Especially to precast concrete structure connections are one of the most essential parts. Connections transfer forces between precast members, so the interaction between precast units is obtained. They are generally the weakest link in the structure. An acceptable performance of precast concrete structure depends especially on the appropriate kind of connections choice, adequate detailing of components and design of the connections is fundamental. It is interesting to study the behavior of connecting elements and to compare different solutions of ductile connections for precast concrete structures in case of horizontal applied force and vertical imposed displacement, as well as those produced by hazards situation, like that earthquake and explosion, whereby topics of structure robustness are carried out. The case of study is an innovative dissipative system of connection between precast concrete elements, usable for buildings and bridges, the investigation of these topics is carried out by F.E.A. by program DIANA with comparison with results obtained independently with ASTER.

1. 1 FINITE ELEMENT ANALYSIS
1.1 Introduction
The experience of hazards, like earthquakes and even
accidental situations, has shown that reinforced concrete
bridges are subject to beam-column joint failure. If
connection design is inadequate, for example for the
shear load that develops under earthquake excitation, the
connection may exhibit deteriorating stiffness and
strength. This behavior may result in inadequate
structural performance. Over the years, many studies
about system of beam-column connections of bridge have
followed. View of the analogy between the beam-column
points of reinforced concrete buildings and bridges, in
this study, the authors treat the topic of beam-column
connections for precast concrete structures.
This work presents the FEM Analysis for studying the
behavior of an innovative dissipative system of
connection between precast concrete elements. The FEM
program DIANA v 9.3 was used. DIANA is a general
purpose finite element code, based on the Displacement
Method, with extensive material, element and procedure
libraries based on advanced database techniques. To
create the geometry and then the mesh of the structure, to
assign boundary conditions and loads, the program Midas
FX+ for DIANA was used. FX+ is a general purpose
pre- and postprocessor that provides state-of-the-art finite
element modeling tools. It is equipped with advanced
geometric modeling functions, powerful mesh generation
algorithms, various analysis conditions, and exceptional
output displays with the latest graphics technology. The
non-linear mechanisms that were considered in this study
are cracking of the concrete and yielding of the steel.
Since the objective of the investigation was to simulate
structural behavior in a realistic way, material parameters
were taken by their mean values instead of the
characteristic or design values. The finite element models
were two-dimensional and three-dimensional, using truss,
beam, plane stress and solid elements. Comparison
between two models is presented: a model with beam
and column connection made by mortar (monolithic
structure, MODEL “A”) and a model without mortar
connection (MODEL “B”). The results of linear analysis
were compared to results of non linear analysis of
materials.
1.2 Structure
The structural configuration studied consists of a beam-
column sub-assemblage with BS-Italia connectors as
shown in Fig.1 with the classical test bed.
Finite element analysis of innovative solutions of precast concrete beam-
column ductile connections
A. Saviotti, P. Olmati, F. Bontempi
Sapienza Università di Roma, Rome, Italy
ABSTRACT: Especially to precast concrete structure connections are one of the most essential parts. Connections
transfer forces between precast members, so the interaction between precast units is obtained. They are generally the
weakest link in the structure. An acceptable performance of precast concrete structure depends especially on the
appropriate kind of connections choice, adequate detailing of components and design of the connections is fundamental.
It is interesting to study the behavior of connecting elements and to compare different solutions of ductile connections
for precast concrete structures in case of horizontal applied force and vertical imposed displacement, as well as those
produced by hazards situation, like that earthquake and explosion, whereby topics of structure robustness are carried
out. The case of study is an innovative dissipative system of connection between precast concrete elements, usable for
buildings and bridges, the investigation of these topics is carried out by F.E.A. by program DIANA with comparison
with results obtained independently with ASTER.
Bridge Maintenance, Safety, Management, Resilience and Sustainability – Biondini & Frangopol (Eds)
© 2012 Taylor & Francis Group, London, ISBN 978-0-415-62124-3
2048

2. Figure 1 – Experimental setup of the beam
assemblage.
The system of connection between beam
show in Figure 2.
Figure 2 – Innovative connections system by BS
1.3 Materials
The basic material characteristics are summarized in
Table 1.
