Push-Out Test Parametric Simulation Study of a New Sheet-Type Shear Connector

Josef Fink *, Thomas Petraschek **, Lubomir Ondris ***

* Professor, Head of the Institute of Steel Structures, TU Vienna ** Research assistent, Institute of Steel Structures, TU Vienna

*** Research assistent, corresponding author, Institute of Steel Structures, TU Vienna, Karlsplatz 13/212, A-1040 Vienna / Austria

Abstract At the Technical University of Vienna, Institute of Steel Constructions, new shapes of shear connectors for composite steel and concrete beam structures are being studied. To verify the efficiency of a particular welded sheet-type shear connector both numerical analyses and physical experiments with push-out tests are carried out. For the numerical analysis of a composite structure consisting of steel beam with a shear connector welded on it and surrounded with a concrete reinforced slab the well-established FE-program ABAQUS is used. As far as possible, for the most control and material parameters default values are used. The influence of remaining unknown parameters for available concrete material models has been studied for the first shear connector shape in an extensive parametric study using both static and dynamic analysis procedures. The influence of the friction coefficient between shear connector and concrete and the influence of the boundary condition describing the support of the specimen have been studied as well. The experience given here will be used to limit the extent of FE-analyses of subseqent shear connector shapes. It can be used also by other users in analyses of composite steel and concrete structures using ABAQUS. The autors apologize for the user's inconvenience caused by removing some pictures for the time of patenting the subject of the report. Keywords: Composite steel and concrete beam structure, welded shear connector, push-out test, finite element modeling, ABAQUS, material model for concrete

1. Introduction

As composite structural member consisting of steel and concrete often a rolled steel beam with I-cross section and excentric concrete slab with reinforcement is used. The shear force acting between steel and concrete part is transmitted by a shear connector usually welded to the steel flange of the I-beam and embedded in surrounding concrete slab. Well-known are welded headed studs with circular cross section widely used despite of their relatively low shear load capacity and other disadvantages. Newer continually welded sheet-type connectors are characterized by a substantially increased load carrying capacity and ductility as the basic design requirements of the composite structural members. In contrast to the locally applied headed studs with discrete welded joints, no fatigue cracks rise from the continually welded sheet connectors. Their shape and the reinforcement of the concrete slab are to be determined to maximize the shear load capacity and ductility and to minimize the overall manufacturing cost. This is why following the first sheet connectors with perforation used for positioning of the cross reinforcement /1/ other researchers continue the design and testing new shapes of sheet connectors in order to improve the properties of the composite structural members /2-7/. The basic characteristics of shear connectors are usually gained in push-out tests. However, a reliable shape verification must consist of both physical experiment and numerical analysis. The reasons are convincingly given in /2/ and elsewhere and will not be repeated here.

Numerical simulation of push-out tests with a specimen described below is a highly nonlinear problem with material and contact nonlinearities and large displacements. For solving such problems usually well-known FE-packages are used. ABAQUS /8-10/ surely belongs to them and is used by many researchers /7, 11-15/. There are, however, some crucial questions to be answered by a user of an FE-package including ABAQUS before starting a nonlinear simulation of push-out tests, e.g.: Static or dynamic solution, control and stopping parameters, finite elements, mesh density, boundary conditions, applying of loads, material model for concrete, friction coefficient between steel and concrete, reinforcement modeling, etc. Results can considerably differ depending on answering of the questions. Especially, upon quite common absence of reliable tests determining specific material model parameters for concrete behaviour, the user mostly accepts input values approved in similar numerical analyses and/or program default values. If there are still "free" input parameters, the user is encouraged to "calibrate" them /8/, i.e. to use values of unknown input parameters matching analysis results to a known physical test. However, without an input parameter study this can lead to reasonableness of the material input values. The situation is even worse if there is no physical test available. Thus, a broader understanding of the problems seems to be desirable. At the Technical University of Vienna, Institute of Steel Constructions, new shapes of sheet-type shear connectors for composite steel and concrete beam structures have been suggested. The first new connector shape has been used as a basis for extensive parametric studies using ABAQUS for numerical push-out test simulations. The aim was to collect a broad information necessary for a qualified decision about parameters of the FE-simulation of push-out tests of sheet-type shear connectors. Here, results of 123 calculations are presented. Generally, for non described input parameters ABAQUS default values were used.

2. Push-out test specimen The steel part of a push-out test specimen consists of an I-beam with a head plate and two new sheet-type shear connectors welded on it (Fig. 1). The connectors are embedded in reinforced concrete slabs jointed together by four anchor rods. In the physical push-out test the specimen was horizontally fixed between the press plates of the hydraulic load machine (Fig. 2) and loaded by displacement controlled movement of the right press plate. During the test the total force, the displacement of the steel beam, the slip between shear connector and concrete slabs and the strains in specified points of the steel connector were measured. The raising of concrete slabs from the connectors caused their inclined position after testing (Fig. 3). The main dimensions of the specimen parts are as follows: I-beam: HE 300 M, H=340 mm, B=310 mm, L=1000 mm head plate: 400x370x40 mm 2 concrete slabs: 1340x950x220 mm each reinforcement: D=8, 10 and 12 mm 2 sheet connectors: 465x170x20 mm with two active teeth each crown shape: upper and lower tooth part equally high embedded depth in concrete slab: 130 mm 4 anchor rods Dywidag: D=15 mm

Fig. 2 Complete push-out specimen in a loading machine

Fig. 3 Deformed push-out specimen after testing

3. Static and dynamic solution procedures /8/ In this study, static analyses were carried out using procedures *STATIC, RIKS and *STATIC, STABILIZE, both available in ABAQUS/ STANDARD. Dynamic analyses were carried out using the procedure *DYNAMIC, EXPLICIT available in ABAQUS/EXPLICIT.

