ABSTRACT: In the present paper the theoretical aspects and the application of the non-linear finite element program MASA for analysis of anchorages placed at an edge of a concrete block are discussed. After an introduction the structure of the finite element (FE) code is briefly described. The results of the simulations are shown and compared with experimental data. They confirm that the FE code is able to simulate realistically the behavior of anchorages. Subsequently a parametric study is caITied out and the results are discussed

J Hofmann

J Ozbolt

R Eligehausen

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Fracture Mechanics of Concrete Structures, de Borst et al (eds)© 2001 Swets & Zeitlinger, Lisse, ISBN 90 2651 825 o 
Behavior and design of fastenings with headed anchors at the edge under 
tension and shear load 
J.Hofmann, R.Eligehausen & J.Ozbolt 
Institute of Construction Materials, University of Stuttgart, Germany 
ABSTRACT: In the present paper the theoretical aspects and the application of the non-linear finite element 
program MASA for analysis of anchorages placed at an edge of a concrete block are discussed. After an in-
troduction the structure of the finite element (FE) code is briefly described. The results of the simulations are 
shown and compared with experimental data. They confirm that the FE code is able to simulate realistically 
the behavior of anchorages. Subsequently a parametric study is caITied out and the results are discussed. 
1 INTRODUCTION 
The failure load of anchorages with headed studs 
may be calculated according to the CC - method by 
Fuchs, Eligehausen, Breen (1995). In order to under-
stand the behavior of headed studs very close to an 
edge under tension and shear loading in more detail 
and possibly to improve the CC - method, a numeri-
cal investigation was caffied out with the non-linear 
FE code MASA. It is based on the microplane 
model. The program is able to analyze the three-
dimensional nonlinear behavior of concrete. 
In the present paper it is shown that the program 
MASA is able to predict realistically the behavior of 
fastenings with headed anchors close to an edge. 
Furthermore the influence of the most important 
concrete properties and geometrical parameters on 
the failure load is shown. 
2 FINITE-ELEMENT-CODEMASA 
2.1 General 
1 The used finite element code is based on the mi-
croplane model. It can be used for the two and the 
three-dimensional analysis of quasi brittle materials. 
The model allows a realistic prediction of the mate-
rial behavior in case of three-dimensional stress -
strain states. The smeared crack approach is em-
ployed. To ensure a mesh independent crack devel-
opment a so-called "localization limiter " is used. 
This is realized by the crack band approach or by a 
generalized nonlocal integral method. For the analy-
ses discussed in the present paper, the improved 
crack band approach was used. The material model 
is described in detail in Ozbolt et al. (2001) 
941 
The concrete is discreted by 8-node brick ele-
ments. The reinforcing bars are modeled with bar 
elements or smeared within the concrete elements. 
Beside the standard finite elements special contact 
elements are available. They allow a simulation of 
the contact between concrete and headed stud. The 
analysis is incremental. For simple handling of the 
program as well as for the pre and post processing 
the commercial program FEMAP (1997) is used. 
2.2 Constitutive law Microplane model 
In the microplane model the material properties are 
characterized separately on planes of various orien-
tations within the material. On these microplanes 
there are only a few uniaxial stress and strain com-
ponents and no tensorial invariance requirements 
need to be considered. The constitutive properties 
are entirely characterized by relations between the 
stress and strain components on each microplane in 
both, normal and shear directions (Fig. 1). It is as-
sumed that the strain components on the microplanes 
are projections of the macroscopic strain tensor (Id-
nematic constraint approach). Knowing the stress-
strain relationship of all microplane components, the 
macroscopic stiffness and the stress tensor are calcu-
lated from the actual strains on the microplanes by 
integrating the stress components on the microplanes 
over all directions. The simplicity of the model is 
due to the fact that only uniaxial stress-strain rela-
tionships are required for each microplane compo-
nent and the macroscopic response is obtained 
automatically by integration over the microplanes. 
