Finite element analysis of HSS semi-rigid composite joints with precast concrete slabs and demountable bolted shear connectors

Finite Elements in Analysis and Design 122 (2016) 16–38

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Finite Elements in Analysis and Design journal homepage: www.elsevier.com/locate/finel

Finite element analysis of HSS semi-rigid composite joints with precast concrete slabs and demountable bolted shear connectors Abdolreza Ataei n, Mark A. Bradford, Hamid R. Valipour Centre for Infrastructure Engineering and Safety, School of Civil and Environmental Engineering, UNSW Australia, UNSW Sydney, NSW 2052, Australia

art ic l e i nf o

a b s t r a c t

Article history: Received 15 March 2016 Received in revised form 9 August 2016 Accepted 11 August 2016

High-strength steel has a higher yield strength, greater corrosion resistance and superior toughness compared to mild steel, and its use can contribute to the sustainability of a steel structure by increasing its structural life whilst reducing steel usage and maintenance. In addition, using deconstructable steelconcrete composite floors can facilitate component recycling and reuse and can improve the sustainability of the building industry significantly by reducing energy consumption and construction waste at demolition. This paper investigates the structural behaviour of an innovative beam-to-column composite semi-rigid joint with deconstructable post-installed friction-grip bolted shear connectors and grade S690 high strength steel flush end plates. Non-linear continuum-based finite element models are developed and validated against results of four full-scale laboratory tests of this innovative joint. The validated finite element models are used for conducting an extensive parametric study in which the effects of the reinforcement ratio, thickness of the precast concrete slab, degree of shear connection, number of bolted shear connectors, size of the bolts in the connection zone, size of the steel beam and thickness of the flush end plate on the structural behaviour of a composite joint with deconstructable post-installed friction-grip bolted shear connectors and grade S690 high strength steel flush end plates are investigated. A simple analytical model is proposed to predict the moment capacity and rotation capacity of this type of composite joint. & 2016 Elsevier B.V. All rights reserved.

Keywords: High strength steel Composite joints Sustainable Deconstructable Friction-grip bolt Finite element model

1. Introduction In steel framed buildings, traditional flush end plate semi-rigid (FEPSR) connections can provide substantial moment resistance, stiffness and rotation capacity, particularly when composite action develops between the concrete slab and steel beam. The tensile forces carried by the reinforcing bars in the concrete slab improve the rigidity of the composite connection quite significantly, and this in turn allows for the bending moment transfer to the column as well as moment redistribution at the strength limit state. In addition, the fabrication and erection of steel frames with flushend plate connections are simple and economic compared to rigid connections. However, as attention is being focused increasingly towards lowering the carbon footprint of a building and the possibility of component recycling in the construction industry, traditional steel-concrete composite floors in buildings constructed using headed stud shear connectors welded to the top flange of the steel beam cannot be deconstructed easily. In addition, the use of ordinary Portland cement in the concrete for the slab increases n

Corresponding author. Fax: þ61 2 93859747. E-mail address: [email protected] (A. Ataei).

http://dx.doi.org/10.1016/j.finel.2016.08.003 0168-874X/& 2016 Elsevier B.V. All rights reserved.

the carbon footprint of the building owing the large quantity of CO2 emissions generated during its manufacture. The use of high-strength steel (HSS) has gained popularity in the construction industry. However, the efficient use of HSS in structural members has been hampered by problems associated with its lower ductility, weldability and fatigue resistance. In particular, the lower ductility of the HSS can potentially affect the structural performance of end plate beam-to-column connections where the steel plates can experience large strains well-beyond the yield strain. Girão Coelho and Bijlaard [1,2] carried out an experimental investigation on moment connections with end plates made from HSS of grades S460, S690 and S960 to provide insight into the nonlinear behaviour of these joints, and it was concluded that the extrapolation of the design philosophy in the current Eurocode 3 (EC3) [3] and Eurocode 4 (EC4) [4] provisions, based on semi-continuous/partially-restrained concepts, can provide accurate strength predictions. The size/thickness of structural steel members/plates and connection components such as end plates can be reduced by using HSS instead of mild steel, without significantly compromising the ductility and rotation capacity of the connections [1,2]. Accordingly, using HSS can reduce the amount of steel (as an energy and carbon intensive material) in the construction that in

A. Ataei et al. / Finite Elements in Analysis and Design 122 (2016) 16–38

17

Fig. 1. Normalised uniaxial stress–strain relationship for concrete under: (a) compression; (b) tension.

turn, improves the sustainability of steel structures. While the effect of end plates made of HSS on reducing the overall weight/ amount of steel structures can be limited, this is considered as one of the first steps towards systematic codification and incorporation of the HSS in the construction industry. The next step to further benefit from use of HSS in the construction industry and improve the sustainability of steel structures is to use HSS for beams and columns in addition to connections. The influence of HSS flush end plates on the structural behaviour of beam-to-column joints and benefits of using HSS flush end plates have been also discussed in previous studies [1,2]. The use of precast concrete slabs batched from concrete with a low content of Portland cement [5] using demountable technologies has the potential to minimise the undesirable attributes of traditional composite framed systems when evaluated within paradigms related to sustainable infrastructure. In a fully deconstructable steel-concrete composite frame, the beam-to-column connections as well as the floor slab to steel beam connections need to be easily dismantled. As an alternative to headed stud shear connectors, post-installed friction-grip bolted shear connectors (PFBSCs) are proposed to replace headed shear connectors to connect the precast concrete slab to the top flange of steel girder through predrilled holes in the precast concrete slab and steel beams [6–12]. Post-installed friction grip bolted shear connectors (PFBSCs) installed through bolt holes placed in precast slabs and predrilled holes in the top flange of the steel beams is a novel method for developing composite action between precast concrete slabs and steel girders. The composite floors employing PFBSCs can be easily deconstructed at the end of their service life, and this in turn can minimise the construction waste associated with the demolition of composite floors and can maximise the possibility for future reuse of the structural components. Furthermore, deconstructable composite floors with precast slabs and prefabricated steel girders can increase the speed, accuracy and quality of construction and reduce the time and environmental impact of the construction [6–12]. This paper presents the development of a three-dimensional finite element (FE) model to investigate the structural behaviour of beam-to-column composite semi-rigid joints with deconstructable PFBSCs and Grade S690 high strength steel flush end plates. Tests on full-scale FEPSR beam-to-column joints made up of grade S690 HSS are reported and the numerical modelling is validated against the experimental results. The model simulates a composite beamto-column connection under hogging moment and it includes both geometrical and material non-linearities as well as non-linearity of the contacts and interfaces. It is shown that the FE representation developed can adequately capture the local and global behaviour of deconstructable HSS composite joints with PFBSCs. Accordingly,

the proposed FE models are used for conducting a comprehensive parametric study in which the effects of the reinforcement ratio, thickness of the precast concrete slab, degree of shear connection, number of deconstructable bolted shear connectors, size of the bolts in the connection zone, size of the steel beam and the thickness of the flush end plate on the structural behaviour of deconstructable HSS semi-rigid composite joints with PFBSCs are investigated. Finally, a simple analytical model is proposed to predict the moment capacity and rotation capacity of this type of composite joint.

