abaqus behavior

Numerical model of shear connection by concrete dowels

W. Lorenc, R. Ignatowicz, E. KubicaFaculty of Civil Engineering, Wroclaw University of Technology, Poland

G. SeidlSchmitt Stumpf Fruhaufund Partner (SSF), Germany

Keywords: concrete dowel, numerical model, shear connection, composite structures

ABSTRACT: The VFT-WIB® construction method represents a new technology in Europe using prefabricatedcomposite beams with innovative type of shear force transfer mechanism. A new type of shear transmission -the concrete dowel - allows composite girders without any upper steel flange and an enduring shear connectionespecially between high strength steel combined and high strength concrete. The concrete dowel is a coproduct

tiona cthe

sfythiss ofnon

s ob

– concrete failure by shearing.

The steel failure has also to be additionally consid-

from the processing of rolled beams in steel construcare necessary to investigate complex stress states inand also to develop the best dowel shape maximizingThe finite element method is an adequate tool to satideveloped by using ABAQUS software to investigatetypes are taken into consideration. Different procedureexplicit processing method. The influence of materialand embedded elements can be figured out. The resultexperimental results obtained during push-out tests.

1 SHEAR TRANSMISSION WITH CONCRETEDOWELS

The shear connection realized by concrete dowels,which appear between the cut steel web and the con-crete, is applied to composite beams developed by SSF(Schmitt and Seidl 2006).

As the concrete dowel (CD) is a spin-off productfrom the processing of rolled beams in steel construc-tion, different cutting shapes are possible to obtain.A three-axial stress situation is generated in con-crete dowels (confined concrete) which creates a high
load-bearing capacity. Different shapes and dimen-sions are possible, which influences the slip-behaviorand load-bearing capacity of this connection. FEMis an economic and efficient method for parametricalstudies to optimize the design unlike time-consumingexperimental tests. However, numerical models arecomplex, the behavior is high-grade nonlinear andinfluenced by many parameters. The aim of this paperis to present general approaches and values of variableswhich are necessary to define.
© Millpress, The Netherlands, ISBN 9789059660540

without any additional resource. Numerical modelsoncrete dowel, to predict the load-bearing capacityshear force transferred in the composite connection.

this demand. A complex three-dimensional model isshear connection. Different element types and mesh

analysis are applied by comparing the implicit and thelinearities of steel and concrete, contact interactions

tained from the finite element analysis is validated by

2 EXPERIMENTAL STUDY

Push-out models and then following tests conductedby Fink and Petraschek (2006) were the basis forthe FEM study. Three fundamental concrete fail-ure mechanisms characterize this shear connection(Zapfe2001):

– concrete crushing (local compression),– pry-out of concrete coverage by a cone,

ered. The proposed FE model, which is partly validatedby experimental results, predicts this specific behaviorof the structure.

3 NUMERICAL MODEL - GENERALAPPROACH

A numerical model is generated with the objective ofanalyzing the structural behavior of the connection

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ranges from −3 [mm] to −10 [mm]. Caused by thesymmetry of 1-2 and 2-3 plane appropriate symmetricboundary conditions are used. Hence load-slip relation(P-u curve) is defined by reaction force Pv2 versusdisplacement u2 measured in the reference point.

3.4 Finite elements

In general the steel girder and the concrete part aremodeled with continuum elements C3D8R because the

and determining the failure mechanisms. ABAQUSsoftware was used (ABAQUS 2004).

The numerical simulation of the connection withCD is complicated because of its complex geom-etry combined with a multiplicity of nonlmeanties.To establish an elementary model is complex, espe-cially due to the concrete part of the connection whichappears high-graded non-linear in whole load range.Therefore the following aspect are focused: the mate-rial nonlinearities, the contact interactions and thecomplex geometry. Push-out tests are an elementarymethod for determining the resistance and for study-ing the behavior of shear connector. Hence a numericalmodel of push-out test is created first. Geometric andmaterial properties of this numerical model correspondto the specimens tested by Fink and Petraschek (2006).Investigating the behavior of the model is possible bycomparing it with experimental results. Some assump-tions for FEM model are similar to the approachpresented by Marecek et al. (2006) using ABAQUSsoftware. Detailed descriptions of the software and theaspects of modeling abilities are omitted in this paper.

3.1 Geometrical model of push-out specimen

Basically the model consisted of three parts: steel, con-crete and reinforcement bars. The push-out specimencontains two symmetric planes. Symmetric boundaryconditions are used and only % of specimen is model-lised. This model is indicated 3P1, because three teethof the push-out specimen are taken into consideration.Basically one element represents half of web thick-ness (plane 1–3 view) and the size of all the elementsis similar.