4. Control and stopping parameters In a recent EU-Project FE-packages ABAQUS, ANSYS, DIANA, GEFDYN and LUSAS have been compared /17/. It has been confirmed that the result of a complex highly nonlinear problem often depends on nonlinear control parameters used. A correct estimating of an ultimate load using a non-convergence stopping criterion is problematic because with a "wrong" criterion the non-convergence on relatively small loads can occure. We add that the reason for a premature calculation break can lie in other components of an FE calculation, too. The problem can partially be overcome by repeating analyses with different stopping criterion and input parameters and comparing results with a physical test if it exists. In this study, the physical test was available and for control and stopping parameters exclusively the ABAQUS default values inclusive default incrementation were used. The geometrical nonlinearity has always been taken into account (*STEP, NLGEOM) and the calculations have been performed in double precision. The maximum number of iterations as general stopping criterion was set sufficiently high (and never reached). Similarly, for starting and minimum possible increments very small values were set. This conservative practice sometimes caused unnecessary long calculations but the results can be considered for reliable.

5. Friction coefficient between steel connector and concrete slab The friction between steel and concrete has been studied by many researchers. In literature following values of the friction coefficient can be found: 0.3 in /7/, 0.3-0.6 in /18/, 0.45 in /15/, min. 0.45 in /19/, 0.59-0.77 in /20/, 0.8 in /21/. Intuitively, the friction coefficient can be important in composite structures. E.g., a remarkable part of the shear force between the box concrete and steel profile is transfered via friction forces /21/. In this study, no experiments for estimating the friction coefficient in push-out tests were available. To test its influence, all calculations have been done three times using the values f = 0.3, 0.5 and 0.7, always the same value in all contact surfaces.

6. FE-model of the specimen 6.1 Symmetry In all FE-models the twofold symmetry of the problem is taken into account, thus, by applying of appropriate boundary conditions only 1/4 of the specimen has to be analysed (Fig. 4). After first analyses the head plate and the I-beam have been removed from the model (Fig. 5). They are very stiff and their omitting and replacing by corresponding boundary conditions on the bottom connector surface welded to the I-beam has only a negligible influence on the critical area between the connector and concrete. For the same reason also the reinforcement has been modeled only in the concrete slab part surrounding the connector.

6.2 FE-meshes Two meshes are used in present analyses as a result of succesive refinements. They can be considered for some FE "overkill", especially because the mesh in all cross sections parallel to the connector has the same density as in the visible vertical symmetry plane. The fine division of reinforcement elements corresponding to small concrete elements contributes to a smooth interaction between reinforcement and concrete. Here the emphasis has been placed on the highest possible accuracy and reliability of the system answer rather than on efficiency of calculations. In practical subseqent analyses the ABAQUS surface constraint (*TIE) will be used to connect the areas of interest (fine mesh) with less important areas (coarse mesh). The mesh for static analyses using ABAQUS/STANDARD (Fig. 6) consists of following parts: steel connector (Fig. 7) : 747 elements C3D20R concrete slab (Fig. 8) : 4994 elements C3D20R reinforcement (Fig. 9) : 354 elements T3D2 anchor rods (Fig. 6) : 1 element T3D2 each T3D2: 3D truss element with linear approximation of displacements, 2 nodes/element, 3 translational DOFs/node C3D20R: 3D hexahedral (brick) element with quadratic approximation of displacements, reduced integration, 20 nodes/element, 3 translational DOFs/node There is only one quadratic element C3D20R in transversal direction of the steel connector. In dynamic analyses using ABAQUS/EXPLICIT quadratic elements can not be used, thus, the disadvantage of using linear elements had to be compensate by an adequate finer mesh. The mesh for dynamic analyses (Fig. 10) consists of following parts: steel connector : 6474 elements C3D8R concrete slab: 30495 elements C3D8R reinforcement: 525 elements T3D2 anchor rods: 1 element T3D2 each C3D8R: 3D hexahedral (brick) element with linear approximation of displacements, reduced intergration with hourglass control, 8 nodes/element, 3 translational DOFs/node There are three linear elements C3D8R in transversal direction of the steel connector.

6.3 Material models for steel parts All steel parts use the same elastic-ideally plastic material model without hardening with the same density=7.8E-6 kg/mm3, E-module E=210000 N/mm2, Poisson coefficient ν=0.3. connector: Steel S 355J2G3, fy=363 N/mm2 (acc. to attest) anchor rods: Steel St 900/1100, fy=900 N/mm2 reinforcement: Steel BSt 550, fy=550 N/mm2

6.4 Material models for concrete C 25/30 Density=2.643E-6 kg/mm3, E-module E=31000 N/mm2, Poisson coefficient ν=0.2. Compressive strength=33 N/mm2, tensile strength=3.3 N/mm2.

In nonlinear compressive and tensile range the input values depend on material models used and are described below. Details can be found in /8/. Generally, the reinforcement used (Fig. 9) is a minimal one. Thus, in ABAQUS-sense, concrete was considered as not or very little reinforced, leading to using a displacement formulation of the postcracking behaviour of the concrete material models.

6.4.1 Concrete Smeared Cracking (CSC) available in ABAQUS/STANDARD (usable for static calculations only) /8/

This material model uses concepts of oriented damaged elasticity and isotropic compressive plasticity to represent the inelastic behaviour. It is intended primarily for the analysis of reinforced concrete structures subjected to essentially monotonic straining under fairly low confining pressures. For compressive range, the nonlinear behaviour of the concrete C 25/30 using /22/ is given in Fig. 11.