2. Finite element model The commercial software ABAQUS [13] was used to develop a three-dimensional FE model to investigate the structural behaviour of HSS semi-rigid composite beam-to-column joints with PFBSCs. The accuracy and reliability of the FE representations depend on the material models adopted in the analysis, the mesh type and size, as well as the boundary conditions including contact and interface areas that are discussed in the following sections. 2.1. Material constitutive laws 2.1.1. Concrete A precast reinforced concrete slab is one of the core components of deconstructable composite beam-to-column joints. In the FE models, the concrete in compression and tension was represented using a damaged-plasticity model that takes advantage of an isotropic damage model in conjunction with an isotropic plasticity-based model that can capture the concrete cracking and crushing under tensile and compressive stress states. For concrete under uniaxial compression, the relationship proposed by Carreira and Chu [14] was adopted as (Fig. 1(a)) 8 σ c r 0:35f c
ð2Þ

is a factor that controls the curvature of the stress–strain curve, ε the strain and fc the mean compressive strength of concrete (in MPa) obtained from standard cylinder tests. The ultimate strain of the concrete in compression at failure is assumed to be 0.01. For concrete in tension, a linear–elastic representation followed by a linear softening branch was adopted as shown in Fig. 1(b).

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reinforcement. A mesh sensitivity analysis was carried out to ensure that a good compromise between accuracy and computational efficiency can be achieved and the FE models developed can capture global and local response of the structural components including local buckling of compressive flanges and all distinctive modes of failure observed in the experiments. It is noteworthy that the adequacy of using only one element over flange thickness of steel girders has been demonstrated in the previous FE studies [19–22]. The FE mesh for the whole composite joint, bolts and flush end plates are outlined in Figs. 5 and 6.

600

Stress (MPa)

500 400

Sample 1-BF Sample 2-BF Sample 3-BF Sample 1-BW Sample 2-BW Sample 3-BW FE model

300 200 100 0

0

100000 200000 Strain (µ )

300000

Fig. 2. Stress–strain relationship for steel beam.

600

Stress (MPa)

500

400 300

Sample 1-SHS Sample 2-SHS Sample 3-SHS FE model

200 100 0

0

100000 200000 Strain (µ )

300000

Fig. 3. Stress–strain relationship for column.

2.1.2. Structural steel, reinforcing bars, blind bolts and standard bolts The actual stress–strain diagrams for the steel beams, steel hollow section (SHS), HSS flush end plates, reinforcing bars, blind bolts and standard bolts were obtained from direct uniaxial tensile tests reported elsewhere [9] and the results are shown in Figs. 2–4. Idealised piecewise linear representations of the experimental uniaxial stress–strain diagrams were adopted in the FE models, as shown in Figs. 2–4. Based on tensile tests, the ultimate strains of the longitudinal reinforcing bars, standard bolts and HSS flush end plates at the failure were assumed to be 0.15, 0.1 and 0.07 respectively. The composite beam-to-column joints tested in this study were fabricated using high strength steel (HSS) plates available in Australia and the HSS plates comply with over-strength and ductility requirements of Australian standard AS4100 [15] and AS3597 [16]. The material test results show that the over-strength fu/fy ratio for HSS used in this study was slightly less than that recommended by Eurocode (i.e. fu/fy 4 1.10). However, a comparison between the specimens with HSS end plates [9] and those with mild steel end plates [10,12] shows that the discrepancy in over-strength requirements of Australian standards and Eurocode have minor influence on the structural behaviour of beam-to-column semirigid joints with deconstructable PFBSCs and Grade S690 HSS flush end plates. 2.2. Element type and mesh Only half of the composite joint was modelled because of the symmetry of the specimens. Except for the reinforcing bars, all components were meshed by the 8-node solid elements (C3D8R) with a reduced integration scheme to prevent shear locking, to reduce the computational cost and to provide the required level of accuracy [17,18]. Three-dimensional truss elements (T3D2) with a linear approximation of the displacement, two nodes and three translational degrees of freedom were used for meshing the steel

2.3. Contact modelling The contact interaction between various components in the composite connections can significantly affect the FE results. To simulate the contact interaction between different components, the surface-to-surface contact interaction using a penalty contact method was used, in which one surface was considered as master and the other as slave surface. The HARD and PENALTY options available in the ABAQUS software were employed for contact modelling in directions normal and parallel to the interface plane respectively. Friction coefficients of 0.45 and 0.25 were adopted for the interface between the concrete and steel component, and between two steel components, respectively. The reinforcing bars were considered to be embedded in the concrete slab, with the slab being a host region and the bars being an embedded region. The technique provides for perfect bond between the reinforcing steel bars and concrete. As the flush end plate and the stiffeners were welded to the steel beam, the TIE option was used for connecting these components. Representing the shear interaction between the concrete slabs and steel girders through mechanical shear connectors is one of the main challenges in the FE modelling of composite beams and joints. In this study, the PFBSCs were not modelled explicitly. Instead, axial connectors were used to represent the horizontal shear interaction between the concrete slab and steel girders (Fig. 7). These connectors were located at the same positions as the PFBSCs placed on the specimen. The shear-slip characteristic of the PFBSCs was taken from standard push tests as reported elsewhere [12]. The actual load-slip diagrams for two types of the bolted shear connectors and the idealised piecewise linear representations of these experimental load-slip diagrams, adopted in the FE models, are shown in Fig. 8. According to the push-out test results [12], fracture of the bolted shear connectors was assumed to be occurred at the ultimate slip of 13 mm for M16 bolted shear connector and at 18 mm for M20 bolted shear connector. 2.4. Boundary and loading conditions Proper representations of the boundary conditions have an essential role in the accuracy of the FE predictions and a small variation in these boundary conditions can significantly affect the FE results. Accordingly, every attempt was made to model the boundary conditions in the FE models as close as possible to the test setup. Since only half of the composite joint was simulated, all nodes along the middle of the column web, the column stiffeners, concrete slab and longitudinal bars (surface 1) were restrained from moving in the X direction and from rotating in the Y and Z directions due to symmetry. In addition, following the experimental set-up described subsequently, all nodes at the bottom surface of the column (surface 2) were restrained from moving and rotating in X, Y and X directions (Fig. 9). The connections were loaded in two stages in the numerical study. Firstly, the pretension was applied to the bolts located in the connection zone and, subsequently, the external loads were applied on the connection under a displacement-control regime.

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Fig. 4. Stress–strain relationships for: (a) HSS end plate; (b) longitudinal bar (LB); (c) transverse bar (TB); (d) blind bolt (BB); and (e) M24 standard bolt (SB).

Fig. 5. FE mesh for composite joints with: (a) I-section columns (b) concrete-filled columns without showing concrete core.

Mirza and Uy [23] have pointed out that Riks’ technique is needed to capture any unloading in the non-linear analysis; accordingly the general Newton–Raphson method and modified Riks method

were used as the solution algorithms in the first and second stages of the loading, respectively. To prevent a stress concentration, a rigid plate was placed at the location where point load was applied

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A. Ataei et al. / Finite Elements in Analysis and Design 122 (2016) 16–38

Interface

Fig. 6. FE meshes for: (a) blind bolt, (b) standard bolt and nut and HSS end plate with (c) six and (d) four holes.

Fig. 7. Schematic diagram of axial connector model for composite joints.

(Fig. 9). The distribution of the von Mises’ stresses in the bolts and flush end–plate after the first stage of loading (the bolt pretension) for specimen CJ1 is shown in Fig. 10, which demonstrates the adequacy of loading procedure adopted in the FE models.