More details related to the used model can be found 
in OZbolt et al. (2001). 
a) b) 
y 
x 
Figure l. Concept of the microplane model: a) unit volume 
sphere - integration point and b) strain components. 
3 COMPARISONBETWEENTESTDATAAND 
NUMERICAL ANALYSIS IN CASE OF BLOW 
OUT FAILURE 
To verify the suitability of the finite element pro-
gram MASA for the numerical simulation of headed 
studs placed close to the edge of a concrete block a 
numerical study was cmTied out and the results are 
compared with expe1imental results. 
3 .1 Geometry and discretization 
The geometry of the modeled anchorage structure is 
shown in Figure 2a. A concrete slab with a width of 
b = c + 400 mm (c = concrete cover), a length of 
800 mm and a height of 380 mm is analyzed. The 
mate1ial properties are adapted to the properties 
known from the experiments and are summarized in 
Table 1. 
Figure 2 also shows the finite element mesh used 
in the analysis. The existing symmetry plane was 
used to reduce the analysis time. The mesh was re-
fined within the area of the headed stud. The mod-
eled test specimen is restrained in vertical direction 
at a distance of 85 mm from the anchor (Fig. 2b ). 
The numerical analysis considers the same boundary 
conditions as in the experiment (Furche, Elige-
hausen 1991). 
The discretization of the concrete slab was per-
formed by eight - node solid elements. The mi-
croplane model was used. Linear elastic material be-
havior was assumed for steel elements. 
Between the steel elements of the headed stud 
and the concrete elements contact elements were 
placed. These elements have a thickness of 0.5 mm. 
They where chosen such that only compressive 
stresses between concrete and anchor could be taken 
up. 
The load was applied by displacement control at the 
nodes of the headed stud. The displacement was in-
creased by 0.05 mm in each step. 
Table l : Material properties assumed in the analysis. 
942 
-concrete geometry steel 
Gr fctm Eat:ton f3w h,r a 
[Mpa] [Mpa] [Mpa] [Mpa] [mm] [mm] 
O,D75 2,5 35000 35 400 7,5 
a) 
[[ 
I ... 400 mm 
::: ~:::: 
.... 
~;i,:::.::::::ii )i:::::·:.:.1~~ 
/. :::::: 
::::::- -·:> 
?:;;:~ 
:/'./::-:~ 
·::>:::::::::::::::,_ 
Headed stud d = 25 mm 
b) 
Figure 2. Dimensions of the FE - model. 
y c 
[OJ [mm] 
90 60 
:~ 
~:·, 
Es1ohl 
[Mpa] 
20000 
3 
3 
c 
3.2 Numerical results and comparison with test 
results 
-
fy -
[Mpa] 
-
2000 
In both the experimental and the numerical investi-
gations a characteristic blow out failure could be ob-
served. The damage zone obtained in the analysis is 
shown in Figure 3 as maximum principal strains. 
The dark areas are the areas of strain localization 
(damage). The comparison shows a good agreement 
between the failure mode observed in the experi-
rnents and the analysis. 
The displacements and the anchor forces were 
taken at the head of the stud. At maximum load the 
displacement measured in the experiment is slightly 
larger than in the simulation. This is due to the com-
plex conditions when local damage at the head of the 
stud takes place. 
displacement 
,,Blow Out" 
Figure 3. Post peak crack pattern, her= 400 mm (embedment 
depth), c = 60 mm (edge distance), a= 7,5 mm (head shoulder). 
Experiment by Furche, Eligehausen, 1991. 
250, 00 ~--~---,..-----.-----. 
200, 00 -+---t-----+----t---t 
~ 
150,00 
'O zrl. m 100,00 .s 
50,00 experimental data 
numerical data 
0,00 -+--~~---+-~~-+~~~1--~---1 
0,00 25,00 50,00 75,00 100,00 
edge distance [mm] 
Figure 4. Influence of edge distance on failure load. Experi-
mental results taken from Furche, Eligehausen, 1991. 