0

5

10

15

20

25

30

35

0,0000 0,0005 0,0010 0,0015 0,0020 0,0025 0,0030 0,0035

e plast

Com

p. S

tress

/ N

/mm

2 /

Fig. 11 Concrete C 25/30 in compressive range

In preprocessor ABAQUS/CAE the input values are submitted as a table under the heading Compressive Stress – Plastic Strain. In ABAQUS input file they begin under *CONCRETE. In CSC material model, the failure surface is given by four ratios (*FAILURE RATIOS). Only for the second of them (absolute value of the ratio of uniaxial tensile stress at failure to the uniaxial compressive stress at failure) the default value 0.09 was replaced by 0.1. For three remaining failure ratios default values were used. The postfailure stress-strain relation is modeled with the *TENSION STIFFENING option, which allows the user to define the strain-softening behaviour for cracked concrete. This option also allows for the effects of the reinforcement interaction with concrete to be simulated in a simple manner. In situations with none or little reinforcement, the tension stiffening can be characterized by a simple linear stress-displacement response. Displacement means here the crack width and the value has to be calibrated.

According recommendations in /8/, in present calculations the option was used in the form *TENSION STIFFENING, TYPE=DISPLACEMENT u0 and tested with u0 = 0.05, 0.5 and 1 mm. (Fig. 12).

0,0

0,5

1,0

1,5

2,0

2,5

3,0

3,5

Displacement u / mm /

Tens

ile s

tres

s ac

ross

cra

ck /

N/m

m2

/

u0

Fig. 12 Postfailure behaviour for none or little reinforcement

6.4.2 Concrete Damaged Plasticity (CDP) available in ABAQUS/STANDARD and ABAQUS/EXPLICIT (usable for both static and dynamic calculations) /8/

This material model uses concepts of isotropic damaged elasticity in combination with isotropic tensile and compressive plasticity to represent the inelastic behaviour. It is intended primarily for the analysis of reinforced concrete structures subjected to monotonic, cyclic, and/or dynamic loading under low confining pressures. In preprocessor ABAQUS/CAE the input values for nonlinear compressive range are submitted as a table under the heading Yield Stress – Inelastic Strain. For concrete C 25/30 again Fig. 11 is used with the same input values as for CSC. Also, ABAQUS input file looks equally. As for plasticity parameters, only the first one in *CONCRETE DAMAGED PLASTICITY option, dilation angle ψ, was defined and tested. All other plasticity parameters were not defined, thus, default values (zeroes) were used. Dilation angle ψ depends on material and on application as well. In literature diverse values can be found: 12 in /23/, 15 in /7, 9/, 27.75-42.87 and 23.51-35.40 in /24/, 30 in /25/, 36.31 in /10/, 40 in /26/, 42 in /27/ (all values in degrees). In present calculations following values were tested: ψ = 12, 20, 36.31 and 45 degrees.

The postfailure tension stiffening and tension damage of C 25/30 can again be expressed using displacement (= crack width) formulation and are supposed to be similar as in /10/ (Fig. 13, 14). Full line denotes the basic CDP material, the dashed line the material CDP M2 (Tab. 1).

0,0

0,5

1,0

1,5

2,0

2,5

3,0

3,5

0,0 0,1 0,2 0,3 0,4 0,5

Cracking displacement / mm /

Tens

ile s

tress

/ N

/mm

2 /

Fig. 13 Tension stiffening for CDP / CDP M2

0,0

0,2

0,4

0,6

0,8

1,0

0,0 0,1 0,2 0,3 0,4 0,5

Cracking displacement / mm /

Tens

ile d

amag

e pa

ram

eter

Fig. 14 Tension damage for CDP / CDP M2 In preprocessor ABAQUS/CAE the input values for tension stiffening are submitted as a table under the heading Yield Stress – Displacement. In ABAQUS input file they begin under *CONCRETE TENSION STIFFENING, TYPE=DISPLACEMENT The input values for concrete tension damage are submitted as a table under the heading Damage Parameter – Displacement. In ABAQUS input file they begin under *CONCRETE TENSION DAMAGE, TYPE=DISPLACEMENT

6.4.3 Brittle Cracking (BRITTLE) available in ABAQUS/EXPLICIT (usable for dynamic calculations only) /8/

This material model is designed primarily for the analysis of reinforced concrete structures in which the behaviour is dominated by tensile cracking. The compressive behaviour is linear elastic in the whole range. This model also allows removal of cracked elements with the *BRITTLE FAILUR option. However, removing elements can lead to incorrect simulation if the material is expected to carry compressive loads after it has failed in tension, e.g. upon massive force flow changing. Hence, this option was not used. Because of linear eleastic behaviour in the whole compressive range, no special description of compressive behaviour is necessary. According to recommendation in /8/ for situations with none or little reinforcement, the postfailure behaviour was defined by a linear loss of tensile strength after cracking using *BRITTLE CRACKING, TYPE=GFI 3.3, 0.092 3.3 N/mm2 is the tensile strength, 0.092 N/mm is the fracture energy. For concrete C 25/30 with compressive strength of 33 N/mm2 the fracture energy was interpolated between 0.04 N/mm for compressive strength about 20 N/mm2 and 0.12 N/mm for compressive strength about 40 N/mm2 as recommended in /8/. With the option *BRITTLE SHEAR, TYPE=POWER LAW eck

max, p the generally nonlinear postcracking loss of shear stiffness was expressed by definig the postcracking shear modulus as a fraction of the uncracked shear modulus. eck

max is the crack opening strain at which the postcracking shear modulus = 0. With the exponent p=1 a linear (slow), with p>1 an exponential (faster) loss of shear stiffness is described. In /8/, the necessity of calibration of the postcracking behaviour is emphasized. In this study folloving values were tested: eck

max = 0.005, 0.01 and 0.04, p=1 and 5.

