- Email: [email protected]
Cyclic behaviour characterization of web panel components in bolted end-plate steel joints
Journal of Constructional Steel Research 133 (2017) 310–333
Contents lists available at ScienceDirect
Journal of Constructional Steel Research
Cyclic behaviour characterization of web panel components in bolted end-plate steel joints Hugo Augusto a,⁎, Luís Simões da Silva a, Carlos Rebelo a, José Miguel Castro b a b
Institute for Sustainability and Innovation in Structural Engineering (ISISE), Department of Civil Engineering, University of Coimbra, Polo II, Rua Luís Reis Santos, 3030-788 Coimbra, Portugal Department of Civil Engineering, Faculty of Engineering, University of Porto, Rua Dr. Roberto Frias, s/n, 4200-465 Porto, Portugal
a r t i c l e
i n f o
Article history: Received 12 August 2016 Received in revised form 21 January 2017 Accepted 24 January 2017 Available online xxxx Keywords: Steel joints Cyclic behaviour Column web panel End-plate Component method Finite element analysis
a b s t r a c t This paper addresses the characterization of the behaviour of the column web panel components in bolted endplate steel joints subject to cyclic loading. Based on experimental test results, a calibrated parametric FE model of a double extended beam-to-column end-plate steel joint is implemented, that allows characterizing the behaviour of the joints both globally and in terms of the dissipative components. The numerical models have been developed using the ABAQUS FE package considering a detailed representation of the various joints components and taking into account the different sources of geometrical and material nonlinearities. Finally, based on the integration of the stress and displacement fields in predefined paths along the column web, a detailed extraction procedure for the cyclic force-deformation behaviour of the column web panel components is proposed, however extensible to other components. These relationships are needed for implementation in a components based approach that accounts for cyclic loading conditions. © 2017 Published by Elsevier Ltd.
1. Introduction Partial-strength joints subject to static monotonic loading are well characterized in modern codes of practice, such as Eurocode 3 part 1– 8 (EC3-1-8) [1] within the framework of the component method. However, in the presence of cyclic load reversals there is no direct and easy approach to characterize their cyclic behaviour and energy dissipation. This need mostly results from the seismic action, where the cyclic behaviour of the members and connections play an important role, along with ductility, tenacity, rotation capacity or energy dissipation of the dissipative members or joints. When partial-strength joints are used in steel moment-resisting frames (MRF), there may be a shift of the plastic hinge location from the beams or columns to the joints. When this shift occur, it is of critical importance to take into account the characteristics of beam-to-column joints. The use of partial-strength joints is a common and relatively low cost solution to apply in MRF, in comparison with their full-strength counterparts. Previous studies have shown that, if adequately detailed, these connections may also become attractive alternatives for structures located in seismic regions, allowing a precise control of the location and response of the dissipative elements [2]. Furthermore, Shen and Astaneh-Asl [4] argued that, when properly designed, bolted joints ⁎ Corresponding author. E-mail addresses: [email protected] (H. Augusto), [email protected] (L. Simões da Silva), [email protected] (C. Rebelo), [email protected] (J.M. Castro). URL's: http://www.uc.pt/fctuc (H. Augusto), http://www.fe.up.pt (J.M. Castro).
http://dx.doi.org/10.1016/j.jcsr.2017.01.021 0143-974X/© 2017 Published by Elsevier Ltd.
may exhibit high ductility and good energy-dissipation capacity under cyclic loading, providing that brittle components have sufficient overstrength in order to prevent undesirable failure modes. In this case, proper assessment of the behaviour is crucial due to the controlling role that these joints will play, as the main dissipative components in the structure, in the structural response during a seismic event. In fact, design codes, such as Eurocode 8 (EC8) [3], allow the use of partial-strength joints, providing that a set of design requirements is met. Firstly, advanced structural analyses are required, such as non-linear static (pushover) or non-linear time history analyses, although detailed information is missing concerning the adoption of these types of analyses, particularly when dealing with steel frames with partialstrength connections. Additionally, EC8 (sections 6.5.5(6), 6.5.5(7) and 6.6.4(4)) requires experimental evidence of the behaviour of the joints whenever dissipative connections are considered in the seismic design process, which is very difficult to accomplish in design practice. It is therefore clear that this kind of joints require more research to achieve adequate detailed guidance to overcome these difficulties. The findings in the research presented in this paper can contribute to the development of a simplified design method for partial-strength steel joints. Based on the component method, which takes directly into account the cyclic behaviour of each dissipative component and, simultaneously, provides adequate overstrength for the non-dissipative components (capacity design), thus ensuring that the idealized behaviour of the joint can be considered in the global analysis of the structure in a simplified manner. However first is necessary to extract the behaviour of the basic components.
H. Augusto et al. / Journal of Constructional Steel Research 133 (2017) 310–333
This paper aims to contribute to the mechanical characterization of components in double-extended beam-to-column joints using a detailed parametric numerical model developed in ABAQUS [5] taking advantage of the Python scripting interface in ABAQUS. The model is applied to end-plate beam-to-column joints and considers a three dimensional detailed representation of the various joint components taking into account several phenomena involved in the connection behaviour, namely the nonlinearities related to the geometry, contact and material properties. A combined isotropic and kinematic materialhardening model is used. The calibration of the numerical model, which is based on the results of an experimental research programme, is comprehensively described in this paper.
a) Global FE model
In the following sections, the cyclic behaviour of the joints is characterized, both at the global joint response and in terms of the critical components, comparing the results of the experimental and numerical models. Using the validated FE models, a detailed procedure is described to isolate the column web components under cyclic loading, namely the column web panel in shear and the column web in transverse compression or tension, and to identify their mechanical behaviour analysing the stress and deformation fields in the FE models. The derived force-displacement relationships, of the individual dissipative components, can be directly applied to a mechanical model of the joint, to characterize its behaviour, provided it is ensured that the non-dissipative components remain elastic.
b) Detail of the cross sections of the wire elements Fig. 1. Meshed parts of the FE model.
300
18 15
50 40 60
15 8
8
Ø26 M24 (10.9)
360 IPE360 (S355)
540
240
8 60 40 50
HEA320 (S355)
15
55 110 55 220
310
Fig. 2. Detail of the joint for Groups 1 and 2.
300
18 12 8 360 IPE360 (S355) 12
50 40 60
15 8 Ø26 M24 (10.9)
540
240
8 60 40 50
HEB320 (S355) 320
311
55 110 55 220 Fig. 3. Detail of the joint for Group 3.
c) Detailed view of the Joint zone
312
H. Augusto et al. / Journal of Constructional Steel Research 133 (2017) 310–333
6 5 4 3 2 1 0 -1 -2 -3 -4 -5 -6
2. Literature review
A considerable amount of experimental work was carried out in the past to characterize the cyclic behaviour of steel joints in several fields of application. Focussing on the cyclic behaviour of the column web panel: Plumier & Schleich [7] studied the contribution of the column shear panel to the energy dissipation, strength and rotation capacity of the joints. The studies undertaken by Dubina et al. [8,9] analysed the influence of symmetric and antisymmetric cyclic loading, concluding that the loading type influence occurs mainly through the contribution of the panel zone. The work developed by Guo et al. [10] on the cyclic behaviour of stiffened and unstiffened extended end-plate connections of beam–column joints allowed concluding that the column web stiffeners have a remarkable influence, contributing to increase the strength of the joint as well as the energy dissipation capacity. A detailed review of the experimental work on steel joints subjected to cyclic loading may be found in Nogueiro et al. [11] and Sullivan and O'Reilly [12].
y
2.1. Past experimental work in the cyclic behaviour of the column web panel
J-n.2 (S1)
Table 1 Bolted beam-to-column double extended end-plate joints test programme. Group
J1
J2
J3
J4
Test
Beam
Column
type
Bending
Axial
J1.1 J1.2 J1.3 J1.4 J2.1 J2.2 J2.3 J3.1 J3.2 J3.3 J4.1 J4.2 J4.3
IPE360 IPE 360 IPE 360 IPE 360 IPE360 IPE 360 IPE 360 IPE360 IPE 360 IPE 360 HEA280 HEA 280 HEA 280
HEA320 HEA 320 HEA 320 HEA 320 HEA320 HEA 320 HEA 320 HEB320 HEB 320 HEB 320 HEA320 HEA 320 HEA 320
Monotonic Cyclic S1 Cyclic S2 Cyclic SA Monotonic Cyclic S1 Cyclic S2 Monotonic Cyclic S1 Cyclic S2 Monotonic Cyclic S1 Cyclic S2
MM-/M+ M-/M+ M-/M+ MM-/M+ M-/M+ MM-/M+ M-/M+ MM-/M+ M-/M+
N- (800 kN) N- (1200 kN) N- (800 kN) -
the energies dissipated by the various joint components. More recently, Simões da Silva et al. [28] detailed a cyclic component model fully compatible with the static monotonic implementation in EC3-1-8 [1]. 2.3. Characterization of the column web panel components A bolted beam-to-column steel joint may be divided in two main parts: column web panel and connection(s) (left and/or right beams). In many situations, the column web panel controls the behaviour of the joint, usually providing large energy dissipation under cyclic loading conditions. However, the associated local distortion may impair the global stability of the frame by inducing excessive second-order effects. Consequently, design codes usually impose limits on the contribution of the column web panel to dissipate energy [30]. The characterization of the behaviour of the column web panel under static monotonic loading conditions was described in detail by the authors in [31], the fundamental works of Krawinkler et al. [32] and Jaspart and his co-workers [29,33] being emphasized there. In
300 18 12 8 270 HEA280 (S355) 12
50 40 60
15 Ø26 M24 (10.9)
8 450
150
8 60 40 50
HEA320 (S355) 310
70
160
Cycles
Fig. 5. Cyclic loading strategies used in the experimental tests.
2.2. Review of models to characterize the cyclic behaviour of joints The extensive experimental research work on the cyclic behaviour of steel joints led to the development of several approaches to establish, and ultimately to predict, the behaviour of steel joints under cyclic loading. Many authors proposed mathematical models (bilinear hysteretic, Ramberg-Osgood based models, Richard-Abbott based models or multi-linear deterioration models) to fit the global moment-rotation curves of steel joints [13–22]. In addition to the mathematical formulations described above, some authors focused on establishing empirical damage accumulation laws to assess the low-cycle fatigue behaviour of steel joints. Calado and Castiglioni [23] developed a cumulative damage model and a general failure criterion to assess the low-cyclic fatigue of steel joints. Bursi et al. [24] studied the fracture behaviour of isolated T-stub connections with partial fillet welds, and characterized cracks for the low-cyclic fatigue assessment of isolated T-Stubs of steel joints. Finally, there is a growing interest on the implementation of cyclic component models, whereby the global moment-rotation behaviour of the joint is obtained from the cyclic behaviour of the individual components. Mechanical models, such as those developed by Madas and Elnashai [25], can be considered one of the first attempts to apply the component approach to characterize the cyclic behaviour of beam-tocolumn joints. Simões da Silva et al. [26] proposed an extension to the component method for the cyclic behaviour of end-plate joints. Latour et al. [27] proposed a simplified cyclic model based on a lumped approach for the tensile and compressive zones, considering that the overall energy dissipation of the connection can be obtained by summing
J-n.3 (S2)
70
Fig. 4. Detail of the joint for Group 4.
H. Augusto et al. / Journal of Constructional Steel Research 133 (2017) 310–333
according to the setup of the experimental tests used in the validation of the FE models. The development of the FE models and the finite element modelling options were already the subject of a detailed description and validation, under monotonic load, in [31]. Hence, only a brief description of the model is presented, addressing the particular features of the finite element modelling and validation of the cyclic behaviour. The models are composed by solid (mainly C3D8RH) finite elements in the joint region, due to the reduce integration formulation (only 1 Gauss point) at least 3 elements were consider in the thickness of the plates, to help avoiding the numerical problem hourglass associated to bending dominated problems [31]. Beam elements (B31) are used in the regions adjacent to the joint, i.e., in the beam and column segments, in order to reduce the computational time. The kinematic relations are transferred from the solid to the beam elements by multi-point constraint equations. The model and its parts are illustrated in Fig. 1, with the adopted mesh, namely the wire columns, the wire beam, the solid column, with or without stiffeners (the latter not represented in Fig. 1), and with the bolt holes in the flange, the solid beam with the corresponding fillet welds, the end-plate with the bolt holes and the bolts composed by the shank, head and nut. The various parts interact with each other by continuity links, called constraints in ABAQUS (e.g. between the beam and the end-plate) or defining contact properties, called interactions in ABAQUS (e.g. between the end-plate and the column flange), to form the beam-to-column end-plate joint structural model.
Table 2 Cyclic loading strategies. Cycle
Stategy 1 (S1)
Strategy 2 (S2)
1 2 3 4 (and following) 20 (and following) 40 (and following, and so on)
0.75θy 1.5θy 2.25θy 3.0θy 3.0θy + 2.5*1mrad 3.0θy + 2.5*2mrad
1.5θy 3.0θy 4.5θy 6.0θy 6.0θy 6.0θy
313
particular, it is important to highlight the deformation modes in the web panel, namely the transverse deformation, due to the beam moment resulting force couple (Fb = Mb/(hb − tfb)), and the distortion due to the pure shear introduced in the panel and the frame-type behaviour for transversely-stiffened web panels. Concerning the cyclic behaviour of components, Kim and Engelhardt [34] proposed a model to characterize the behaviour of the column web panel in shear under cyclic loading. It is a model based on the Dafalias' [35] bounding surface theory, that uses the Cofie and Krawinklers's [36] rule for the movement of the bound line. Moreover, it is assumed that the moment-rotation relationship of the panel zone can be determined from its material properties using the Cofie's rule. Simões da Silva et al. [26] applied the Richard-Abbot model to simulate the cyclic behaviour of individual components, such as the column web panel in shear and the end-plate in bending. Finally, Latour et al. [37] extended the application of the Kim and Engelhardt model to the load introduction components. However, they did not separate load introduction in tension and in compression, therefore disregarding the fact that, in bolted joints, tension is transferred by the bolts at discrete positions while compression is transferred within a tributary area, approximately centred on the beam compressed flanges.
3.2. Material modelling For the material modelling, the combined isotropic/kinematic hardening model available in ABAQUS was adopted. This material model [38] uses the von Mises yield criterion and an associative flow rule is assumed. The isotropic component of the model defines the change of the size of the yield surface σ0 as a function of equivalent plastic strain εp, and is given by:
3. Numerical modelling 3.1. Modelling overview
P σ 0 ¼ σ j0 þ Q ∞ 1−e−biso ε
The numerical model developed in ABAQUS [5] consists of a representative part of a MRF structure, composed by a column and a beam connected to each other by means of an end-plate welded to the beam and bolted to the column flange. This is representative of an external node of a MRF with double-extended end plate joints. The lengths of the beam (approx. 1.2 m) and the column (approx. 3 m) are established
ð1Þ
where σ|0 is the yield stress at zero equivalent plastic strain, Q∞ is the maximum change in the size of the yield surface and biso is the rate at which the size of the yield surface changes as the plastic strain increases.
Table 3 Bolted beam-to-column double extended end-plate joints test programme. Test
Loading strategy
Failure mode
−Mmax (kNm)
+Mmax (kNm)
n.° of cycles
−Rot.max (mrad)
+Rot.max (mrad)
Total energy (kNm × mrad)
J1.2 J1.3 J1.4 J2.2 J2.3 J3.2 J3.3 J4.2 J4.3
S1 S2 SA S2 S2 S1 S2 S1 S2
Weld Weld Cracking EP Weld Weld Cracking EP Weld Weld Weld
−335 −362 −333 −353 −358 −408 −421 −290 −310
+340 +352 +378 +365 +368 +418 +431 +276 +295
83 22 28 27 27 26 13 54 34
−23 −28 −28 −24 −30 −19 −21 −27 −35
+16 +21 +19 +22 +21 +17 +26 +30 +35
435,156 293,979 201,946 368,538 382,945 215,156 195,075 448,850 505,611
Table 4 Geometrical properties of the FE models.
J1.3 J3.2 J4.3
Column
Beam
ht (mm)
Lc (mm)
Lc1 (mm)
Lc2 (mm)
Lc3 (mm)
L1 (mm)
L2 (mm)
Lb1 (mm)
d (mm)
HEA320 HEB320 HEA320
IPE360 IPE360 HEA280
3220 3260 3260
3000 3040 2894
1395 1395 1249
720 740 690
885 905 955
1331 1320 1329
1355 1385 1483
467 468 357
1175 1160 1173
314
H. Augusto et al. / Journal of Constructional Steel Research 133 (2017) 310–333
The kinematic component of the model defines the changes of backstress α, which is expressed as: α¼
Table 7 Main features of the achieved F-Δ relationships.
Sini (kN/mm) Δmax (mm) Δmin (mm) Fmax (kN) Fmin (kN)
Joint
C kin P P þ 1−e−γε þ α 1 e−γε γ
ð2Þ
where Ckin and γ are material constants. The ratio Ckin/γ represents the maximum change in backstress and γ determines the rate at which the backstress changes as the plastic strain increases. Monotonic coupon tensile test results were used to derive key coordinates in the stress-strain relationship. Elastic-plastic constitutive material laws were used in all parts of the model, non-linear in the solid elements and tri-linear in the beam elements.
J1_1_pv1_tp18_ts0
J1_1_pv1_tp18_ts20
3.3. Analysis procedures The analyses were performed using the ABAQUS/Standard solver that iteratively solves a system of equilibrium equations implicitly for each solution increment, using Newton's method to solve nonlinear problems and the stiffness method to solve linear problems [5]. Second-order effects were considered in all the analyses to account for large displacement effects. Due to the several nonlinearities present in the models, namely material nonlinearity, geometric nonlinearity and contact nonlinearity, general analysis steps were adopted with automatic control for the increments, i.e. the increment size was determined according to the response of the model.
E3-TB-E_cyc_M3_ts0
4. Validation of the numerical models 4.1. Experimental tests E3-TB-E_cyc_M3_ts30
A set of experimental tests [39] carried out at the University of Coimbra were used to calibrate the numerical model. The tested joints were designed aiming to study the behaviour of several external bolted beam-to-column partial-strength joint typologies with double extended end-plates. The relevant features of these tests are shortly described in the following paragraphs and presented in detail in [39]. The experimental programme comprised thirteen external doubleextended bolted end-plate joints, see Table 1. It was divided in four groups, whereby the column section size and/or the beam size were varied, as well as the presence of axial force in the column in group J2, as shown in Table 1. The joint's details are illustrated in Figs. 2–4. In each group, the first test was performed under monotonic loading. The results were analysed in detail in [31]. Two additional
Group 1, 2
2575
0.62
-1.78
887.1
-874.9
Group 3, 4
3304
0.80
-1.65
891.4
-867.6
Row 1
1847
0.30
-1.36
562.1
-654.8
Row 2
1551
1.54
-1.14
325.0
-297.0
Row 3
2011
1.61
-1.04
388.9
-330.7
Row 4
1669
0.39
-1.27
502.5
-610.9
Group 1, 2
3519
0.10
-0.10
380.5
-373.0
Group 3, 4
5726
0.10
-0.09
377.2
-369.7
Row 1
2126
0.09
-0.22
293.1
-367.9
Row 2
1718
0.86
-0.03
147.6
-284.7
Row 3
2277
0.92
-0.03
165.0
-292.4
Row 4
2055
0.10
-0.22
263.7
-344.3
Group 1, 2, 3
3971
0.56
-13.21
3349.7
-3888.6
Group 4, 5, 6
5530
0.74
-7.35
2599.7
-3697.6
Row 1
2991
0.24
-10.00
1888.2
-2308.0
Row 2
2000
2.99
-10.94
965.4
-949.3
Row 3
948
5.39
-5.90
778.9
-901.7
Row 4
1739
5.19
-2.22
593.7
-708.9
Row 5
2150
3.36
-5.64
994.2
-1052.2
Row 6
2525
0.30
-5.27
1301.7
-2029.2
Group 1, 2, 3
4963
0.23
-0.27
1272.7
-1415.9
Group 4, 5, 6
9766
0.21
-0.23
1123.8
-1368.9
Row 1
3241
0.12
-0.24
554.5
-882.5
Row 2
2764
3.79
-0.12
845.4
-851.3
Row 3
607
6.64
-0.03
475.8
-801.1
Row 4
2288
5.50
-0.05
503.9
-772.3
Row 5
2029
3.60
-0.10
697.3
-689.1
Row 6
2813
0.12
-0.24
477.7
-740.9
tests, with two alternative cyclic loading protocols, were also performed, except in the first group where an additional cyclic test was conducted, J1.4, with arbitrary loading (SA). The two cyclic loading strategies, are illustrated in Fig. 5, and described in Table 2. The loading was applied in the vertical direction, at the end of the cantilever beam, by means of a 100 ton hydraulic actuator. The tests were carried out under displacement control, with a constant speed
Table 5 Comparison of the strength and maximum rotation between the experimental and numerical results.
J1.3 J3.2 J4.3
−Mrd (Exp.) (kNm)
−Mrd (FE) (kNm)
Error (%)
−Mrd (Exp.) (kNm)
−Mrd (FE) (kNm)
Error (%)
−Rot.max (Exp.) (mrad)
−Rot.max (FE) (mrad)
Error (%)
+Rot.max (Exp.) (mrad)
+Rot.max (FE) (mrad)
Error (%)
−362 −408 −310
−373 −416 −298
+2.9 +1.9 −3.9
+352 +418 +295
+364 +414 +295
+3.3 −1.0 +0.0
−24 −17.7 −35
−22.5 −17.7 −35
−6.3 0.0 +0.0
+19 +15.7 +32
+18.5 +16.6 +32
−2.6 +5.4 +0.0
Table 6 Geometrical properties of the FE models.