Figure 4 shows a comparison between the ultimate 
loads measured in the experiments and obtained 
from the analysis. In all cases failure was caused by 
blow-out. The numerical results show a good 
agreement with the experimental results 
4,50 
8 
§ 4,00 
0 
{) 3,50 
~ 
~ 3,00 
* 2,50 b p 0 2,00 {) 
<.;... 
0 
~ 1,50 
0 
s 1,00 0 
{) 
ro 
~ 0,50 
:.a 
0,00 
O,OE+OO 5,0E+04 1,0E+05 1,5E+05 2,0E+05 
force at head [NJ 
Figure 5. Displacement of concrete surface close to the head 
perpendicular to the surface. Test results are taken from 
Furche, Eligehausen, 1991. 
In Figure 5 the lateral deformation of the concrete 
surface close to the head of the stud is plotted as a 
function of applied load. The numerical result agree 
sufficiently well with the experimental results. The 
lateral displacements increase fast after the maxi-
mum load is reached, indicating the failure of the 
concrete close to the head. 
4 COMPARISON BETWEEN EXPERIMENTAL 
AND NUMERICAL RESULTS IN CASE OF 
EDGE FAILURE 
4.1 Geometry and discretization 
The geometry of the modeled structure is shown in 
Figure 6. A concrete slab with a height of 420 mm, a 
length of 740 mm and a width of c +270 mm 
(c =concrete cover) was modeled by eigth node 
solid elements. Between the steel elements of the 
headed stud and the concrete elements a contact 
layer with a thickness of 0.5 mm was placed. The 
material properties were adapted to the material 
properties obtained from the experimental investiga-
tions of Wi.istholz (1999). The head stud was loaded 
in shear towards the edge. The supports were se-
lected (Fig. 6) as in the experiment with a distance 
of four time the edge distance. In the analysis the 
available symmetry was used. 
4.2 Numerical results and comparison with test 
results 
A typical shear failure mode occutTed in the numeri-
cal analysis as well as in the experiment. It is shown 
943 
I, 
6 
6 
370 ll\lll 
c + 270 mm 
Figure 6. Geometry and finite element mesh of the test speci-
men loaded in shear towards the edge. 
in Figures 7 and 8. The crack pattern obtained in the 
analysis shows a good agreement with the crack pat-
tern observed in the test. The influence of the edge 
distance on the failure load is shown in Figure 9. For 
an edge distances of 60 mm and 100 mm a good 
agreement of the calculated maximum loads with the 
experimental data was reached. For an edge distance 
of 160 mm a local failure in front of the anchor oc-
curred in the FE - simulation, which was not ob-
served in the tests. 
5 PARAMETRIC STUDY 
5.1 Influence of the material parameters on tensile 
(blow out) resistance 
The influence of the material parameters on the ten-
sile load capacity of anchorages at the edge was ex-
amined. In each calculation only one parameter was 
varied, while the remaining parameters c01Te-
sponded to the values of the reference model. In 
load Q 
Figure 7. Post peak crack pattern (her == 130 mm, c == 100 mm, 
shear load). 
analysis 
failure 
Figure 8. Post peak crack pattern (her== 130 mm, c == 100 mm, 
shear load). 
80,0 
70,0 
D experimental data h,r= 130 mm 
- + numerical data 1111 
60,0 
~ 50,0 
'"d ro 
..9 40,0 
11) 
2 
3 30,0 
Lo 0al failure i i front her=65 mm 
of he anchor 
'Ill 
~ ,..---.. 
~- r\!) 
h,r= 130 mm 
t 
~ 
20,0 ; h,r=65 mm 
10,0 
0,0 
0,0 50,0 100,0 150,0 200.0 
edge distance [mm] 
Figure 9. Influence of the edge distance on the failure load. 
944 
Figures lOa to lOd the calculated load displacement 
curves are shown. Varied was the concrete compres-
sion strength (Fig. lOa), the concrete tensile strength 
(Fig. lOb ), the fracture energy (Fig lOc) and the 
Young's modulus (Fig. lOd). 