Table 1
1.3.1 Concrete
The behavior of the concrete was modeled with the total
strain based constitutive model which describe
tensile and compressive behavior of a material with one
stress-strain relationship. The non-linear
concrete was considered in both tension and compression
including the influence of lateral cracking on the
compressive strength. In this study, within
capabilities, it was chosen a “LINEAR” curve for tension
softening functions based on fracture energy
“CONSTA” curve (Fig. 3) for compression functions.
fck Rck Ecm ν
N/mm2
N/mm2
N/mm2
N/mm
CONCRETE
C40/50
40 50 35220 0.2
CONCRETE FOR
STRATUM
30960 0.2
STEEL B450C 206000 0.3
RUBBER 500 0.4
setup of the beam-column sub-
The system of connection between beams and column is
Innovative connections system by BS-Italia.
The basic material characteristics are summarized in
The behavior of the concrete was modeled with the total
which describes the
tensile and compressive behavior of a material with one
linear behavior of
concrete was considered in both tension and compression
including the influence of lateral cracking on the
, within DIANA
” curve for tension
racture energy and a
) for compression functions.
a) b)
Figure 3 –a) Tension behavior for concrete after
Compression behavior for concrete after
The tensile curve in DIANA
fracture energy, according to Feenstra. The relationship
for reduction due to lateral cracking is the model
according to Vecchio & Collins
1.3.2 Steel
For the reinforcement, an elastic
both in tension and compression, with Von Mises yield
criterion. For Steel a predefined class according to the
NEN 6770 code was used, and the materials model
implemented are show in Figure
Figure 4 – Steel behavior.
1.3.3 Mortar and Rubber
The rubber pad was modeled with a linear elastic stress
strain relation. For the mortar a total strain model was
used, similar to the one for concrete.
2 TWO-DIMENSIONAL
The first model was developed in two dimensions.
Midas FX+ for DIANA as for
realize a two-dimensional modeling
should be performed:
definition of geometry, creation of mesh
materials, assignment of properties
boundary conditions, application of loads/displacements
2.1 Geometry
The creation of geometry in Midas FX+
made by entering the coordinates from external files (.txt)
fyk ftk
N/mm2
N/mm2
450 540
a) b)
Tension behavior for concrete after DIANA; b)
Compression behavior for concrete after DIANA.
DIANA is a formulation based on
fracture energy, according to Feenstra. The relationship
for reduction due to lateral cracking is the model
according to Vecchio & Collins
For the reinforcement, an elastic-plastic model was used
both in tension and compression, with Von Mises yield
criterion. For Steel a predefined class according to the
NEN 6770 code was used, and the materials model
implemented are show in Figure 4.
The rubber pad was modeled with a linear elastic stress-
For the mortar a total strain model was
used, similar to the one for concrete.
DIMENSIONAL MODEL
The first model was developed in two dimensions. In
as for DIANA v 9.3 too, to
modeling the following steps
creation of mesh, assignment of
of properties, introduction of
application of loads/displacements.
creation of geometry in Midas FX+ for DIANA was
made by entering the coordinates from external files (.txt)
2049

3. to create points and then connecting the dots
create poly-lines. In the formation of poly
can create surfaces directly.
2.2 Mesh
About mesh, it was chosen a discretization more refined
at the connecting joint between beam and column and a
coarse mesh elsewhere. Concrete, mortar, rubber
steel plates where any constraints and loads
were modeled by a four-node quadrilateral plane stress
elements and three-node triangle plane stress elements
whereas steel reinforcements were modeled by two
straight truss elements.
An overview of the mesh scheme is shown in
6.
Figure 5 - Model with connection mortar stratum
Figure 6 - Model without connection mortar stratum
MODEL
2.3 Boundary conditions and loads
In this work the support of beams was
constraining the node in y-direction and the support of
column was made by restricting the node in the x
direction and in the y-direction and a concentrated
horizontal force was applied at the top of the column.
connecting the dots to
In the formation of poly-lines DIANA
About mesh, it was chosen a discretization more refined
at the connecting joint between beam and column and a
coarse mesh elsewhere. Concrete, mortar, rubber and
loads are applied,
node quadrilateral plane stress
node triangle plane stress elements
whereas steel reinforcements were modeled by two-node
he mesh scheme is shown in Figs.5 and
Model with connection mortar stratum MODEL “A”
Model without connection mortar stratum – “B”
In this work the support of beams was achieved by
direction and the support of
column was made by restricting the node in the x-
direction and a concentrated
horizontal force was applied at the top of the column.