J1_1-pv1_tp18_ts0 J1_1_pv1_tp18_ts20 E3-TB-E-M3-ts0 E3-TB-E-M3-ts30
Column
Beam
ht (mm)
Lc (mm)
Lc1 (mm)
Lc2 (mm)
L1 (mm)
L2 (mm)
Lb1 (mm)
d (mm)
HEA320 HEA320 HEB500 HEB500
IPE360 IPE360 IPE600 IPE600
3220 3220 3500 3500
3000 3000 3200 3200
1395 1395 995 995
720 720 1210 1210
1331 1331 2600 2600
1355 1355 1750 1750
467 467 780 780
1175 1175 2350 2350
H. Augusto et al. / Journal of Constructional Steel Research 133 (2017) 310–333
of 0.02 mm/s for the monotonic tests, 0.2 mm/s for the first cyclic tests and 0.4 mm/s for the second cyclic tests. Group 2 was tested with a constant level of axial force in the column: (i) 800 kN,
315
corresponding to 18% of the plastic axial resistance of the column; and (ii) 1200 kN, corresponding to 27% of the plastic axial resistance of the column section.
Table 8 Methodology overview. Step
Action
1
Development of the FE model of the joint
1.1 1.2 2 2.1
Validation of the model Selection of the component model and active components Extraction of the components column web in tension and compression Definition of the stress paths P1 and P2
2.1.1 2.1.2 2.2 2.2.2 2.2.1
P1 P2 Extraction of the normal stresses (σzz) along P1 Determination of the integration boundaries (IB1 to IBn) Determination of the forces through integration of σzz over the lengths hc for compression and ht. for tension
2.3 2.3.1
Extraction of the displacements fields along P1 and P2 Determination of the deformation of the web
2.4
Derivation of the force-deformation curve for the integration boundaries chosen
3 3.1 3.2 3.2.2
Extraction of the component column web panel in shear Definition of the stress path P3 Extraction of the normal stresses (τyz) in P3 Determination of the integration boundaries
3.2.1
Determination of the shear forces by integration of τyz over the lengths defined for the shear area.
3.3 3.3.1
Extraction of the displacements in four orthogonal points in the web Determination of the horizontal rotation of the web
3.3.2
Determination of the vertical rotation of the web
Tools/comments
Experimental results or proper benchmark
Defined in the column web after the flange to web radius Near the connected flange Opposite flange For the selected load increments of the FE analysis According to the mechanical model, see also Fig. 14
For the selected load increments of the FE analysis δcw ¼ δP1 δP2 (usually aligned with the element that causes the deformation, e.g. bolt rows, flanges, etc.) For each selected load increment relate the calculated forces with the computed deformation F-δcw See Fig. 15 (a) For the selected load increments of the FE analysis According to the shear area adopted (for the EC3 shear area see also Fig. 15 (b))
For the selected load increments of the FE analysis, see also Fig. 15 (a) θh ¼ a tan DT1V3 DT2V3 d3 θv ¼ a tan DT3V2 DT4V2 d4
3.3.3 3.4 3.4.1 3.4.1.1
Determination of the distortion of the web In the presence of transverse web stiffeners Definition of the hinges location in the column flanges P4, P5, P6 and P7 Definition of the extraction paths P4.1, P4.2, P4.3, P5.1, P5.2, P5.3, P6.1, P6.2, P6.3 and P7.1, P7.2, P7.3 3.4.2 Extraction of the normal stresses (σyy) in each path 3.4.2.1 Determination of the neutral axis using paths Pi.2 and Pi.3 3.4.2.2 Determination of the bending moments by integration of σyy over the width of the column flanges
3.4.3
Determination of the additional shear stress
3.5
Derivation of the force-deformation curve for the integration boundaries chosen
γ ¼ θ h þ θv Account for the additional shear strength See Fig. 16
For the selected load increments of the FE analysis Interpolating between the paths Pi.2 and Pi.3 where the stress becomes zero.
For each selected load increment relate the achieved shear forces with the achieved distortion
316
H. Augusto et al. / Journal of Constructional Steel Research 133 (2017) 310–333
Column
Fixedto the beam
DT1
DT5 Column Beam
d3
DT3 DT4 DT2
d DT11 DT7
L d1
Fixedto the beam
d4
TwoLoadingCells 20 Ton
d2 DT8
d5
Beam
DT17
DT14
DT15
DT12
DT20
DT19
DT10
L2
120100 500
DT16
DT9
DT6
DT18
DT13
1000 x
LVDT Loadcell
(a)
(b)
Fig. 6. a) Instrumentation apparatus, and b) detail of the instrumentation in the column web using a crosshead.
To extract the relevant test information, the prototypes were instrumented according to the scheme shown in Fig. 6. 4.2. Global behaviour of the joint
Bending moment (kNm)
The experimental moment-rotation curves are depicted in Fig. 7 for each group, using the results from the load cells and displacement transducers DT11 and DT12 for the groups J1 to J4 tests and DT20 for the
lesser instrumented J3.1. The analysis of the results of the J1 group allows concluding that, for all cyclic loading strategies, the hysteretic response was very stable. No pinching or strength degradation was detected and only slight stiffness degradation was observed (Fig. 7a). For joint configuration J2, no pinching or stiffness degradation was observed (Fig. 7b). For joint configuration J3, some strength degradation was observed; however, no pinching was detected (Fig. 7c). Failure occurred either by cracking of the end-plate (J.3.2) or cracking of the weld
600
600
400
400
200
200
0
0
-200
-200
-400
J1.4 (DT11-12) J1.2 (DT11-12)
-600 -40
-30
-20
-10
-400
J1.3 (DT11-12) J1.1 (DT11-12) 0
10
20
30
J2.3 (DT11-12) J2.1 (DT11-12)
-600 40
-40
-30
-20
-10
J2.2 (DT11-12) 0
10
Rot. (mrad)
Bending moment (kNm)
Bending moment (kNm)
200 0 -200 -400 -600
600 400 200 0 -200 -400
J4.3 (DT11-12) J4.1 (DT11-12)
-600 -30
-20
-10
40
(b) J3.2 (DT11-12)
400
-40
30
Rot. (mrad)
(a) J3.3 (DT11-12) J3.1 (DT20)
600
20
0
10
20
30
40
Rot. (mrad)
-40
-30
(c)
-20
-10
0
10
20
30
40
Rot. (mrad)
(d) Fig. 7. Experimental moment-rotation curves.
J4.2 (DT11-12)
H. Augusto et al. / Journal of Constructional Steel Research 133 (2017) 310–333
317
L1 Lc1
ht Lc Lc2
Column
d Beam disp.
Lb1
Lb2 Lb 2(Y)
Lc3
L2
3(Z) 1(X)
J1.3
J3.2
J4.3
Geometrical properties
Fig. 8. FE models used in the validation.
(J.3.3). Noticeable strength and stiffness degradation and pinching was observed for joint configuration J4 (Fig. 7d). Table 3 summarises the nine results obtained for all cyclic tests, including the identification of the failure modes and the corresponding number of cycles.
from the numerical models are compared with some of the test results previously described, one for each different geometry. Bending moments and rotations were determined according to the procedure described in Annex B of [31]. For the experimental tests, the load cells and the displacement transducers were used. For the FE models, the reaction forces and the displacements of some predefined nodes were selected. The bending moments were computed at the face of the connected column flange, M = F*d, using distance d and the forces applied in the tip of the beam. Rotations were computed using the relation between the displacements measured in LVDTs (or the displacements
4.3. Comparative analysis of the experimental and numerical results
Bending Moment (kNm)
4.3.1. Introduction In this section, a detailed analysis of the behaviour of the joints is carried out focusing on both global and component behaviours. The results
600 400 200 0 -200 -400
Joint Rot. - EXP. Joint Rot. - FE
-600 -40
-30
-20
-10
0
10
20
30
40
Rotation (mrad)
Bending Moment (kNm)
(a) J1.3 global response
(b) J1.3 von Mises stress distribution
600 400 200 0 -200 -400
Joint Rot. - EXP. Joint Rot. - FE
-600 -40
-30
-20
-10
0
10
20
30
40
Rot.ation (mrad)
Bending Moment (kNm)
(c) J3.2 global response
(d) J3.2 von Mises stress distribution
600 400 200 0 -200 -400
Joint Rot. - FE Joint Rot. - EXP.
-600 -40
-30
-20
-10
0
10
20
30
40
Rotation (mrad)
(e) J4.3 global response
(f) J4.3 von Mises stress distribution
Fig. 9. Global experimental and numerical results.
318
H. Augusto et al. / Journal of Constructional Steel Research 133 (2017) 310–333
obtained in the pre-defined nodes in the FE mesh) and the distance between them, excluding the rotations due to the elastic deformation of the members and the rotations due to the support clearances (θ = atan((DTi − DTi + 1)/dn) − θelast_column − θblock). To compute the total rotation of the joint, the column web contribution was added to the connection contribution, with the help of the crosshead, for experimental tests was used the Eq. B.6 of [31], and for the FE models was used the Eq. B.7 of [31] (using the displacements from DT1, DT2, according to Fig. 15, and distance d3). A set of models were developed according to the tests setup, using the same geometry, see Fig. 8 and Table 4, following the same boundary
conditions and loading. The elasto-plastic material properties were based on the mean values of the coupon tests [31] [39]. 4.3.2. Global cyclic behaviour Fig. 9(a), (c) and (e) compare the experimental and numerical moment-rotation curves for the J1.3, J3.2 and J4.3 joints, respectively. Fig. 9(b), (d) and (f) show the von Mises stress distribution in the joint region for the 3 joints analysed, for the maximum rotation achieved in the joint, i.e., the largest rotation amplitude achieved during the numerical analysis. The stress patterns are very similar for all joints, although for J4.3 it is possible to see higher stress concentration around
Fig. 10. Evolution of stiffness and strength degradation with the number of cycles.
H. Augusto et al. / Journal of Constructional Steel Research 133 (2017) 310–333
the stiffeners in the opposite flange of the column, which is due to the smaller lever arm of the beam inducing larger rotations in the joint. The stress peak values occurred in the bolts, the stress scale was limited to a small range of stress values. The comparisons between the numerical and experimental results, including Table 5, allow concluding that the FE models of extended end-plate joints produce very accurate results in comparison with the experimental data also for the cyclic load cases [31]. From the detailed analysis of the cyclic behaviour, it is possible to identify the strength and stiffness degradation exhibited by the joints, for the stable cycles, see Fig. 10. The positive and negative stiffness are determined in the unloading branch of each positive and negative halfcycle, respectively. The positive and negative bending moments, depicted in Fig. 10, are the maximum and minimum moments in each
319
half-cycle, respectively. It is possible to conclude that, for the group J1, degradation of stiffness is observed for all joints, but at different rates. In the case of J1.4, degradation only occurred in the last 7 cycles. Strength degradation is not noticeable in J1.2, but it occurs in J1.4 only in the last 7 cycles, after an amplitude increase. In the case of the group J2, a very similar behaviour was observed for both joints with some degradation of stiffness and strength occurring with the evolution of the loading protocol. J3.2 presents a very stable behaviour in terms of stiffness and strength. Similar to J3.2, the J3.3 joint exhibited very stable behaviour in terms of stiffness and strength, although after the 10th cycle it is possible to observe a strong degradation of stiffness and strength as a result of the damage observed in the welds between the end-plate and the beam. Similar to the group J2, the group J4 showed a similar behaviour for both joints in the group, with similar strength and stiffness
J1.3
J1.3
J3.2
J3.2
J4.3
J4.3 Fig. 11. Comparison of the moment-rotation responses.
H. Augusto et al. / Journal of Constructional Steel Research 133 (2017) 310–333
degradation, although in this case the number of cycles achieved by J4.2 was 37% higher than for J4.3, the failure occurred by the beam-to-endplate welds in both cases. The comparisons with the numerical results are quite good, although the numerical results for J1.3 are slightly lower than the ones obtained in the tests.
4.3.3. Cyclic behaviour of the components In a ductile extended end-plate joint it is expected that the most dissipative components are the end-plate and/or column flanges in bending and the column web panel in shear. In the particular case of the studied joints, the transverse web stiffeners limits the column flanges deformation, so the large contribution is provided by the other two components. According to the instrumentation setup, depicted in Fig. 6, and using a similar procedure as in the global joint response, the displacement measured in DT1, DT2 and distance d3 were used to determine the end-plate rotation, and from DT3, DT4 and distance d4 results, were used to determine the rotations of the column web panel rotation in the experimental tests. In a similar procedure the rotation of the column web, in the numerical models, was obtained by the displacements of four pre-defined nodes in the mesh of the web, see Fig. 15 (a). So equations (B.9) and (B.10) provided in [31] were used to determine the joints column web rotation, for the experimental and numerical models, respectively. Similarly, the rotation of the end-plate was determined, using the measurements of the displacement transducers DT1 and DT2 for the experimental tests, and the relative displacements of FE-Total Energy - 100% FE - CWPF - 89% FE - End-plate - 11% EXP. - Total Energy - 100% EXP. CWPF - 83% EXP. End-plate - 17%
J1.3 12000
kNm.mrad
10000 8000
two pre-define nodes in the end-plate aligned with the beam flanges (DT13 and DT14) were used for the FE models. As such the equations (B.11) and (B.12) given in [31] were used to determine the end-plate contribution for the experimental and numerical models, respectively. Fig. 11 shows a comparison of the moment-rotation curves for each joint and for the two critical components, both for the experimental and the numerical results. Fig. 12 compares the energy dissipated in the experimental tests with that obtained in the FE models. The comparisons are performed for the range of results in which the joints exhibited stable behaviour, i.e., until the first failure was observed in the test. The comparisons reveal good agreement between the experimental and numerical results. For all tests, the column web panel in shear (CWPF - column web panel and flanges) provided the largest contribution in terms of deformation and energy dissipation of the joint (78% to 83%), while the end-plate in bending represented 17% to 22% of the overall energy dissipated. As seen from the numbers, the remaining components have little contribution.
5. Characterization of the column web components under cyclic loading using Fe models 5.1. Introduction This section presents a methodology to characterize the behaviour of column web panel components from experimental results and/or FE models under cyclic loading conditions.
6000
500000 400000 300000 200000
4000
100000
2000
0
0 1
4
7
10
13
16
Cycles
8000
4
4000
2000
10
13
16
19
FE - Total Energy - 100% => 228895 FE - CWPF - 87% => 199057 FE - End-plate - 13% => 29838 EXP. - Total Energy - 100% => 232073 EXP. CWPF - 78% => 181786 EXP. End-plate - 22% => 50287
J3.2
6000
7
Cycles
Energy (kNm.mrad)
12000 10000
1
19
FE - Total Energy - 100% FE - CWPF - 87% FE - End-plate - 13% EXP. - Total Energy - 100% EXP. CWPF - 78% EXP. End-plate - 22%
J3.2 Energy (kNm.mrad)
FE-Total Energy - 100% => 252406 FE - CWPF - 89% => 223380 FE - End-plate - 11% => 29026 EXP. - Total Energy - 100% => 258416 EXP. CWPF - 83% => 214707 EXP. End-plate - 17% => 43482
J1.3 kNm.mrad
320
0
500000 400000 300000 200000 100000
0 1
4
7
10
13
16
19
22
25
1
4
7
10
13
16
19
22
Energy (kNm.mrad)
12000 10000 8000 6000 4000
2000
FE - Total Energy - 100% => 341235 FE - CWPF - 74% => 253252 FE - End-plate - 26% => 87982 EXP. - Total Energy - 100% => 348002 EXP. CWPF - 80% => 279651 EXP. End-plate - 20% => 68351
J4.3 Energy (kNm.mrad)
FE - Total Energy - 100% FE - CWPF - 74% FE - End-plate - 26% EXP. - Total Energy - 100% EXP. CWPF - 80% EXP. End-plate - 20%
J4.3
25
Cycles
Cycles
500000 400000 300000 200000 100000 0
0 1
4
7
10
13
16
19
22
25
1
4
7
10
Cycles
Fig. 12. Comparison of the relative energy dissipation of the components.
13
16
19
22
25
Cycles
H. Augusto et al. / Journal of Constructional Steel Research 133 (2017) 310–333
(31) (41) (51) (81) (101)
Integration boundaries (IB): Comp. 2 = IB1, IB3, IB(n+1) Comp. 3 = IB1 to IB(n+1) 3
IB1
Comp. 1
F
(2) (7) (32) (42) (52) (82)(102)
4 hbf
10
2
321
Comp. 2
(1)
F
(33) (43) (53) (83)(103)
19
(2) (7)
IB2 7, 8
(34) (44) (54) (84)(104)
Comp. 3
F
1
IB3
5
hbf
(21) (31) (41) (51) (81) (101) 7, 8
IB4
(7)
(22) (32) (42) (52) (82)(102)
19
2
10
IB(n+1) 3
4
hbf
Comp. 1, 2 F and 3
(1)
Alternative assemblage Integration boundaries (IB): Comp. 2 = comp. 3 = IB1 to IB(n+1)
(23) (33) (43) (53) (83)(103) (7)
(24) (34) (44) (54) (84)(104)
Idealized behaviour for components 1, 2 and 3:
Fig. 13. From left to right: Identification of the components in the joint and definition of possible integration boundaries (IB); assemblage of the identified components according to the integration boundaries chosen; idealized response of the column web components 1, 2 and 3.
Fig. 13 represent a double-extended end-plate beam-to-column steel joint and two possible component models. The active components are the following: (1) column web in shear, (2) column web in transverse compression, (3) column web in transverse tension, (4) column flange in bending, (5) end-plate in bending, (7) beam flange and web in compression, (8) beam web in tension, (10) bolts in tension and (19) welds. The characterization of the components behaviour, under cyclic loading conditions, is a complex task, to ease the process, and to analyse in detail each component behaviour, the identified components were grouped according to their location in the joint: components of the column web (1, 2 and 3), components of the connection (4, 5, 10 and 19) and components of the beam (7 and 8). In this paper only the components of the column web will be addressed i.e. components 1, 2 and 3. As the joint is subjected to load reversal, it is necessary to take into account the added complexity of exhibiting tensile and compressive stresses within the same location of the joint. With reference to Fig. 13, this added complexity mostly results from the fact that the load-introduction points, in the column web, vary as the stresses change from tension to compression. When transferring tension from the beam to the column, the load-introduction in the column web panel comes from the position of the bolt rows in tension, while compression is more evenly distributed around the compression centre, with the peak maximum compressive stress aligned with the compressed beam flange, as is evidenced later in Fig. 20. In line with the main assumptions of the component method [1], the joint is discretized according to the bolt rows and the centre lines of the beam flanges, as shown in Fig. 13, using appropriate effective widths. Consequently, the characterization of the column web panel components in bolted joints depends on the assumed simplifications of the component model. It is of course possible to lump some lines of action of the components in order to simplify the problem, as shown in the alternative assemblage of Fig. 13. This simplification aligns the load-introduction tensile and compressive components in the column web panel, allowing to combine the force-deformation (F-Δ) response of these two components into one single force-deformation (F-Δ) curve, as illustrated in Fig. 13, at the expense of losing consistency with the component characterization of EC3-1-8 for static monotonic conditions.
In the following sub-section, a general extraction procedure is described that allows for the arbitrary consideration of any component model. Therefore, the choice is freely left to the user to implement any component model and easily convert the component characterization of the column web panel components across different models such as those shown in Fig. 13. 5.2. Derivation of the force-displacement relationships This derivation consists of an extension to the methodology presented in [31] to deal with reversal load conditions for the extraction of the column web panel components behaviour, due to the load-introduction effect and the shear effect. It is fully based on the results provided by the FE models and allows the derivation of force-displacement and shear-distortion curves of the components. It was developed using numerical integration of the stress fields obtained from the FE models and it is illustrated in Fig. 14 to Fig. 16, for the load-introduction effect and for the shear effect. The forces (Fc and Ft) are obtained through integration of the stress field according to Eq. (3) for the load-introduction effect and from Eq. (4) for the shear effect. In these equations, σ33 is the normal horizontal stress in the column web along path P1, integrated over the lengths hc for compression and ht. for tension (Eq. (3)). Furthermore τ23 is the shear stress in the column web along path P3, integrated over the corresponding lengths (Eq. (4)), tfc and twc are the column flange and web thicknesses, respectively, and t1 is the thickness according to the shear area represented in Fig. 15 (b). It is noted that this procedure is quite flexible in defining the integration boundaries (IB in Fig. 14) to calculate the forces. The assessment of the forces will depend on the idealized mechanical model and the procedure can be easily adapted to the two examples presented before or to any other compatible mechanical model. Moreover, in the case of the shear evaluation, other integration boundaries can be considered; in this case, the EC3-1-8 [1] shear area definition was used to set the boundaries for integration. ! ! Fc ¼
hc;i
∫ σ 33 dy t wc or F t;i ¼
ht;i
∫ σ 33 dy t wc
ð3Þ
322
H. Augusto et al. / Journal of Constructional Steel Research 133 (2017) 310–333
IB1 h (mm)
800
P2
700
IB2
600
IB3
400
(1)
Ft
ht(1st)
Ft
ht(2nd)
500
300
Fc
IB...