6.5 Reinforcement (Fig. 9) The embedded element technique is used to specify that steel reinforcement elements are "embedded" in host concrete elements. ABAQUS checks the position of nodes of the embedded elements in host elements. If a node of an embedded element lies within a host element, its translational degrees of freedom are constrained to the interpolated values of the corresponding degrees of freedom of the host element. The definition of this constraint is straightforward and ABAQUS default values were used.

6.6 Boundary conditions and loading As already mentioned, because of twofold symmetry only 1/4 of the model without removed head plate and I-beam has been analysed. Following boundary conditions have been used (Fig. 15):

Symmetry plane 2-3: U1 (=UR2=UR3) =0 Symmetry plane 1-3 (anchor rods): U2 (=UR1=UR3) =0 In analyses published, the concrete slab support is conventionally defined as clamped. However, depending on shape of the steel connector and on arrangement of the physical test, with increasing load the concrete slabs trend to raise from the steel connector /2/, /6/. In present physical tests this effect also has been observed (Fig. 3), leaving only the upper part of the support surface active (Fig. 31) and causing the force flow changing. To test the influence of the raising effect on numerical results, in this study besides the conventional clamped boundary condition U1=U2=U3 (=UR1=UR2=UR3) =0 also a contact between the right side of the concrete slab and rigid support was tested. The boundary condition for the whole lower surface of the steel connector (welded to the removed I-beam) consists of two parts. Using U2=0, the very high stiffness of the I-beam is taken into account. Using U3=25 mm, the system is loaded by prescribed displacement instead of using classical pressure load. This displacement is applied in automatic increments. In dynamical analyses, it is applied with a constant velocity of 0.5 mm/sec. Mostly, due to numerical collapse, the displacement has not been acchieved. The loading force corresponding to the actual displacement is taken as a total reaction force in the concrete slab support.

6.7 Contact problem (surface-to-surface contact) There are always two surface interaction pairs in each analysis describing the interaction between steel connector and surrounding concrete slab: the frontal and the lateral surface pair. The master contact surfaces of the steel connector are shown in Fig. 16 and 17. Corresponding concrete surfaces are defined as slave contact surfaces. Beside this, in analyses marked as "contact" in Table 1, the concrete slab is not clamped at the right end. In this case the interaction is defined as a contact with a rigid support. In all three interaction definitions the same friction coefficient and the same ABAQUS settings are used as follows: ABAQUS/STANDARD (static calculations): sliding formulation: constraint enforcement method: node to surface finite sliding slave node/surface adjustment: only to remove overclosure normal behaviour: constraint enforcement method: augmented Lagrange pressure-overclosure: "hard" contact allowed separation after contact tangential behaviour: friction formulation: penalty friction directionality: isotropic ABAQUS/EXPLICIT (dynamic calculations): mechanical constraint formulation: kinematic contact method normal behaviour: constraint enforcement method: default other settings as with static calculations

7. Analyses summarized Two static procedures (with a mesh of C3D20R elements for static calculations), one dynamic procedure (with a mesh of C3D8R elements for dynamic calculations), three concrete material models and clamped and contact boundary conditions have been combined, leading to 11 calculation groups in Table 1. The number of calculations in a group (9 or 12) is given by a crosswise variation of two input parameters. Group ABAQUS concrete material FE concrete slab nr. of Fig. Nr. procedure model elements support calcul. 18 *STATIC,RIKS CDP C3D20R clamped 12 19 *STATIC,STABILIZE CDP C3D20R clamped 12 20 *STATIC,RIKS CDP M2 C3D20R clamped 12 21 *STATIC,RIKS CSC C3D20R clamped 9 22 *DYNAMIC,EXPLICIT CDP C3D8R clamped 12 23 *DYNAMIC,EXPLICIT BRITTLE 1 C3D8R clamped 9 24 *DYNAMIC,EXPLICIT BRITTLE 5 C3D8R clamped 9 25 *STATIC,RIKS CDP C3D20R contact 12 26 *DYNAMIC,EXPLICIT CDP C3D8R contact 12 27 *DYNAMIC,EXPLICIT CDP M2 C3D8R contact 12 28 *DYNAMIC,EXPLICIT CDP M2 C3D8R clamped 12 CALCULATIONS TOTAL: 123

Table 1. Analyses summarized

One of them is always the friction coefficient f (3 values), the second one (3 or 4 values) depends on the concrete material model used: CSC: displacement u0 /mm/ in *TENSION STIFFENING, TYPE=DISPLACEMENT CDP: dilation angle ψ /degrees/ in *CONCRETE DAMAGED PLASTICITY BRITTLE: strain eck

max in *BRITTLE SHEAR, TYPE=POWER LAW BRITTLE 1 means exponent p=1 in *BRITTLE SHEAR, TYPE=POWER LAW BRITTLE 5 means exponent p=5 in *BRITTLE SHEAR, TYPE=POWER LAW CDP M2 means halved postfailure resistance (dashed lines in Fig. 13, 14) clamped means conventionally clamped support of the concrete slab contact means support of the concrete slab with a contact interaction In Figures 18-28 the influence of tested parameters on the load force and the displacement of the steel connector as the most important design requirements is given. It is to remind that, because of symmetry, the whole force overtaken by a real pair of sheet-type shear connectors is a quadruple of the force from the FE-analysis.