3.2 Material models

Nonlinear material laws are applied to the struc-tural steel and to the concrete. A linear modelis applied to reinforcement bars. The “Mises cri-terion” of isotropic hardening is implemented forconstruction steel and “Concrete Damaged Plasticity”(CDP) -model (ABAQUS 2004) describes the concretebehavior. Important is, that no degradation of stiffnessis applied as well as no decreasing part of tension curveappears - there is steady value of fct after cracking stress(Figure 2). It is constituted “Substitute CDP model”. A
curve for uniaxial compression can be defined accord-ing to MC 90 (CEB-FIP, 1993). This concrete modelis justified if an element is generally under compres-sion. The decreasing part of the curve under tensionresults in local problems inside the concrete dowel andunreasonable post-failure behavior: The P-u curve israpidly decreasing after the maximum load level. CDPmaterial parameters are:
- eccentricity e = 0.15- dilation angle � = 15- Kc = 0.667

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Figure 1. Geometry of push-out (3P1) model: a) mesh, b) com-ponents.

The ratio of stresses �b0/�c0 = 1.16 is assumed, fc,fct,and Ec are then determined according to experimentalresults (concrete compression tests).

3.3 Interactions and boundary conditions (BCs)

In the hard contact between steel and concrete isassumed a friction coefficient R = 0.3. The specimenin the model is supported at the bottom surface ofconcrete part (Figure 1a). The predetermined verti-cal displacement is applied to the upper surface ofthe horizontal steel plate. Therefore a rigid body isimplemented. Hence displacement M2 (vertical dis-placement - Figure 1b) applies to a single point whichdefines the reference point at the intersection of thesymmetry planes of push-out specimen. This displace-ment u2 is increasing from null to the U2,max which

explicit method is used in most of the ca-culations.Different element sizes are studied up to more than106 elements for one model (3P4 model-four elements

Figure 2. Strain- stress relation (uniaxial) for concrete.

Structural Engineering, Mechanics and Computation 3, A. Zingoni (ed.)

along the half of web thickness). Reinforcement barsare modeled with beam elements B32 instead of trusselements because they enable dowel action accordingto MC 90 (CEB-FIP, 1993). This difference influencesthe behavior and load capacity of the structure. Hencetrusses do not seem to be the appropriate solution. Thebeam elements are embedded in the concrete elementsand the appropriate BCs are prescribed to their end in1-2 plane.

3.5 Analysis procedures

Two different methods are common (ABAQUS2004) for solving numerical problems: implicitmethod (ABAQUS/Standard) and explicit method(ABAQUS/Explicit). Both approaches are applied andcompared due to the ability to solve the problem andthe efficiency of calculation. Finally explicit methodwas chosen as the favorable method to solve problemconcerning concrete dowels. In ABAQUS/Explicitapproach the time incrementation is controlled by thestability limit of the central difference operator. Thisprocedure is efficient for large models and for the anal-ysis of extremely discontinuous events or processes.If the explicit method is used “smooth step” curve wasapplied for displacement u2 of reference point and timeperiod was set to ttot = 0,01 [sec]. Contact interactionswith kinematic contact method and default weightingfactor is implemented in the solution. The ttot valueis very important and extensive study was conductedto set this value properly. Furthermore the implicitmethod is used in a comparative study.

3.6 Results and conclusions of the comparativestudies

Selected results are presented in Figure 3. The com-parison of FEM results with experimental resultsconfirms that the generated push-out model representsthe behavior in the push-out tests quite well. The loadcapacity of the connection is depending on the confin-ing effect of concrete by the reinforcement bars. Alsothe BCs are important as well as the concrete mate-rial law. It is stated that decreasing part of concretelaw (tension) used with CDP model by default resultsin a local failure mechanism. On the other hand thisnumerical problem does not appear in the real struc-
ture. This simplification has to be investigated in anadditional study, but currently this proposed modelsolves the problem of “numerical local failure” in aconvenient way. The number of elements and their sizedon’t influence postfailure capacity. But a smaller sizeof the elements results in early starting failure mech-anism. The model with a coarse mesh figures out arapidly decreasing part of P-u curve and a higher loadcapacity is reached. On the other hand this model ismore convergent with the experimental values of thepush-out tests. The implementation of constant part ofthe curve describing the concrete law under tension

Figure 3. Push-out model results: a) Mises stress, b) u2 dis-placements, c) additional plate which enables modeling of contactsupport, d) Mises stress (yielded steel) for 3P4 model (with highnumber of elements).

solves the problem of local failure mechanism. Fur-thermore it can be justified only if the model has tobe mainly compressed in u2 direction without largetensioned blocks which overestimate capacity. So it isvery important to define appropriate BCs and some-times additional contact interaction elements (Figure 3c) are necessary, especially for models which havelarge cross-sectional area in plane 1-3 compared toheight of model.