V
(2) (7) (34) (44) (54) (84)(104)
h
hc(4th)
0 -400
-200
0
200
400
33 (N/mm2)
600
800
(a) Stress integration for negative moment
h (mm)
800
P2
IB1
(31) (41) (51) (81) (101) (1)
hc(1st)
600 500
300 200 100
IBn -600
h
Ft
hc(3rd)
Ft
hc(4th)
(2) (7) (32) (42) (52) (82) (102) V
hc(2nd)
400
IB...
(b) Mechanical model for negative moment
P1
700
Fc
IB3
-800
M
(33) (43) (53) (83) (103)
hc(3rd)
100
-600
IB2
(2) (7) (32) (42) (52) (82) (102)
200
IBn -800
(31) (41) (51) (81) (101)
P1
M
(33) (43) (53) (83) (103) (2) (7) (34) (44) (54) (84) (104)
0 -400
-200
0
200
400
600
33 (N/mm2) (c) Stress integration for positive moment
800
(d) Mechanical model for positive moment
Fig. 14. Procedure to obtain the forces in the column web in transverse tension and compression components, (a) and (c), under negative and positive bending moment; and in (b) and (d) the same components are identified in the global assembly of the joint components, also for negative and positive moment, respectively.
0 1 ðtfc =2þrÞback @ Vn ¼ ∫ τ 23 dzA t 1 þ
!
hwc
∫ τ 23 dz
0 1 ðtfc =2þrÞfront @ t wc þ ∫ τ 23 dzA t 1
2 23 (N/mm )
ð4Þ
hshc
400 300 200
DT1 fc
100
0 -100
To determine the shear force (Vn) in the web panel, the stress field is evaluated at a cross section of the column aligned with the mid-height of the connected beam, where the stresses reach their maximum values (at bending neutral axis), using the middle elements of the web to extract the shear stresses. The stresses in the column web panel are assumed to be uniformly distributed due to the action of the column
P3
Vn
(+)
DT4
DT3
r twc
Vn (-)
-200
rc
hwc hshc rc tfc/2
-300
DT2
-400 0
100
200
hc (mm) (a)
300
(b)
Fig. 15. Procedure to obtain the shear force of the column web panel in shear component. a) plot of the shear stresses envelope; and b) integration boundaries (in this case according to the EC3-1-8).
H. Augusto et al. / Journal of Constructional Steel Research 133 (2017) 310–333
323
tfc Mfc P5
P7
bc
P4.1
P4.2
P6
P4
dA
z
P4.3
tfc
(a)
(b)
Fig. 16. Determination of the bending moment in the flanges through stress integration. a) illustrates the paths P4 to P7 in the joint perspective, and top view of part of a cut, aligned with path P4, showing the additional paths in the column flange used to determine the bending moment according to the integration scheme represented in b).
flanges, as proposed by Jaspart [29]. Therefore, the shear stresses are only extracted along path P3, see Fig. 15 (a). The deformation and rotation corresponding to the load-introduction effect and shear effect, respectively, are obtained from the displacement fields. In the case of the load-introduction effect, the displacements are extracted from paths P1 and P2, see Fig. 14, and the deformation is determined, see Eq. (5), as the difference between the nodes in the paths aligned with the element that causes the deformation, e.g. bolt rows, flanges, etc. at the same location of the arrows
indicating the forces in Fig. 14. For the rotation due to the shear effect, the displacements are extracted from the predefined nodes indicated in Fig. 15 (a) and computed according to Eq. (6). δcw ¼ δP1 −δP2
ð5Þ
DT1U3 −DT2U3 DT3U2 −DT4U2 þ a tan γ ¼ a tan d3 d4
ð6Þ
1200
25 80 75 89 90
Ø39 M36 (10.9)
600
910
1000
True stress (MPa)
30
242 90
IPE600 (S355)
89 75 80
HEB500 (S355)
800 600 400 200 0
75 150 75 300
500
Steel (S355) Bolts (10.9) 0%
5%
10%
15%
20%
25%
30%
True strain (%)
(a)
(b)
Bending Moment (kNm)
Fig. 17. (a) Geometry of the E3-TB-E-M3-ts30 and (b) true stress – true strain curves of the materials adopted.
500 400 300 242.27
Lb
239.47
200
J1_1_pv1_tp18_ts0 J1_1_pv1_tp18_ts20 ECCS Linearization
100 3.97
0 0
5.56 10
20
30
40
Rot. (mrad)
(a)
(b)
Fig. 18. (a) Determination of the elastic limit based on the nonlinear monotonic behaviour of the joints; (b) geometrical properties for the AISC 341-10 load protocol.
324
H. Augusto et al. / Journal of Constructional Steel Research 133 (2017) 310–333
Whenever transverse stiffeners are present, the additional shear strength provided by the moment resisting frame formed by the column flanges and the transverse stiffeners aligned with the beam flanges is accounted for considering a plastic mechanism whereby the plastic hinges will occur in the column flanges due to the higher stiffness and strength of the stiffeners, if properly designed, see also [31]. The stresses are extracted at a section near the flanges maxima normal stresses, σ22, as depicted in Fig. 16. Subsequently, Eq. (7) is used to determine the bending moment in the flanges, and Eq. (8) is used to obtain the
additional shear strength, Vc, computed using the four plastic hinges in the column flanges and the distance between the centre lines of the transverse stiffeners. t fc
Mfc ¼ ∫ zðσ 22 dAÞ; Vc ¼
dA ¼ bc dz
MfcðP4Þ þ M fcðP5Þ þ MfcðP6Þ þ MfcðP7Þ hb −t s
700 Row 1
h (mm)
h (mm)
500
400 300
Row 3
600 500
Row 2
400 300
Row 3
200
Row 4
200 Row 4
100
-600
-400
-200
100
J1_1_pv1_tp18_ts0
0 -800
0
200
400
600
800
-4
-2
0
h (mm)
h (mm)
500 400
300
600 500
Row 2
400 300
Row 3
200 Row 4
200 Row 4
100
-600
-400
-200
100
J1_1_pv1_tp18_ts20
0 -800
0
200
400
600
800
-4
-2
0
1000
800
Row 2 Row 3
800
h (mm)
h (mm)
Row 1
400
Row 6
600
Row 4 Row 5
400
Row 6
200
200
0
-800
-600
-400
-200
200
400
600
800
-15
-10
-5
1200 1000
Row 1
1000
Row 2 Row 3
800
Row 2 Row 3
800
600 400
Row 6
-600
200 -400
-200
10
15
600
Row 4 Row 5
400
Row 6
200
E3-TB-E_cyc_M3_ts30
0 -800
5
1200
Row 1
h (mm)
h (mm)
0
Web deformation (mm)
33 (N/mm2)
Row 4 Row 5
E3-TB-E_cyc_M3_ts0
0
0
4
1200
1000
600
Row 4 Row 5
2
Web deformation (mm) E3-TB-E-cyc_M3_ts0
1200
Row 2 Row 3
J1_1_pv1_tp18_ts20
0
33 (N/mm2)
Row 1
4
700 Row 1
600
Row 3
2
Web deformation (mm)
700
Row 2
J1_1_pv1_tp18_ts0
0
33 (N/mm2)
Row 1
ð8Þ
700 Row 1
600
Row 2
ð7Þ
0
200
33 (N/mm2)
400
600
800
E3-TB-E_cyc_M3_ts30
0 -15
-10
-5
0
5
Web deformation (mm)
Fig. 19. Stress fields (left), and web deformation fields (right), for increasing levels of bending moment.
10
15
H. Augusto et al. / Journal of Constructional Steel Research 133 (2017) 310–333
5.3. Application to the joints 5.3.1. Introduction The proposed procedure was applied to some variants of the joints analysed in the calibration of the FE models, and extended to other geometries developed using the same principles. The geometrical properties are described in Table 6, with reference to the scheme of Fig. 8. The first two geometries correspond to joint J1.1, with and without transverse web stiffeners, analysed in [31]. The last two joints are also double-extended end-plate joints with stronger beam and column profiles, IPE600 and HEB500, respectively, with six bolt rows, with four inner rows, bolt size M36 in grade 10.9, with and without transverse web stiffeners. The E3-TB-E-M3-ts30 joint was designed according to EC3-1-8, to reach a strength level similar to the beam plastic moment. The geometry of the joint is depicted in the Fig. 17(a). In the design of the joints without stiffeners, the governing component, in the compression side, was the column web in transverse compression. In the tension side, the governing component, for the external bolt rows, was, in both geometries (J1.1 or E3), the end-plate in bending. For the inner bolt rows, the strength of the compression component limited the development of the full resistance of the tension components. In the case of the J1.1 joint, the component that governed the design was the column flange in bending and in the E3 joint was the endplate in bending. In the latter case, the third bolt row was inactive. In the
1st yielding
time step 0.9912 time step 2.9912 time step 4.9912 time step 6.9912 time step 9.0138 time step 11.0034 time step 12.8306 time step 12.9483 time step 12.9979 time step 14.6891 time step 14.7779 time step 15.0123 J1_1_pv1_tp18_ts0
700 600
h (mm)
500
400 300 200
100 0 -600
-400
-200
0
200
400
600
800
1000
presence of transverse web stiffeners the governing component, in the compression side, was the column web panel in shear. In the tension side the behaviour was similar to the joints without stiffeners, but due to the higher strength of the compression component, it was possible to reach higher values in the tension components for the inner bolt rows. The steel mechanical properties adopted in these analyses correspond to the nominal values defined in Eurocode 3 part 1–1 [40] (E = 2.10E5 N/mm2; fy = 355 N/mm2; fu = 490 N/mm2) for the FE models representing the joints based on J1.1. For the remaining joints, a more realistic stress-strain relationship, of a steel grade S355, depicted in Fig. 18 (b) was considered. Two different load protocols were used: ECCS [41] was adopted for the joints based on J1.1, and the protocol specified in the AISC 341-10 [42] was employed for the remaining joints. The ECCS load protocol is defined as follows: (i) one cycle in the ranges: θy/4; 2θy/4; 3θy/4 and θy (ii) three cycles in the ranges: 2θy; (2 + 2n)θy where n = 1.2, … The assessment of the elastic limit, θy, is based on the bi-linearization of the nonlinear monotonic response of the joints, see Fig. 18 (a). In case of AISC 341–10 [42], the procedure is conducted by controlling the inter-storey drift, θ, imposed to the test specimen, six cycles in the ranges 0.00375 rad, 0.005 rad, 0.0075 rad, four cycles in the range 0.01 rad and two cycles in the ranges 0.015 rad, 0.02 rad, 0.03 rad, 0.04 rad. The loading is applied with increments of 0.01 rad, with two cycles of loading for each step. In the analysis, the vertical beam deflection is the controlled parameter. Thus, when defining the load function in ABAQUS, the amplitude δ is used and it is defined by Eq. (9), according to Fig. 18 (b).
θ¼
δ ⇔δ ¼ θ Lb Lb
Row 1
600 500
Row 2
400
300
Row 3
200 Row 4
100
-400
-200
1000
h (mm)
800 600 400
200
0
200
400
400
600
800
1000
1200 1000 800
h (mm)
time step 0.063 time step 3.141 time step 5.175 time step 6.975 time step 10.894 time step 15.103 time step 19.022 time step 21.131 time step 25.05 time step 26.859 time step 28.659 time step 31.119 time step 33.031 time step 35.088 time step 36.972
33 (N/mm2)
J1_1_pv1_tp18_ts20
0 -600
600
800
1000
33 (N/mm2)
1200
200 E3-TB-E-cyc_M3_ts0 0 -600 -400 -200 0
time step 0.9912 time step 2.9912 time step 4.9912 time step 6.9912 time step 8.9944 time step 10.9944 time step 12.8944 time step 12.9944 time step 14.9944 time step 16.6944 time step 16.9944
700
33 (N/mm2) 1st yielding
ð9Þ
5.3.2. Load-introduction effects As already explained, the introduction of the loads in the column web, due to the beam force couple, is different in tension and in compression as tension is transferred by the bolt rows and compression is
h (mm)
For simplification, it is considered that the stresses are uniform along the width of the column flanges, so the integration of the stresses along each path results in a single force at that strip. The bending moment is obtained by multiplying the force at each layer by the distance to the neutral axis. The bending moment can be computed with the forces determined in the two outer paths (P4.1 and P4.2). However, and because it is necessary to determine the neutral axis position, due to the presence of axial force in the column flanges, a third path (P4.3) is required to determine the location where the stresses are equal to zero, the neutral axis position is sensitive to the back and forward from the cycles. It is also important to note that the third path should cross the radius and web elements so that the integrated forces and the neutral axis evaluation take that into account.
325
600 400
-400
Row 1 Row 2 Row 3 Row 4 Row 5
Row 6 200 E3-TB-E-cyc_M3_ts30 0 -200 0 200 400 600
33 (N/mm2)
Fig. 20. Stress fields for the first load increments and identification of first yielding.
time step 0.063 time step 3.141 time step 6.975 time step 10.969 time step 13.003 time step 16.997 time step 19.031 time step 21.141 time step 25.059 time step 26.869 time step 28.669 time step 28.969 time step 30.778 time step 32.963 time step 34.997 time step 800 100038.991 1200 time step 45.06 time step 47.039
326
H. Augusto et al. / Journal of Constructional Steel Research 133 (2017) 310–333
1000
Group of rows 1, 2, 3 Group of rows 3, 4, 5
3000
500
2000
250
1000
F (kN)
F (kN)
4000
J1_1_pv1_tp18_ts0
750
0 -250 -500
0 -1000
E3-TB-E-cyc_M3_ts0
-2000
-750 -2
-1
-3000
Group of rows 1 and 2 Group of rows 3 and 4 1 2
-1000 0
-4000 -15
-12.5
Web deformation (mm) Group of rows 1 and 2 Group of rows 3 and 4
500
2000
-7.5
-5
-2.5
0
2.5
E3-TB-E_cyc_M3_ts30
1500
250
1000
F (kN)
F (kN)
-10
Web deformation (mm)
0
500 0 -500 -1000
-250
-1500
J1_1_pv1_tp18_ts20
-2000
-500 -0.3
-0.2
-0.1
0
0.1
0.2
-0.3
0.3
-0.2
-0.1
0
Group of rows 1, 2, 3 Group of rows 3, 4, 5 0.1 0.2 0.3
Web deformation (mm)
Web deformation (mm)
Fig. 21. F-Δ curves for the components due to the load-introduction effect considering the group of bolts around the beam flanges.
transferred directly from the contact of the beam flange to the column web. Fig. 19 shows the stress, along the path P1, and deformation fields, obtained by Eq. (5), for the joints defined in Table 6, for several load increments. Globally, the stress distribution is very similar in tension and in compression, especially for the joints without transverse web stiffeners. However, some differences are noted. The first load increments, depicted in Fig. 20, show that the differences between tension and compression are more evident in the elastic range, with local maxima stresses perfectly aligned with the position of the bolts rows for tensile
stresses, and with the position of the beam flanges for compressive stresses. After yielding of the web is reached, both tension and compression diagrams become similar and the maximum stresses deviate from the position of the bolt rows. Regarding the web deformation, the differences between tension (positive) and compression (negative) are more notorious. For the joints without transverse web stiffeners, the maximum deformation in compression is aligned with the beam flanges, while in tension the maximum is aligned with the inner bolt row, revealing the stiffer behaviour of those bolt rows. The transverse web stiffeners, aligned with the beam
750
750
J1_1_pv1_tp18_ts20
500
500
250
250
F (kN)
F (kN)
J1_1_pv1_tp18_ts0
0
0 -250
-250 -500
-500
Bolt row 1 Bolt row 4
-750 -2
-1
0
1
Bolt row 1 Bolt row 4
-750 -2
2
-1
0
2
750
750
J1_1_pv1_tp18_ts0
J1_1_pv1_tp18_ts20
500
500
250
250
F (kN)
F (kN)
1
Web deformation (mm)
Web deformation (mm)
0
0 -250
-250 -500
-500
Bolt row 2 Bolt row 3
Bolt row 2 Bolt row 3
-750
-750 -2
-1
0
1
Web deformation (mm)
2
-0.5
0
0.5
1
1.5
2
Web deformation (mm)
Fig. 22. F-Δ curves for the components due to the load-introduction effect for each bolt row, for the J1.1 joints, according to the alternative mechanical model depicted in Fig. 13.
H. Augusto et al. / Journal of Constructional Steel Research 133 (2017) 310–333
flanges, prevent the deformation of the column web in compression in the inner bolt row. The application of the methodology described in Section 5.2 allows obtaining the numerical F-Δ curves for the components. The procedure is general in the sense that it allows to obtain force resultants and deformations for any selected tributary area between two integration limits, both for the column web in tension or in compression. Fig. 21 depicts the cyclic force-deformation behaviour for the load introduction in the column web panel for the four joints. A single lumped component is considered for the top and bottom zones. Consequently, with reference to Fig. 14, the integration limits are defined between points of zero or near zero normal stress σ33 for the top and bottom zones, respectively. It is noted that these limits will not necessarily coincide for positive and negative bending moments, neither also between the different load cycles. However, Fig. 19 shows that they are fairly stable and hence it is possible to assume constant limits of integration for all loading cycles. Concerning the deformation, the maximum web deformation in tension and compression is selected. It is noted that the maximum values will not necessarily occur at the same section. Typically, the maximum web deformation in compression is observed at the level of the beam flange while in tension it often develops aligned with one of the bolt rows. Fig. 22 and Fig. 23 represent the force-deformation cyclic curves for joints J1.1 and E3, respectively, according to the alternative component model shown in Fig. 13, i.e., with the load introduction components
3000
(tension and compression) positioned according to the bolt rows. In this case, for the top and bottom zones, the integration limits for each bolt row are established based on the effective widths of the components. The deformation, in this case, is measured aligned with the corresponding bolt row. The component model illustrated in Fig. 13 reflects the definition of the individual components in accordance with EC3-1-8 [1]. It further highlights that the effective width of the column web panel in compression is clearly distinct from the corresponding effective widths of the column web panel in tension components for each bolt row in tension. Hence, the integration limits in tension and in compression should be different. Fig. 24 illustrates the cyclic behaviour of the column web panel in compression, referenced to the beam flange level, while Fig. 25 depicts the cyclic force-deformation curves for the column web panel in tension for each bolt row. The comparison of the results obtained for the stiffened and unstiffened joints shows that the transverse web stiffeners have a major influence on the amplitude and shape of the force-displacement curves. Whilst the compression is transmitted directly to the stiffeners without causing transverse deformation in the column web, tension causes deformation in the column web aligned with the bolt rows. The examination of the behaviour of the inner bolt rows, see Fig. 23, reveals a ratcheting effect after yielding, mainly in the third and fourth rows of the E3-TB-E_cyc_M3 joints, due to the migration of the normal stresses (σ33) across the web with the increase of bending moment, see
1500
E3-TB-E-cyc_M3_ts0
E3-TB-E-cyc_M3_ts30
2000
1000 500
F (kN)
F (kN)
1000 0 -1000
0 -500
-2000
Bolt row 1 Bolt row 6
-1000
-3000 -15
-10
-5
0
5
10
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
Web deformation (mm) 1500
E3-TB-E-cyc_M3_ts0
E3-TB-E-cyc_M3_ts30
2000
1000
1000
500
F (kN)
F (kN)
3000
Bolt row 1 Bolt row 6
-1500
15
Web deformation (mm)
0
0 -500
-1000 -2000
-1000
Bolt row 2 Bolt row 5 -15
-10
-5
0
5
10
Bolt row 2 Bolt row 5
-1500
-3000
-1
15
0
1
3000
2
3
4
5
6
7
8
Web deformation (mm)
Web deformation (mm) 1500
E3-TB-E-cyc_M3_ts0
E3-TB-E-cyc_M3_ts30
2000
1000
1000
500
F (kN)
F (kN)
327
0
0 -500
-1000 -2000
-1000
Bolt row 3 Bolt row 4
-1500
-3000 -15
-10
-5
0
5
Web deformation (mm)
10
Bolt row 3 Bolt row 4
15
-1
0
1
2
3
4
5
6
7
8
Web deformation (mm)
Fig. 23. F-Δ curves for the components due to the load-introduction effect for each bolt row, for E3 joints, according to the alternative mechanical model depicted in Fig. 13.
328
H. Augusto et al. / Journal of Constructional Steel Research 133 (2017) 310–333
J1_1_pv1_tp18_ts0
0
Component 2 (upper beam flange) Component 2 (lower beam flange)
0
E3-TB-E-cyc_M3_ts0
-1000
F (kN)
F (kN)
-250 -500 -750
-2000 -3000
-1000 -2
-1
Component 2 (upper beam flange) Component 2 (lower beam flange) 0 1 2
-4000 -15
-12.5
Web deformation (mm)
-10
-7.5
-5
-2.5
0
2.5
Web deformation (mm)
Fig. 24. F-Δ curves for component (2) due to the load-introduction effect, compression side of the previous relationships.
Fig. 27. This phenomenon can be associated with the interaction with the shear stress (τ23) that progressively increases the normal stress beyond the line of the beam flanges alignment. The joints without stiffeners may exhibit out-of-plane deformations, as illustrated in Fig. 26. This phenomenon is captured in the derived F-Δ relationships, represented by the last cycles with larger amplitude, for the joint E3-TB-E_cyc_M3_ts0, visible in the response of the external and in the internal bolt rows, see Fig. 23 or Fig. 25. The transverse web stiffeners may prevent this undesired phenomenon, as shown in both figures. Table 7 summarises the main results for the column web panel in tension and compression F-Δ relationships. In general, the initial stiffness, of the achieved F-Δ relationships, is lower for the joints without stiffeners, although for the E3 joints this fact is not verified in some bolt rows, as highlighted in the table. Regarding the maximum strength achieved in the component, it is clear that the joints without stiffeners present the highest values in comparison with the joints with stiffeners. This results from the fact that the transverse web stiffeners directly transfer the compression forces to shear in the column web.
