Parametric PushOut Analysis on Perfobond Rib with Headed Stud Mixed Shear Connector

In steel and concrete composite structures, it is unfavourable to install many headed studs or perfobond ribs with narrow spacings at the joints. To solve this problem, a new type of a mixed shear connector was developed by combining a headed stud and perfobond rib at the same steel beam flange. In this paper, totally nine push-out tests were conducted. .e main purpose was to compare the failure mode and the load-slip behavior of the headed stud, perfobond rib, and mixed shear connector. Furthermore, 19 nonlinear finite element simulations were performed. .e effects of connector dimension and material properties on the structural behaviors of mixed shear connectors were studied. Based on the experimental and parametric study, an analytical equation was finally proposed to evaluate the shear capacity of perfobond rib with a headed stud mixed shear connector.


Introduction
In the past few decades, composite structures made of steel and concrete have been increasingly used in construction and bridge engineering.e main reason is their optimum structural performance and favourable cost.To achieve the load transfer between steel and concrete components, various types of shear connectors have been proposed, such as headed studs [1], perfobond ribs [2][3][4], channel connectors [5], bolted connectors [6], and composite dowels [7].e headed stud connector is most popular in engineering practice.e longitudinal shear is resisted by a stud shank, and the uplift separation is prevented with an anchorage head.However, the headed stud has some disadvantages, such as the requirement for specific welding equipment and the fatigue problem under cyclic loading [8,9].
To ease the installation and to improve the fatigue performance of shear connectors, an alternative connector named perfobond rib connector was developed by a German design company in the 1980s.e perfobond rib connector consists of a flat steel plate with several holes.Concrete dowels will form in these holes after casting to resist both shear and uplift forces.e perfobond rib connector has some advantages over the headed stud, such as easier installation by using continuous fillet welds, higher shear stiffness, and favourable fatigue performance.us, the perfobond connectors are increasingly designed and used in composite structures [10,11].
Recently, extensive research has been done to reveal the structural behavior of headed stud and perfobond rib shear connectors [12][13][14][15][16]. e effects of the shank diameter, stud length, material properties, and loading directions on the shear behavior of the headed stud have been studied [12,13].e effects of the hole number, hole diameter, configuration of the rebar in the hole, dimension of the perfobond rib, and material properties on the shear behavior of the perfobond rib have been investigated [14][15][16].According to these investigations, the shear capacity of shear connectors can be conveniently increased by using more headed studs or perfobond ribs.However, installing many headed studs or perfobond ribs at one steel beam flange would narrow the spacings, which is unfavourable for the bearing performance of shear connectors.It would also increase the difficulty in placing the reinforcing bars between headed studs and perfobond ribs.
In this paper, a new type of mixed shear connector was developed, combining headed stud and perfobond rib at the same steel beam flange.A total of nine push-out specimens were designed and tested.e main purpose was to compare the shear capacity and the load-slip behavior of the headed stud, perfobond rib, and mixed shear connector.Moreover, nonlinear finite element models were generated to study further the structural behaviors of mixed shear connectors concerning the connector dimension and material properties.Based on the experimental and numerical results, an analytical equation was derived to predict the shear capacity of perfobond rib with headed stud mixed shear connector.

Push-Out Test
To confirm the reliability of the push-out analysis for a perfobond rib with a headed stud mixed shear connector, nine push-out tests were introduced.As shown in Table 1, these tests could be equally divided into three groups in terms of the connector type.e groups HS and PR were the specimens installed with the headed studs and perfobond ribs, respectively.e group MS was the specimen of the perfobond rib with the headed stud mixed shear connector which was installed with four headed studs and one perfobond rib at each steel flange.e variables of the headed stud were the stud shank diameter d s and the stud length l s .
e parameters of the perfobond rib were the hole diameter d p and the rebar diameter d r .e yield strength and ultimate strength of the stud, the rebar, and the structural steel were obtained from tension tests and denoted as f sy , f ry , f y and f su , f ru , f u , respectively.e layout of the push-out test specimens is shown in Figure 1.Apart from the connector type, all the test specimens were identical in terms of the dimensions.Each specimen comprised one steel H-beam and two concrete slabs.e headed stud or perfobond rib was welded to the steel beam flange.A perforating rebar was installed in the hole of the perfobond rib.
e bond was prevented by greasing the contact surfaces before concrete casting.Styrofoam was attached to the bottom of the perfobond rib to eliminate the bearing stress.
As shown in Figure 2, the specimens were tested by using a hydraulic loading machine.e shear force between steel and concrete was applied by pushing down the steel H-beam.Four displacement gauges were installed at the level of the headed stud or the hole of the perfobond rib to measure the relative slip.e applied load and relative slips were both automatically and continuously recorded.
erefore, the push-out failure and load-slip curves of shear connectors could be obtained to verify the proposed finite element model.

