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

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Figure 1 – Experimental setup of the beamassemblage.

The system of connection between beamshow 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 describetensile 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 0.3RUBBER 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 DIANAfracture 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 elasticboth 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 stressstrain 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 modelingshould be performed:

definition of geometry, creation of meshmaterials, assignment of propertiesboundary 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)

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to create points and then connecting the dotscreate poly-lines. In the formation of polycan 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, rubbersteel plates where any constraints and loadswere modeled by a four-node quadrilateral plane stress elements and three-node triangle plane stress elements whereas steel reinforcements were modeled by twostraight 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 wasconstraining the node in y-direction and the support of column was made by restricting the node in the xdirection 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 prcase 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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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”

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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 polyDIANA creates surfaces directly. Then witcommand “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, threepyramid elements whereas steel longitudinal reinforcements were modeled by twoelements and the stirrups two-dimensional class-II beam element. elements, the only physical property thmaterial. 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, 9106for 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 beamcolumn joint

Figure 18 – 3D MODEL “B”: Zoom of the mesh in the beamcolumn 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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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.2partial 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: zoomedfor applied load of 600 kN (max 184 N/mmq)

Figure 23 – “B” MODEL: top d

Figure 24 – “A” MODEL: zoomed vfor applied load of 600 kN (max. 1028 N/mmq)

3.4 Non linear analysis

In the following the results of the non linear athe so-called “A4.4” and “B4.4” modelsstarting 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.

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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, tvaluable graph, because it underlinessimilarity between the simulations conductedways, with redundancy of software and people.

Finally, in Figg.27-28 pictures shows the crackresults 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 v450 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 beamconnections, 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 britfailure do not occurs. The progress of the cracking of the concrete is well reproduced.

An important result is the similarityresults obtained with twoelement 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

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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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