750
The joints were also subjected to different load protocols, ECCS [41] and AISC 341-10 [42], resulting in different demands. ECCS is clearly more severe than the AISC load protocol. Note that the ECCS load protocol imposes four cycles in the elastic range, while the AISC load protocol may involve a significant number of cycles in the elastic range before the yield resistance of the joint is reached. This difference is related to the fact that the ECCS load protocol has a pre-processing procedure to assess the elastic limit of the joint, relating the amplitudes of the cycles with the assessed value, unlike the AISC load protocol that specifies fixed values for the amplitudes. In the plastic range, the ECCS load protocol is also more severe than the AISC load protocol, as it doubles the deformation amplitude between sets of cycles after yielding. In contrast, AISC increases the deformation amplitude by 150% between sets of cycles after yielding. Although the yield rotations for both geometries (J1.1 and E3) are similar, in terms of beam displacement amplitude, E3 needs approximately double the amplitude of the J1.1, due to the higher beam length, a fact that was considered in the comparisons of the two load protocols. The evolution of the two protocols reveals that ECCS always reached higher amplitudes earlier than AISC. This evidence can
2000
Component 3 (row 1) Component 3 (row 4)
J1_1_pv1_tp18_ts0
Component 3 (row 1) Component 3 (row 6)
1500 500
F (kN)
F (kN)
E3-TB-E-cyc_M3_ts0 1000
250 500 0
0 -2
-1
0
1
2
-10
-7.5
Web deformation (mm) 750
2000
Component 3 (row 2) Component 3 (row 3)
J1_1_pv1_tp18_ts0
-5
-2.5
0
2.5
Web deformation (mm) Component 3 (row 2) Component 3 (row 5) Component 3 (row 3) Component 3 (row 4)
1500
F (kN)
F (kN)
500
E3-TB-E-cyc_M3_ts0
1000
250 500
0
0
-2
-1
0
1
Web deformation (mm)
2
-10
-7.5
-5
-2.5
0
2.5
5
Web deformation (mm)
Fig. 25. F-Δ curves for component (3) due to the load-introduction effect, tension side of the previous relationships.
7.5
10
H. Augusto et al. / Journal of Constructional Steel Research 133 (2017) 310–333
329
protocol allow the joints to sustain more cycles before failure. However, the specimens become more prone to very-low cycle fatigue effects.
Fig. 26. Mises stress distribution with out-of-plane column web deformation, for a global rotation of 84 mrad.
lead to higher degradation levels in the joints subjected to the ECCS load protocol, see Fig. 28. The lower amplitudes obtained with AISC load
5.3.3. Shear results Similar to the previous sub-section, it is possible to obtain the sheardistortion (V-γ) relationships by applying the methodology described in Section 5.2. As shown in Fig. 29, the stress fields for the joints with and without column web stiffeners are quite similar, although, in the presence of the transverse web stiffeners, the shear stress is confined by the stiffeners and the flanges, while it is more spread in the case of the unstiffened column web. Fig. 30 depicts the derived relationships and compares the results with and without transverse web stiffeners. Note that, in the case of the E3-TB-E_cyc_M3_ts0 joint, the out-of-plane deformation is also noticeable, preventing the web to reach the same level of distortion and shear strength as the joint with stiffeners. These out-of-plane deformations detected in the column web, after a global rotation of 35 mrad, have a strong influence on the degradation of the shear strength in the column web.
E3-TB-E_cyc_M3_ts0
E3-TB-E_cyc_M3_ts30 Fig. 27. Evolution of the normal (σ33) and shear (τ23) stress for a half-cycle.
H. Augusto et al. / Journal of Constructional Steel Research 133 (2017) 310–333 5000 4000 3000 2000 1000 0 -1000 -2000 -3000 -4000 -5000
8000 E3-TB-E-M3-ts0
J1_1_pv1_tp18_ts0
Stiffness (N/mm)
Force (kN)
330
7000 6000 5000 4000 3000 2000 1000
E3-TB-E-M3-ts0
J1_1_pv1_tp18_ts0
0 0
5
10
15
20
25
0
30
5
10
15
Cycles
20
25
30
Cycles
Fig. 28. Comparison of the strength and stiffness degradation for the F-Δ relationship for the group of bolt rows 1, 2 and 3.
The column web panel in shear also shows differences in the response due to the load protocol applied to the joints. The ECCS load protocol is more severe so the difference between stable cycles is larger than in the joints subjected to the AISC load protocol. Fig. 31 represents the evolution of the peak strength and stiffness (measured in the unloading branch) for the stiffened joints. The results show that no degradation is detected and that the ECCS load protocol is more severe than AISC load protocol in the first cycles. Conversely, a small degradation of stiffness can be observed in the E3 joint. The behaviour in positive and negative shear stress is similar, as expected, due to the symmetry of the joints. Since the bare shear resistance of the column web panel is independent of the presence of transverse web stiffeners, the additional resistance that is observed is a result from the contribution of the frame action provided by the column flanges and the transverse web stiffeners. The evolution of the bending moment (Mfc) in the flanges against the web rotation is depicted in Fig. 32. Note that the stress distribution near the bolts row in tension and compression is influenced by the presence of the holes in the flange, resulting in a shift of the position of the
5.4. Methodology overview A methodology to extract the column web components response was presented and explained in the previous sections, the methodology was also applied to several joints. The objective of this section is to summarize, in a walk-through, the proposed methodology. Table 8 summarises the steps required for the application of the methodology. 6. Conclusions This paper proposes a procedure for the mechanical characterization of the cyclic behaviour of components in double-extended beam-to-column joints using a calibrated finite element model capable of representing the cyclic behaviour of extended end-plate joints. The model developed in ABAQUS uses solid (or continuum) elements in
350
J1_1_pv1_tp18_ts0
250
250
150
150
50 -50 0
100
200
300
-150
23 (N/mm2)
23 (N/mm2)
350
plastic hinge towards the bolts row alignment. For that reason, paths P6 and P7 are considered aligned with the bolts holes, although in the transition between tension and compression this shift is not so notorious, as observed in Fig. 33.
-50 0
350
E3-TB-E_cyc_M3_ts0
250
250
150
150
50 -50 0 100 200 300 400 500
200
300
-250
-250
(a)
E3-TB-E_cyc_M3_ts30
-50 0 100 200 300 400 500 -150
hshc (mm)
hshc (mm)
50
-150
-350
100
-150
-350
hshc (mm)
23 (N/mm2)
23 (N/mm2)
350
50
-250
-250 -350
J1_1_pv1_tp18_ts20
-350
hshc (mm)
(b)
Fig. 29. Shear stress fields for increasing levels of bending moment: (a) unstiffened and (b) stiffened column web.
J1_1_pv1_tp18_ts20 J1_1_pv1_tp18_ts0
1250 1000 750 500 250 0 -250 -500 -750 -1000 -1250
3000
331
E3-TB-E_cyc_M3_ts0 E3-TB-E_cyc_M3_ts30
2000 1000
V (kN)
V (kN)
H. Augusto et al. / Journal of Constructional Steel Research 133 (2017) 310–333
0 -1000 -2000 -3000
-40
-30
-20
-10
0
10
20
30
40
-50
-30
-10
(mrad)
10
30
50
(mrad) Fig. 30. V-γ behaviour for the shear load.
5000
1000000 E3-TB-E-M3-ts30
J1_1_pv1_tp18_ts20
Stiffness (N/mm)
4000
Force (kN)
3000 2000 1000 0 -1000
800000 600000 400000 200000
-2000
E3-TB-E-M3-ts30
J1_1_pv1_tp18_ts20
0
-3000 0
5
10
15
20
25
0
30
5
10
15
Cycles
20
25
30
Cycles
Fig. 31. Comparison of the strength and stiffness degradation for the V-γ relationship.
M(P4)
M(P5)
M(P6)
40
M(P7)
6
30
4
20
Mpf (kNm)
Mpf (kNm)
8
2 0
M(P4)
M(P5)
M(P6)
M(P7)
10 0
-10
-2 -4
-20
-6
-30 -40
-8 -50 -40 -30 -20 -10
0
10
20
30
40
50
(mrad)
(a) J1_1_pv1_tp18_ts20
-50 -40
-30 -20 -10
0
10
20
30
40
(mrad)
(b) E3-TB-E_cyc_M3_ts30
Fig. 32. Evolution of bending moment (Mfc) in the flanges against the web distortion (γ).
(a) DT20U2 = -60.22 mm; M = 385.50 kNm
(b) DT20U2 = -35.38 mm; M = 66.05 kNm
Fig. 33. Normal stress fields in the column flanges for different levels of bending moment.
50
332
H. Augusto et al. / Journal of Constructional Steel Research 133 (2017) 310–333
the connection zone. For computational efficiency, beam elements are used in the column and beam regions located away from the connection. The model considers non-linear material and geometrical behaviour, non-linear contact, re-contact and slip. A material model combining both isotropic and kinematic hardening was employed. The model was calibrated against experimental tests carried out at the University of Coimbra on double extended end-plate beam-to-column joints. The experimental tests were presented and the results were analysed, for the global joint behaviour and at the component level. The good agreement between the experimental data and the numerical results allowed concluding that the model is capable of simulating accurately the behaviour of end-plate beam-to-column joints, and that it can be used in detailed analyses of the behaviour of the connection components. A versatile and efficient methodology for the extraction of the cyclic behaviour of the web panel components from experimental tests and numerical simulations was presented, applicable to bolted end-plate joints, but extensible to other joint configurations. The methodology uses the integration of stress fields from the FE models of the joints, namely the column web panel in shear and the column web in transverse compression or tension components. The accuracy of the methodology depends on the column web element size and the number of stress fields analysed from the available load increments. Finally, it was highlighted that the procedure is very flexible in terms of the definition of the integration boundaries; in particular, and in line with the definition of the components in EC3-1-8, the boundaries may be different for tension or compression, therefore generating tension or compression cyclic F-Δ curves only. Double-extended end-plate joints, with and without transverse web stiffeners, and subjected to different load protocols (ECCS and AISC 34110) were analysed and used to assess the proposed methodology. The results allowed concluding that the procedure is able to capture the behaviour of the column web under tension and compression, both for groups of bolts and for isolated bolt rows, as well as the shear-rotation behaviour, including the additional shear resistance provided by the stiffeners and achieved by the frame action developed by the column flanges and the stiffeners. The direct comparison of the behaviour of the joints, with and without stiffeners, shows that the procedure is able to capture the influence of these designs in the amplitude and shape of the force-displacement relationships. Moreover, the results also demonstrates that joints without stiffeners can develop out-ofplane deformations. This phenomenon was captured in the derived relationships, represented by the larger deformation observed in the last cycles, not following the growth trend due to the load increments. The presence of the transverse web stiffeners can avoid this undesired phenomenon, since the compression is directly transmitted to the stiffeners. The comparisons between the joints loaded according to the ECCS load protocol with those subjected to the AISC 341-10 load protocol allowed concluding that the ECCS load protocol is more severe than the AISC one. This is partly due to the pre-processing procedure to assess the elastic limit of the joint that is required by the ECCS load protocol and used in the definition of the cycles' amplitudes. This is reflected in a loading sequence that imposes a smaller number of cycles before plastic deformation is achieved in the joint, however, on the other hand, greater amplitudes between cycles are applied after yielding of the joint. Even though the double-extended end-plate steel joints analysed in this paper fall out of the scope of Eurocode 8, due to the excessive contribution of the column web panel to the plastic deformation of the joint, the specific characteristics of the joints allowed to analyse and characterize in detail the cyclic behaviour of the column web components. The force-displacement relationships obtained revealed a cyclic stable behaviour and high energy dissipation capacity, mostly provided by the column web panel in shear. The proposed procedure revealed to be an excellent tool to obtain the isolated behaviour of the components
of the column web panel, and it can be extended to other components such as the beam and column flange in compression or the beam web in tension.
Acknowledgment This work was partially financed by FEDER funds through the Operational Competitiveness Programme – COMPETE and by national funds through FCT – Foundation for the Science and Technology within the scope of the project POCI-01-0145-FEDER-007633 and also within QREN - POPH - Typology 4.1 – Advanced Education, funded by the European Social Fund and Portuguese national funds MEC, under contract grants SFRH/BD/91167/2012, for the first author. It has also been partially funded by the following research Projects: FREEDAM under research grant RFSR-CT-2015-00022 and EQUALJOINTS under the research grant agreement no. RFSR-CT-2013-00021. References [1] CEN, EN 1993–1-8, Eurocode 3: Design of Steel Structures – Part 1–8: Design of Joints, May 2005, Standardization, Brussels, European Committee for, 2005. [2] C. Bernuzzi, R. Zandonini, P. Zanon, Experimental analysis and modelling of semirigid steel joints under cyclic reversal loading, J. Constr. Steel Res. 38 (2) (1996) 95–123. [3] CEN, EN 1998-1. Eurocode 8: Design of Structures for Earthquake Resistance – Part 1: General rules, December 2004, Standardization, Brussels, European Committee for, 2004. [4] J. Shen, A. Astaneh-Asl, Hysteretic behaviour of bolted-angle connections, J. Constr. Steel Res. 51 (1999) 201–218. [5] ABAQUS User's, Theory and Scripting Manuals. ABAQUS, Inc., Dassault Systèmes Simulia Corp., Providence, USA; 2014. [7] A. Plumier, J.B. Schleich, Seismic resistance of steel and composite frame structures, J. Constr. Steel Res. 27 (1993) 159–176. [8] D. Dubina, A.L. Ciutina, A. Stratan, Cyclic tests of double-sided beam-to-column joints, J. Struct. Eng. 127 (2) (2001) 129–136. [9] D. Dubina, A.L. Ciutina, A. Stratan, Cyclic testes on bolted steel and composite double-sided beam-to-column joints, Steel Compos. Struct. 2 (2) (2002) 147–160. [10] B. Guo, Q. Gu, F. Liu, Experimental behavior of stiffened and unstiffened end-plate connections under cyclic loading, J. Struct. Eng. 132 (9) (2006) 1352–1357. [11] P. Nogueiro, L. Simões da Silva, R. Bento, R. Simões, Numerical implementation and calibration of a hysteretic model with pinching for the cyclic response of steel joints, Int. J. Adv. Steel Constr. 3 (1) (2007) 459–484. [12] T.J. Sullivan, G.J. O'Reilly, Characterising the Seismic Behaviour of Steel Beam-Column Joints for Seismic Design, IUSS press, Pavia, Italy, 2014. [13] R.W. Clough, S.B. Johnston, “Effect of Stiffness Degradation on Earthquake Ductility Requirements”, Proceedings of Second Japan National Conference on Earthquake Engineering, 1966 227–232. [14] E.P. Popov, R.B. Pinkney, “Behavior of Steel Building Connections Subjected to Inelastic Strain Reversals”, Bull No. 13 (Nov.), American Iron and Steel Institute, University of California at Berkeley, 1968. [15] F.M. Mazzolani, Mathematical model for semi-rigid joints under cyclic loads, in: R. Bjorhovde, et al., (Eds.), Connections in Steel Structures: Behaviour, Strength and Design, Elsevier Applied Science Publishers, London 1988, pp. 112–120. [16] A. De Martino, C. Faella, F.M. Mazzolani, “Simulation of Beam-to-Column Joint Behaviour Under Cyclic Loads”, Construzioni Metalliche, 6, 1984 346–356. [17] G. Della Corte, G. De Matteis, R. Landolfo, F.M. Mazzolani, Seismic analysis of MR steel frames based on refined hysteretic models of connections, J. Constr. Steel Res. 58 (10) (2002) 1331–1345. [18] L.F. Ibarra, R.A. Medina, H. Krawinkler, Hysteretic models that incorporate strength and stiffness deterioration, Earthq. Eng. Struct. Dyn. 34 (12) (2005) 1489–1511. [19] D. Lignos, H. Krawinkler, Deterioration modeling of steel components in support of collapse prediction of steel moment frames under earthquake loading, J. Struct. Eng. 137 (11) (2011) 1291–1302. [20] O.S. Bursi, M. Galvani, “Low Cycle Behaviour of Isolated Bolted Tee Stubs and Extended End Plate Connections”, Proceedings of CTA, Italian Conference on Steel Construction, Ancona, Italy, 1997 110–121. [21] M. Sivaselvan, A.M. Reinhorn, Hysteretic models for deteriorating inelastic structures, J. Eng. Mech. ASCE 126 (6) (2000) 633–640. [22] G. Della Corte, G. De Matteis, R. Landolfo, Influence of connection modelling on seismic response of moment resisting steel frames, in: F.M. Mazzolani (Ed.), Moment Resistant Connections of Steel Buildings Frames in Seismic Areas, E. & F.N. Spon, London, UK, 2000. [23] L. Calado, C.A. Castiglioni, “Steel Beam-to-Column Connections Under Low-Cycle Fatigue Experimental and Numerical Research”, Eleventh World Conference on Earthquake Engineering, Paper No. 1227, 1996. [24] O.S. Bursi, F. Ferrario, V. Fontanari, Non-linear analysis of the low-cycle fracture behaviour of isolated tee stub connections, Comput. Struct. 80 (1) (2002) 2333–2360. [25] P.J. Madas, A.S. Elnashai, “A Component-Based Model for Beam-to-Column Connections”, Proceedings of. 10th World Conference on Earthquake Engineering, 19–24 July, Vol. 8, Madrid, Spain, 1992.
H. Augusto et al. / Journal of Constructional Steel Research 133 (2017) 310–333 [26] L. Simões da Silva, C. Rebelo, L. Mota, Extension of the component method to endplate beam-to-column steel joints subjected to seismic loading, Trends in Civil and Structural Engineering Computing, Computational Science, Engineering and Technology Series 22, Saxe-Coburg Publications, UK 2009, pp. 149–167. [27] M. Latour, V. Piluso, G. Rizzano, Cyclic modeling of bolted beam-to-column connections: component approach, J. Earthq. Eng. 15 (4) (2011) 537–563. [28] L. Simões da Silva, A. Shahbazian, F. Gentili, H. Augusto, “Implementation of a Component Model for the Cyclic Behaviour of Steel Joints”, Proceedings of Eighth International Workshop on Connection in Steel Structures, Boston, USA, 2016. [29] J.P. Jaspart, “Étude de la Semi-Rigidité des Noeuds Poutre-Colonne et son Influence sur la Resistence et la Stabilité des Ossatures en Acier”. PhD Thesis, Faculty of Applied Sciences, University of Liège, Belgium, 1991 (in French). [30] J.M. Castro, F.J. Davila-Arbona, A.Y. Elghazouli, Seismic design approaches for panel zones in steel moment frames, J. Earthq. Eng. 12 (S1) (2008) 34–51. [31] H. Augusto, L. Simões da Silva, C. Rebelo, J.M. Castro, Characterization of web panel components in double-extended bolted endplate steel joints, J. Constr. Steel Res. 116 (2016) 271–293. [32] H. Krawinkler, V.V. Bertero, E.P. Popov, Shear behaviour of steel frame joints, J. Struct. Eng. ASCE 101 (ST11) (1975) 2317–2336. [33] J.P. Jaspart, “Shear and Load-Introduction Deformability and Strength of Column Web Panels in Strong Axis Beam-to-Column Joints”, Internal Report MSM, n° 202, University of Liége, 1990 (April). [34] K.D. Kim, M.D. Engelhardt, Monotonic and cyclic loading models for panel zones in steel moment frames, J. Constr. Steel Res. 58 (2002) 605–635.
333
[35] Y.F. Dafalias, “On cyclic and Anisotropic Plasticity: (I) A General Model Including Material Behavior Under Stress Reversals. (II) Anisotropic Hardening for Initially Orthotropic Materials”. PhD Thesis, Department of Civil Engineering, University of California, Berkeley, CA, 1975. [36] N.G. Cofie, H. Krawinkler, Uniaxial cyclic stress–strain behavior of structural steel, J. Eng. Mech. ASCE 111 (9) (1985) 1105–1120. [37] M. Latour, V. Piluso, G. Rizzano, “Cyclic Model of Beam-to-Column Joints”, Proceedings of 5th Steel Conference, EUROSTEEL 2008, Graz, Austria, 2008. [38] J.L. Chaboche, Time independent constitutive theories for cyclic plasticity, Int. J. Plast. 2 (2) (1986) 149–188. [39] P. Nogueiro, “Cyclic Behaviour of Steel Connections”. PhD Thesis, Civil Engineering Department, University of Coimbra, Portugal (in Portuguese), 2009. [40] CEN, EN 1993-1-1. Eurocode 3: Design of Steel Structures – part 1–1: General Rules and Rules for Buildings, May 2005, Standardization, Brussels, European Committee for, 2005. [41] ECCS, Recommended Testing Procedure for Assessing the Behaviour of Structural Steel Elements Under Cyclic Loads. Technical Committee 1, TWG 1.3 – Seismic Design, publ. n.° 45, European Convention for Constructional Steelwork, Brussels, Belgium, 1986. [42] AISC, Seismic Provisions for Structural Steel Buildings, ANSI/AISC 341–10, USA, American Institute of Steel Construction, Chicago, 2010.