3. Experimental study The beam-to-column joints tested physically were part of a novel deconstructable and sustainable structural system with composite steel-precast concrete slabs manufactured a proprietary concrete having a reduced amount of ordinary Portland cement [5]. In these specimens, composite action between the steel girders and precast concrete slabs was provided by PFBSCs. All beam-to-column joint specimens were designed and constructed according to the provisions of EC3 and EC4 to simulate the behaviour of an internal joint in a semi-rigid frame. The experimental programme was intended to provide benchmark results for validation of numerical models and development of design procedures.

The experimental study comprised of four full-scale composite beam-to-column joints with HSS Grade S690 flush end plates. For the first two specimens, i.e. CJ1 and CJ2, the columns were Australian 250UC89.5 I-section steel columns and for the other two specimens (i.e. CJ3 and CJ4), concrete-filled tubular steel 250  250  12.5 mm columns were used. The geometry, dimensions and details of all specimens are illustrated in Figs. 11 and 12. More details of the testing is given in [9]. The steel beams were connected to the column by means of friction grip Grade 8.8 bolts post-tensioned using an electrical wrench in conjunction with Squirter Direct Tension Indicating (SDTI) washers. For the specimens with concrete-filled tubular columns, 33 mm diameter holes drilled in the flush end plate were used to install M20 blind bolts. The blind bolts were tightened to a torque of 300 N m in accordance with the manufacturer [24,25] using a manual torque wrench. To install the PFBSCs, 22 mm diameter holes were drilled through the top flange of the steel beam using a portable electric magnetic drill. The configuration of the cruciform joints before and after installation of the precast concrete slabs is shown in Fig. 13. The precast concrete panels (Fig. 13(b)) were attached to the steel beam by

A. Ataei et al. / Finite Elements in Analysis and Design 122 (2016) 16–38

140

250

120

Load (kN)

200

Load (kN)

21

150 100 M20 bolt

50

FE model 0

100 80 60

40

M16 bolt

20

FE model

0

0

10 20 Average Slip (mm)

30

0

5

10 15 Average Slip (mm)

20

Fig. 8. Experimental and piece-wise linear representation of load-slip relationships for (a) M20 and (b) M16 bolted shear connectors.

Load

Surface 1

Surface 2 Fig. 9. Boundary conditions.

Fig. 10. Stress distribution at the first step of loadings for: CJ2 (a) bolt; (b) flush end plate.

means of Grade 8.8 structural bolts installed through prefabricated holes in the precast concrete slabs and the predrilled holes in the steel beams. The PFBSCs were tightened using an electrical wrench and the minimum pretension force induced in the PFBSCs was confirmed by using SDTI washers. The loading arrangement and test set-up for the experimental programme are illustrated in Fig. 14. The end of the column was fixed to the floor and two vertical static loads were applied at both ends of the composite beams. All specimens were loaded under a regime of displacement-control. For the first stage of the loading, the set-up and performance of the components and instrumentation was checked by applying a small load (about 10%) of the predicted ultimate capacity of the specimens. Following this first

stage, the specimens were unloaded and reloaded, and the deformation was increased monotonically until no further load could be sustained by the specimen (being defined as failure of the specimens). During the loading regime, three displacement rates, viz. 0.3, 0.6 and 1.2 mm/min, were used consecutively and application of the displacements was stopped when the load dropped dramatically.

4. Verification of FEM The first and the most important step towards application of the FE model for parametric studies is the validation of the FE

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A. Ataei et al. / Finite Elements in Analysis and Design 122 (2016) 16–38

Fig. 11. Geometry and details of joints CJ1 and CJ2 (unit: mm).

predictions against physical tests. Because of this, the bending moment versus rotation curves, load-strain plots in the top and bottom flanges of the steel girders at sections 120 mm and 400 mm from the face of the column and load-strain plots for the

reinforcing bars at the mid-span predicted by the FE models are compared with the experimental results of the composite beamto-column joints in Figs. 15–18. It can be seen that the FE results correlate well with the experimental data and the numerical

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23

Fig. 12. Geometry and details of joints CJ3 and CJ4 (unit: mm).

model developed is able to accurately predict the local and global responses as well as failure (associated with a significant drop in the load) of the deconstructable composite joint with a HSS flush end plate and PFBSCs. It can be seen that the FE models can predict the plastic deformation of the flush end plate and the excessive

deformations in the joint zone with reasonable accuracy (Fig. 19 (a)). Moreover, the FE models predicted the tensile fracture of the longitudinal reinforcing bars in all specimens (Fig. 19(b)). The bending moment capacities of the composite beam-tocolumn joints predicted by the FE models are compared with

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A. Ataei et al. / Finite Elements in Analysis and Design 122 (2016) 16–38

Fig. 13. Configuration of cruciform joints (a) before and (b) after installation of precast concrete slabs for specimen CJ1 and CJ2.

Fig. 14. (a) Loading arrangement and (b) test set up.

the experimental results in Table 1 and a good correlation between peak loads predicted by the FE models and experimental results is observable with the average ratio of the FE to the test results very close to unity. In addition, the ultimate negative bending moment capacity of the composite crosssection was calculated using the plastic analysis approach and the results are provided in Table 1. It is seen that the ultimate negative bending moment capacities of the composite cross

section are about 15–20% higher than the bending moment capacity of the composite joints obtained from the experiments. The tested composite beam-to-column joints were also analysed under pure bending moment (applied at the end of the composite beam) and the peak load capacities obtained from the pure bending moment case were found to closely correlate with the results of FE models in which composite

A. Ataei et al. / Finite Elements in Analysis and Design 122 (2016) 16–38

Fig. 15. Comparison of the FE predictions with the experimental results for specimen CJ1.

Fig. 16. Comparison of the FE predictions with the experimental results for specimen CJ2.

25

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A. Ataei et al. / Finite Elements in Analysis and Design 122 (2016) 16–38

Fig. 17. Comparison of the FE predictions with the experimental results for specimen CJ3.

400

600

300

400

Load (kN)

Moment (KNm)

500

300 200

CJ4

100

200 CJ4

FEM

100

FEM 0

0

0

20

40

-2000

60

400

300

300 Load (kN)

Load (kN)

400

200

-1000

1000

2000

200

100

100

0

0

CJ4 FEM

FEM -1500

0 Strainn (µ )

Rotation (mrad)

CJ4

-1000

-500

0

500

1000

Strainn (µ )

0

10000 20000 30000 Strainn (µ )

40000

Fig. 18. Comparison of the FE predictions with the experimental results for specimen CJ4.

joints were subjected to bending moment and shear force simultaneously (identical to tested joints). Accordingly, it was concluded that shear force has negligible effect on the peak load capacity of the tested composite beam-to-column joints.

This is consistent with the previous FE studies that demonstrated the negligible influence of shear force on the peak load capacity and structural response of the composite beams/ joints [26].

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Fig. 19. (a) Plastic deformation of the end plate and strain distribution in reinforcing steel bars and (b) distribution of strain in bars in CJ1.

Table 1 Parameters considered for parametric studies. Specimen

CJ CJ CJ CJ

1 2 3 4

Joint moment capacity (kN m) Test

FE

(FE/Test) ratio

513 507 535 535

484 487 522 521

Negative plastic bending moment capacity (kN m)

(Test/Plastic bending moment) ratio

631 631 631 631

0.81 0.80 0.85 0.85

0.94 0.96 0.98 0.97

Table 2 Parameters considered for parametric studies. Variable Shear connection (%) Shear connectors Spacing (mm) Reinforcement (%) Reinforcing Steel beam Slab depth (mm) Bolt size End plate thick. (mm)

Range of variable selected 34 2M16 1100 0.36 6N10 250UB37 80 M12 4

54 2M20 1100 0.51 6N12 360UB57 120 M16 8

67 4M16 1100 0.70 6N14 460UB82 160 M20 12

108 4M20 1100 0.91 6N16 530UB92 200 M24 16

101 6M16 550 1.16 6N18 610UB125 280 M30 20

Note: Values in bold adopted for standard joint.