2.4 Linear Analysis
In any kind of structural pr
case is need: Figs.7-8 and Figs.
both for MODEL “A” with
“B” without.
Figure 7 – “A” MODEL: linear analysis
23.4 mm for 600 kN of load applied at
Figure 8 – “A” MODEL: linear analysis
Stress in x-direction for load of 600 kN that it was applied at
the top of the column.
Figure 9 – “B” MODEL: linear analysis
35.1 mm for 600 kN of load applied at the top of the column.
In any kind of structural problem analysis, a first linear
and Figs.9-10 show partial results
mortar stratum and for Model
linear analysis - top displacement of
applied at the top of the column.
linear analysis - zoomed view of
direction for load of 600 kN that it was applied at
linear analysis - top displacement of
applied at the top of the column.
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4. Figure 10 – “B” MODEL: linear analysis - zoomed view of
stress in x-direction for load of 600 kN that it was applied of
the column.
In particular, after this opening analysis is done DIANA
checks whether any badly shaped elements exist. There
were no such warning messages in the analysis-progress
window or in the standard output file, so it’s possible to
inspect and accept the analysis results.
Looking at Figg.7-10, it is clear the impact of
the presence or absence of the mortar stratum; in
fact, with regard tension (Fig. 8 and 10), the steel
elements of connection of MODEL “A” have a max
of about 130 / , but the system of connection of
model B have a max of about 1580 / . The
presence of mortar stratum increases the initial stiffness
about of 50%. (Figg. 8,10)
2.5 Non linear analysis
Just as with linear analysis, a displacement vector that
balances the internal and external forces must be
calculated. In the linear case, the solution vector can be
calculated immediately, but in the nonlinear case you
cannot. To determine the equilibrium state not only
makes the problems in the discrete space (with finite
elements) but also over time (in increments). To achieve
balance at the end of the increment, an iterative solution
can use. The combination of the two is called
the incremental-iterative solution procedure. The
incremental-iterative solution procedure consists of two
parts: the increment part and the iteration part.
In this work a Regular Newton-Raphson incremental
method was used. For convergence criteria the program
DIANA offers 3 types of norms: displacement, force and
energy norms. In this analysis all norms were used
contemporaneously with arc-length strategy. The Fig.11
shows the force-displacement diagram for some of the
cases studied and summarized in table 2.
Table 2
Figure 11 – Comparison among different force-displacement
response of MODEL “A” and MODEL “B”.
After this initial exploratory phase, the finally selected
models for this study are “A4.4”, “B4.4” because they are
the model whose behavior is more realistic.
The displacement at the application of the horizontal
force at the Step 1, when the force is about of 18 kN for
both Models, is practically imperceptible. Later on with
the further application of load steps of the horizontal
force the structure deforms. The column tends to deform
much more compared with the other elements.
Beside global aspects as the overall diagram force-
displacement, it is interesting to examine local aspects.
The crack-strain results at the integration points (first
crack at integration point) are named in DIANA.
Different load steps in order to show the cracking
sequence are presented:
• MODEL “A”:
- Step 7 – F=105.41 kN, when the behavior of
structure is still linear-elastic;
- Step 40- F=280.9 kN, after reaching the
maximum force;
• MODEL “B”:
- Step 7 – F=107.6 kN,, the behavior of structure
is still linear-elastic;
- Step 18 – F=173.1 kN,, after reaching the
maximum force;
Figure 12 – Comparison between MODELS “A” and “B”
2051

5. a) b)
Figure 13- MODEL “A” - CRACK STATUS:
Step 40, after reaching the maximum force.
a) b)
Figure 14– MODEL “B” - CRACK STATUS:
Step 18, after reaching the maximum force.
Finally, also the correct representation of steel must
checked. Fig.15 shows how the stress is developed in the
steel parts of the models, following the prescribed law.