It is obvious, that many parameters can influencethe behavior of the model, e.g. time period ttot, vari-ables and coefficients in concrete CDP model, the sizeof elements, BCs etc. A simplified model is necessaryto derive from which parameters the structural behav-ior is influenced. Therefore different material lawsare combined and the failure mechanisms are evalu-ated due to influence of the parameters. The followingcombinations are investigated:

– NLsNLc (nonlinear steel/nonlinear concrete)– NLsLc (nonlinear steel/linear concrete)– LsNLc (linear steel/nonlinear concrete).

4 ONE-DOWEL MODEL

The general approach to calculate the shear transmis-sion of CD is a “one-steel-tooth-model” embedded inreinforced concrete. Appropriate boundary conditionsand interactions are necessary to represent the behav-

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Figure 4. One-dowel model (1D) - geometry and BCs.

ior of the structure. The geometry and the boundaryconditions are shown in Figure 4 and interactions aredifined in Figure 5.

The idea is that Part 1 moves parallel to axis 1with respect to Part 2 and bottom surface of Part1 is fixed with rigid body to reference point (RP)where appropriate boundary conditions (BC3) are pre-scribed: u2 = r3 = 0 and u1 is increasing up to valueu during analysis. Half of the structure is modeled
1,max
(t = tw/2, where tw is web thickness), hence symmetryBCs in plane 1-2 are applied (BC1) to all nodes ofmodel placed in this symmetry plane. Reinforcements(Part 4) are embedded in Part 2. Important point isto enable vertical movement of Part 2 (along axis 2)just to take uplift into consideration. Also appropriateconfined concrete effect must be ensured at surface2A, but boundary conditions u1 = u2 = u3 = 0 are not areasonable solution, as well as BC u1 = 0 (no confinedconcrete effect). Hence specific solution in form of stiffplate fixed with BC2 (u1 = u2 = u3 = 0) and connected

Figure 5. One-dowel model (1D) - parts and interactions.

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Figure 6. One-dowel models (1D1) for ttot calculations: a)puzzle-shape (mesh), b) shark-shape (parts).

with model by means of Interaction 3 was proposed(contact, R = 0.3 is suggested). This solution ensuresboth uplift effect as well as confined concrete effectconsidered. For this model following dimensions aresuggested: B = hc = 1.5 h, L = 2.5e.

An important point is to establish the minimumacceptable total time, if explicit method is used.This time should be estimated corresponding to thefirst eigenfrequency. Therefore a model without anycontact interactions has to be used. Hence a modelconsisting of all parts with tie constraint (Figure 6: redcolor of puzzle-shape) is analyzed. Time tM = 0,01sis proposed for 1D model. Results of comparativeFEM study are presented in Figure 7 to justify thevalue ttot = 0,01 [s]. Therefore the identical modelwas analyzed using explicit method with different ttat

values as well as implicit method. The contact formu-lations are changed for the implicit model (without
any influence on the behavior). Model assumptions tosimplify:
- Omitting of Part 3 (BC u1 = u2 = u3 = 0 directly onsurface 2A)

- Omitting of Part 4 (reinforcement)

For instance the “puzzle shape” with e = 100 mm,h = 50 mm - and tw = 20 mm was analyzed (Figure 6a).

One model (serie 1) was solved with contactinteraction and the others (series 2-9) were solvedwith tie constraint between steel and concrete in

Figure 7. P-u curves (1D1) for different ttot values in the refer-ence point.


Figure 10. Energy balance (1D1 shark shape) for ttot calculations.
Figure 8. P-u curves (1D1 shark shape) for different ttot values.
compressed zone as presented in Figure 6 (red color).Three different ttot values for explicit method wereassumed: 0.001s, 0.01s and 0.1s and additionallyproblem was solved by means of standard method(that is why contact interaction was replaced by tie),also two different material configurations (NLsNLcand NLsLc) were considered.

Figure 7 figures out that ttot = 0,01s is the appro-priate value (ttot = 0,001s is too short). The results forthis value don’t diverge in a wide range in compari-son to tm = 0,1s. Stress layouts resulting of the standardmethod are similar. This conclusion concerns NLsNLcand NLsLc configurations. The influence of tm is def-initely more important if NLc configuration is used(important if concrete determines capacity of con-
nection). The assumption of long time ttot is alwaysfavourable (Figure 7).
A one-dowel sharkfin-shape model was analyzed.Complex 1D1 model (one element per half of webthickness) was considered including four parts withcontact interactions and a NLsNLc material config-uration. For geometry see Figure 6b, P-u curves arepresented in Figure 8.