Contents lists available at ScienceDirect
Journal of Constructional Steel Research
Cyclic behaviour characterization of web panel components in bolted end-plate steel joints Hugo Augusto a,⁎, Luís Simões da Silva a, Carlos Rebelo a, José Miguel Castro b a b
Institute for Sustainability and Innovation in Structural Engineering (ISISE), Department of Civil Engineering, University of Coimbra, Polo II, Rua Luís Reis Santos, 3030-788 Coimbra, Portugal Department of Civil Engineering, Faculty of Engineering, University of Porto, Rua Dr. Roberto Frias, s/n, 4200-465 Porto, Portugal
a r t i c l e
i n f o
Article history: Received 12 August 2016 Received in revised form 21 January 2017 Accepted 24 January 2017 Available online xxxx Keywords: Steel joints Cyclic behaviour Column web panel End-plate Component method Finite element analysis
a b s t r a c t This paper addresses the characterization of the behaviour of the column web panel components in bolted endplate steel joints subject to cyclic loading. Based on experimental test results, a calibrated parametric FE model of a double extended beam-to-column end-plate steel joint is implemented, that allows characterizing the behaviour of the joints both globally and in terms of the dissipative components. The numerical models have been developed using the ABAQUS FE package considering a detailed representation of the various joints components and taking into account the different sources of geometrical and material nonlinearities. Finally, based on the integration of the stress and displacement fields in predefined paths along the column web, a detailed extraction procedure for the cyclic force-deformation behaviour of the column web panel components is proposed, however extensible to other components. These relationships are needed for implementation in a components based approach that accounts for cyclic loading conditions. © 2017 Published by Elsevier Ltd.
1. Introduction Partial-strength joints subject to static monotonic loading are well characterized in modern codes of practice, such as Eurocode 3 part 1– 8 (EC3-1-8) [1] within the framework of the component method. However, in the presence of cyclic load reversals there is no direct and easy approach to characterize their cyclic behaviour and energy dissipation. This need mostly results from the seismic action, where the cyclic behaviour of the members and connections play an important role, along with ductility, tenacity, rotation capacity or energy dissipation of the dissipative members or joints. When partial-strength joints are used in steel moment-resisting frames (MRF), there may be a shift of the plastic hinge location from the beams or columns to the joints. When this shift occur, it is of critical importance to take into account the characteristics of beam-to-column joints. The use of partial-strength joints is a common and relatively low cost solution to apply in MRF, in comparison with their full-strength counterparts. Previous studies have shown that, if adequately detailed, these connections may also become attractive alternatives for structures located in seismic regions, allowing a precise control of the location and response of the dissipative elements [2]. Furthermore, Shen and Astaneh-Asl [4] argued that, when properly designed, bolted joints ⁎ Corresponding author. E-mail addresses: [email protected] (H. Augusto), [email protected] (L. Simões da Silva), [email protected] (C. Rebelo), [email protected] (J.M. Castro). URL's: http://www.uc.pt/fctuc (H. Augusto), http://www.fe.up.pt (J.M. Castro).
http://dx.doi.org/10.1016/j.jcsr.2017.01.021 0143-974X/© 2017 Published by Elsevier Ltd.
may exhibit high ductility and good energy-dissipation capacity under cyclic loading, providing that brittle components have sufficient overstrength in order to prevent undesirable failure modes. In this case, proper assessment of the behaviour is crucial due to the controlling role that these joints will play, as the main dissipative components in the structure, in the structural response during a seismic event. In fact, design codes, such as Eurocode 8 (EC8) [3], allow the use of partial-strength joints, providing that a set of design requirements is met. Firstly, advanced structural analyses are required, such as non-linear static (pushover) or non-linear time history analyses, although detailed information is missing concerning the adoption of these types of analyses, particularly when dealing with steel frames with partialstrength connections. Additionally, EC8 (sections 6.5.5(6), 6.5.5(7) and 6.6.4(4)) requires experimental evidence of the behaviour of the joints whenever dissipative connections are considered in the seismic design process, which is very difficult to accomplish in design practice. It is therefore clear that this kind of joints require more research to achieve adequate detailed guidance to overcome these difficulties. The findings in the research presented in this paper can contribute to the development of a simplified design method for partial-strength steel joints. Based on the component method, which takes directly into account the cyclic behaviour of each dissipative component and, simultaneously, provides adequate overstrength for the non-dissipative components (capacity design), thus ensuring that the idealized behaviour of the joint can be considered in the global analysis of the structure in a simplified manner. However first is necessary to extract the behaviour of the basic components.
H. Augusto et al. / Journal of Constructional Steel Research 133 (2017) 310–333
This paper aims to contribute to the mechanical characterization of components in double-extended beam-to-column joints using a detailed parametric numerical model developed in ABAQUS [5] taking advantage of the Python scripting interface in ABAQUS. The model is applied to end-plate beam-to-column joints and considers a three dimensional detailed representation of the various joint components taking into account several phenomena involved in the connection behaviour, namely the nonlinearities related to the geometry, contact and material properties. A combined isotropic and kinematic materialhardening model is used. The calibration of the numerical model, which is based on the results of an experimental research programme, is comprehensively described in this paper.
a) Global FE model
In the following sections, the cyclic behaviour of the joints is characterized, both at the global joint response and in terms of the critical components, comparing the results of the experimental and numerical models. Using the validated FE models, a detailed procedure is described to isolate the column web components under cyclic loading, namely the column web panel in shear and the column web in transverse compression or tension, and to identify their mechanical behaviour analysing the stress and deformation fields in the FE models. The derived force-displacement relationships, of the individual dissipative components, can be directly applied to a mechanical model of the joint, to characterize its behaviour, provided it is ensured that the non-dissipative components remain elastic.
b) Detail of the cross sections of the wire elements Fig. 1. Meshed parts of the FE model.
300
18 15
50 40 60
15 8
8
Ø26 M24 (10.9)
360 IPE360 (S355)
540
240
8 60 40 50
HEA320 (S355)
15
55 110 55 220
310
Fig. 2. Detail of the joint for Groups 1 and 2.
300
18 12 8 360 IPE360 (S355) 12
50 40 60
15 8 Ø26 M24 (10.9)
540
240
8 60 40 50
HEB320 (S355) 320
311
55 110 55 220 Fig. 3. Detail of the joint for Group 3.
c) Detailed view of the Joint zone
312
H. Augusto et al. / Journal of Constructional Steel Research 133 (2017) 310–333
6 5 4 3 2 1 0 -1 -2 -3 -4 -5 -6
2. Literature review
A considerable amount of experimental work was carried out in the past to characterize the cyclic behaviour of steel joints in several fields of application. Focussing on the cyclic behaviour of the column web panel: Plumier & Schleich [7] studied the contribution of the column shear panel to the energy dissipation, strength and rotation capacity of the joints. The studies undertaken by Dubina et al. [8,9] analysed the influence of symmetric and antisymmetric cyclic loading, concluding that the loading type influence occurs mainly through the contribution of the panel zone. The work developed by Guo et al. [10] on the cyclic behaviour of stiffened and unstiffened extended end-plate connections of beam–column joints allowed concluding that the column web stiffeners have a remarkable influence, contributing to increase the strength of the joint as well as the energy dissipation capacity. A detailed review of the experimental work on steel joints subjected to cyclic loading may be found in Nogueiro et al. [11] and Sullivan and O'Reilly [12].
y
2.1. Past experimental work in the cyclic behaviour of the column web panel
J-n.2 (S1)
Table 1 Bolted beam-to-column double extended end-plate joints test programme. Group
J1
J2
J3
J4
Test
Beam
Column
type
Bending
Axial
J1.1 J1.2 J1.3 J1.4 J2.1 J2.2 J2.3 J3.1 J3.2 J3.3 J4.1 J4.2 J4.3
IPE360 IPE 360 IPE 360 IPE 360 IPE360 IPE 360 IPE 360 IPE360 IPE 360 IPE 360 HEA280 HEA 280 HEA 280
HEA320 HEA 320 HEA 320 HEA 320 HEA320 HEA 320 HEA 320 HEB320 HEB 320 HEB 320 HEA320 HEA 320 HEA 320
Monotonic Cyclic S1 Cyclic S2 Cyclic SA Monotonic Cyclic S1 Cyclic S2 Monotonic Cyclic S1 Cyclic S2 Monotonic Cyclic S1 Cyclic S2
MM-/M+ M-/M+ M-/M+ MM-/M+ M-/M+ MM-/M+ M-/M+ MM-/M+ M-/M+
N- (800 kN) N- (1200 kN) N- (800 kN) -
the energies dissipated by the various joint components. More recently, Simões da Silva et al. [28] detailed a cyclic component model fully compatible with the static monotonic implementation in EC3-1-8 [1]. 2.3. Characterization of the column web panel components A bolted beam-to-column steel joint may be divided in two main parts: column web panel and connection(s) (left and/or right beams). In many situations, the column web panel controls the behaviour of the joint, usually providing large energy dissipation under cyclic loading conditions. However, the associated local distortion may impair the global stability of the frame by inducing excessive second-order effects. Consequently, design codes usually impose limits on the contribution of the column web panel to dissipate energy [30]. The characterization of the behaviour of the column web panel under static monotonic loading conditions was described in detail by the authors in [31], the fundamental works of Krawinkler et al. [32] and Jaspart and his co-workers [29,33] being emphasized there. In
300 18 12 8 270 HEA280 (S355) 12
50 40 60
15 Ø26 M24 (10.9)
8 450
150
8 60 40 50
HEA320 (S355) 310
70
160
Cycles
Fig. 5. Cyclic loading strategies used in the experimental tests.
2.2. Review of models to characterize the cyclic behaviour of joints The extensive experimental research work on the cyclic behaviour of steel joints led to the development of several approaches to establish, and ultimately to predict, the behaviour of steel joints under cyclic loading. Many authors proposed mathematical models (bilinear hysteretic, Ramberg-Osgood based models, Richard-Abbott based models or multi-linear deterioration models) to fit the global moment-rotation curves of steel joints [13–22]. In addition to the mathematical formulations described above, some authors focused on establishing empirical damage accumulation laws to assess the low-cycle fatigue behaviour of steel joints. Calado and Castiglioni [23] developed a cumulative damage model and a general failure criterion to assess the low-cyclic fatigue of steel joints. Bursi et al. [24] studied the fracture behaviour of isolated T-stub connections with partial fillet welds, and characterized cracks for the low-cyclic fatigue assessment of isolated T-Stubs of steel joints. Finally, there is a growing interest on the implementation of cyclic component models, whereby the global moment-rotation behaviour of the joint is obtained from the cyclic behaviour of the individual components. Mechanical models, such as those developed by Madas and Elnashai [25], can be considered one of the first attempts to apply the component approach to characterize the cyclic behaviour of beam-tocolumn joints. Simões da Silva et al. [26] proposed an extension to the component method for the cyclic behaviour of end-plate joints. Latour et al. [27] proposed a simplified cyclic model based on a lumped approach for the tensile and compressive zones, considering that the overall energy dissipation of the connection can be obtained by summing
J-n.3 (S2)
70
Fig. 4. Detail of the joint for Group 4.
H. Augusto et al. / Journal of Constructional Steel Research 133 (2017) 310–333
according to the setup of the experimental tests used in the validation of the FE models. The development of the FE models and the finite element modelling options were already the subject of a detailed description and validation, under monotonic load, in [31]. Hence, only a brief description of the model is presented, addressing the particular features of the finite element modelling and validation of the cyclic behaviour. The models are composed by solid (mainly C3D8RH) finite elements in the joint region, due to the reduce integration formulation (only 1 Gauss point) at least 3 elements were consider in the thickness of the plates, to help avoiding the numerical problem hourglass associated to bending dominated problems [31]. Beam elements (B31) are used in the regions adjacent to the joint, i.e., in the beam and column segments, in order to reduce the computational time. The kinematic relations are transferred from the solid to the beam elements by multi-point constraint equations. The model and its parts are illustrated in Fig. 1, with the adopted mesh, namely the wire columns, the wire beam, the solid column, with or without stiffeners (the latter not represented in Fig. 1), and with the bolt holes in the flange, the solid beam with the corresponding fillet welds, the end-plate with the bolt holes and the bolts composed by the shank, head and nut. The various parts interact with each other by continuity links, called constraints in ABAQUS (e.g. between the beam and the end-plate) or defining contact properties, called interactions in ABAQUS (e.g. between the end-plate and the column flange), to form the beam-to-column end-plate joint structural model.
Table 2 Cyclic loading strategies. Cycle
Stategy 1 (S1)
Strategy 2 (S2)
1 2 3 4 (and following) 20 (and following) 40 (and following, and so on)
0.75θy 1.5θy 2.25θy 3.0θy 3.0θy + 2.5*1mrad 3.0θy + 2.5*2mrad
1.5θy 3.0θy 4.5θy 6.0θy 6.0θy 6.0θy
313
particular, it is important to highlight the deformation modes in the web panel, namely the transverse deformation, due to the beam moment resulting force couple (Fb = Mb/(hb − tfb)), and the distortion due to the pure shear introduced in the panel and the frame-type behaviour for transversely-stiffened web panels. Concerning the cyclic behaviour of components, Kim and Engelhardt [34] proposed a model to characterize the behaviour of the column web panel in shear under cyclic loading. It is a model based on the Dafalias' [35] bounding surface theory, that uses the Cofie and Krawinklers's [36] rule for the movement of the bound line. Moreover, it is assumed that the moment-rotation relationship of the panel zone can be determined from its material properties using the Cofie's rule. Simões da Silva et al. [26] applied the Richard-Abbot model to simulate the cyclic behaviour of individual components, such as the column web panel in shear and the end-plate in bending. Finally, Latour et al. [37] extended the application of the Kim and Engelhardt model to the load introduction components. However, they did not separate load introduction in tension and in compression, therefore disregarding the fact that, in bolted joints, tension is transferred by the bolts at discrete positions while compression is transferred within a tributary area, approximately centred on the beam compressed flanges.
3.2. Material modelling For the material modelling, the combined isotropic/kinematic hardening model available in ABAQUS was adopted. This material model [38] uses the von Mises yield criterion and an associative flow rule is assumed. The isotropic component of the model defines the change of the size of the yield surface σ0 as a function of equivalent plastic strain εp, and is given by:
3. Numerical modelling 3.1. Modelling overview
P σ 0 ¼ σ j0 þ Q ∞ 1−e−biso ε
The numerical model developed in ABAQUS [5] consists of a representative part of a MRF structure, composed by a column and a beam connected to each other by means of an end-plate welded to the beam and bolted to the column flange. This is representative of an external node of a MRF with double-extended end plate joints. The lengths of the beam (approx. 1.2 m) and the column (approx. 3 m) are established
ð1Þ
where σ|0 is the yield stress at zero equivalent plastic strain, Q∞ is the maximum change in the size of the yield surface and biso is the rate at which the size of the yield surface changes as the plastic strain increases.
Table 3 Bolted beam-to-column double extended end-plate joints test programme. Test
Loading strategy
Failure mode
−Mmax (kNm)
+Mmax (kNm)
n.° of cycles
−Rot.max (mrad)
+Rot.max (mrad)
Total energy (kNm × mrad)
J1.2 J1.3 J1.4 J2.2 J2.3 J3.2 J3.3 J4.2 J4.3
S1 S2 SA S2 S2 S1 S2 S1 S2
Weld Weld Cracking EP Weld Weld Cracking EP Weld Weld Weld
−335 −362 −333 −353 −358 −408 −421 −290 −310
+340 +352 +378 +365 +368 +418 +431 +276 +295
83 22 28 27 27 26 13 54 34
−23 −28 −28 −24 −30 −19 −21 −27 −35
+16 +21 +19 +22 +21 +17 +26 +30 +35
435,156 293,979 201,946 368,538 382,945 215,156 195,075 448,850 505,611
Table 4 Geometrical properties of the FE models.
J1.3 J3.2 J4.3
Column
Beam
ht (mm)
Lc (mm)
Lc1 (mm)
Lc2 (mm)
Lc3 (mm)
L1 (mm)
L2 (mm)
Lb1 (mm)
d (mm)
HEA320 HEB320 HEA320
IPE360 IPE360 HEA280
3220 3260 3260
3000 3040 2894
1395 1395 1249
720 740 690
885 905 955
1331 1320 1329
1355 1385 1483
467 468 357
1175 1160 1173
314
H. Augusto et al. / Journal of Constructional Steel Research 133 (2017) 310–333
The kinematic component of the model defines the changes of backstress α, which is expressed as: α¼
Table 7 Main features of the achieved F-Δ relationships.
Sini (kN/mm) Δmax (mm) Δmin (mm) Fmax (kN) Fmin (kN)
Joint
C kin P P þ 1−e−γε þ α 1 e−γε γ
ð2Þ
where Ckin and γ are material constants. The ratio Ckin/γ represents the maximum change in backstress and γ determines the rate at which the backstress changes as the plastic strain increases. Monotonic coupon tensile test results were used to derive key coordinates in the stress-strain relationship. Elastic-plastic constitutive material laws were used in all parts of the model, non-linear in the solid elements and tri-linear in the beam elements.
J1_1_pv1_tp18_ts0
J1_1_pv1_tp18_ts20
3.3. Analysis procedures The analyses were performed using the ABAQUS/Standard solver that iteratively solves a system of equilibrium equations implicitly for each solution increment, using Newton's method to solve nonlinear problems and the stiffness method to solve linear problems [5]. Second-order effects were considered in all the analyses to account for large displacement effects. Due to the several nonlinearities present in the models, namely material nonlinearity, geometric nonlinearity and contact nonlinearity, general analysis steps were adopted with automatic control for the increments, i.e. the increment size was determined according to the response of the model.
E3-TB-E_cyc_M3_ts0
4. Validation of the numerical models 4.1. Experimental tests E3-TB-E_cyc_M3_ts30
A set of experimental tests [39] carried out at the University of Coimbra were used to calibrate the numerical model. The tested joints were designed aiming to study the behaviour of several external bolted beam-to-column partial-strength joint typologies with double extended end-plates. The relevant features of these tests are shortly described in the following paragraphs and presented in detail in [39]. The experimental programme comprised thirteen external doubleextended bolted end-plate joints, see Table 1. It was divided in four groups, whereby the column section size and/or the beam size were varied, as well as the presence of axial force in the column in group J2, as shown in Table 1. The joint's details are illustrated in Figs. 2–4. In each group, the first test was performed under monotonic loading. The results were analysed in detail in [31]. Two additional
Group 1, 2
2575
0.62
-1.78
887.1
-874.9
Group 3, 4
3304
0.80
-1.65
891.4
-867.6
Row 1
1847
0.30
-1.36
562.1
-654.8
Row 2
1551
1.54
-1.14
325.0
-297.0
Row 3
2011
1.61
-1.04
388.9
-330.7
Row 4
1669
0.39
-1.27
502.5
-610.9
Group 1, 2
3519
0.10
-0.10
380.5
-373.0
Group 3, 4
5726
0.10
-0.09
377.2
-369.7
Row 1
2126
0.09
-0.22
293.1
-367.9
Row 2
1718
0.86
-0.03
147.6
-284.7
Row 3
2277
0.92
-0.03
165.0
-292.4
Row 4
2055
0.10
-0.22
263.7
-344.3
Group 1, 2, 3
3971
0.56
-13.21
3349.7
-3888.6
Group 4, 5, 6
5530
0.74
-7.35
2599.7
-3697.6
Row 1
2991
0.24
-10.00
1888.2
-2308.0
Row 2
2000
2.99
-10.94
965.4
-949.3
Row 3
948
5.39
-5.90
778.9
-901.7
Row 4
1739
5.19
-2.22
593.7
-708.9
Row 5
2150
3.36
-5.64
994.2
-1052.2
Row 6
2525
0.30
-5.27
1301.7
-2029.2
Group 1, 2, 3
4963
0.23
-0.27
1272.7
-1415.9
Group 4, 5, 6
9766
0.21
-0.23
1123.8
-1368.9
Row 1
3241
0.12
-0.24
554.5
-882.5
Row 2
2764
3.79
-0.12
845.4
-851.3
Row 3
607
6.64
-0.03
475.8
-801.1
Row 4
2288
5.50
-0.05
503.9
-772.3
Row 5
2029
3.60
-0.10
697.3
-689.1
Row 6
2813
0.12
-0.24
477.7
-740.9
tests, with two alternative cyclic loading protocols, were also performed, except in the first group where an additional cyclic test was conducted, J1.4, with arbitrary loading (SA). The two cyclic loading strategies, are illustrated in Fig. 5, and described in Table 2. The loading was applied in the vertical direction, at the end of the cantilever beam, by means of a 100 ton hydraulic actuator. The tests were carried out under displacement control, with a constant speed
Table 5 Comparison of the strength and maximum rotation between the experimental and numerical results.
J1.3 J3.2 J4.3
−Mrd (Exp.) (kNm)
−Mrd (FE) (kNm)
Error (%)
−Mrd (Exp.) (kNm)
−Mrd (FE) (kNm)
Error (%)
−Rot.max (Exp.) (mrad)
−Rot.max (FE) (mrad)
Error (%)
+Rot.max (Exp.) (mrad)
+Rot.max (FE) (mrad)
Error (%)
−362 −408 −310
−373 −416 −298
+2.9 +1.9 −3.9
+352 +418 +295
+364 +414 +295
+3.3 −1.0 +0.0
−24 −17.7 −35
−22.5 −17.7 −35
−6.3 0.0 +0.0
+19 +15.7 +32
+18.5 +16.6 +32
−2.6 +5.4 +0.0
Table 6 Geometrical properties of the FE models.