0

100

200

300

400

500

600

0 0,5 1 1,5 2 2,5 3 3,5 4

Displacement /mm/

Load

/kN

/ ψ=45, f=0.7ψ=45, f=0.5ψ=45, f=0.3ψ=36.31, f=0.7ψ=36.31, f=0.5ψ=36.31, f=0.3ψ=20, f=0.7ψ=20, f=0.5ψ=20, f=0.3ψ=12, f=0.7ψ=12, f=0.5ψ=12, f=0.3

Fig. 18 Load-displacement for *STATIC,RIKS CDP clamped

0

100

200

300

400

500

600

0 0,5 1 1,5 2 2,5 3 3,5 4

Displacement /mm/

Load

/kN

/

ψ=45, f=0.7ψ=45, f=0.5ψ=45, f=0.3ψ=36.31, f=0.7ψ=36.31, f=0.5ψ=36.31, f=0.3ψ=20, f=0.7ψ=20, f=0.5ψ=20, f=0.3ψ=12, f=0.7ψ=12, f=0.5ψ=12, f=0.3

Fig. 19 Load-displacement for *STATIC,STABILIZE CDP clamped

0

100

200

300

400

500

600

0 0,5 1 1,5 2 2,5 3 3,5 4

Displacement /mm/

Load

/kN

/

ψ=45, f=0.7ψ=45, f=0.5ψ=45, f=0.3ψ=36.31, f=0.7ψ=36.31, f=0.5ψ=36.31, f=0.5 Sψ=36.31, f=0.3ψ=20, f=0.7ψ=20, f=0.5ψ=20, f=0.3ψ=12, f=0.7ψ=12, f=0.5ψ=12, f=0.3

Fig. 20 Load-displacement for *STATIC,RIKS CDP M2 clamped

0

10

20

30

40

50

60

70

80

90

100

0 0,02 0,04 0,06 0,08 0,1 0,12 0,14

Displacement /mm/

Load

/kN

/

u=1, f=0.7u=1, f=0.5u=1, f=0.3u=0.5, f=0.7u=0.5, f=0.5u=0.5, f=0.3u=0.05, f=0.7u=0.05, f=0.5u=0.05, f=0.3

Fig. 21 Load-displacement for *STATIC,RIKS CSC clamped

0

100

200

300

400

500

600

0 5 10 15 20 25

Displacement /mm/

Load

/kN

/

ψ=45, f=0.7ψ=45, f=0.5ψ=45, f=0.3ψ=36.31, f=0.7ψ=36.31, f=0.5ψ=36.31, f=0.3ψ=20, f=0.7ψ=20, f=0.5ψ=20, f=0.3ψ=12, f=0.7ψ=12, f=0.5ψ=12, f=0.3

Fig. 22 Load-displacement for *DYNAMIC,EXPLICIT CDP clamped

0

100

200

300

400

500

600

0 1 2 3 4 5 6 7 8 9 10 11 12

Displacement /mm/

Load

/kN

/ e=0.04, f=0.7e=0.04, f=0.5e=0.04, f=0.3e=0.01, f=0.7e=0.01, f=0.5e=0.01, f=0.3e=0.005, f=0.7e=0.005, f=0.5e=0.005, f=0.3

Fig. 23 Load-displacement for *DYNAMIC,EXPLICIT BRITTLE 1 clamped

0

100

200

300

400

500

600

0 1 2 3 4 5 6 7 8 9 10 11 12

Displacement /mm/

Load

/kN

/ e=0.04, f=0.7e=0.04, f=0.5e=0.04, f=0.3e=0.01, f=0.7e=0.01, f=0.5e=0.01, f=0.3e=0.005, f=0.7e=0.005, f=0.5e=0.005, f=0.3

Fig. 24 Load-displacement for *DYNAMIC,EXPLICIT BRITTLE 5 clamped

0

100

200

300

400

500

600

0 0,5 1 1,5 2 2,5 3 3,5 4Displacement /mm/

Load

/kN

/

ψ=45, f=0.7ψ=45, f=0.5ψ=45, f=0.3ψ=36.31, f=0.7ψ=36.31, f=0.5ψ=36.31, f=0.3ψ=20, f=0.7ψ=20, f=0.5ψ=20, f=0.3ψ=12, f=0.7ψ=12, f=0.5ψ=12, f=0.3

Fig. 25 Load-displacement for *STATIC,RIKS CDP contact

0

100

200

300

400

500

600

0 5 10 15 20 25

Displacement /mm/

Load

/kN

/

ψ=45, f=0.7ψ=45, f=0.5ψ=45, f=0.3ψ=36.31, f=0.7ψ=36.31, f=0.5ψ=36.31, f=0.3ψ=20, f=0.7ψ=20, f=0.5ψ=20, f=0.3ψ=12, f=0.7ψ=12, f=0.5ψ=12, f=0.3

Fig. 26 Load-displacement for *DYNAMIC,EXPLICIT CDP contact

0

100

200

300

400

500

600

0 5 10 15 20 25

Displacement /mm/

Load

/kN

/

ψ=45, f=0.7ψ=45, f=0.5ψ=45, f=0.3ψ=36.31, f=0.7ψ=36.31, f=0.5ψ=36.31, f=0.3ψ=20, f=0.7ψ=20, f=0.5ψ=20, f=0.3ψ=12, f=0.7ψ=12, f=0.5ψ=12, f=0.3

Fig. 27 Load-displacement for *DYNAMIC,EXPLICIT CDP M2 contact

0

100

200

300

400

500

600

0 5 10 15 20 25Displacement /mm/

Load

/kN

/

ψ=45, f=0.7ψ=45, f=0.5ψ=45, f=0.3ψ=36.31, f=0.7ψ=36.31, f=0.5ψ=36.31, f=0.3ψ=20, f=0.7ψ=20, f=0.5ψ=20, f=0.3ψ=12, f=0.7ψ=12, f=0.5ψ=12, f=0.3

Fig. 28 Load-displacement for *DYNAMIC,EXPLICIT CDP M2 clamped

8. Evaluation of analyses

8.1 Friction coefficient Despite of analytical procedure and concrete material model used, the influence of the friction coefficient between steel connector and concrete slab especially before failure is generally the same: the higher value for the friction coefficient is used the higher load is necessary to achieve the same displacement. The influence on the connector displacement itself is not so unique. After the failure the basic relationship remains, however, the differences caused by the friction coefficient depend on the concrete material model used and are not always clearly demonstrated. E.g. with CDP, in Fig. 22 the curves interlace, in Fig. 26, 27 they clearly express the basic relationship. With BRITTLE material model, upon the highest value of eck

max in Fig. 23, 24 only displacements are influenced by the friction coefficient value, not the loads. If no experimental results are available, for practical engineering purposes without an artificial smoothing or roughing of the contact surfaces the friction coefficient value 0,3-0,5 seems to be reliable. The actual value is not critical.