700

Moment (kNm)

600

500 400 300

6N10(0.36%) 6N12(0.51%) 6N14(0.70%) 6N16(0.91%) 6N18(1.16%) 6N20(1.43%)

200 100 0

0

10

20 30 40 Rotation (mrad)

50

60

Fig. 20. Moment vs. rotation response of composite joints with different reinforcing ratio in the precast slab.

162 6M50 550 1.43 6N20

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Table 3 FE modelling results for composite joints with different reinforcing ratio. Model Reinf. ratio %

End slip Initial stiffness mm kN m/ mrad

Rotation cap. Moment cap. Failure mode Mrad kN m

6N10 6N12 6N14 6N16 6N18 6N20

1.0 4.3 6.3 9.5 13.0 13.0

36.8 45.0 47.4 49.9 29.6 29.5

64.3 69.8 72.0 82.3 83.7 84.7

349.7 422.6 501.4 586.0 589.6 591.5

RBF RBF RBF RBF & LB BSCF BSCF

Moment capacity (kNm)

The FE model validated by the experimental results was used for conducting a comprehensive parametric study to investigate the effect of different variables on the behaviour of deconstructable HSS semi rigid composite beam-to-column joints with PFBSCs and I-section columns (Table 2). The ranges adopted for different parameters are deemed to be applicable for real beam-to-column joints. The main mechanical properties of the beam-to-column joints including the initial stiffness, moment capacity and rotation capacity were obtained from the FE analysis of deconstructable

90

55

85

50

Bar fracture

80 PFBSC fracture/Local buckling

75 70 65

Rotation capacity (mrad)

Initial stiffness (kNm/mrad)

Notes: RBF ¼ reinforcing bar fracture, LB ¼ local buckling of compression flange, BSCF ¼ bolted shear connector fracture.

5.1. General

PFBSC fracture/Local buckling

45 40 35 30

Bar fracture

25

60 0.25 0.50 0.75 1.00 1.25 1.50 Reinforcement ratio (%)

20 0.25 0.50 0.75 1.00 1.25 1.50 Reinforcement ratio (%)

650

14

600

12

550

500

PFBSC fracture/Local buckling

450 400 350 Bar fracture

300 0.25 0.50 0.75 1.00 1.25 1.50 Reinforcement ratio (%)

End slip at failure (mm)

0.36 0.51 0.70 0.91 1.16 1.43

5. Parametric study

10 8 6

PFBSC fracture/ Local buckling

4 2

Bar fracture 0 0.25 0.50 0.75 1.00 1.25 1.50 Reinforcement ratio (%)

Fig. 21. Variation of (a) initial stiffness (b) rotation capacity (c) bending moment capacity and (d) end slip with respect to reinforcing ratio in the precast slab.

Fig. 22. Contours of von Mises’ stresses (in Pa) within connection and local buckling of compression flange at ultimate state for joint with 0.91% reinforcement ratio.

A. Ataei et al. / Finite Elements in Analysis and Design 122 (2016) 16–38

HSS composite joints with PFBSCs. Moreover, the final slip at the end of the composite beam and the failure mode of the composite joints was also obtained from the FE models. 5.2. Effect of reinforcement ratio The reinforcing ratio for the concrete slabs has a significant influence on the behaviour of the composite joints. Six different reinforcement ratios, i.e. 6N10 (0.36%), 6N12 (0.51%), 6N14 (0.70%), 6N16 (0.91%), 6N18 (1.16%) and 6N20 (1.43%), were considered in the parametric study. The minimum reinforcing ratio in the parametric study was specified with respect to the beam grade and size, reinforcement properties and the connection type (i.e. compact or plastic). The maximum reinforcing ratio was specified assuming that the compressive region in the steel beam remains in the lower half of the steel beam. 600

Moment (kNm)

500 400 2M16(34%) 2M20(54%) 4M16(67%) 6M16(101%) 4M20(108%) 6M20(162%)

300 200

100 0

0

20

40 Rotation (mrad)

60

80

Fig. 23. Moment vs. rotation response for composite joints with different degrees of shear connection.

The moment-rotation response for the deconstructable composite joints with different reinforcing ratios for the concrete slabs is shown in Fig. 20. Furthermore, the initial stiffness, moment capacity, rotation capacity, failure mode of the specimen and the final slip at the end of the composite beam obtained from the FE models are summarised in Table 3, and their variation with respect to the reinforcing ratio are shown in Fig. 21. It can be seen that the initial stiffness of the semi-rigid joint gradually increases as the reinforcing ratio increases. For example, the initial stiffness of the composite joint with a reinforcing ratio of 0.91% is about 28% higher than that of the joint with a reinforcing ratio of 0.36%. Fig. 21(a) also shows that an increase of the reinforcing ratio above about 1% has an insignificant influence on the initial stiffness of the joint owing to fracture of the PFBSCs. Moreover, it is observable that an increase in the area of the steel reinforcement (up to about 1%) leads to a significant increase in the bending moment capacity of the joint (Fig. 21(c)). However, a further increase in the reinforcement (above 1%) does not increase the moment capacity of the composite joint, because at ratios above 1% the failure mode changes from reinforcing bar fracture to bolted shear connector fracture or to premature local buckling of the bottom flange of the steel beam. Because of this, it is concluded that in deconstructable composite joints with PFBSCs, the minimum shear connection should be determined with respect to the reinforcing ratio in the precast concrete slab, otherwise increasing the area of reinforcement will not increase the moment capacity of the composite joint. Fig. 22 shows the model at failure with 0.91% reinforcement. It is seen that as the reinforcing ratio increases, the rotation capacity and the ductility of the joints also increases (Fig. 21b). However, a reinforcing ratio exceeding 1% can decrease the

Rotation capacity (mrad)

Initial stiffness (kNm/mrad)

100 90 80 70 60 50 40

60 55 PFBSC fracture 50 45 40 35 30 Bar fracture 25 20 0 50 100 150 200 Degree of shear connection(%)

540

14

520

12

500

10

End slip (mm)

Moment capacity (kNm)

0 50 100 150 200 Degree of shear connection(%)

480 460 440

29

8

6 4 2

420

0

400 0

50

100

150

200

Degree of shear connection(%)

0

50

100

150

200

Degree of shear connection(%)

Fig. 24. Variation of (a) initial stiffness (b) rotation capacity (c) moment capacity and (d) end slip with respect to degree of shear connection.

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Table 4 FE modelling results for composite joints with different degrees of shear connection. Model

Degree of shear connection

Longitudinal spacing (mm)

End slip mm

Initial stiffness kN m/mrad

Rotation cap. mrad

Moment Cap. kN m

Failure mode

2M16 2M20 4M16 6M16 4M20 6M20

34 54 67 101 108 162

1100 1100 1100 550 1100 550

13.0 10.9 6.3 4.2 5.1 1.5

51.2 52.2 72.0 94.2 73.6 95.8

25.7 56.9 47.4 44.4 43.8 35.5

419.9 520.7 501.4 494.0 495.3 478.9

BSCF RBF RBF RBF RBF RBF

Notes: RBF ¼ reinforcing bar fracture, BSCF¼ bolted shear connector fracture.