J1_1-pv1_tp18_ts0 J1_1_pv1_tp18_ts20 E3-TB-E-M3-ts0 E3-TB-E-M3-ts30
Column
Beam
ht (mm)
Lc (mm)
Lc1 (mm)
Lc2 (mm)
L1 (mm)
L2 (mm)
Lb1 (mm)
d (mm)
HEA320 HEA320 HEB500 HEB500
IPE360 IPE360 IPE600 IPE600
3220 3220 3500 3500
3000 3000 3200 3200
1395 1395 995 995
720 720 1210 1210
1331 1331 2600 2600
1355 1355 1750 1750
467 467 780 780
1175 1175 2350 2350
H. Augusto et al. / Journal of Constructional Steel Research 133 (2017) 310–333
of 0.02 mm/s for the monotonic tests, 0.2 mm/s for the first cyclic tests and 0.4 mm/s for the second cyclic tests. Group 2 was tested with a constant level of axial force in the column: (i) 800 kN,
315
corresponding to 18% of the plastic axial resistance of the column; and (ii) 1200 kN, corresponding to 27% of the plastic axial resistance of the column section.
Table 8 Methodology overview. Step
Action
1
Development of the FE model of the joint
1.1 1.2 2 2.1
Validation of the model Selection of the component model and active components Extraction of the components column web in tension and compression Definition of the stress paths P1 and P2
2.1.1 2.1.2 2.2 2.2.2 2.2.1
P1 P2 Extraction of the normal stresses (σzz) along P1 Determination of the integration boundaries (IB1 to IBn) Determination of the forces through integration of σzz over the lengths hc for compression and ht. for tension
2.3 2.3.1
Extraction of the displacements fields along P1 and P2 Determination of the deformation of the web
2.4
Derivation of the force-deformation curve for the integration boundaries chosen
3 3.1 3.2 3.2.2
Extraction of the component column web panel in shear Definition of the stress path P3 Extraction of the normal stresses (τyz) in P3 Determination of the integration boundaries
3.2.1
Determination of the shear forces by integration of τyz over the lengths defined for the shear area.
3.3 3.3.1
Extraction of the displacements in four orthogonal points in the web Determination of the horizontal rotation of the web
3.3.2
Determination of the vertical rotation of the web
Tools/comments
Experimental results or proper benchmark
Defined in the column web after the flange to web radius Near the connected flange Opposite flange For the selected load increments of the FE analysis According to the mechanical model, see also Fig. 14
For the selected load increments of the FE analysis δcw ¼ δP1 δP2 (usually aligned with the element that causes the deformation, e.g. bolt rows, flanges, etc.) For each selected load increment relate the calculated forces with the computed deformation F-δcw See Fig. 15 (a) For the selected load increments of the FE analysis According to the shear area adopted (for the EC3 shear area see also Fig. 15 (b))
For the selected load increments of the FE analysis, see also Fig. 15 (a) θh ¼ a tan DT1V3 DT2V3 d3 θv ¼ a tan DT3V2 DT4V2 d4
3.3.3 3.4 3.4.1 3.4.1.1
Determination of the distortion of the web In the presence of transverse web stiffeners Definition of the hinges location in the column flanges P4, P5, P6 and P7 Definition of the extraction paths P4.1, P4.2, P4.3, P5.1, P5.2, P5.3, P6.1, P6.2, P6.3 and P7.1, P7.2, P7.3 3.4.2 Extraction of the normal stresses (σyy) in each path 3.4.2.1 Determination of the neutral axis using paths Pi.2 and Pi.3 3.4.2.2 Determination of the bending moments by integration of σyy over the width of the column flanges
3.4.3
Determination of the additional shear stress
3.5
Derivation of the force-deformation curve for the integration boundaries chosen
γ ¼ θ h þ θv Account for the additional shear strength See Fig. 16
For the selected load increments of the FE analysis Interpolating between the paths Pi.2 and Pi.3 where the stress becomes zero.
For each selected load increment relate the achieved shear forces with the achieved distortion
316
H. Augusto et al. / Journal of Constructional Steel Research 133 (2017) 310–333
Column
Fixedto the beam
DT1
DT5 Column Beam
d3
DT3 DT4 DT2
d DT11 DT7
L d1
Fixedto the beam
d4
TwoLoadingCells 20 Ton
d2 DT8
d5
Beam
DT17
DT14
DT15
DT12
DT20
DT19
DT10
L2
120100 500
DT16
DT9
DT6
DT18
DT13
1000 x
LVDT Loadcell
(a)
(b)
Fig. 6. a) Instrumentation apparatus, and b) detail of the instrumentation in the column web using a crosshead.
To extract the relevant test information, the prototypes were instrumented according to the scheme shown in Fig. 6. 4.2. Global behaviour of the joint
Bending moment (kNm)
The experimental moment-rotation curves are depicted in Fig. 7 for each group, using the results from the load cells and displacement transducers DT11 and DT12 for the groups J1 to J4 tests and DT20 for the
lesser instrumented J3.1. The analysis of the results of the J1 group allows concluding that, for all cyclic loading strategies, the hysteretic response was very stable. No pinching or strength degradation was detected and only slight stiffness degradation was observed (Fig. 7a). For joint configuration J2, no pinching or stiffness degradation was observed (Fig. 7b). For joint configuration J3, some strength degradation was observed; however, no pinching was detected (Fig. 7c). Failure occurred either by cracking of the end-plate (J.3.2) or cracking of the weld
600
600
400
400
200
200
0
0
-200
-200
-400
J1.4 (DT11-12) J1.2 (DT11-12)
-600 -40
-30
-20
-10
-400
J1.3 (DT11-12) J1.1 (DT11-12) 0
10
20
30
J2.3 (DT11-12) J2.1 (DT11-12)
-600 40
-40
-30
-20
-10
J2.2 (DT11-12) 0
10
Rot. (mrad)
Bending moment (kNm)
Bending moment (kNm)
200 0 -200 -400 -600
600 400 200 0 -200 -400
J4.3 (DT11-12) J4.1 (DT11-12)
-600 -30
-20
-10
40
(b) J3.2 (DT11-12)
400
-40
30
Rot. (mrad)
(a) J3.3 (DT11-12) J3.1 (DT20)
600
20
0
10
20
30
40
Rot. (mrad)
-40
-30
(c)
-20
-10
0
10
20
30
40
Rot. (mrad)
(d) Fig. 7. Experimental moment-rotation curves.
J4.2 (DT11-12)
H. Augusto et al. / Journal of Constructional Steel Research 133 (2017) 310–333
317
L1 Lc1
ht Lc Lc2
Column
d Beam disp.
Lb1
Lb2 Lb 2(Y)
Lc3
L2
3(Z) 1(X)
J1.3
J3.2
J4.3
Geometrical properties
Fig. 8. FE models used in the validation.
(J.3.3). Noticeable strength and stiffness degradation and pinching was observed for joint configuration J4 (Fig. 7d). Table 3 summarises the nine results obtained for all cyclic tests, including the identification of the failure modes and the corresponding number of cycles.
from the numerical models are compared with some of the test results previously described, one for each different geometry. Bending moments and rotations were determined according to the procedure described in Annex B of [31]. For the experimental tests, the load cells and the displacement transducers were used. For the FE models, the reaction forces and the displacements of some predefined nodes were selected. The bending moments were computed at the face of the connected column flange, M = F*d, using distance d and the forces applied in the tip of the beam. Rotations were computed using the relation between the displacements measured in LVDTs (or the displacements
4.3. Comparative analysis of the experimental and numerical results
Bending Moment (kNm)
4.3.1. Introduction In this section, a detailed analysis of the behaviour of the joints is carried out focusing on both global and component behaviours. The results
600 400 200 0 -200 -400
Joint Rot. - EXP. Joint Rot. - FE
-600 -40
-30
-20
-10
0
10
20
30
40
Rotation (mrad)
Bending Moment (kNm)
(a) J1.3 global response
(b) J1.3 von Mises stress distribution
600 400 200 0 -200 -400
Joint Rot. - EXP. Joint Rot. - FE
-600 -40
-30
-20
-10
0
10
20
30
40
Rot.ation (mrad)
Bending Moment (kNm)
(c) J3.2 global response
(d) J3.2 von Mises stress distribution
600 400 200 0 -200 -400
Joint Rot. - FE Joint Rot. - EXP.
-600 -40
-30
-20
-10
0
10
20
30
40
Rotation (mrad)
(e) J4.3 global response
(f) J4.3 von Mises stress distribution
Fig. 9. Global experimental and numerical results.
318
H. Augusto et al. / Journal of Constructional Steel Research 133 (2017) 310–333
obtained in the pre-defined nodes in the FE mesh) and the distance between them, excluding the rotations due to the elastic deformation of the members and the rotations due to the support clearances (θ = atan((DTi − DTi + 1)/dn) − θelast_column − θblock). To compute the total rotation of the joint, the column web contribution was added to the connection contribution, with the help of the crosshead, for experimental tests was used the Eq. B.6 of [31], and for the FE models was used the Eq. B.7 of [31] (using the displacements from DT1, DT2, according to Fig. 15, and distance d3). A set of models were developed according to the tests setup, using the same geometry, see Fig. 8 and Table 4, following the same boundary
conditions and loading. The elasto-plastic material properties were based on the mean values of the coupon tests [31] [39]. 4.3.2. Global cyclic behaviour Fig. 9(a), (c) and (e) compare the experimental and numerical moment-rotation curves for the J1.3, J3.2 and J4.3 joints, respectively. Fig. 9(b), (d) and (f) show the von Mises stress distribution in the joint region for the 3 joints analysed, for the maximum rotation achieved in the joint, i.e., the largest rotation amplitude achieved during the numerical analysis. The stress patterns are very similar for all joints, although for J4.3 it is possible to see higher stress concentration around
Fig. 10. Evolution of stiffness and strength degradation with the number of cycles.
H. Augusto et al. / Journal of Constructional Steel Research 133 (2017) 310–333
the stiffeners in the opposite flange of the column, which is due to the smaller lever arm of the beam inducing larger rotations in the joint. The stress peak values occurred in the bolts, the stress scale was limited to a small range of stress values. The comparisons between the numerical and experimental results, including Table 5, allow concluding that the FE models of extended end-plate joints produce very accurate results in comparison with the experimental data also for the cyclic load cases [31]. From the detailed analysis of the cyclic behaviour, it is possible to identify the strength and stiffness degradation exhibited by the joints, for the stable cycles, see Fig. 10. The positive and negative stiffness are determined in the unloading branch of each positive and negative halfcycle, respectively. The positive and negative bending moments, depicted in Fig. 10, are the maximum and minimum moments in each
319
half-cycle, respectively. It is possible to conclude that, for the group J1, degradation of stiffness is observed for all joints, but at different rates. In the case of J1.4, degradation only occurred in the last 7 cycles. Strength degradation is not noticeable in J1.2, but it occurs in J1.4 only in the last 7 cycles, after an amplitude increase. In the case of the group J2, a very similar behaviour was observed for both joints with some degradation of stiffness and strength occurring with the evolution of the loading protocol. J3.2 presents a very stable behaviour in terms of stiffness and strength. Similar to J3.2, the J3.3 joint exhibited very stable behaviour in terms of stiffness and strength, although after the 10th cycle it is possible to observe a strong degradation of stiffness and strength as a result of the damage observed in the welds between the end-plate and the beam. Similar to the group J2, the group J4 showed a similar behaviour for both joints in the group, with similar strength and stiffness
J1.3
J1.3
J3.2
J3.2
J4.3
J4.3 Fig. 11. Comparison of the moment-rotation responses.
H. Augusto et al. / Journal of Constructional Steel Research 133 (2017) 310–333
degradation, although in this case the number of cycles achieved by J4.2 was 37% higher than for J4.3, the failure occurred by the beam-to-endplate welds in both cases. The comparisons with the numerical results are quite good, although the numerical results for J1.3 are slightly lower than the ones obtained in the tests.
4.3.3. Cyclic behaviour of the components In a ductile extended end-plate joint it is expected that the most dissipative components are the end-plate and/or column flanges in bending and the column web panel in shear. In the particular case of the studied joints, the transverse web stiffeners limits the column flanges deformation, so the large contribution is provided by the other two components. According to the instrumentation setup, depicted in Fig. 6, and using a similar procedure as in the global joint response, the displacement measured in DT1, DT2 and distance d3 were used to determine the end-plate rotation, and from DT3, DT4 and distance d4 results, were used to determine the rotations of the column web panel rotation in the experimental tests. In a similar procedure the rotation of the column web, in the numerical models, was obtained by the displacements of four pre-defined nodes in the mesh of the web, see Fig. 15 (a). So equations (B.9) and (B.10) provided in [31] were used to determine the joints column web rotation, for the experimental and numerical models, respectively. Similarly, the rotation of the end-plate was determined, using the measurements of the displacement transducers DT1 and DT2 for the experimental tests, and the relative displacements of FE-Total Energy - 100% FE - CWPF - 89% FE - End-plate - 11% EXP. - Total Energy - 100% EXP. CWPF - 83% EXP. End-plate - 17%
J1.3 12000
kNm.mrad
10000 8000
two pre-define nodes in the end-plate aligned with the beam flanges (DT13 and DT14) were used for the FE models. As such the equations (B.11) and (B.12) given in [31] were used to determine the end-plate contribution for the experimental and numerical models, respectively. Fig. 11 shows a comparison of the moment-rotation curves for each joint and for the two critical components, both for the experimental and the numerical results. Fig. 12 compares the energy dissipated in the experimental tests with that obtained in the FE models. The comparisons are performed for the range of results in which the joints exhibited stable behaviour, i.e., until the first failure was observed in the test. The comparisons reveal good agreement between the experimental and numerical results. For all tests, the column web panel in shear (CWPF - column web panel and flanges) provided the largest contribution in terms of deformation and energy dissipation of the joint (78% to 83%), while the end-plate in bending represented 17% to 22% of the overall energy dissipated. As seen from the numbers, the remaining components have little contribution.
5. Characterization of the column web components under cyclic loading using Fe models 5.1. Introduction This section presents a methodology to characterize the behaviour of column web panel components from experimental results and/or FE models under cyclic loading conditions.
6000
500000 400000 300000 200000
4000
100000
2000
0
0 1
4
7
10
13
16
Cycles
8000
4
4000
2000
10
13
16
19
FE - Total Energy - 100% => 228895 FE - CWPF - 87% => 199057 FE - End-plate - 13% => 29838 EXP. - Total Energy - 100% => 232073 EXP. CWPF - 78% => 181786 EXP. End-plate - 22% => 50287
J3.2
6000
7
Cycles
Energy (kNm.mrad)
12000 10000
1
19
FE - Total Energy - 100% FE - CWPF - 87% FE - End-plate - 13% EXP. - Total Energy - 100% EXP. CWPF - 78% EXP. End-plate - 22%
J3.2 Energy (kNm.mrad)
FE-Total Energy - 100% => 252406 FE - CWPF - 89% => 223380 FE - End-plate - 11% => 29026 EXP. - Total Energy - 100% => 258416 EXP. CWPF - 83% => 214707 EXP. End-plate - 17% => 43482
J1.3 kNm.mrad
320
0
500000 400000 300000 200000 100000
0 1
4
7
10
13
16
19
22
25
1
4
7
10
13
16
19
22
Energy (kNm.mrad)
12000 10000 8000 6000 4000
2000
FE - Total Energy - 100% => 341235 FE - CWPF - 74% => 253252 FE - End-plate - 26% => 87982 EXP. - Total Energy - 100% => 348002 EXP. CWPF - 80% => 279651 EXP. End-plate - 20% => 68351
J4.3 Energy (kNm.mrad)
FE - Total Energy - 100% FE - CWPF - 74% FE - End-plate - 26% EXP. - Total Energy - 100% EXP. CWPF - 80% EXP. End-plate - 20%
J4.3
25
Cycles
Cycles
500000 400000 300000 200000 100000 0
0 1
4
7
10
13
16
19
22
25
1
4
7
10
Cycles
Fig. 12. Comparison of the relative energy dissipation of the components.
13
16
19
22
25
Cycles
H. Augusto et al. / Journal of Constructional Steel Research 133 (2017) 310–333
(31) (41) (51) (81) (101)
Integration boundaries (IB): Comp. 2 = IB1, IB3, IB(n+1) Comp. 3 = IB1 to IB(n+1) 3
IB1
Comp. 1
F
(2) (7) (32) (42) (52) (82)(102)
4 hbf
10
2
321
Comp. 2
(1)
F
(33) (43) (53) (83)(103)
19
(2) (7)
IB2 7, 8
(34) (44) (54) (84)(104)
Comp. 3
F
1
IB3
5
hbf
(21) (31) (41) (51) (81) (101) 7, 8
IB4
(7)
(22) (32) (42) (52) (82)(102)
19
2
10
IB(n+1) 3
4
hbf
Comp. 1, 2 F and 3
(1)
Alternative assemblage Integration boundaries (IB): Comp. 2 = comp. 3 = IB1 to IB(n+1)
(23) (33) (43) (53) (83)(103) (7)
(24) (34) (44) (54) (84)(104)
Idealized behaviour for components 1, 2 and 3:
Fig. 13. From left to right: Identification of the components in the joint and definition of possible integration boundaries (IB); assemblage of the identified components according to the integration boundaries chosen; idealized response of the column web components 1, 2 and 3.
Fig. 13 represent a double-extended end-plate beam-to-column steel joint and two possible component models. The active components are the following: (1) column web in shear, (2) column web in transverse compression, (3) column web in transverse tension, (4) column flange in bending, (5) end-plate in bending, (7) beam flange and web in compression, (8) beam web in tension, (10) bolts in tension and (19) welds. The characterization of the components behaviour, under cyclic loading conditions, is a complex task, to ease the process, and to analyse in detail each component behaviour, the identified components were grouped according to their location in the joint: components of the column web (1, 2 and 3), components of the connection (4, 5, 10 and 19) and components of the beam (7 and 8). In this paper only the components of the column web will be addressed i.e. components 1, 2 and 3. As the joint is subjected to load reversal, it is necessary to take into account the added complexity of exhibiting tensile and compressive stresses within the same location of the joint. With reference to Fig. 13, this added complexity mostly results from the fact that the load-introduction points, in the column web, vary as the stresses change from tension to compression. When transferring tension from the beam to the column, the load-introduction in the column web panel comes from the position of the bolt rows in tension, while compression is more evenly distributed around the compression centre, with the peak maximum compressive stress aligned with the compressed beam flange, as is evidenced later in Fig. 20. In line with the main assumptions of the component method [1], the joint is discretized according to the bolt rows and the centre lines of the beam flanges, as shown in Fig. 13, using appropriate effective widths. Consequently, the characterization of the column web panel components in bolted joints depends on the assumed simplifications of the component model. It is of course possible to lump some lines of action of the components in order to simplify the problem, as shown in the alternative assemblage of Fig. 13. This simplification aligns the load-introduction tensile and compressive components in the column web panel, allowing to combine the force-deformation (F-Δ) response of these two components into one single force-deformation (F-Δ) curve, as illustrated in Fig. 13, at the expense of losing consistency with the component characterization of EC3-1-8 for static monotonic conditions.
In the following sub-section, a general extraction procedure is described that allows for the arbitrary consideration of any component model. Therefore, the choice is freely left to the user to implement any component model and easily convert the component characterization of the column web panel components across different models such as those shown in Fig. 13. 5.2. Derivation of the force-displacement relationships This derivation consists of an extension to the methodology presented in [31] to deal with reversal load conditions for the extraction of the column web panel components behaviour, due to the load-introduction effect and the shear effect. It is fully based on the results provided by the FE models and allows the derivation of force-displacement and shear-distortion curves of the components. It was developed using numerical integration of the stress fields obtained from the FE models and it is illustrated in Fig. 14 to Fig. 16, for the load-introduction effect and for the shear effect. The forces (Fc and Ft) are obtained through integration of the stress field according to Eq. (3) for the load-introduction effect and from Eq. (4) for the shear effect. In these equations, σ33 is the normal horizontal stress in the column web along path P1, integrated over the lengths hc for compression and ht. for tension (Eq. (3)). Furthermore τ23 is the shear stress in the column web along path P3, integrated over the corresponding lengths (Eq. (4)), tfc and twc are the column flange and web thicknesses, respectively, and t1 is the thickness according to the shear area represented in Fig. 15 (b). It is noted that this procedure is quite flexible in defining the integration boundaries (IB in Fig. 14) to calculate the forces. The assessment of the forces will depend on the idealized mechanical model and the procedure can be easily adapted to the two examples presented before or to any other compatible mechanical model. Moreover, in the case of the shear evaluation, other integration boundaries can be considered; in this case, the EC3-1-8 [1] shear area definition was used to set the boundaries for integration. ! ! Fc ¼
hc;i
∫ σ 33 dy t wc or F t;i ¼
ht;i
∫ σ 33 dy t wc
ð3Þ
322
H. Augusto et al. / Journal of Constructional Steel Research 133 (2017) 310–333
IB1 h (mm)
800
P2
700
IB2
600
IB3
400
(1)
Ft
ht(1st)
Ft
ht(2nd)
500
300
Fc
IB...