8.2 Concrete material models CSC, CDP and BRITTLE

8.2.1 CSC material model With a prescribed behaviour in linear range and nonlinear compressive range (Fig. 11) and the shape of the failure surface given by four default ratios (*FAILURE RATIOS) the user has practically only one "free" parameter to control the CSC material model in situations with little or none reinforcement. It is the displacement u0 in *TENSION STIFFENING, TYPE=DISPLACEMENT influencing the postcracking behaviour (Fig. 12). Even with the highest value used (1 mm), considerably exceeding the recommendation in /8/ (0.05-0.08 mm), the calculations end with small loads and displacements

(Fig. 21). Moreover, this material model is available for static analyses only. It does not to be suitable for push-out test simulations.

8.2.2 CDP material model The CDP material model can be used for both statical and dynamical analyses. Its sofisticated formulation offers a broad potential for matching the simulation results to physical tests. Two material alternatives have been tested differing in postfailure behaviour, marked as CDP and CDP M2 in Table 1. With both of them always four values of the dilation angle ψ have been tested. The importance of the postfailure behaviour input for calculated load and displacement can be seen by comparing Fig. 18 and 20. Both calculation groups use the same static numerical procedure (*STATIC,RIKS) and the same boundary condition for the concrete slab (clamped). They differ only in material alternative used. Calculations with a reduced postfailure resistance concrete CDP M2 (Fig. 20) stop on evident reduced loads and displacements as compared with the material CDP (Fig. 18). The same influence can be seen by using dynamic procedure (*DYNAMIC,EXPLICIT). Here both slab boundary conditions were tested. When using clamped slab the calculations with a reduced postfailure resistance concrete CDP M2 (Fig. 28) stop on reduced loads and displacements as compared with the CDP material (Fig. 22). For a slab with contact the same can be seen by comparing Fig. 27 and 26. As for dilation angle ψ, the higher value is used the higher load is necessary to achieve the same displacement. Similar is its influence on the connector displacement using the same friction coefficient. In dynamical analyses, large displacements only upon higher dilation angles can be achieved. Only using CDP and CDP M2 material models and (*DYNAMIC,EXPLICIT) it was possible to achieve large displacements with a slightly (Fig. 22) or even quite radical decreasing load (Fig. 26-28) similar to the physical test /28/. Generally, because of its versatility, the CDP model can be considered for the basic concrete material model in FE simulations of physical push-out tests. For standard concrete materials the postfailure behaviour can be described as in /10/ and slightly modified to match the particular concrete used. Extreme dilation angles ψ=12 and ψ=45 degrees used here just for completeness are not typical for standard concrete materials.

8.2.3 BRITTLE material model The BRITTLE material model can be used for dynamical analyses only. Two material alternatives have been tested differing in postfailure behaviour and marked as BRITTLE 1 and BRITTLE 5 in Table 1. With both of them always three values of the crack opening strain eck

max have been tested. The importance of the postfailure behaviour input for calculated load and displacement can be seen by comparing Fig. 23 and 24. Both calculation groups use the same numerical procedure (*DYNAMIC,EXPLICIT) and the same boundary condition for the concrete slab (clamped). They differ only in material alternative BRITTLE 1 and BRITTLE 5. Concrete with an exponential (faster) loss of shear stiffness (Fig. 24) shows an evident reducing of loads and displacements. In both calculation groups, large displacements only upon the highest value of eck

max can be achieved. Here, the loads remain almost unchanged which does not correspond the physical tests. Despite of a quite simple formulation of this material model (linear elastic behaviour in the whole compressive range) the results are remarkable. In FE simulations of physical push-out tests the BRITTLE material model can be used for comparison with CDP.

8.3 Procedures *STATIC,RIKS, *STATIC,STABILIZE and *DYNAMIC,EXPLICIT /8/ 8.3.1 *STATIC,RIKS *STATIC, RIKS available in ABAQUS/STANDARD is a nonlinear static incremental procedure. Based on the modified Riks method it is recommended for solving complex global unstable problems caused by geometric, material and contact nonlinearities and for solving of generally ill-conditioned problems. Results of using *STATIC,RIKS are summarized in Fig. 18, 20, 21 and 25. Thus, following cross comparisons are possible: - material model CDP (Fig. 18) and CDP M2 (Fig. 20), both with clamped concrete slab - clamped slab (Fig. 18) and slab with contact (Fig. 25), both with material model CDP - material model CDP (Fig. 18) and CSC (Fig. 21), both with clamped concrete slab In all the figures the procedure offers reliable results (insufficiency in Fig. 21 is caused by the CSC material model) but the calculations apparently end before reaching the maximum load. In some cases after reaching a critical point the solution reverses (ψ=20, f=0.5 and ψ=36.31, f=0.7 in Fig. 18). This is a feature of the Riks method which uses the load magnitude as an additional unknown; it solves simultaneously for loads and displacements.