General.
e finite element model of a typical push-out test was established with only one half of the specimen in order to save the analysis time, as shown in Figure 3.One purpose of this analysis was to investigate the inner failure by using validated finite element models instead of expensive and time-consuming push-out tests.Another purpose was to find out how these finite element models could support the deduction of design rules for the perfobond rib with the headed stud mixed shear connector.To assign the modelling strategy to other connector types, the general analysis package ABAQUS [17] was adopted to simulate the push-out tests of the mixed shear connector.e dynamic explicit method was used to consider both material and geometric nonlinearities [18][19][20][21][22]. e loading rate was carefully concerned by comparison with the push-out test results and finally taken as 0.1 mm/s to assure the quasi-static loading process.e kinetic energy was controlled within 5% to 10% of the total internal energy.A semiautomatic mass scaling method was used with the target time increment of 0.002 s to achieve a balance between solution time and accuracy.

Finite Element Type and Mesh.
As shown in Figure 3, a typical push-out test was modelled with the relevant support constraints in the symmetry layers.Discrete rigid elements (R3D4) were introduced to mesh the jacking header and the base plate.Eight-node reduced integration elements (C3D8R) were chosen to simulate the concrete slab, steel beam, headed stud, perfobond rib, and perforating rebar.
ree-dimensional two-node truss elements (T3D2) were used to model the other rebars.A global coarse mesh was applied to save analysis time using an overall size of 10 mm.In order to achieve more accurate results, a locally refined mesh with a smallest size of about 5 mm was applied at the region of the headed stud and perfobond rib.

Interaction and Boundary Conditions.
e boundary condition (BC), as shown in Figure 4, was applied to the symmetric planes of the model.e reference point of the base plate was fixed in all directions.A downward enforced displacement of 10 mm was applied to the reference point of the jacking header which represented the action of the hydraulic loading machine.Shear forces were induced at the interface of the shear connectors and the concrete slab.
e perforating rebar was tied to the surrounding concrete, while the other rebars were embedded inside the concrete slab.Contact interactions were applied at the interfaces of the jacking header to steel beam, concrete slab to base plate, steel beam to concrete slab, and concrete slab to shear connectors.General contact interactions were applied by matching predefined master and slave surface pairs [17].A "hard" contact was used in the normal direction to prevent penetration.e contact pressure could be transmitted, and possible separation was allowed when the pressure was zero or negative.e tangential behavior was defined by penalty frictional formulation.After trial calculations, the favourable frictional coefficient was taken as 0.5 for the contact between the base plate and concrete slab, while the other contact interactions were assumed to be frictionless.

Material Modelling of Concrete.
As shown in Figure 5, the nonlinear behavior of the concrete material in 2 Advances in Civil Engineering compression and tension was presented by a uniaxial compressive stress-strain curve and a tensile stress-crack width relationship, respectively.e concrete material constitutions in compression were governed by equation (1) [23,24].As shown in Figure 5(a), the rst part of the stress-strain curve is assumed to be elastic.e following two parts are a nonlinear parabolic portion and a descending branch, respectively:

Advances in Civil Engineering
where σ c is the compressive stress at any point (MPa); ε c is the compressive strain at any point; E c is Young's modulus (MPa); f c is the compressive strength of concrete (MPa); k is the plasticity number, k E c • ε cp /f c ; η is the ratio of strain to peak strain, η ε c /ε cp , ε cp 0.002; and ε cu 13.6 ε cp .
For uncracked concrete subjected to tension, a linear stress-strain relationship was adopted.As shown in Figure 5(b), for a cracked section, a nonlinear approach for the stress-crack width relationship can be determined by using the following equation, referring to the study of Hordijk [25]: where σ t is the tensile stress of concrete (MPa); f t is the tensile strength (MPa); w is the crack width (mm); w c is the crack width at the complete release of stress, w c 5.14 G F /f t (mm); G F is the fracture energy required to create a unit area of stress-free crack, G F 0.073 f 0.18 c (N/mm); and the constants are c 1 3 and c 2 6.93.
e concrete damaged plasticity model was used to describe the degraded response of the concrete material.Two independent uniaxial damage variables, d c and d t , were adopted to depict the damage of concrete due to compressive crushing and tensile cracking [17].
For concrete in compression, the evolution of d c is associated with the plastic strain ε pl c , which is determined proportional to the inelastic strain ε in c ε c − σ c /E c , using a constant factor b c (0 < b c < 1) in the following equation as suggested by Birtel and Mark [26]: where d c is the concrete compressive damage component and b c is the ratio of the plastic strain to inelastic strain, b c ε pl c /ε in c , and b c is taken as 0.7 [26].
For concrete in tension, the damage evolution component d t is related to the "plastic" crack width w pl , which is 4 Advances in Civil Engineering proportional to the crack width w, using a constant factor b t (0 < b t < 1) in the following equation, referring to [26]: where d t is the tensile damage variable of concrete; l 0 is assumed to be the unit length; and b t is the ratio of the "plastic" crack width to the crack width, b t w pl /w, and b t is set as 0.1 [26].

Material Modelling of Steel.
As shown in Figure 6, the stress-strain relationship of structural and reinforcing steel was modelled by trilinear curves.e initial stage is assumed to be elastic with Young's modulus E s , followed by a branch of yielding and nally a regime of strain hardening.e stress-strain relationships for steel in tension and compression were assumed to be the same.
e headed stud, especially the region around the stud root, experiences complex stress state and large deformation.To improve the accuracy of simulation, the material of the stud was modelled by a trilinear stress-strain curve, as shown in Figure 7. e material behavior of the stud is initially elastic with Young's modulus E s followed by strain hardening and then yielding.

Analysis Results and Verification
4.1.Failure Mode.As shown in Figure 8, the numerical results resembled the push-out failure of the headed stud, perfobond rib, and mixed shear connector quite well.e specimens with the headed stud failed due to stud shank fracture and concrete crushing below the stud root.e failure modes of the specimens with the perfobond rib were characterized by a crack in the concrete slab, yield of the perforating rebar, and shear failure of the concrete dowel.
e push-out failure of the mixed shear connector was caused by the stud shank fracture, concrete crushing below the stud root, yield of the perforating rebar, and concrete dowel shear at the same time.

Local Response Stress.
Figure 9 shows the local response stress of headed studs, perfobond ribs, and mixed shear connectors at the specimen failure.It was indicated that the mixed shear connectors had distributions of Mises stress in the stud shank similar to those of headed studs, and distributions of shear stress in the concrete dowel were similar to those of perfobond ribs.As shown in Figures 9(a) and 9(c), the Mises stress at the top and bottom of the stud shank decreased with the increase of distance to the stud root.
e maximum Mises stress occurred near the stud root and exceeded the ultimate strength of headed studs that equaled 465 MPa, which revealed that the headed studs were shorn o at this region.As shown in Figures 9(b) and 9(d), the shear stress on the left and right of the concrete dowel increased until reaching about 2/3 of the distance to the bottom and then gradually decreased to zero at the top.It was shown that the shear stress in most part of the concrete dowel exceeded the allowable shear strength of concrete, which indicated dowel shear failures of perfobond ribs and mixed shear connector.
e analysis results of local response stress agreed with the material behaviors of steel and concrete and thus further validated the reliability of the nite element method.

Load-Slip Behavior.
As listed in Table 2, the accuracy of the proposed nite element model can be veri ed by comparison with push-out test results.e load-slip curves obtained from the nite element analysis were in good agreement with those of the experimental results, as shown in Figure 10.For specimens with the headed stud, the analyzed shear strength accounted for 94% to 96% of the experimental results.For specimens with the perfobond rib, the analyzed shear strength took up 99% to 105% of the mean test result.And the analyzed shear strength of the specimen with the mixed shear connector was among 90% to 104% of the averaged test shear capacity.e shear strength and the corresponding peak slip from the push-out tests were successfully captured in the nite element analysis.However, the analyzed load-slip curves showed smaller sti ness than those obtained from the push-out tests at the initial loading stage.e reason might be that the accurate

Parametric Study
Based on the validated finite element model, a total of 19 push-out tests were simulated to study the effects of connector dimension and material properties, as shown Table 3.
e investigated variables included the stud diameter, hole diameter, rebar diameter, stud strength, concrete strength, and rebar strength.e connector dimension and material properties of models SD-22, SS-N, HD-60, RD-20, RS-N, and CS-70 were identical to those of the reference model RF.
e shank diameter of all the models was 200 mm.e yield strength and tensile strength of steel beam were kept constant as 410 MPa and 545 MPa, respectively.