V
(2) (7) (34) (44) (54) (84)(104)
h
hc(4th)
0 -400
-200
0
200
400
33 (N/mm2)
600
800
(a) Stress integration for negative moment
h (mm)
800
P2
IB1
(31) (41) (51) (81) (101) (1)
hc(1st)
600 500
300 200 100
IBn -600
h
Ft
hc(3rd)
Ft
hc(4th)
(2) (7) (32) (42) (52) (82) (102) V
hc(2nd)
400
IB...
(b) Mechanical model for negative moment
P1
700
Fc
IB3
-800
M
(33) (43) (53) (83) (103)
hc(3rd)
100
-600
IB2
(2) (7) (32) (42) (52) (82) (102)
200
IBn -800
(31) (41) (51) (81) (101)
P1
M
(33) (43) (53) (83) (103) (2) (7) (34) (44) (54) (84) (104)
0 -400
-200
0
200
400
600
33 (N/mm2) (c) Stress integration for positive moment
800
(d) Mechanical model for positive moment
Fig. 14. Procedure to obtain the forces in the column web in transverse tension and compression components, (a) and (c), under negative and positive bending moment; and in (b) and (d) the same components are identified in the global assembly of the joint components, also for negative and positive moment, respectively.
0 1 ðtfc =2þrÞback @ Vn ¼ ∫ τ 23 dzA t 1 þ
!
hwc
∫ τ 23 dz
0 1 ðtfc =2þrÞfront @ t wc þ ∫ τ 23 dzA t 1
2 23 (N/mm )
ð4Þ
hshc
400 300 200
DT1 fc
100
0 -100
To determine the shear force (Vn) in the web panel, the stress field is evaluated at a cross section of the column aligned with the mid-height of the connected beam, where the stresses reach their maximum values (at bending neutral axis), using the middle elements of the web to extract the shear stresses. The stresses in the column web panel are assumed to be uniformly distributed due to the action of the column
P3
Vn
(+)
DT4
DT3
r twc
Vn (-)
-200
rc
hwc hshc rc tfc/2
-300
DT2
-400 0
100
200
hc (mm) (a)
300
(b)
Fig. 15. Procedure to obtain the shear force of the column web panel in shear component. a) plot of the shear stresses envelope; and b) integration boundaries (in this case according to the EC3-1-8).
H. Augusto et al. / Journal of Constructional Steel Research 133 (2017) 310–333
323
tfc Mfc P5
P7
bc
P4.1
P4.2
P6
P4
dA
z
P4.3
tfc
(a)
(b)
Fig. 16. Determination of the bending moment in the flanges through stress integration. a) illustrates the paths P4 to P7 in the joint perspective, and top view of part of a cut, aligned with path P4, showing the additional paths in the column flange used to determine the bending moment according to the integration scheme represented in b).
flanges, as proposed by Jaspart [29]. Therefore, the shear stresses are only extracted along path P3, see Fig. 15 (a). The deformation and rotation corresponding to the load-introduction effect and shear effect, respectively, are obtained from the displacement fields. In the case of the load-introduction effect, the displacements are extracted from paths P1 and P2, see Fig. 14, and the deformation is determined, see Eq. (5), as the difference between the nodes in the paths aligned with the element that causes the deformation, e.g. bolt rows, flanges, etc. at the same location of the arrows
indicating the forces in Fig. 14. For the rotation due to the shear effect, the displacements are extracted from the predefined nodes indicated in Fig. 15 (a) and computed according to Eq. (6). δcw ¼ δP1 −δP2
ð5Þ
DT1U3 −DT2U3 DT3U2 −DT4U2 þ a tan γ ¼ a tan d3 d4
ð6Þ
1200
25 80 75 89 90
Ø39 M36 (10.9)
600
910
1000
True stress (MPa)
30
242 90
IPE600 (S355)
89 75 80
HEB500 (S355)
800 600 400 200 0
75 150 75 300
500
Steel (S355) Bolts (10.9) 0%
5%
10%
15%
20%
25%
30%
True strain (%)
(a)
(b)
Bending Moment (kNm)
Fig. 17. (a) Geometry of the E3-TB-E-M3-ts30 and (b) true stress – true strain curves of the materials adopted.
500 400 300 242.27
Lb
239.47
200
J1_1_pv1_tp18_ts0 J1_1_pv1_tp18_ts20 ECCS Linearization
100 3.97
0 0
5.56 10
20
30
40
Rot. (mrad)
(a)
(b)
Fig. 18. (a) Determination of the elastic limit based on the nonlinear monotonic behaviour of the joints; (b) geometrical properties for the AISC 341-10 load protocol.
324
H. Augusto et al. / Journal of Constructional Steel Research 133 (2017) 310–333
Whenever transverse stiffeners are present, the additional shear strength provided by the moment resisting frame formed by the column flanges and the transverse stiffeners aligned with the beam flanges is accounted for considering a plastic mechanism whereby the plastic hinges will occur in the column flanges due to the higher stiffness and strength of the stiffeners, if properly designed, see also [31]. The stresses are extracted at a section near the flanges maxima normal stresses, σ22, as depicted in Fig. 16. Subsequently, Eq. (7) is used to determine the bending moment in the flanges, and Eq. (8) is used to obtain the
additional shear strength, Vc, computed using the four plastic hinges in the column flanges and the distance between the centre lines of the transverse stiffeners. t fc
Mfc ¼ ∫ zðσ 22 dAÞ; Vc ¼
dA ¼ bc dz
MfcðP4Þ þ M fcðP5Þ þ MfcðP6Þ þ MfcðP7Þ hb −t s
700 Row 1
h (mm)
h (mm)
500
400 300
Row 3
600 500
Row 2
400 300
Row 3
200
Row 4
200 Row 4
100
-600
-400
-200
100
J1_1_pv1_tp18_ts0
0 -800
0
200
400
600
800
-4
-2
0
h (mm)
h (mm)
500 400
300
600 500
Row 2
400 300
Row 3
200 Row 4
200 Row 4
100
-600
-400
-200
100
J1_1_pv1_tp18_ts20
0 -800
0
200
400
600
800
-4
-2
0
1000
800
Row 2 Row 3
800
h (mm)
h (mm)
Row 1
400
Row 6
600
Row 4 Row 5
400
Row 6
200
200
0
-800
-600
-400
-200
200
400
600
800
-15
-10
-5
1200 1000
Row 1
1000
Row 2 Row 3
800
Row 2 Row 3
800
600 400
Row 6
-600
200 -400
-200
10
15
600
Row 4 Row 5
400
Row 6
200
E3-TB-E_cyc_M3_ts30
0 -800
5
1200
Row 1
h (mm)
h (mm)
0
Web deformation (mm)
33 (N/mm2)
Row 4 Row 5
E3-TB-E_cyc_M3_ts0
0
0
4
1200
1000
600
Row 4 Row 5
2
Web deformation (mm) E3-TB-E-cyc_M3_ts0
1200
Row 2 Row 3
J1_1_pv1_tp18_ts20
0
33 (N/mm2)
Row 1
4
700 Row 1
600
Row 3
2
Web deformation (mm)
700
Row 2
J1_1_pv1_tp18_ts0
0
33 (N/mm2)
Row 1
ð8Þ
700 Row 1
600
Row 2
ð7Þ
0
200
33 (N/mm2)
400
600
800
E3-TB-E_cyc_M3_ts30
0 -15
-10
-5
0
5
Web deformation (mm)
Fig. 19. Stress fields (left), and web deformation fields (right), for increasing levels of bending moment.
10
15
H. Augusto et al. / Journal of Constructional Steel Research 133 (2017) 310–333
5.3. Application to the joints 5.3.1. Introduction The proposed procedure was applied to some variants of the joints analysed in the calibration of the FE models, and extended to other geometries developed using the same principles. The geometrical properties are described in Table 6, with reference to the scheme of Fig. 8. The first two geometries correspond to joint J1.1, with and without transverse web stiffeners, analysed in [31]. The last two joints are also double-extended end-plate joints with stronger beam and column profiles, IPE600 and HEB500, respectively, with six bolt rows, with four inner rows, bolt size M36 in grade 10.9, with and without transverse web stiffeners. The E3-TB-E-M3-ts30 joint was designed according to EC3-1-8, to reach a strength level similar to the beam plastic moment. The geometry of the joint is depicted in the Fig. 17(a). In the design of the joints without stiffeners, the governing component, in the compression side, was the column web in transverse compression. In the tension side, the governing component, for the external bolt rows, was, in both geometries (J1.1 or E3), the end-plate in bending. For the inner bolt rows, the strength of the compression component limited the development of the full resistance of the tension components. In the case of the J1.1 joint, the component that governed the design was the column flange in bending and in the E3 joint was the endplate in bending. In the latter case, the third bolt row was inactive. In the
1st yielding
time step 0.9912 time step 2.9912 time step 4.9912 time step 6.9912 time step 9.0138 time step 11.0034 time step 12.8306 time step 12.9483 time step 12.9979 time step 14.6891 time step 14.7779 time step 15.0123 J1_1_pv1_tp18_ts0
700 600
h (mm)
500
400 300 200
100 0 -600
-400
-200
0
200
400
600
800
1000
presence of transverse web stiffeners the governing component, in the compression side, was the column web panel in shear. In the tension side the behaviour was similar to the joints without stiffeners, but due to the higher strength of the compression component, it was possible to reach higher values in the tension components for the inner bolt rows. The steel mechanical properties adopted in these analyses correspond to the nominal values defined in Eurocode 3 part 1–1 [40] (E = 2.10E5 N/mm2; fy = 355 N/mm2; fu = 490 N/mm2) for the FE models representing the joints based on J1.1. For the remaining joints, a more realistic stress-strain relationship, of a steel grade S355, depicted in Fig. 18 (b) was considered. Two different load protocols were used: ECCS [41] was adopted for the joints based on J1.1, and the protocol specified in the AISC 341-10 [42] was employed for the remaining joints. The ECCS load protocol is defined as follows: (i) one cycle in the ranges: θy/4; 2θy/4; 3θy/4 and θy (ii) three cycles in the ranges: 2θy; (2 + 2n)θy where n = 1.2, … The assessment of the elastic limit, θy, is based on the bi-linearization of the nonlinear monotonic response of the joints, see Fig. 18 (a). In case of AISC 341–10 [42], the procedure is conducted by controlling the inter-storey drift, θ, imposed to the test specimen, six cycles in the ranges 0.00375 rad, 0.005 rad, 0.0075 rad, four cycles in the range 0.01 rad and two cycles in the ranges 0.015 rad, 0.02 rad, 0.03 rad, 0.04 rad. The loading is applied with increments of 0.01 rad, with two cycles of loading for each step. In the analysis, the vertical beam deflection is the controlled parameter. Thus, when defining the load function in ABAQUS, the amplitude δ is used and it is defined by Eq. (9), according to Fig. 18 (b).
θ¼
δ ⇔δ ¼ θ Lb Lb
Row 1
600 500
Row 2
400
300
Row 3
200 Row 4
100
-400
-200
1000
h (mm)
800 600 400
200
0
200
400
400
600
800
1000
1200 1000 800
h (mm)
time step 0.063 time step 3.141 time step 5.175 time step 6.975 time step 10.894 time step 15.103 time step 19.022 time step 21.131 time step 25.05 time step 26.859 time step 28.659 time step 31.119 time step 33.031 time step 35.088 time step 36.972
33 (N/mm2)
J1_1_pv1_tp18_ts20
0 -600
600
800
1000
33 (N/mm2)
1200
200 E3-TB-E-cyc_M3_ts0 0 -600 -400 -200 0
time step 0.9912 time step 2.9912 time step 4.9912 time step 6.9912 time step 8.9944 time step 10.9944 time step 12.8944 time step 12.9944 time step 14.9944 time step 16.6944 time step 16.9944
700
33 (N/mm2) 1st yielding
ð9Þ
5.3.2. Load-introduction effects As already explained, the introduction of the loads in the column web, due to the beam force couple, is different in tension and in compression as tension is transferred by the bolt rows and compression is
h (mm)
For simplification, it is considered that the stresses are uniform along the width of the column flanges, so the integration of the stresses along each path results in a single force at that strip. The bending moment is obtained by multiplying the force at each layer by the distance to the neutral axis. The bending moment can be computed with the forces determined in the two outer paths (P4.1 and P4.2). However, and because it is necessary to determine the neutral axis position, due to the presence of axial force in the column flanges, a third path (P4.3) is required to determine the location where the stresses are equal to zero, the neutral axis position is sensitive to the back and forward from the cycles. It is also important to note that the third path should cross the radius and web elements so that the integrated forces and the neutral axis evaluation take that into account.
325
600 400
-400
Row 1 Row 2 Row 3 Row 4 Row 5
Row 6 200 E3-TB-E-cyc_M3_ts30 0 -200 0 200 400 600
33 (N/mm2)
Fig. 20. Stress fields for the first load increments and identification of first yielding.
time step 0.063 time step 3.141 time step 6.975 time step 10.969 time step 13.003 time step 16.997 time step 19.031 time step 21.141 time step 25.059 time step 26.869 time step 28.669 time step 28.969 time step 30.778 time step 32.963 time step 34.997 time step 800 100038.991 1200 time step 45.06 time step 47.039
326
H. Augusto et al. / Journal of Constructional Steel Research 133 (2017) 310–333
1000
Group of rows 1, 2, 3 Group of rows 3, 4, 5
3000
500
2000
250
1000
F (kN)
F (kN)
4000
J1_1_pv1_tp18_ts0
750
0 -250 -500
0 -1000
E3-TB-E-cyc_M3_ts0
-2000
-750 -2
-1
-3000
Group of rows 1 and 2 Group of rows 3 and 4 1 2
-1000 0
-4000 -15
-12.5
Web deformation (mm) Group of rows 1 and 2 Group of rows 3 and 4
500
2000
-7.5
-5
-2.5
0
2.5
E3-TB-E_cyc_M3_ts30
1500
250
1000
F (kN)
F (kN)
-10
Web deformation (mm)
0
500 0 -500 -1000
-250
-1500
J1_1_pv1_tp18_ts20
-2000
-500 -0.3
-0.2
-0.1
0
0.1
0.2
-0.3
0.3
-0.2
-0.1
0
Group of rows 1, 2, 3 Group of rows 3, 4, 5 0.1 0.2 0.3
Web deformation (mm)
Web deformation (mm)
Fig. 21. F-Δ curves for the components due to the load-introduction effect considering the group of bolts around the beam flanges.
transferred directly from the contact of the beam flange to the column web. Fig. 19 shows the stress, along the path P1, and deformation fields, obtained by Eq. (5), for the joints defined in Table 6, for several load increments. Globally, the stress distribution is very similar in tension and in compression, especially for the joints without transverse web stiffeners. However, some differences are noted. The first load increments, depicted in Fig. 20, show that the differences between tension and compression are more evident in the elastic range, with local maxima stresses perfectly aligned with the position of the bolts rows for tensile
stresses, and with the position of the beam flanges for compressive stresses. After yielding of the web is reached, both tension and compression diagrams become similar and the maximum stresses deviate from the position of the bolt rows. Regarding the web deformation, the differences between tension (positive) and compression (negative) are more notorious. For the joints without transverse web stiffeners, the maximum deformation in compression is aligned with the beam flanges, while in tension the maximum is aligned with the inner bolt row, revealing the stiffer behaviour of those bolt rows. The transverse web stiffeners, aligned with the beam
750
750
J1_1_pv1_tp18_ts20
500
500
250
250
F (kN)
F (kN)
J1_1_pv1_tp18_ts0
0
0 -250
-250 -500
-500
Bolt row 1 Bolt row 4
-750 -2
-1
0
1
Bolt row 1 Bolt row 4
-750 -2
2
-1
0
2
750
750
J1_1_pv1_tp18_ts0
J1_1_pv1_tp18_ts20
500
500
250
250
F (kN)
F (kN)
1
Web deformation (mm)
Web deformation (mm)
0
0 -250
-250 -500
-500
Bolt row 2 Bolt row 3
Bolt row 2 Bolt row 3
-750
-750 -2
-1
0
1
Web deformation (mm)
2
-0.5
0
0.5
1
1.5
2
Web deformation (mm)
Fig. 22. F-Δ curves for the components due to the load-introduction effect for each bolt row, for the J1.1 joints, according to the alternative mechanical model depicted in Fig. 13.
H. Augusto et al. / Journal of Constructional Steel Research 133 (2017) 310–333
flanges, prevent the deformation of the column web in compression in the inner bolt row. The application of the methodology described in Section 5.2 allows obtaining the numerical F-Δ curves for the components. The procedure is general in the sense that it allows to obtain force resultants and deformations for any selected tributary area between two integration limits, both for the column web in tension or in compression. Fig. 21 depicts the cyclic force-deformation behaviour for the load introduction in the column web panel for the four joints. A single lumped component is considered for the top and bottom zones. Consequently, with reference to Fig. 14, the integration limits are defined between points of zero or near zero normal stress σ33 for the top and bottom zones, respectively. It is noted that these limits will not necessarily coincide for positive and negative bending moments, neither also between the different load cycles. However, Fig. 19 shows that they are fairly stable and hence it is possible to assume constant limits of integration for all loading cycles. Concerning the deformation, the maximum web deformation in tension and compression is selected. It is noted that the maximum values will not necessarily occur at the same section. Typically, the maximum web deformation in compression is observed at the level of the beam flange while in tension it often develops aligned with one of the bolt rows. Fig. 22 and Fig. 23 represent the force-deformation cyclic curves for joints J1.1 and E3, respectively, according to the alternative component model shown in Fig. 13, i.e., with the load introduction components
3000
(tension and compression) positioned according to the bolt rows. In this case, for the top and bottom zones, the integration limits for each bolt row are established based on the effective widths of the components. The deformation, in this case, is measured aligned with the corresponding bolt row. The component model illustrated in Fig. 13 reflects the definition of the individual components in accordance with EC3-1-8 [1]. It further highlights that the effective width of the column web panel in compression is clearly distinct from the corresponding effective widths of the column web panel in tension components for each bolt row in tension. Hence, the integration limits in tension and in compression should be different. Fig. 24 illustrates the cyclic behaviour of the column web panel in compression, referenced to the beam flange level, while Fig. 25 depicts the cyclic force-deformation curves for the column web panel in tension for each bolt row. The comparison of the results obtained for the stiffened and unstiffened joints shows that the transverse web stiffeners have a major influence on the amplitude and shape of the force-displacement curves. Whilst the compression is transmitted directly to the stiffeners without causing transverse deformation in the column web, tension causes deformation in the column web aligned with the bolt rows. The examination of the behaviour of the inner bolt rows, see Fig. 23, reveals a ratcheting effect after yielding, mainly in the third and fourth rows of the E3-TB-E_cyc_M3 joints, due to the migration of the normal stresses (σ33) across the web with the increase of bending moment, see
1500
E3-TB-E-cyc_M3_ts0
E3-TB-E-cyc_M3_ts30
2000
1000 500
F (kN)
F (kN)
1000 0 -1000
0 -500
-2000
Bolt row 1 Bolt row 6
-1000
-3000 -15
-10
-5
0
5
10
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
Web deformation (mm) 1500
E3-TB-E-cyc_M3_ts0
E3-TB-E-cyc_M3_ts30
2000
1000
1000
500
F (kN)
F (kN)
3000
Bolt row 1 Bolt row 6
-1500
15
Web deformation (mm)
0
0 -500
-1000 -2000
-1000
Bolt row 2 Bolt row 5 -15
-10
-5
0
5
10
Bolt row 2 Bolt row 5
-1500
-3000
-1
15
0
1
3000
2
3
4
5
6
7
8
Web deformation (mm)
Web deformation (mm) 1500
E3-TB-E-cyc_M3_ts0
E3-TB-E-cyc_M3_ts30
2000
1000
1000
500
F (kN)
F (kN)
327
0
0 -500
-1000 -2000
-1000
Bolt row 3 Bolt row 4
-1500
-3000 -15
-10
-5
0
5
Web deformation (mm)
10
Bolt row 3 Bolt row 4
15
-1
0
1
2
3
4
5
6
7
8
Web deformation (mm)
Fig. 23. F-Δ curves for the components due to the load-introduction effect for each bolt row, for E3 joints, according to the alternative mechanical model depicted in Fig. 13.
328
H. Augusto et al. / Journal of Constructional Steel Research 133 (2017) 310–333
J1_1_pv1_tp18_ts0
0
Component 2 (upper beam flange) Component 2 (lower beam flange)
0
E3-TB-E-cyc_M3_ts0
-1000
F (kN)
F (kN)
-250 -500 -750
-2000 -3000
-1000 -2
-1
Component 2 (upper beam flange) Component 2 (lower beam flange) 0 1 2
-4000 -15
-12.5
Web deformation (mm)
-10
-7.5
-5
-2.5
0
2.5
Web deformation (mm)
Fig. 24. F-Δ curves for component (2) due to the load-introduction effect, compression side of the previous relationships.
Fig. 27. This phenomenon can be associated with the interaction with the shear stress (τ23) that progressively increases the normal stress beyond the line of the beam flanges alignment. The joints without stiffeners may exhibit out-of-plane deformations, as illustrated in Fig. 26. This phenomenon is captured in the derived F-Δ relationships, represented by the last cycles with larger amplitude, for the joint E3-TB-E_cyc_M3_ts0, visible in the response of the external and in the internal bolt rows, see Fig. 23 or Fig. 25. The transverse web stiffeners may prevent this undesired phenomenon, as shown in both figures. Table 7 summarises the main results for the column web panel in tension and compression F-Δ relationships. In general, the initial stiffness, of the achieved F-Δ relationships, is lower for the joints without stiffeners, although for the E3 joints this fact is not verified in some bolt rows, as highlighted in the table. Regarding the maximum strength achieved in the component, it is clear that the joints without stiffeners present the highest values in comparison with the joints with stiffeners. This results from the fact that the transverse web stiffeners directly transfer the compression forces to shear in the column web.