8.3.2 *STATIC,STABILIZE *STATIC, STABILIZE available in ABAQUS/STANDARD is a nonlinear static incremental procedure based on a classical Newton method and stabilization of local instabilities. Here the procedure was used with a quite cautious stabilizing: the damping factor (dissipated energy / strain energy) was 0.0002 (ABAQUS default). In Fig. 18 and 19 results of two calculation groups are summarized using the same CDP material model and clamped concrete slab and differing in the procedure used only. In Fig. 19 (*STATIC,STABILIZE) the reversation disappeared, calculations generally break later on. For CDP M2 material model, in Fig. 20 together with reversing curve (ψ=36.31, f=0.5) also its stabilized alternative (ψ=36.31, f=0.5 S) with a substantial larger displacement is given for comparison. However, in Fig. 19 the curve (ψ=36.31, f=0.7) moved down from its natural position and three calculations break even earlier than in Fig. 18. Generally, even a default ABAQUS stabilisation makes the structure more flexibel and prolongates calculations, thus, it confirms the existence of local instabilities. However, its manifestation is ambiguous and calculations in postfailure range still are not possible. 8.3.3 *DYNAMIC,EXPLICIT Push-out tests are traditionally simulated using well-established nonlinear static implicit procedures even if they are not suitable for calculations in postfailure range. However, every static problem can be solved also as a dynamic one with a sufficiently slow load incrementation to get negligible inertial forces. In /16/ an excellent reasoning is given why only just an explicit integration package should be used for solving highly nonlinear problems and will not be completely repeated here. In this study, for dynamic analyses the procedure *DYNAMIC, EXPLICIT available in ABAQUS/EXPLICIT was used. Because only linear FE elements are available, the mesh has to be finer than with quadratic FE elements. This, however, does not mean any higher requirements on computer capacities because in contrast to implicit methods the requirements are principially smaller and a finer mesh means linear increasing of requirements only. Also, an

extraordinary robustness of convergence behaviour and numerical stability are advantages of the method: While implicit methods try to minimize the errors, explicit integration methods a priori avoid forming of errors, thus, no equilibrium iterations are necessary /16/. The results are summarized in Fig. 22-24 and 26-28. Following cross comparisons are possible: - material models CDP (Fig. 22) and BRITTLE (Fig. 23, 24), both with clamped concrete slab - material models CDP (Fig. 22) and CDP M2 (Fig. 28), both with clamped concrete slab - material models CDP (Fig. 26) and CDP M2 (Fig. 27), both with slab with contact - clamped slab (Fig. 22) and slab with contact (Fig. 26), both with material model CDP - clamped slab (Fig. 28) and slab with contact (Fig. 27), both with material model CDP M2. In comparison with all static calculations, due to the numerical stability also simulations in failure and postfailure range could be achieved. However, in dynamical analyses the ratio ALLKE/ALLIE (kinetic energy / strain energy) always must be checked. E.g. in Fig. 27 the calculation (ψ=36.31, f=0.3) reaches the load maximum at a displacement of about 2.25 mm and formally ends at about 23.6 mm. The ratio ALLKE/ALLIE first grows and then (due to strain energy) even changes its sign at about 11.8 mm (Fig. 28) making the simulation at least questionable. Deformations in concrete part of the FE model beginn to grow excessively after reaching displacement of 5 mm and at 11.8 mm and over they are inacceptable (Fig. 30). Thus, very long dynamic calculations can be useless. ABAQUS recommendation ALLKE/ALLIE<0.1 /8/ seems to be too optimistic for applications in question.

-0,15

-0,1

-0,05

0

0,05

0,1

0,15

0 5 10 15 20 25

Displacement / mm /

ALL

KE

/ ALL

IE

Fig. 29 ALLKE/ALLIE-displacement for (ψ=36.31, f=0.3) / Fig. 27

8.4 Boundary condition of the concrete slab Concrete slab supported by friction contact has been used in three calculation groups, Fig. 25-27. In all other calculations the concrete slab support is conventionally defined as clamped. Following cross comparisons are possible: - clamped slab (Fig. 18) and slab with contact (Fig. 25), both with material model CDP and *STATIC,RIKS - clamped slab (Fig. 22) and slab with contact (Fig. 26), both with material model CDP and *DYNAMIC,EXPLICIT - clamped slab (Fig. 28) and slab with contact (Fig. 27), both with material model CDP M2 and *DYNAMIC,EXPLICIT. In all cases using of slab with contact instead of clamped slab leads to reducing of the contact area (Fig. 31), to smaller displacements and loads and to higher stresses in anchor rods. It is to notice that in Fig. 25 in contrast to Fig. 18 no reversation occures. In some dynamic calculations with contact

(Fig. 26, 27) intensive oscillations can be seen. This can be caused by smaller stifness of the system as a whole in combination with higher values of ψ and f. Generally, in situations where the arrangement of the physical test allows raising of the concrete slab from the steel connector, there is no rational reason for using clamped slab.

9. Conclusions Simultaneously with the presented numerical simulation study physical tests of push-out specimens with diverse connector shapes have been carried out /28/. A comparison of load-displacement curves from this study and from the physical test with the same steel connector shape shown in /28/ indicates that there is enough potential in ABAQUS for calibration of numerical simulation to match physical push-out tests in a material consistent manner. Some differencies can be caused by material characteristics used in the numerical simulation: Because the true characteristics of the used concrete C25/30 were not available, standard parameters from EC 2 have been used instead. Especially the tensile strength value can influence the postfailure behaviour via tension stiffening considerably. Based on comparison mentioned, subseqent shear connector shapes will be analysed using friction coefficient 0.3-0.5, concrete material model CDP / CDP M2 with dilation angle 20-30 degrees, concrete material model BRITTLE, explicit dynamic procedure with an energy check, contact in concrete slab support and ABAQUS default values as far as possible. It is believed, that the numerical results gained and given here will substantially reduce the amount of calculations in simulating physical push-out tests of subsequent new connector shapes. A reduction of the number of physical tests is expected, too.