Figure lOa shows that the concrete compression 
strength fc has a strong influence on the tension load 
capacity of a single anchor bolt at the edge. Increas-
ing the concrete compression strength from 20 MPa 
to 30 MPa the tension load capacity increases by 
about 11 %, whereas an increase of the concrete 
compression strength from 30 MPa to 40 MPa 
causes an increase of the load capacity of 23 %. This 
increase in failure load with increasing concrete 
compression strength can be explained follow : Fail-
ure is caused by lateral bursting forces which are 
generated due to the high pressure (lO·fc - 18·fc) un-
der the anchor. With increasing the concrete com-
pression strength a higher pressure under the head is 
needed to generate the same bursting force. The load 
displacement curves show that the behaviour be-
comes more brittle when the concrete compression 
strength increases. 
According to Figure lOb the concrete tensile 
strength has also an influence on the tension load 
capacity. An increase of the concrete tensile strength 
from ft= 1.8 MPa to ft= 2.8 MPa causes an increase 
of the load capacity by about 18 %. A further in-
crease to ft= 3.8 MPa causes an increase of the ten-
sion load capacity of 6 % only. The load displace-
ment behaviour does not change significantly. 
The fracture energy Gf has an important influence 
on the maximum load and the load displacement be-
haviour. Figure lOc shows that a doubling of the 
fracture energy from Gr = 0.05 N/mm to 
Gr= 0.10 N/mm causes an increase of the failure 
load by 14 %. Doubling of the fracture energy from 
Gr = 0.10 N/mm to Gf = 0.20 N/mm gives an in-
crease of 33 %. With the increase of the fracture en-
ergy Gr the behavior becomes more ductile. 
The Young's modulus of concrete has a smaller in-
fluence on the failure load. In Figure lOd the load 
displacement curves with the Young's modulus of 
20.000 MPa, 35.000 MPa and 40.000 MPa are plot-
ted. They show that an increase of the Young's 
modulus causes an increases the tension load capac-
ity by 4 % and 5 % respectively. 
5.2 Influence of material properties on the shear 
concrete edge resistance 
The influence of the material parameters on the 
shear loading capacity of anchorages at the edge is 
studied. In each calculation only one parameter was 
varied, while the remaining parameters c01re-
sponded to the values of the reference model. In 
Figures 1 la to l ld the calculated load displacement 
1 curves are plotted. Varied was the concrete com-
945 
250 
a) 
200 
~ 
50 
'"d 
,,; 00 ..s 
50 
0 
0 
250 
b) 
200 
~ 
150 
'"d 100 ,,; 
..s 
50 
0 
0 
250 
c) 
200 
~ 
150 
'"d 
,,; 100 ..s 
50 
0 
0 
250 
d) 
200 
~ 150 
'"d 
,,; 
..s 100 
50 
0 
0 
2 3 
=20 MPa 
= 30 MPA 
= 40 MPA 
4 
displacement 
--f = 1,8 MPa 
::.::::.:::.· ;; : ~:: ~~: 
2 3 4 
displacement 
--G,=0,05 
····-···-· G
1
=0,10 
··········G
1
=0,20 
2 3 4 
displacement 
--E = 20.000 MPa 
-·-·-·-·- E = 35.000 MPa 
........ E = 40.000 MPa 
2 3 4 
displacement 
5 
5 
5 
5 
Figure 10. Calculated load - displacement curves showing the 
influence of the material properties : a) compression strength fc 
b) tensile strength ft , c) fracture energy Gr and d) Young's 
modulus E. 
pression strength (Fig. l la), the concrete tensile 
strength (Fig. llb), the fracture energy (Fig. llc) 
and the Young's modulus (Fig. lld). 
Figures lOa shows that the concrete compression 
strength fc has a visible influence on the shear load 
capacity of a single anchor bolt at the edge. Increas-
ing the concrete compressive strength from 25 MPa 
to 35 MPa the shear load capacity increases by 
about 5 %, while a decrease of the concrete com-
pressive strength from 25 MPa to 15 MPa causes a 
decrease of the shear load capacity of 10 %. 