Obviously a short time value increases the loadcapacity of the model by the same displacement. Thereis no convergence with increasing time values. Thecomparison of von Mises stress and displacements

Figure 9. . Results (1D1 shark shape) for different Rvalues:ttot,2 = 0,01 s (a, b, c) and ttotA = 0,08 s (d, e, f), Mises stress (a, d),u1 (b, e) and u2 (c, f).


Figure 11. Eccentricity e: P-u curves (1D1), R = 0, � = 0.

of the model of different values (tm,2 = 0,01 s andtm,4 = 0,08 s) is presented. Results (u1, u2, Mises) fortm,2 = 0,01 s and tm,4 = 0,08 s for the same displacementare presented in Figure 9.

The stresses and the displacements are analyzedfor a first time step. Mises stress values in steel do notexceed yield point value. The results obtained withtu,t,2 = 0,01 s fulfill the expectations (Figure 9: a, b, c).In contrast, the results obtained with tm,4 = 0,08 s arecontrary to expectations (Figure 9: d, e, f).

In that case (ttot,4 = 0,08[s]) unexpected movementof material appears in the steel part, clearly noticeableas Mises stress concentration at the very beginningof load range and it affects the behavior of thewhole model in following load steps. Energy bal-ance shown in Figure 10 (ALLIE = internal energy;ALLKE = kinetic energy).

If the kinetic energy of the deformed material doesnot exceed a small fraction of its internal energy (typ-ically 5%–10%) except early stages of simulation,all tests can be treated as quasistatic. Especially forthe value tm,4 = 0,08 s the results are not correspond-

Figure 12. Dilation ang. �: P-M curves (1D1), R = 0.3, e = 0,15.

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Figure 13. Friction coef. R: P-u curves (1D1), � = 15, e = 0,15,.

chubkrafte, Doctoral thesis, Univer-sitat der Bundeswehr,

Figure 14. Influence of fct.

ing to the tests and the expected (logical) behaviorof the structure. For the setting of the value tm itis necessary to work out a comparative study (eg.ABAQUS/Standard). A similar approach is to simu-late the behavior of CD with different ttot values andto check the layout of stresses and displacements. Fur-theremore, the value tm = 0,0 1s seems to be justifiedfor 1D models just as well as tm = 0,01 s up to 0,1 s isreasonable for 3P models.

As mentioned at item 3.6, it is desirable to check theinfluence of CDP model parameters and friction coeffi-cient R on the behavior of model. Additional 1D modelis created (1D1 shark shape, tm = 0,01 s) with somesimplifications in order to set CDP material parame-ters: eccentricity e, dilation angle �, influence of fct

and also friction coefficient R (Figures 11-14).The influence of/* (Figure 14) is presented f similar

model to the one presented in Figure 6a.The size/number of elements is important if c tact

pressure is studied in detail and for the anal of localstress state in this contact region (mo 1D4 and 3P4).

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For other purposes, eg. P-u cur 1D1 (3P1) model issufficient.

5 CONCLUSION

The numerical models 3P and 1D are up to modelthe complex nonlinear behavior of concrete dowelshear connection. CDP model substitudes the concreteunder certain circumstances (with constant insteadof decreasing tension part for uniaxial stress-strainrelationship) with values: Kc = 0.667, �b0/�c0 = 1.16,ψ = 15 and e = 0.15. Friction coefficient between steeland concrete is recommended with the value R = 0.3.For the use of the explicit method tm = 0,01s value canbe assumed for 1D models. Other material modelsshould be also considered for the concrete in regionunder high confining pressure.

ACKNOWLEDGEMENTS

The authors would like to thank Dr. Lubomir On-dris(TU Vienna) for valuable discussion concerning prob-lems presented in the paper (Ondris 2006).

The support of the Wroclaw Centre for Networkingand Supercomputing is acknowledged.

REFERENCES

Zapfe, C., 2001. Trag- und Verformungsverhalten von Ver-bundtragern mit Betondubeln zu Ubertra-gung der Langss-

Munchen,Fink, J., Petraschek, T., 2006. Push-out tests VFT-VIB statish.

Neubau StraBenbriicke bei Vigaun OBB Strecke Salzburg -Worgl km 23,135. Tech-nishe Universitat Wien.

Schmitt V., Seidl G., Hever M. 2005. Composite bridges withthe VFT-WIB construction method -robust and long lasting,Compendium Eurosteel, Maastricht, Netherlands.

Marecek, J., Chromiak, P., Studnicka, J., Numerical model ofperforated shear connector, Progress in Steel, Composite andAluminium Structures.

CEB-FIP Model Code 1990, Th. Telford, 1993.ABAQUS Online Documentation, Version 6.5, 2004.Ondris L., Institute of Steel Structures, TU Vienna: Private Com-

munication 2006-2007.


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