Figure 15 - Relationship between stress and strain for
“A” and “B” of beam-column ductile connection.
3 3D MODEL
The three-dimensional modeling of concrete structures is,
in the opinion of the authors, still complex.
For the three-dimensional modeling the
performed are the same of 2D Model.
The creation of geometry was made by entering the
coordinates from external files (.txt) to create points and
then connecting the dots to create poly
DIANA creates surfaces directly. Then wit
command “EXTRUDE”, the surfaces became
3.1 Mesh
Concrete, mortar, rubber and steel
plates where any constraints and loads are applied, were
CRACK STATUS: a) Step 7; b)
CRACK STATUS: a) Step 7; b)
representation of steel must be
how the stress is developed in the
, following the prescribed law.
Relationship between stress and strain for MODEL
column ductile connection.
dimensional modeling of concrete structures is,
in the opinion of the authors, still complex.
steps should be
The creation of geometry was made by entering the
coordinates from external files (.txt) to create points and
poly-lines and so
. Then with the
surfaces became solids.
Concrete, mortar, rubber and steel
are applied, were
modeled by a four-node, three
pyramid elements whereas steel longitudinal
reinforcements were modeled by two
elements and the stirrups
two-dimensional class-II beam element.
elements, the only physical property th
material. For the reinforcing steel the physical input is the
cross-sectional area and for the stirrups the physical input
is the diameter of the section.
The mesh scheme is shown in Fig.
158634 solid elements, 9106
for a total of around 142941
Figg.17-18 show details for
respectively, focusing on the concrete parts of the
specimen.
Details of the steel reinforcing layout are instead
in Figg.19-20.
Figure 16 – 3D Model “A”: Mesh
Figure 17 - 3D MODEL “A”: zoom of the mesh in the beam
column joint
Figure 18 – 3D MODEL “B”: Zoom of the mesh in the beam
column joint.
node, three-side iso-parametric solid
pyramid elements whereas steel longitudinal
reinforcements were modeled by two-node straight truss
the stirrups were modeled by two-node,
II beam element. For solid
the only physical property that is needed is the
material. For the reinforcing steel the physical input is the
sectional area and for the stirrups the physical input
is the diameter of the section.
esh scheme is shown in Fig.16: it consists in
9106 bar elements, 31639 nodes
142941 degree of freedom.
show details for MODEL “A” and “B”
respectively, focusing on the concrete parts of the
Details of the steel reinforcing layout are instead shown
Model “A”: Mesh
: zoom of the mesh in the beam-
: Zoom of the mesh in the beam-
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6. Figure 19 – Overview of the reinforcing steel
MODEL.
Figure 20 –Reinforcing Steel of 3D MODEL: zoom at the
section of innovative solutions for ductile connections.
3.3 Boundary conditions and loads
The boundary conditions and loads are the same of the
two-dimensional model. Of course, suitable out of plane
constraints are considered.
3.4 Linear Analysis
A first linear analysis was performed. Figg.2
partial results of this linear analysis.
Figure 21 – “A” MODEL: top displacement of 19.2 mm.
teel layout of 3D
Reinforcing Steel of 3D MODEL: zoom at the
section of innovative solutions for ductile connections.
The boundary conditions and loads are the same of the
Of course, suitable out of plane
Figg.21-24 show
of 19.2 mm.
Figure 22 – “A” MODEL: zoomed
for applied load of 600 kN (max 184 N/mmq)
Figure 23 – “B” MODEL: top d
Figure 24 – “A” MODEL: zoomed v
for applied load of 600 kN (max. 1028 N/mmq)
3.4 Non linear analysis
In the following the results of the non linear a
the so-called “A4.4” and “B4.4” models
starting with global response as in Fig.
Figure 25 – “MODEL “A”
responses from linear and non linear a
oomed view of stress in x-direction
(max 184 N/mmq).
top displacement 26.1 mm.
: zoomed view of stress in x-direction
(max. 1028 N/mmq).
the results of the non linear analysis of
“A4.4” and “B4.4” models are shown,
starting with global response as in Fig.25.