Effect of Stud Diameter.
Figure 11 shows the effect of the stud shank diameter on the load-slip behavior of the mixed shear connector.When the stud shank diameter was added from 16 mm to 19 mm, 22 mm, 25 mm, and 30 mm, the shear capacity increased by 10%, 22%, 32%, and 53%, respectively.It was indicated that the increase of the stud shank diameter would lead to great increase of the shear capacity of the mixed shear connector.e mixed    Advances in Civil Engineering shear connector failed due to stud fracture, concrete crushing at the stud root, and shear of the concrete dowel.
As the larger stud was used, a larger region of the concrete below the stud root was involved in resisting the shear load.

Effect of Stud Strength.
Figure 12 shows the effect of the stud strength on the load-slip behavior of mixed shear connector.When the headed stud's yield strength was increased from 370 MPa to 650 MPa, the shear capacity of the mixed shear connector increased by 10%.It was indicated that increasing the stud strength would lead to little increase in the shear capacity of the mixed shear connector.e analyzed failure mode of the mixed shear connector was still stud fracture, concrete crushing at the stud root, bending deformation of the perforating rebar, and shear of the concrete dowel.As the high strength stud was used, a larger region of the concrete below the stud root damaged before the connector failure.

Effect of Hole Diameter.
Figure 13 shows the effect of the perfobond rib's hole diameter on the load-slip behavior of mixed shear connector.When the hole diameter was added from 40 mm to 50 mm, 60 mm, 70 mm, and 80 mm, the shear capacity increased by 4%, 9%, 14%, and 24%, respectively.It was indicated that the increase of the perfobond rib's hole diameter would lead to increase of the shear capacity of the mixed shear connector.As the larger hole was used for the perfobond rib, more concrete near the concrete dowel would be involved in resisting the shear load.

Effect of Rebar Diameter.
Figure 14 shows the effect of the perforating rebar's diameter on the load-slip behavior of mixed shear connector.When the rebar diameter was added from 16 mm to 18 mm, 20 mm, 22 mm, and 25 mm, the shear capacity increased by 6%, 8%, 12% and 15%, respectively.It was indicated that the increase of the rebar diameter would lead to increase of the shear capacity of the mixed shear connector.
e failure mode of the mixed shear connector was characterized by the stud fracture, concrete crushing, shear of the concrete dowel, and bending of the perforating rebar in hole.As the larger rebar was used, a larger region of the concrete near the concrete dowel was involved in resisting the shear load, and less bending deformation was observed for the perforating rebar.

Effect of Rebar Strength.
Figure 15 shows the effect of the rebar strength on the load-slip behavior of mixed shear connector.When the perforating rebar's yield strength was increased from 382 MPa to 480 MPa, the shear capacity of the mixed shear connector increased by 3%.It was revealed that increasing the rebar strength would lead to little increase in the shear capacity of the mixed shear connector.
e analyzed failure modes of the mixed shear connector included stud fracture, concrete crushing, shear of the concrete dowel, and bending of the perforating rebar in hole.Similar failure modes were observed for the finite element models using normal strength and high strength rebars.

Effect of Concrete Strength.
Figure 16 shows the effect of the concrete strength on the load-slip behavior of the mixed shear connector.When the concrete strength was added from 30 MPa to 40 MPa, 50 MPa, 60 MPa, and 70 MPa, the shear capacity increased by 18%, 30%, 44%, and 57%, respectively.It was indicated that the increase of the concrete strength would lead to great increase of the shear capacity of the mixed shear connector.As the higher strength concrete was used, smaller region of the damaged concrete below the concrete dowel was observed in the analyzed failure modes.6.1.Existing Equation for Headed Stud.Eurocode 4 [27] provides the following design equation for specifying the shear capacity of the headed stud installed by automatic welding:

Shear Capacity Equation
where V su is the shear capacity per stud (N); d s is the diameter of the shank of the headed stud (mm); E c is the elastic modulus of concrete (MPa); f c is the concrete compressive strength (MPa); f su is the ultimate tensile strength of the headed stud but not greater than 500 MPa; c V is the partial factor (�1.25); and α � 0.2(l s /d s + 1) for 3 ≤ l s /d s ≤ 4 and α � 1 for l s /d s > 4.
AASHTO LRFD [28] specifies the nominal shear capacity of the headed stud embedded in concrete as equation follows: where A s is the cross-sectional area of the shank of headed stud (mm 2 ) and φ is the resistance factor (�0.85).e Chinese standard for design of steel structures (GB 50017-2017) [29] evaluates the shear capacity of headed stud by using the following equation:

Existing Equation for Perfobond Rib.
e standard specifications for hybrid structures of JSCE [30] suggest the following design equation for predicting the shear capacity per hole of the perfobond rib with the perforating rebar: where V pu is the shear capacity per stud (N); c b is the material coefficient (�1.3); d p is the hole diameter (mm); d r is the diameter of the rebar in hole (mm); and f ru is the ultimate tensile strength of the rebar (MPa).Advances in Civil Engineering e Chinese speci cations for design of highway steel bridge (JTG D64-2015) [31] evaluates the shear capacity per hole of the perfobond rib connector by using the following equation: where f ry is the yield strength of the rebar (MPa).r f ry , respectively.us, an alternative equation combining these four contributions was proposed to evaluate the shear capacity of the mixed shear connector as follows:   Based on the nonlinear regression analysis on a total of 32 experimental and numerical results both in reference [32] and in this study, the best tting of the coe cients in equation ( 10) could be derived as C 1 0.16, C 2 0, C 3 2.0, and C 4 2.4.erefore, the nal proposal for estimating the shear capacity of mixed shear connector could be given as follows: Table 4 presents the calculated shear capacities from (11), which were compared to the experimental and numerical results.
e mean and variance of the ratio of predicted shear strengths to experimental results were 0.998 and 0.055, respectively.It was indicated that the predicted values agreed reasonably well with the results from push-out tests and parametric study, as shown in Figure 17.erefore, (11) could be used to predict the shear capacity of the perfobond rib with the headed stud mixed shear connector in steel and concrete composite structures.
e validity and accuracy of the model cannot be demonstrated on the basis of the reduced number of experimental data, and it is however limited within the range of parameter variation investigated.

Conclusions
In this study, nine push-out tests of the perfobond rib with the headed stud mixed shear connector were carried out.Based on the experimental results, parametric study, and analytical analysis, the following conclusions are drawn: (1) e push-out failure modes of the perfobond rib with the headed stud mixed shear connector are characterized by the stud shank fracture, concrete crushing below the stud root, yield of the perforating rebar, and concrete dowel shear at the same time.

Figure 6 :Figure 7 :
Figure 6: Material modelling of structural and reinforcing steel.

Figure 9 :
Figure 9: Local response stress.(a) Mises stress of the headed stud (HS).(b) Shear stress of the concrete dowel (PR).(c) Mises stress of the headed stud (MS).(d) Shear stress of the concrete dowel (MS).

( 2 )
e proposed nite element model is veri ed by comparison with push-out test results.e load-slip curves obtained from nite element analysis are in good agreement with experimental results.(3)Based on the validated nite element model, a total of 19 push-out tests are simulated to study the e ects of connector dimension and material properties.e shear capacity of the mixed shear connector increases with the increase of the stud diameter, rebar diameter, hole diameter, stud strength, rebar strength, and concrete strength.

( 4 )Figure 17 :
Figure 17: Comparison and validation of the proposed shear capacity equation.

Table 2 :
Comparison of analyzed and tested push-out results.

Table 3 :
Generalization of parametric models.
s = 16 mm d s = 19 mm d s = 22 mm d s = 25 mm d s = 30 mm

Table 4 :
Comparison and validation of the proposed shear capacity equation.mu is the shear capacity per ange of mixed shear capacity (N); n s is the number of headed studs per ange; n p is the number of holes of the perfobond rib per ange; d s is the stud shank diameter (mm); E c is the elastic modulus of concrete (MPa); f c is the concrete compressive strength (MPa); f su is the ultimate tensile strength of the stud; d p is the hole diameter (mm); d r is the rebar diameter (mm); f ry is the yield strength of the rebar (MPa); and C 1 , C 2 , C 3 , and C 4 are coe cients.
Specimen n s d s (mm) f cu (MPa) f su (MPa) n p d p (mm) d r (mm) f ry (MPa) V u (kN) V u,eq (kN) V u,eq (V u )