References 1 Leonhardt F., Andrä W., Andrä H.P., Harre W.: Neues, vorteilhaftes Verbundmittel für Stahlverbundtragwerke mit hoher Dauerfestigkeit, Beton- und Stahlbetonbau, Vol 12, 1987, 325-331 2 Zapfe C.: Trag- und Verformungsverhalten von Verbundträgern mit Betondübeln zur Übertragung der Längsschubkräfte, Dissertation, Institut für Konstruktiven Ingenieurbau, Universität der Bundeswehr München, 2001 3 Jurkiewicz B., Hottier J.M.: Static behaviour of a steel-concrete composite beam with an innovative horizontal connection, Journal of Constructional Steel Research 61 (2005) 1286-1300 4 Mangerig I., Zapfe C.: Experimentelle Untersuchungen zum Trag- und Verformungs- verhalten von Betondübeln mit optimierter Ausnehmungsgeometrie, Versuchsbericht, München 2004 5 Mangerig I., Zapfe C.: Experimentelle Untersuchungen zum Trag- und Verformungs- verhalten von Betondübeln mit optimierter Ausnehmungsgeometrie, Teil II: Ermüdung, Versuchsbericht, München 2005 6 Marecek J., Chromiak P., Studnicka J.: Numerical model of perforated shear conector, in Gizejowski, Kozlowski, Sleczka, Ziolko (eds.): Progress in Steel, Composite and Alu- minium Structures, Taylor & Francis Group, London, 2006, ISBN 0-415-40120-8 7 Wojciech Lorenc: Private Communication, Wroclaw University of Technology, Institute of Building Engineering, 2006 8 Hibbitt, Karlsson & Sorensen, INC.: ABAQUS/CAE, ABAQUS/STANDARD, ABAQUS/EXPLICIT, Dokumentation Ver. 6.5, http://www.abaqus.com 9 ABAQUS Verification Manual, 2.2.24 10 ABAQUS Example Problems Manual, 2.1.15

11 Greiner R., Ofner R.: Tragwirkung von Verbund-Fahrbahndecks für Brücken, Festschrift Prof. Sparowitz, Technische Universität Graz, Institut für Betonbau, 2000, 81–90 12 Mardfeldt B., Grabe J.: Nichtlineare Finite-Elemente-Analyse zum Tragverhalten einer Kaimauer im Gebrauchszustand, Bauingenieur, Band 80, September 2005 13 Rusinowski P.: Two-way Concrete Slabs with Openings: Experiments, Finite Element Analyses and Design, Master's Thesis, Department of Civil and Environmental Engineering, , Luleå University of Technology, Sweden, 2005 14 Ellobody E., Young B.: Performance of shear connection in composite beams with

profiled steel sheeting, Journal of Constructional Steel Research 62 (2006) 682-694 15 Marecek J., Chromiak P., Studnicka J.: Numerical model of perforated shear conector, in Gizejowski, Kozlowski, Sleczka, Ziolko (eds.): Progress in Steel, Composite and Alu- minium Structures, Taylor & Francis Group, London, 2006, ISBN 0-415-40120-8 16 Zimmermann S.: Finite Elemente und ihre Anwendung auf physikalisch und geometrisch nichtlineare Probleme, Report TUE-BCO 01.05, Technische Universität Eindhoven, Niederlande, März 2001 17 Jefferson A.D., Bennett T. and Hee S.C.: Fracture Mechanics Based Problems for the

Analysis of Dam Concrete, NW-IALAD-Final Technical Report-Task Group 2.4, Cardiff University (UWC), 15. March 2005

18 Beton-Lexikon (www.Beton-Lexikon.de) 19 Sattler K.: Theorie der Verbundkonstruktionen, Verlag Wilhelm Ernst & Sohn, 1959 20 Roik K., Bürkner K.-E.: Reibwert zwischen Stahlgurten und aufgespannten Betonfertigteilen, Bauingenieur 53 (1978), 37-41 21 Hegger J., Goralski C., Kerkeni N.: Finite Elemente Berechnungen kammerbetonierter Verbundträger, Bauingenieur Band 80, Juni 2005 22 DIN 1045-1:2001-07, Eq. 62 ff. 23 Borst R., Vermeer P. A.: Possibilities and Limitations of Finite Elements for Limit Analysis, Geotechnique, No. 2, Vol. 34, 1984, 199–210 24 Armaanidis V.I.: A Model for the Shear Strength of Rough Rock Diskontinuities under Low Normal Stress, MSC Dissertation, School of Civil Engineering and Geosciences, University of Newcastle upon Tyne, UK, 2003 25 Materialprüfungsanstalt, Universität Stuttgart: Sicherheitstechnische Untersuchung

bezüglich des Behälterabstürzes auf den Hallenboden …, Auftrags-Nr.: 831 801 001, 01/2004, Tabelle 5: Materialkenngrößen für C30/37 www.bfs.de/www/extfs/transport/publika/SiTE_Castor_Teil1.pdf 26 Beckwith G., Bedenkop D.V.:An Investigation of the Load Carrying Capacity of Drilled

Cast-in-Place Concrete Piles Bearing on Coarse Grannular Soils and Cemented Alluvial Fan Deposits, Report No. AHD-RD-10-122, 1973

27 Rollins K.M. at al.: Drilled Shaft Side Friction in Gravelly Soils, Report No. UT-90.02, 1997 28 Fink J., Petraschek T., Ondris L.: In preparation