700

Moment (kNm)

600

500 400 4 mm end plate 8 mm end plate 12 mm end plate 16 mm end plate 20 mm end plate

300 200 100 0 0

10

20 30 40 Rotation (mrad)

50

60

Fig. 25. Moment vs. rotation response for composite joints with different flush end plate thickness.

Table 5 FE modelling results for composite joints with different end plate thickness. Model

tep/db

End slip mm

Initial stiffness kN m/mrad

Rotation capacity mrad

Moment capacity kN m

Failure mode

4 mm end plate 8 mm end plate 12 mm end plate 16 mm end plate 20 mm end plate

0.17 0.33 0.50 0.67 0.83

7.1 6.3 5.9 5.4 5.3

54.1 72.0 94.4 121.8 141.2

32.8 47.4 26.5 15.4 11.0

389.4 501.4 575.8 593.2 594.1

FEPF RBF BF BF BF

Notes: FEPF ¼ flush end plate fracture, RBF ¼ reinforcement bar fracture, BF¼ bolt fracture in tension zone.

rotation capacity and ductility, because failure of the joint is governed by sudden fracture of the shear connectors or by local buckling of the compressive flange, as pointed out by Loh et al. [27]. Because of this, it is concluded that the slab reinforcement must be carefully specified to be proportionate with fracture of the shear connectors and the local buckling of the bottom flange of the steel beam. As shown in Table 3, the final slip at the end of the composite beam also increases with an increase of the reinforcing ratio. 5.3. Effect of degree of shear connection In the parametric study, six degrees of composite shear connection (composite efficiency), i.e. 34% (2M16), 54% (2M20), 67% (4M16), 108% (4M20), 101% (6M16) and 162% (6M20) per slab, were considered. The first three levels of composite efficiency represent partial shear connection and the second three represent full shear connection. The moment-rotation curves for the composite joints with different levels of shear interactions are shown in Fig. 23, while the initial stiffness, the moment capacity, the rotation capacity, the failure mode of the specimen and the final slip at the end of the composite beam versus degree of shear connection are shown in Fig. 24 and Table 4. It can be seen that the initial stiffness of the joint increases gradually as the degree of

shear connection increases and that decreasing the degree of the shear connection leads to a significant decrease in the secant stiffness of the joint (Figs. 23 and 24(a)). This recent observation is consistent with the experimental results [9]. The spacing of the bolted shear connectors along the beam can be important. Fig. 24(a) shows that the initial stiffness of the beam-to-column joints with a composite efficiency of 101% (6M16) is higher than that with 108% (4M20) composite efficiency. This may be because a large number of bolted shear connectors having a small bolt size is more efficient than a small number of large-size bolted connectors in transferring shear force between the precast concrete slab and steel beam. Accordingly, it is recommended to use a smaller bolt size and increase the number of bolts instead of reducing the number of bolts and increasing their size. A comparison of the results shows that when fracture of the reinforcing bars governs the failure mode, the moment and rotation capacities of the joints are not significantly influenced by the degree of the shear connection (Figs. 24(b) and (c)). It is seen that these capacities with composite efficiencies of 67%, 101% and 108% are almost the same. The joint with 2M20 bolts (54% composite efficiency) has the highest bending moment and rotation capacities (Figs. 24(b) and (c)) that can be attributed to the minimum degree of shear connection provided to prevent the fracture of the bolted shear connectors and to mobilise the plastic strain in the

160 140 120 100

80 60 40 0.00

31

50

Rotation capacity (mrad)

Initial stiffness (kNm/mrad)

A. Ataei et al. / Finite Elements in Analysis and Design 122 (2016) 16–38

0.25

0.50

0.75

40 30 20

10 0 0.00

1.00

0.25

0.50

0.75

1.00

0.75

1.00

tep/db

tep/db

Moment capacity (kNm)

600 550

Bar fracture and end plate yielding

500 450

Bolt fracture

400

350 0.00

0.25

0.50 tep/db

0.75

1.00

End slip at failure (mm)

8 650

7

7 6 6 5

5 4 0.00

0.25

0.50 tep/db

Fig. 26. Variation of joint (a) initial stiffness (b) rotation capacity (c) moment capacity and (d) end slip with respect to flush end plate thickness to bolt diameter ratio.

Fig. 27. Failure mode of joint with 4 mm end plate (a) contours of Von Mises’ stresses (in Pa) and (b) equivalent plastic strain (PEEQ) distribution in connection.

longitudinal reinforcing bars. It is concluded that if a very low level of shear interaction is provided for the composite beams, the bolted connectors fracture before the reinforcing bars yield. The FE results also show that the moment and rotation capacities of the joints are not influenced significantly by the spacing of the bolted shear connectors along the beam as shown in Table 4 and Figs. 24 (b) and (c) for models with almost same degree of shear

connection and different bolted shear connector spacing (i.e. 101% and 108%). In regard to Table 4 and Fig. 24(d), it can be observed that there is significant slip at the end of the composite beam with a very low (in this case 34%) degree of shear connection. However, a high degree of shear connection between the precast slab and steel beam reduces significantly the final slip at the end of the

32

A. Ataei et al. / Finite Elements in Analysis and Design 122 (2016) 16–38

Fig. 28. Failure mode of joint with 20 mm thick end plate (a) contours of Von Mises’ stresses (in Pa) (b) total longitudinal strain (NE) distribution in bolts and end plate.

600

Table 6 FE modelling results for composite joints with different slab depth.

Moment (kNm)

500 Model

End slip Initial stiffness Mm kN m/ mrad

Rotation capacity mrad

Moment capacity kN m

Failure mode

80 mm slab 120 mm slab 160 mm slab 200 mm slab 280 mm slab

7.3 6.3 6.3 6.4 6.0

56.2 47.4 45.3 41.0 33.2

490.0 501.4 514.7 528.9 554.5

RBF RBF RBF RBF RBF

400 300 80 mm slab 120 mm slab 160 mm slab 200 mm slab 280 mm slab

200

100 0

0

20

40 Rotation (mrad)

60

80

50.4 72.0 84.6 98.4 138.9

Note: RBF ¼ Reinforcing bar fracture.