According to Figure 11 b the concrete tensile 
strength has a strong influence on the shear load ca-
pacity. A decrease of the concrete tensile strength 
from ft= 2.5 MPa to ft= 1.5 MPa causes a decrease 
of the shear load capacity of about 13%. 
The fracture energy Gf has also an important in-
fluence on the maximum load and load displacement 
behavior. Figure l lc shows that an increase of the 
fracture energy from Gf = 0.04 N/mm to Gf = 0.10 
N/mm causes an increase of the failure load by 
14 %. 
The Young's modulus of concrete exhibits a rela-
tively strong influence on the shear load capacity. In 
Figure 1 ld the calculated load displacement curves 
with Young's modulus of 20.000 MPa, 30.000 MPa 
and 40.000 MPa are plotted. The figure show that 
an increase of the Young's modulus by 100 % in-
creases the shear load capacity by 19 %. 
The results of the parametric study are summa-
rized in Figure 12. The figure shows that the failure 
load in the blow-out failure mode is more sensitive 
to the variation of the material properties than in the 
shear failure mode. With the blow-out failure mode 
the failure load increase approximately with \j/0•4 
(\jf =parameter) (fc, Gf) or \j/0'25 (fc, Gf). 
On the contrary to that with the shear failure 
mode the increase is proportional to the varied pa-
rameter \jf 0'25 . 
6 CONCLUSION 
The FE code MASA used in the present study is 
based on the microplane material model for concrete 
and on the smeared crack approach. As localization 
limiter the modified crack band method is used. 
The comparison between the numerical and ex-
perimental data shows that the FE code is able to 
simulate the failure mechanism of headed stud an-
chorages placed close to edge under tensile loading 
or shear loading. 
The parametric study indicates that failure load 
and the blow out failure mode is more sensitive to 
the variation of mate1ial properties than in the shear 
failure mode. 
946 
displacement 
Figure 11. Calculated load - displacement curves of the refer-
ence model showing the influence of the material properties : 
a ) compression strength fc , b) tensile strength ft ,c) fracture 
energy Gr and d) Young's modulus E. 
tension load 
1,125 
0,875 
0, 750 +-------4-----~------4 
0,50 1,00 1,50 2,00 
relative influence parameter 1jf 
shear load 
1,250 ~----------------~ 
b) 
0,875 
· - · - +compressive strength (ll 
.......... 11 tensile strength (2) 
fracture energy (3) 
Young's Modulus(4J 
0,750-1------.,..---------.-------4 
0,500 1,000 1,500 2,000 
relative influence parameter 1jf 
Figure 12. Comparison of the relative influence of material 
properties of headed studs under a) tension load. and b) shear. 
7 REFERENCES 
Ozbolt, J.; Li, Y.-J. and Ko:Z:ar, I. (2001). Microplane model for 
concrete with relaxed kinematic constraint. International 
Journal of Solids a11d Structures, in press. 
Fuchs, W.; Eligehausen, R and Breen, J.E. (1995). Concrete 
Capacity Design (CCD) Approach for Fastenings to Con-
crete. ACI Structural Journal, Vol. 92, No. 6, S794-802 
FEMAP (1997) - Finite Element Modelling and Postprocess-
ing, Ver. 5.00a, Copyright© Enterprise Software Products, 
Inc. 
Furche J.; Eligehausen, R. (1991). Lateral Blouout Failure of 
headed Studs Near the Free Edge. In:Senkiw,G.A. ; Lance-
lot, H.B., SP-130 Design an Behavior. American Concrete 
Institute, Detroit, page 235 - 252. 
Wtistholz, T (1999). Tragverhalten von randnahen Befesti-
gungsmitteln unter Querlasten bei der Versagensart Beton-
947 
ausbruch. Diploma theses at the /11stitute of construction 
material, University Stu1tgart 


Behavior and design of fastenings with headed anchors at the edge under tension and shear load

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Behavior and design of fastenings with headed anchors at the edge under tension and shear load

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