MODEL “A” vs “B” ” force-displacement
responses from linear and non linear analysis.
2053

7. An interesting diagram is shown in Fig.
represented all the curves obtained with DIANA
superimposed with the curves obtained with a
independent analysis developed by the code ASTER
Figure 26 – Comparison between results obtained with
v 9.3 program and results obtained with ASTER
In the opinion of the authors, t
valuable graph, because it underlines
similarity between the simulations conducted
ways, with redundancy of software and people.
Finally, in Figg.27-28 pictures shows the crack
results at the integration points .
steps in order (Steps 1, 5, 15, 20) to show the cracking
sequence are presented.
Details for the stress level on the reinforcing bars
shown in Fig.29 and 30, from where it appears that the
bars are fully plasticized as in Fig. 37: this development
is of course important for the ductility requirements.
a) b)
c) d)
Figure 27 –MODEL “A”- Zoomed View of Crack Strain: a)
Step 1; b) Step 5 c) Step 15; d) Step 20.
a) b)
c) d)
Fig.26. Here are
represented all the curves obtained with DIANA
superimposed with the curves obtained with a
analysis developed by the code ASTER.
Comparison between results obtained with DIANA
ASTER Code.
In the opinion of the authors, this is a
it underlines the
between the simulations conducted in two
ways, with redundancy of software and people.
pictures shows the crack-strain
. Different load
20) to show the cracking
forcing bars are
from where it appears that the
: this development
is of course important for the ductility requirements.
View of Crack Strain: a)
Figure 28 –MODEL “B”- Zoomed View of Crack Strain: a)
Step 1; b) Step 5 c) Step 15; d) Step 20
Figure 29 – MODEL “A”: zoomed v
450 N/mmq, STEP 15).
Figure 30 – MODEL “B”: zoomed view of steel stress
450 N/mmq, STEP 12).
4 CONCLUSIONS
In this paper the mechanical behavior of a beam
connections, usable for buildings and bridges,
examined by a finite element analysis.
To develop the numerical analysis
software, modeling the nonlinear behavior of concrete
and mortar using total strain
steel is modeled by a bilinear plasticity model. A detailed
geometry of the system is been meshed and a non linear
constitutive law of the material is been adopted.
The full load capacity of the bars
the failure of the concrete and the
connection system is well performing because a brit
failure do not occurs. The progress of the cracking of the
concrete is well reproduced.
An important result is the similarity
results obtained with two
element programs, the previously mentioned
Zoomed View of Crack Strain: a)
Step 15; d) Step 20
: zoomed view of steel stress (max
MODEL “B”: zoomed view of steel stress (max
In this paper the mechanical behavior of a beam-column
, usable for buildings and bridges, is
examined by a finite element analysis.
To develop the numerical analysis it is used DIANA
modeling the nonlinear behavior of concrete
train crack model. The reinforcing
modeled by a bilinear plasticity model. A detailed
geometry of the system is been meshed and a non linear
constitutive law of the material is been adopted.
The full load capacity of the bars is developed without
concrete and the mortar: therefore the
connection system is well performing because a brittle
failure do not occurs. The progress of the cracking of the
concrete is well reproduced.
An important result is the similarity between the
obtained with two different finite
the previously mentioned DIANA
2054

8. and ASTER. In this way, a complete sensitivity analysis
for this specific kind of connection is developed.
First of all, the role of the mortar stratum is weighted: the
results show that the presence of stratum leads to a
certain degree of increase both in the initial stiffness and
in the final resistance.
Another point of interest was the effect of the
introduction of the connectors inside the mass of
concrete: some worries were about the possibility that
this presence can develop brittle failure mechanism. This
was not the case.
In particular, the overall response curves appear smooth
and regular and in the bars plastic strains are developed,
leading to an effective ductile connection system.
ACKNOWLEDGEMENTS
Arch. Sergio Zambelli and Dr. Claudio Pagani of BS
Italia / Styl-Comp Group, Zanica (BG), Italy, Dr.
Francesco Petrini, Sapienza Università di Roma, Rome,
Italy, and Dr. Luca Sgambi of Politecnico di Milano,
Italy, are deeply acknowledged for support and
discussion.
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