Fig. 29. Moment vs. rotation response for composite joints with different precast concrete slab depth.

composite beam, that in turn can reduce the ductility and rotation capacity of the joint as observed for the model with 6M20 connectors (Fig. 24(d)). 5.4. Effect of flush end plate thickness To investigate the effect of the HSS flush end plate thickness on the behaviour of the deconstructable composite beam-to-column joints with PFBSCs, five flush end plate thicknesses, i.e. 4 mm, 8 mm, 12 mm, 16 mm and 20 mm corresponding to flush end plate thickness to bolt diameter ratios tep/db of 0.17 to 0.83 were considered in the parametric study. The moment versus rotation response for composite joints with different flush end plate thicknesses is plotted in Fig. 25, and the initial stiffness, moment capacity, rotation capacity, specimen failure mode and the final slip at the end of the composite beam are summarised in Table 5 and their variations with respect to the ratio tep/db are shown in Fig. 26. It can be seen that the initial stiffness of the joints increases significantly as the end plate thickness to bolt diameter ratio increases. Furthermore, it is observed that the relative slip between the steel girder and precast concrete slab at the end of the composite beam deceases as the ratio tep/db increases. The bending moment capacity of the composite joints increases significantly as the ratio tep/db increases up to 0.5, but a further increase of the thickness of the end plate has only a minor influence on the moment capacity of the composite joint as shown in Fig. 26(c). This is because the failure mode changes from being fracture of the reinforcing bar to fracture of the top bolt in the connection zone. When a thicker flush end plate is used, the deformation and bending of the end plate as well as the tensile

force in the longitudinal reinforcing bars decrease, but the tensile forces in the two top bolts increase that leads, in turn, to fracture of the top bolts before sufficient elongation takes place in the longitudinal reinforcing bars. In terms of rotation capacity (Fig. 26(b)), it can be seen that except for the joint with a 4 mm flush end plate, the rotation capacity of all joints decreases as the thickness of the flush end plate increases. For example, the maximum rotation capacity of joints with 16 mm and 20 mm flush end plates were about 68% and 77% lower than that of a joint with an 8 mm flush end plate, respectively. This is because the failure mode of the joint changes from complete plastic deformation of the flush end plate in the joints with a 4 mm end plate (Fig. 27) to fracture of the longitudinal reinforcing bar for the joint with an 8 mm end plate, and to fracture of the bolts in the tension zone of the connection for semi-rigid beam-to-column joints with a 12 mm (and thicker flush end plate). The mode of failure of the joint with a 20 mm thick flush end plate is shown in Fig. 28. The FE results show that the end plate thickness recommended in EC3 and EC4 cannot sufficiently prevent the non-ductile mode of failure associated with rupture of the bolts in FEPSR beam-to-column composite joints with deconstructable PFBSCs. This observation is consistent with experimental data of Ataei et al. [9]. According to the EC3 and EC4 provisions, there are three different modes of failure for beam-tocolumn joints. The first failure mode associated with complete yielding of the end plate or column flange can be considered as ductile, whereas the third mode of failure in which only bolt rupture occurs can be considered as brittle (non-ductile). According to EC3 and EC4, to prevent non-ductile failure, the thickness of the end plate should not be taken more than 60% of the bolt diameter (e.g. 12 mm for M20 bolts and 15 mm for M24

A. Ataei et al. / Finite Elements in Analysis and Design 122 (2016) 16–38

60

Rotation capacity (mrad)

Initial stiffness (kNm/mrad)

160 140

120 100 80 60

55 50

45 40 35

30

40

50

150

250

50

350

150

250

350

Slab depth (mm)

Slab depth (mm) 560

8

550 540

End slip (mm)

Moment capacity (kNm)

33

530 520 510

500

7

6 5

490 480

4 50

150 250 Slab depth (mm)

350

50

150 250 Slab depth (mm)

350

Fig. 30. Variation of (a) initial stiffness (b) rotation capacity (c) bending moment capacity and (d) end slip versus precast concrete slab depth to steel beam depth ratio.

600

Moment (kNm)

500 400 300

12 mm bolt 16 mm bolt 20 mm bolt 24 mm bolt 30 mm bolt

200

100 0 0

10

20

30 40 Rotation (mrad)

50

60

Fig. 32. Moment vs. rotation response for composite joints with different bolt size.

Table 7 Results of the FE analysis for composite joints with different bolt size.

Fig. 31. Longitudinal total strain distribution for two top bolts in the tension zone of the composite beam-to-column joint with (a) 80 mm and (b) 280 mm thick concrete slab.

Model

tep/db End slip Initial stiffness mm kN m/ mrad

Rotation capacity mrad

Moment capacity kN m

Failure mode

12 mm bolt 16 mm bolt 20 mm bolt 24 mm bolt 30 mm bolt

0.67 0.50 0.40 0.33 0.27

16.1 39.2 49.3 47.4 46.5

356.6 419.8 443.5 501.4 538.8

BF BF RBF RBF RBF

6.6 6.8 6.7 6.3 6.2

58.6 60.0 61.8 72.0 79.9

Notes: RBF ¼ reinforcing bar fracture, LB¼ Local buckling of compression flange, BSCF¼ Bolted shear connector fracture.

34

A. Ataei et al. / Finite Elements in Analysis and Design 122 (2016) 16–38

Fig. 33. Longitudinal strain in (a) two top bolts in the tension zone and (b) end plate, bolts and longitudinal reinforcement bars for joint with 12 mm bolt. Fig. 34. Longitudinal strain distribution (NE11) in (a) two top bolts in tension zone and (b) end plate, bolts and longitudinal bars for joint with 30 mm bolt.

bolts). However, as can be seen in Table 5, composite beam-tocolumn joints with 12 mm (50% of the bolt diameter), 16 mm (67% of the bolt diameter) and 20 mm (83% of the bolt diameter) thick flush end plates were failed due to bolt fracture (brittle mode). Because of this, it can be concluded that an end plate thickness of 30–40% of the bolt diameter should be used for high strength steel flush end plates to ensure that the mode of failure of the FEPSR composite joints with high strength end plates is associated with fracture of the reinforcing bars and yielding of the end plate, and hence it is sufficiently ductile. Fig. 28 shows that using flush end plates thicker than the steel column flange can lead to deformation and bending of the column flange at the ultimate stages of loading. 5.5. Effect of precast concrete slab depth The influence of the precast concrete slab depth on the behaviour of deconstructable PFBSCs was studied by analysing composite beam-to-column joints with slab depths of 80, 120, 160, 200 and 280 mm. In push out test specimens [9], increasing the length of the bolted connectors and the depth of the precast concrete slab only increased the load carrying capacity and ductility of the deconstructable PFBSCs slightly. Because of this, the influence of the length of the bolted shear connectors was not taken into account in this part of the parametric study. The moment versus rotation responses of the joints with different slab thicknesses obtained from FE models are given in Fig. 29, with the initial stiffness, the moment capacity, the rotation capacity, the failure mode of the specimen and the final slip at the end of the composite beam obtained from the FE models being summarised in Table 6. The variation of the initial stiffness, moment capacity, rotation capacity and end slip of the joints with respect to the depth of the precast concrete slab is shown in

800

Moment (kNm)

700 600 500 400 250UB37.3 360UB56.7 460UB82.1 530UB92.4 610UB125

300 200 100

0 0

20

40 60 Rotation (mrad)

80

100

Fig. 35. Moment vs. rotation response for composite joints with different steel beam size.

Table 8 FE modelling results for composite joints with different steel beam size. Model

End slip Initial stiffness mm kN m/mrad

Rotation capacity mrad

Moment capacity kN m

Failure mode

250 UB 37.3 360 UB 56.7 460 UB 82.1 530 UB 92.4 610 UB 125

5.0

28.2

45.9

273.2

LB

7.3

47.9

53.2

411.7

RBF

6.3

72.0

47.4

501.4

RBF

6.3

99.4

36.7

603.1

RBF

5.4

138.7

30.9

698.9

BF&RBF

Notes: RBF ¼ reinforcing bar fracture, LB ¼ local buckling of compression flange, BF ¼ bolt fracture in tension zone.

A. Ataei et al. / Finite Elements in Analysis and Design 122 (2016) 16–38

Dcl

d1

35

d2 F rb F bl

drb

Mj dbl

Db

F fb

Fig. 37. Schematic outline of geometry and forces acting on composite joint.

Fig. 36. Contours of von Mises’ stresses (in Pa) within composite connection at the failure for specimens with (a) 250UB37.5 and (b) 610UB125 steel beam.