750
The joints were also subjected to different load protocols, ECCS [41] and AISC 341-10 [42], resulting in different demands. ECCS is clearly more severe than the AISC load protocol. Note that the ECCS load protocol imposes four cycles in the elastic range, while the AISC load protocol may involve a significant number of cycles in the elastic range before the yield resistance of the joint is reached. This difference is related to the fact that the ECCS load protocol has a pre-processing procedure to assess the elastic limit of the joint, relating the amplitudes of the cycles with the assessed value, unlike the AISC load protocol that specifies fixed values for the amplitudes. In the plastic range, the ECCS load protocol is also more severe than the AISC load protocol, as it doubles the deformation amplitude between sets of cycles after yielding. In contrast, AISC increases the deformation amplitude by 150% between sets of cycles after yielding. Although the yield rotations for both geometries (J1.1 and E3) are similar, in terms of beam displacement amplitude, E3 needs approximately double the amplitude of the J1.1, due to the higher beam length, a fact that was considered in the comparisons of the two load protocols. The evolution of the two protocols reveals that ECCS always reached higher amplitudes earlier than AISC. This evidence can
2000
Component 3 (row 1) Component 3 (row 4)
J1_1_pv1_tp18_ts0
Component 3 (row 1) Component 3 (row 6)
1500 500
F (kN)
F (kN)
E3-TB-E-cyc_M3_ts0 1000
250 500 0
0 -2
-1
0
1
2
-10
-7.5
Web deformation (mm) 750
2000
Component 3 (row 2) Component 3 (row 3)
J1_1_pv1_tp18_ts0
-5
-2.5
0
2.5
Web deformation (mm) Component 3 (row 2) Component 3 (row 5) Component 3 (row 3) Component 3 (row 4)
1500
F (kN)
F (kN)
500
E3-TB-E-cyc_M3_ts0
1000
250 500
0
0
-2
-1
0
1
Web deformation (mm)
2
-10
-7.5
-5
-2.5
0
2.5
5
Web deformation (mm)
Fig. 25. F-Δ curves for component (3) due to the load-introduction effect, tension side of the previous relationships.
7.5
10
H. Augusto et al. / Journal of Constructional Steel Research 133 (2017) 310–333
329
protocol allow the joints to sustain more cycles before failure. However, the specimens become more prone to very-low cycle fatigue effects.
Fig. 26. Mises stress distribution with out-of-plane column web deformation, for a global rotation of 84 mrad.
lead to higher degradation levels in the joints subjected to the ECCS load protocol, see Fig. 28. The lower amplitudes obtained with AISC load
5.3.3. Shear results Similar to the previous sub-section, it is possible to obtain the sheardistortion (V-γ) relationships by applying the methodology described in Section 5.2. As shown in Fig. 29, the stress fields for the joints with and without column web stiffeners are quite similar, although, in the presence of the transverse web stiffeners, the shear stress is confined by the stiffeners and the flanges, while it is more spread in the case of the unstiffened column web. Fig. 30 depicts the derived relationships and compares the results with and without transverse web stiffeners. Note that, in the case of the E3-TB-E_cyc_M3_ts0 joint, the out-of-plane deformation is also noticeable, preventing the web to reach the same level of distortion and shear strength as the joint with stiffeners. These out-of-plane deformations detected in the column web, after a global rotation of 35 mrad, have a strong influence on the degradation of the shear strength in the column web.
E3-TB-E_cyc_M3_ts0
E3-TB-E_cyc_M3_ts30 Fig. 27. Evolution of the normal (σ33) and shear (τ23) stress for a half-cycle.
H. Augusto et al. / Journal of Constructional Steel Research 133 (2017) 310–333 5000 4000 3000 2000 1000 0 -1000 -2000 -3000 -4000 -5000
8000 E3-TB-E-M3-ts0
J1_1_pv1_tp18_ts0
Stiffness (N/mm)
Force (kN)
330
7000 6000 5000 4000 3000 2000 1000
E3-TB-E-M3-ts0
J1_1_pv1_tp18_ts0
0 0
5
10
15
20
25
0
30
5
10
15
Cycles
20
25
30
Cycles
Fig. 28. Comparison of the strength and stiffness degradation for the F-Δ relationship for the group of bolt rows 1, 2 and 3.
The column web panel in shear also shows differences in the response due to the load protocol applied to the joints. The ECCS load protocol is more severe so the difference between stable cycles is larger than in the joints subjected to the AISC load protocol. Fig. 31 represents the evolution of the peak strength and stiffness (measured in the unloading branch) for the stiffened joints. The results show that no degradation is detected and that the ECCS load protocol is more severe than AISC load protocol in the first cycles. Conversely, a small degradation of stiffness can be observed in the E3 joint. The behaviour in positive and negative shear stress is similar, as expected, due to the symmetry of the joints. Since the bare shear resistance of the column web panel is independent of the presence of transverse web stiffeners, the additional resistance that is observed is a result from the contribution of the frame action provided by the column flanges and the transverse web stiffeners. The evolution of the bending moment (Mfc) in the flanges against the web rotation is depicted in Fig. 32. Note that the stress distribution near the bolts row in tension and compression is influenced by the presence of the holes in the flange, resulting in a shift of the position of the
5.4. Methodology overview A methodology to extract the column web components response was presented and explained in the previous sections, the methodology was also applied to several joints. The objective of this section is to summarize, in a walk-through, the proposed methodology. Table 8 summarises the steps required for the application of the methodology. 6. Conclusions This paper proposes a procedure for the mechanical characterization of the cyclic behaviour of components in double-extended beam-to-column joints using a calibrated finite element model capable of representing the cyclic behaviour of extended end-plate joints. The model developed in ABAQUS uses solid (or continuum) elements in
350
J1_1_pv1_tp18_ts0
250
250
150
150
50 -50 0
100
200
300
-150
23 (N/mm2)
23 (N/mm2)
350
plastic hinge towards the bolts row alignment. For that reason, paths P6 and P7 are considered aligned with the bolts holes, although in the transition between tension and compression this shift is not so notorious, as observed in Fig. 33.
-50 0
350
E3-TB-E_cyc_M3_ts0
250
250
150
150
50 -50 0 100 200 300 400 500
200
300
-250
-250
(a)
E3-TB-E_cyc_M3_ts30
-50 0 100 200 300 400 500 -150
hshc (mm)
hshc (mm)
50
-150
-350
100
-150
-350
hshc (mm)
23 (N/mm2)
23 (N/mm2)
350
50
-250
-250 -350
J1_1_pv1_tp18_ts20
-350
hshc (mm)
(b)
Fig. 29. Shear stress fields for increasing levels of bending moment: (a) unstiffened and (b) stiffened column web.
J1_1_pv1_tp18_ts20 J1_1_pv1_tp18_ts0
1250 1000 750 500 250 0 -250 -500 -750 -1000 -1250
3000
331
E3-TB-E_cyc_M3_ts0 E3-TB-E_cyc_M3_ts30
2000 1000
V (kN)
V (kN)
H. Augusto et al. / Journal of Constructional Steel Research 133 (2017) 310–333
0 -1000 -2000 -3000
-40
-30
-20
-10
0
10
20
30
40
-50
-30
-10
(mrad)
10
30
50
(mrad) Fig. 30. V-γ behaviour for the shear load.
5000
1000000 E3-TB-E-M3-ts30
J1_1_pv1_tp18_ts20
Stiffness (N/mm)
4000
Force (kN)
3000 2000 1000 0 -1000
800000 600000 400000 200000
-2000
E3-TB-E-M3-ts30
J1_1_pv1_tp18_ts20
0
-3000 0
5
10
15
20
25
0
30
5
10
15
Cycles
20
25
30
Cycles
Fig. 31. Comparison of the strength and stiffness degradation for the V-γ relationship.
M(P4)
M(P5)
M(P6)
40
M(P7)
6
30
4
20
Mpf (kNm)
Mpf (kNm)
8
2 0
M(P4)
M(P5)
M(P6)
M(P7)
10 0
-10
-2 -4
-20
-6
-30 -40
-8 -50 -40 -30 -20 -10
0
10
20
30
40
50
(mrad)
(a) J1_1_pv1_tp18_ts20
-50 -40
-30 -20 -10
0
10
20
30
40
(mrad)
(b) E3-TB-E_cyc_M3_ts30
Fig. 32. Evolution of bending moment (Mfc) in the flanges against the web distortion (γ).
(a) DT20U2 = -60.22 mm; M = 385.50 kNm
(b) DT20U2 = -35.38 mm; M = 66.05 kNm
Fig. 33. Normal stress fields in the column flanges for different levels of bending moment.
50
332
H. Augusto et al. / Journal of Constructional Steel Research 133 (2017) 310–333
the connection zone. For computational efficiency, beam elements are used in the column and beam regions located away from the connection. The model considers non-linear material and geometrical behaviour, non-linear contact, re-contact and slip. A material model combining both isotropic and kinematic hardening was employed. The model was calibrated against experimental tests carried out at the University of Coimbra on double extended end-plate beam-to-column joints. The experimental tests were presented and the results were analysed, for the global joint behaviour and at the component level. The good agreement between the experimental data and the numerical results allowed concluding that the model is capable of simulating accurately the behaviour of end-plate beam-to-column joints, and that it can be used in detailed analyses of the behaviour of the connection components. A versatile and efficient methodology for the extraction of the cyclic behaviour of the web panel components from experimental tests and numerical simulations was presented, applicable to bolted end-plate joints, but extensible to other joint configurations. The methodology uses the integration of stress fields from the FE models of the joints, namely the column web panel in shear and the column web in transverse compression or tension components. The accuracy of the methodology depends on the column web element size and the number of stress fields analysed from the available load increments. Finally, it was highlighted that the procedure is very flexible in terms of the definition of the integration boundaries; in particular, and in line with the definition of the components in EC3-1-8, the boundaries may be different for tension or compression, therefore generating tension or compression cyclic F-Δ curves only. Double-extended end-plate joints, with and without transverse web stiffeners, and subjected to different load protocols (ECCS and AISC 34110) were analysed and used to assess the proposed methodology. The results allowed concluding that the procedure is able to capture the behaviour of the column web under tension and compression, both for groups of bolts and for isolated bolt rows, as well as the shear-rotation behaviour, including the additional shear resistance provided by the stiffeners and achieved by the frame action developed by the column flanges and the stiffeners. The direct comparison of the behaviour of the joints, with and without stiffeners, shows that the procedure is able to capture the influence of these designs in the amplitude and shape of the force-displacement relationships. Moreover, the results also demonstrates that joints without stiffeners can develop out-ofplane deformations. This phenomenon was captured in the derived relationships, represented by the larger deformation observed in the last cycles, not following the growth trend due to the load increments. The presence of the transverse web stiffeners can avoid this undesired phenomenon, since the compression is directly transmitted to the stiffeners. The comparisons between the joints loaded according to the ECCS load protocol with those subjected to the AISC 341-10 load protocol allowed concluding that the ECCS load protocol is more severe than the AISC one. This is partly due to the pre-processing procedure to assess the elastic limit of the joint that is required by the ECCS load protocol and used in the definition of the cycles' amplitudes. This is reflected in a loading sequence that imposes a smaller number of cycles before plastic deformation is achieved in the joint, however, on the other hand, greater amplitudes between cycles are applied after yielding of the joint. Even though the double-extended end-plate steel joints analysed in this paper fall out of the scope of Eurocode 8, due to the excessive contribution of the column web panel to the plastic deformation of the joint, the specific characteristics of the joints allowed to analyse and characterize in detail the cyclic behaviour of the column web components. The force-displacement relationships obtained revealed a cyclic stable behaviour and high energy dissipation capacity, mostly provided by the column web panel in shear. The proposed procedure revealed to be an excellent tool to obtain the isolated behaviour of the components
of the column web panel, and it can be extended to other components such as the beam and column flange in compression or the beam web in tension.
Acknowledgment This work was partially financed by FEDER funds through the Operational Competitiveness Programme – COMPETE and by national funds through FCT – Foundation for the Science and Technology within the scope of the project POCI-01-0145-FEDER-007633 and also within QREN - POPH - Typology 4.1 – Advanced Education, funded by the European Social Fund and Portuguese national funds MEC, under contract grants SFRH/BD/91167/2012, for the first author. It has also been partially funded by the following research Projects: FREEDAM under research grant RFSR-CT-2015-00022 and EQUALJOINTS under the research grant agreement no. RFSR-CT-2013-00021. References [1] CEN, EN 1993–1-8, Eurocode 3: Design of Steel Structures – Part 1–8: Design of Joints, May 2005, Standardization, Brussels, European Committee for, 2005. [2] C. Bernuzzi, R. Zandonini, P. Zanon, Experimental analysis and modelling of semirigid steel joints under cyclic reversal loading, J. Constr. Steel Res. 38 (2) (1996) 95–123. [3] CEN, EN 1998-1. Eurocode 8: Design of Structures for Earthquake Resistance – Part 1: General rules, December 2004, Standardization, Brussels, European Committee for, 2004. [4] J. Shen, A. Astaneh-Asl, Hysteretic behaviour of bolted-angle connections, J. Constr. Steel Res. 51 (1999) 201–218. [5] ABAQUS User's, Theory and Scripting Manuals. ABAQUS, Inc., Dassault Systèmes Simulia Corp., Providence, USA; 2014. [7] A. Plumier, J.B. Schleich, Seismic resistance of steel and composite frame structures, J. Constr. Steel Res. 27 (1993) 159–176. [8] D. Dubina, A.L. Ciutina, A. Stratan, Cyclic tests of double-sided beam-to-column joints, J. Struct. Eng. 127 (2) (2001) 129–136. [9] D. Dubina, A.L. Ciutina, A. Stratan, Cyclic testes on bolted steel and composite double-sided beam-to-column joints, Steel Compos. Struct. 2 (2) (2002) 147–160. [10] B. Guo, Q. Gu, F. Liu, Experimental behavior of stiffened and unstiffened end-plate connections under cyclic loading, J. Struct. Eng. 132 (9) (2006) 1352–1357. [11] P. Nogueiro, L. Simões da Silva, R. Bento, R. Simões, Numerical implementation and calibration of a hysteretic model with pinching for the cyclic response of steel joints, Int. J. Adv. Steel Constr. 3 (1) (2007) 459–484. [12] T.J. Sullivan, G.J. O'Reilly, Characterising the Seismic Behaviour of Steel Beam-Column Joints for Seismic Design, IUSS press, Pavia, Italy, 2014. [13] R.W. Clough, S.B. Johnston, “Effect of Stiffness Degradation on Earthquake Ductility Requirements”, Proceedings of Second Japan National Conference on Earthquake Engineering, 1966 227–232. [14] E.P. Popov, R.B. Pinkney, “Behavior of Steel Building Connections Subjected to Inelastic Strain Reversals”, Bull No. 13 (Nov.), American Iron and Steel Institute, University of California at Berkeley, 1968. [15] F.M. Mazzolani, Mathematical model for semi-rigid joints under cyclic loads, in: R. Bjorhovde, et al., (Eds.), Connections in Steel Structures: Behaviour, Strength and Design, Elsevier Applied Science Publishers, London 1988, pp. 112–120. [16] A. De Martino, C. Faella, F.M. Mazzolani, “Simulation of Beam-to-Column Joint Behaviour Under Cyclic Loads”, Construzioni Metalliche, 6, 1984 346–356. [17] G. Della Corte, G. De Matteis, R. Landolfo, F.M. Mazzolani, Seismic analysis of MR steel frames based on refined hysteretic models of connections, J. Constr. Steel Res. 58 (10) (2002) 1331–1345. [18] L.F. Ibarra, R.A. Medina, H. Krawinkler, Hysteretic models that incorporate strength and stiffness deterioration, Earthq. Eng. Struct. Dyn. 34 (12) (2005) 1489–1511. [19] D. Lignos, H. Krawinkler, Deterioration modeling of steel components in support of collapse prediction of steel moment frames under earthquake loading, J. Struct. Eng. 137 (11) (2011) 1291–1302. [20] O.S. Bursi, M. Galvani, “Low Cycle Behaviour of Isolated Bolted Tee Stubs and Extended End Plate Connections”, Proceedings of CTA, Italian Conference on Steel Construction, Ancona, Italy, 1997 110–121. [21] M. Sivaselvan, A.M. Reinhorn, Hysteretic models for deteriorating inelastic structures, J. Eng. Mech. ASCE 126 (6) (2000) 633–640. [22] G. Della Corte, G. De Matteis, R. Landolfo, Influence of connection modelling on seismic response of moment resisting steel frames, in: F.M. Mazzolani (Ed.), Moment Resistant Connections of Steel Buildings Frames in Seismic Areas, E. & F.N. Spon, London, UK, 2000. [23] L. Calado, C.A. Castiglioni, “Steel Beam-to-Column Connections Under Low-Cycle Fatigue Experimental and Numerical Research”, Eleventh World Conference on Earthquake Engineering, Paper No. 1227, 1996. [24] O.S. Bursi, F. Ferrario, V. Fontanari, Non-linear analysis of the low-cycle fracture behaviour of isolated tee stub connections, Comput. Struct. 80 (1) (2002) 2333–2360. [25] P.J. Madas, A.S. Elnashai, “A Component-Based Model for Beam-to-Column Connections”, Proceedings of. 10th World Conference on Earthquake Engineering, 19–24 July, Vol. 8, Madrid, Spain, 1992.
H. Augusto et al. / Journal of Constructional Steel Research 133 (2017) 310–333 [26] L. Simões da Silva, C. Rebelo, L. Mota, Extension of the component method to endplate beam-to-column steel joints subjected to seismic loading, Trends in Civil and Structural Engineering Computing, Computational Science, Engineering and Technology Series 22, Saxe-Coburg Publications, UK 2009, pp. 149–167. [27] M. Latour, V. Piluso, G. Rizzano, Cyclic modeling of bolted beam-to-column connections: component approach, J. Earthq. Eng. 15 (4) (2011) 537–563. [28] L. Simões da Silva, A. Shahbazian, F. Gentili, H. Augusto, “Implementation of a Component Model for the Cyclic Behaviour of Steel Joints”, Proceedings of Eighth International Workshop on Connection in Steel Structures, Boston, USA, 2016. [29] J.P. Jaspart, “Étude de la Semi-Rigidité des Noeuds Poutre-Colonne et son Influence sur la Resistence et la Stabilité des Ossatures en Acier”. PhD Thesis, Faculty of Applied Sciences, University of Liège, Belgium, 1991 (in French). [30] J.M. Castro, F.J. Davila-Arbona, A.Y. Elghazouli, Seismic design approaches for panel zones in steel moment frames, J. Earthq. Eng. 12 (S1) (2008) 34–51. [31] H. Augusto, L. Simões da Silva, C. Rebelo, J.M. Castro, Characterization of web panel components in double-extended bolted endplate steel joints, J. Constr. Steel Res. 116 (2016) 271–293. [32] H. Krawinkler, V.V. Bertero, E.P. Popov, Shear behaviour of steel frame joints, J. Struct. Eng. ASCE 101 (ST11) (1975) 2317–2336. [33] J.P. Jaspart, “Shear and Load-Introduction Deformability and Strength of Column Web Panels in Strong Axis Beam-to-Column Joints”, Internal Report MSM, n° 202, University of Liége, 1990 (April). [34] K.D. Kim, M.D. Engelhardt, Monotonic and cyclic loading models for panel zones in steel moment frames, J. Constr. Steel Res. 58 (2002) 605–635.
333
[35] Y.F. Dafalias, “On cyclic and Anisotropic Plasticity: (I) A General Model Including Material Behavior Under Stress Reversals. (II) Anisotropic Hardening for Initially Orthotropic Materials”. PhD Thesis, Department of Civil Engineering, University of California, Berkeley, CA, 1975. [36] N.G. Cofie, H. Krawinkler, Uniaxial cyclic stress–strain behavior of structural steel, J. Eng. Mech. ASCE 111 (9) (1985) 1105–1120. [37] M. Latour, V. Piluso, G. Rizzano, “Cyclic Model of Beam-to-Column Joints”, Proceedings of 5th Steel Conference, EUROSTEEL 2008, Graz, Austria, 2008. [38] J.L. Chaboche, Time independent constitutive theories for cyclic plasticity, Int. J. Plast. 2 (2) (1986) 149–188. [39] P. Nogueiro, “Cyclic Behaviour of Steel Connections”. PhD Thesis, Civil Engineering Department, University of Coimbra, Portugal (in Portuguese), 2009. [40] CEN, EN 1993-1-1. Eurocode 3: Design of Steel Structures – part 1–1: General Rules and Rules for Buildings, May 2005, Standardization, Brussels, European Committee for, 2005. [41] ECCS, Recommended Testing Procedure for Assessing the Behaviour of Structural Steel Elements Under Cyclic Loads. Technical Committee 1, TWG 1.3 – Seismic Design, publ. n.° 45, European Convention for Constructional Steelwork, Brussels, Belgium, 1986. [42] AISC, Seismic Provisions for Structural Steel Buildings, ANSI/AISC 341–10, USA, American Institute of Steel Construction, Chicago, 2010.