes predicted by the new model are the same as observed in the experiments6.
5.2 Shear loads
Table 4 presents the comparison of the mean failure loads obtained from the experiments with the
mean failure loads calculated as per the new model for the shear tests.
Table 4: Comparison of mean failure loads for shear tests with the new model
Diameter of
supplementary
reinforcement
C.S. area of one
stirrup leg [mm2]
Mean shear failure loads [kN]
Experiment
EN1992-
4
New
Model
Ratio
Vu,exp/Vu,calc,EN1992-4
Ratio
Vu,exp/Vu,calc,NewModel
0 (Unreinforced)
0
161.7
60.2
142.5
2.69
1.13
12 mm
113
263.4
60.2
240.0*
4.38
1.10
20 mm
314
328.8
60.2
315.6#
5.46
1.04
* The failure load is controlled by reinforcement failure # The failure load is controlled by pryout failure
The failure loads predicted by the new model for concrete edge failure under shear loads in
unreinforced concrete are much more close to the experimentally obtained mean failure loads due to
the consideration of failure crack from back anchors. This approach is also recommended by fib
Bulletin 583 and ACI 3182 but not in EN1992-41.
Akanshu Sharma, Rolf Eligehausen and Jörg Asmus
For the anchorages with supplementary reinforcement, the predicted failure loads are in very good
agreement with the experimentally obtained mean failure loads. The new model predicts an increase
in the failure load even with relatively small amount of supplementary reinforcement, the same as
observed in the experiments6. For relatively high amounts of supplementary reinforcement, the
failure load is controlled by pryout failure in the new model, which is also the failure mode observed
in the tests6.
Thus, the new model is able to predict the mean failure loads as well as the failure modes which are
in good agreement with the experimentally obtained mean failure loads and the failure modes, both
under tension loads as well as shear loads.
6 Conclusions
Based on the evaluation of test results presented in the accompanying paper, a new model is
presented in this work to calculate the failure loads for anchorages with supplementary
reinforcement. The model considers both the reinforcement and concrete failure modes. The model
for the failure of supplementary reinforcement is based on the model proposed by Schmid4 for
anchorages under shear loads and is modified to consider the realistic behavior of the anchorages
with supplementary reinforcement as observed from the tests. The model was also modified to make
it applicable for anchorages with supplementary reinforcement under tension loads as well. The
model for strut failure is based on the model proposed by Berger5. A new approach is proposed to
calculate the pryout failure loads for the anchorages with more than one anchor row when the failure
crack is assumed to appear from the back anchor row. The new model is able to predict the mean
failure loads in excellent agreement with the experimentally obtained mean failure loads as well as
correctly predict the dominant failure mode, both under tension loads as well as shear loads.
7 Acknowledgements
The tests reported in this work were funded by Peikko Group Corporation. The support and efforts of
Mr. Jan Bujnak, Peikko is greatly appreciated.
References:
1. FprEN 1992-4. 2015. Eurocode 2: Design of concrete structures - Part 4 Design of fastenings
for use in concrete, European committee for standardization, CEN/TC 250, Brussels.
2. American Concrete Institute. 2014. ACI 318: Building Code Requirements for Structural
Concrete (ACI 318-14).
3. International federation for structural concrete (fib). 2011. fib Bulletin 58. Design of
anchorages in concrete - Guide to good practice, fib Special Activity Group 4.
4. Schmid, K. 2010. Behavior and design of fastenings at the edge with anchor reinforcement
under shear loads towards the edge. PhD Thesis, Institute of Construction Materials, University of
Stuttgart (In German).
Akanshu Sharma, Rolf Eligehausen and Jörg Asmus
5. Berger, W. 2015. Load-displacement behavior and design of anchorages with headed studs
with and without supplementary reinforcement under tension load). PhD Thesis, Institute of
Construction Materials, University of Stuttgart (In German).
6. Sharma, A., Eligehausen, R., Asmus, J., “Comprehensive experimental investigations on
anchorages with supplementary reinforcement”, Proceedings, 3rd International Symposium on
Connections between Steel and Concrete (ConSC2017), September 27-29, 2017, Stuttgart, Germany.
7. EN1992-1-1: Eurocode 2: Design of concrete structures - Part 1-1: General rules and rules for
buildings, December 2004
8. Eligehausen, R., Mallée, R., Silva J.F.: Anchorage in Concrete Construction, Berlin: Ernst &
Sohn, 2006.
9. Sharma, A., Eligehausen, R., Asmus, J., “Experimental investigations on concrete edge
failure of multiple row anchorages with supplementary reinforcement”, Structural Concrete. 2017;
18: 153–163.
10. Sharma, A., Eligehausen, R., Asmus, J., “A new model for concrete edge failure of multiple
row anchorages with supplementary reinforcement – reinforcement failure”, Structural Concrete,
2017; 0: 1–9. https://doi.org/10.1002/suco.201700002