Fig. 30. It can be observed that the initial stiffness increases significantly as the thickness of the slab increases. For example, as shown in Fig. 30(a) and Table 6, increasing the thickness of the slab from 120 mm to 200 mm and to 280 mm increases the initial stiffness by around 37% and 93%, respectively. The moment capacity of the joints increases slightly as the depth of slab increases. For instance, the ultimate moment capacity of the joints with 200 mm and 280 mm thick slabs achieved about 105% and 110% of the rotation capacity of the joints with a 120 mm slab. However, an increase in the depth of the precast concrete slab led to a reduction in the rotation capacity and ductility and failure of the joint at a smaller deflection (Fig. 30(b)). With regard to Table 6, it is seen that as the thickness of the precast concrete slab increases, the final slip at the end of the composite beam decreases, which in turn can lead to a reduction of the rotation capacity of the joints. The failure mode of all joints was associated with fracture of the longitudinal reinforcing bars. The longitudinal strain distribution for the two top bolts (in the tension zone) is shown in Fig. 31. It can be seen that the strain in the top bolts of the joint with a thicker precast slab (i.e. 280 mm) is smaller than the joint with an 80 mm thick slab. This can be attributed to the larger contribution of the thicker precast slab in carrying the tensile strains induced by the negative bending moment.

diameters of 12 mm, 16 mm, 20 mm, 24 mm and 30 mm, corresponding to the flush end plate thickness to bolt diameter ratios tep/db of 0.67 to 0.27 were developed and analysed. All dimensions for different bolt sizes such as the diameter of the head and nut and the cross-sectional area were adopted from the available guidelines for Grade 8.8 standard bolts in Australia. The moment versus rotation responses for these joints captured by the FE models and the initial stiffness, rotation and bending moment capacities and failure mode of the joints are given in Fig. 32 and Table 7, respectively. It can be seen that the initial stiffness and moment capacity of the joints increases as the size of the bolts located in the tensile zone of the connection region increases. It can also be observed that an increase in the bolt size to 20 mm significantly increases the rotation capacity and ductility of the composite beam-to-column joints. However, increasing the size of the bolts above 20 mm does not have a significant effect on the rotation capacity and the ductility (it reduces the ductility only slightly as shown in Table 7). This may be because the failure mode of the joints with a smaller bolt size was associated with the fracture of the top bolt in the tension zone of the connection (in the joints with bolts M12 and M16) and the rotation capacity of the joint was limited by the longitudinal strength of the bolts as shown in Table 7 and Fig. 32. However, as the size of the bolt increases beyond a certain size (M20 and M24 in this case), the strength of the flush end plate and longitudinal reinforcing bars becomes more influential on the behaviour of composite joint and yielding of the flush end plate and fracture of the longitudinal reinforcing bars governs the failure mode and limits the ductility of the joints. The strain distribution along the two top 12 mm bolts is shown in Fig. 33(a). It is seen that the M12 bolts have achieved a high level of strain that can trigger fracture of the bolts, but the strain in the reinforcing bars is very low. In the joint with an M30 bolt, the reinforcing bars have attained very high strains that can lead to fracture of the bars while the strain in the bolts remains low (Fig. 34). With regard to the results of the parametric study (including the failure mode of the joints) presented in Table 7, it is concluded that an end plate thickness of less than 40% of the bolt diameter should be used for HSS flush end plates to prevent brittle failure of the top bolts in the semi-rigid beam-to-column joints with flush end plate. 5.7. Effect of steel beam size

5.6. Effect of standard bolt size The size of the bolts in the tensile zone of the flush end plate can influence the behaviour and failure mode of semi-rigid composite beam-to-column joints significantly. Because of this, FE models of deconstructable composite joints with different standard bolts having

To investigate the effect of the steel beam size, FE models of five composite joints with different Australian steel beam profiles, i.e. 250UB37.3, 360UB56.7, 460UB82.1, 530UB92.4 and 610UB125 were developed and analysed, and the results are given in Fig. 35 and Table 8. It can be seen that the initial stiffness and moment

36

A. Ataei et al. / Finite Elements in Analysis and Design 122 (2016) 16–38

Table 9 Comparison of FE model-analytical results. Variable

Reinfor. ratio

Degree of shear connection

Flush end plate thickness

Slab thickness

Steel beam size

Bolt size

Model

6N10 6N12 6N14 6N16 6N18 6N20 2M16 2M20 4M16 6M16 4M20 6M20 4 mm * 8 mm 12 mm * 16 mm * 20 mm * 80 mm 120 mm 160 mm 200 mm 280 mm 250 UB 37.3* 360 UB 56.7 460 UB 82.1 530 UB 92.4 610 UB 125* 12 mm* 16 mm* 20 mm 24 mm 30 mm

Failure mode

RBF RBF RBF RBF & LB BSCF BSCF BSCF RBF RBF RBF RBF RBF FEPF RBF BF BF BF RBF RBF RBF RBF RBF LB RBF RBF RBF BF & RBF BF BF RBF RBF RBF

Moment capacity

Rotation capacity

FEM

Anal.

FEM

Anal.

350 423 501 586 590 592 420 521 501 494 495 479 389 501 576 593 594 490 501 515 529 554 273 412 501 603 699 357 420 444 501 539 Average Std. Dev.

330 402 487 584 589 589 379 487 487 487 487 487 487 487 487 487 487 463 487 510 534 581 308 427 544 628 719 373 397 420 444 468

37 45 47 50 30 30 26 57 47 44 44 35 333 47 27 15 11 56 47 45 41 33 46 53 47 37 31 16 39 49 47 46

39 46 51 58 29 29 29 61 51 46 48 40 52 51 50 48 48 53 50 51 50 37 77 64 50 43 37 50 51 51 50 49 1.38 (1.08) 0.74 (0.07)

capacity of the joints have increase and the rotation capacity and ductility of the joints have decrease significantly when increasing the beam size. In composite semi-rigid joints with a smaller beam size (e.g. 250 UB 37.3), the rotation and moment capacity decrease due to the local buckling of the bottom flange of the steel beam (Fig. 36(a)). A similar failure mode associated with buckling of the bottom flange has been observed by Loh et al. [27] in most of their composite joints with a 250UB25.7 steel beam. The failure mode of the composite joint with a 610UB125 steel beam is shown in Fig. 36(b). For this case, the failure mode of the joint was associated with fracture of the longitudinal reinforcing bars and the top bolts. The ultimate rotation capacity of this joint is about 30.9 mrad (Table 8), which is slightly higher than that specified in the EC3 and EC4 codes (i.e. 30 mrad). Using a large steel beam in composite beam-to-column joints can decrease the contribution of the longitudinal bars in carrying tensile forces and can increase the contribution of the top bolts in the tension zone and, since high strength bolts have lower uniform elongation compared to conventional reinforcing bars, the rotation capacity of the joints decreases owing to brittle failure of the bolts.

6. Prediction of moment and rotation capacities To predict the moment capacity and rotation capacity of the deconstructable composite joints with a Grade S690 HSS flush end plate, very simple models based on the concept of rigid plastic analysis are proposed herein. The bending capacity of the joint is obtained by taking the moments of the ultimate forces acting on the reinforcing bars located in the concrete slab and the top row of

0.94 0.95 0.97 1.00 1.00 1.00 0.90 0.94 0.97 0.99 0.98 1.02 1.25 0.97 0.85 0.82 0.82 0.94 0.97 0.99 1.01 1.05 1.13 1.04 1.08 1.04 1.03 1.05 0.95 0.95 0.89 0.87 0.98 (0.98) 0.09 (0.05)

Ratio

1.06 1.02 1.08 1.16 0.98 0.98 1.13 1.07 1.08 1.04 1.10 1.13 1.59 1.08 1.89 3.12 4.35 0.94 1.05 1.13 1.22 1.11 1.68 1.20 1.05 1.17 1.20 3.11 1.30 1.03 1.05 1.05

the bolts (Fig. 37) about the centre of the bottom flange of the steel beam as M j ¼ F rb drb þ F bl dbl

ð3Þ

if Frb r 1.5Fbsc, and as M j ¼ F bsc drb þ F bl dbl

ð4Þ

if Frb 4 1.5Fbsc, in which Frb is the ultimate tensile strength of the longitudinal reinforcing bars, Fbl the ultimate tensile force in the bolts at the top row, Fbsc the bolted shear connector capacity, drb the distance between the centroid of the reinforcing bars and the centroid of the steel beam bottom flange and dbl the distance between the centroid of the top row of bolts and the centroid of the steel beam bottom flange (Fig. 37). Based on the elongation of the longitudinal bars and the precast concrete slab and the steel beam interface slip, the rotation capacity of the composite joint can be expressed as

θj ¼

δ drb

þ

s ; Db

ð5Þ

where s is the final slip between the steel beam and precast concrete slab and δ the elongation of the longitudinal reinforcing bars which can be calculated from

δ ¼ 10εyr ð0:5Dcl þ d1 þ d2 Þ

ð6Þ

if Frb r 1.5Fbsc, and from

δ¼0 if Frb 4 1.5Fbsc, in which εyr is the yield strain in the longitudinal reinforcing bar, Dcl the depth of the column, d1 the distance between the column face and the first row of the shear bolts and

A. Ataei et al. / Finite Elements in Analysis and Design 122 (2016) 16–38

d2 the distance between the first row of the shear bolts and the second row of the shear bolts. The results derived from the proposed analytical models and the FE models are shown and compared in Table 9. Comparison of the results shows that the rigid-plastic model adopted can predict the moment capacity of all specimens with sufficient accuracy. However, Table 9 shows that in a few cases the proposed model predicts much higher estimates of the rotation capacity compared to the FE results. The reason for this is that fracture of bolts in connection zone, fracture of the flush end plate and local buckling of the bottom flange of the steel beam were not considered in this analytical model. The FE models associated with these modes of failure are marked with an asterisk in the table. If the results of these models are not taken into calculation, the average and standard deviation of the results (values in brackets) are improved significantly.

 The initial stiffness and secant stiffness of deconstructable semi



  

7. Conclusions A three-dimensional FE model has been developed using ABAQUS software to simulate the structural behaviour of sustainable HSS semi-rigid beam-to-column composite joints with deconstructable PFBSCs. The FE models simulate the behaviour of FEPSR beam-to-column joints under hogging moment. In the FE models developed both geometrical and material non-linearities as well as non-linearity of the contacts and interfaces were considered. The FE model was validated using experimental data for full-scale FEPSR beam-to-column joints having a Grade S690 HSS flush end plate. It was shown that the FE models predict adequately the behaviour of deconstructable composite joints with PFBSCs and that they provide a reliable and accurate alternative to experimental testing. The validated FE model was used to conduct an extensive parametric study in which the effects of the reinforcement ratio, thickness of the precast concrete slab, degree of shear connection, number of deconstructable bolted shear connectors, size of the bolts in the connection zone, size of the steel beam and thickness of the flush end plate on the structural behaviour of deconstructable HSS semi-rigid beam-to-column composite joints with PFBSCs was studied. The characteristics of beam-to-column joints including their initial stiffness, moment capacity and the rotation capacity of the joints were obtained from the FE models. The final slip at the end of the composite beam and the failure modes were also evaluated by using the FE models. Based on the results of the parametric study, the findings of the study are summarised in the following.

 An increase in the reinforcing ratio to a certain value can





increase the ultimate bending capacity of a deconstructable HSS composite joint. However, increasing this ratio any further will not have a significant influence on the moment capacity of the composite joints. To improve the moment capacity, the minimum shear connectors should be provided based on the reinforcing ratio in the precast slab and the longitudinal bars must be carefully designed to be proportionate with the fracture of the bolted shear connectors and local buckling of the bottom flange of the steel girder. The rotation capacity and ductility of deconstructable HSS composite joints increases as the reinforcing ratio increases. However, a reinforcing ratio beyond a certain value can decrease the rotation capacity and ductility of the joints because of sudden fracture of the shear connectors or by local buckling of the compression flange of the steel beam.

37

 









rigid beam-to-column composite joints increases gradually as the degree of shear connection increases. Composite joints designed with about 50% composite efficiency provide the minimum degree of shear connection to prevent fracture of the bolted shear connectors and to mobilise the plastic strain in the longitudinal reinforcing bars. It is recommended to use a smaller bolt size and a large number of bolted connectors instead of using a larger bolt size and a smaller number of bolts. This is because using a large number of PFBSCs with smaller bolts can more efficiently transfer the shear force between the precast concrete slab and the steel beam. When fracture of the reinforcing bars govern the failure mode, the moment and rotation capacity of joints are not significantly influenced by the degree of the shear connection. Increasing the ratio of the flush end plate thickness to the bolt diameter will increase the initial stiffness of the beam-tocolumn joints significantly. The moment capacity increases significantly as the thickness of the flush end plate to bolt diameter ratio is increased up to 0.5. However, a further increase in the thickness of the end plate will not have a significant effect on the moment capacity of the composite joint and may lead to bolt fracture (brittle failure) at ultimate loading states. The thickness of the end plate is recommended not to be less than 30% of the bolt diameter to prevent the fracture of the end plate. The end plate thickness recommended in EC3 and EC4 cannot sufficiently prevent the non-ductile mode of failure associated with rupture of the bolts. An end plate thickness of 30–40% of the bolt diameter is recommended for a HSS flush end plate to ensure sufficient ductility in the joint. An increase in the bolt size to a certain value (with respect to the end plate thickness) can increase the rotation capacity and ductility of the joint significantly. However, increasing the size of the bolt any further does not have a significant effect on the rotation capacity and the ductility. Increasing the steel beam size increases the initial stiffness and moment capacity of the joints. However, using very large steel beams reduces the rotation capacity and ductility of the joints significantly. Five distinctive failure modes, i.e. longitudinal reinforcing bar fracture, top bolt fracture, bolted shear connector fracture, premature local buckling of the bottom flange, and plastic deformation and failure of the flush end plate were observed in the parametric study conducted by using the FE models. Simple models can be used to predict the moment and rotation capacities of the joints. Comparisons of the results show that in most of the cases the models are able to predict accurately the behaviour of this kind of joints.

Acknowledgement The work reported in this paper was undertaken with the financial support of the Australian Research Council through an Australian Laureate Fellowship (FL100100063) awarded to the second author.

References [1] A.M. Girao Coelho, F.S.K. Bijlaard, Experimental behaviour of high strength steel end-plate connections, J. Constr. Steel Res. 63 (2007) 1228–1240. [2] A.M. Girão Coelho, F.S.K. Bijlaard, High strength steel in buildings and civil engineering structures: design of connections, Adv. Struct. Eng. 13 (2010) 413–439.

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