The influence of rib stiffeners on the response of extended end-plate joints

The influence of rib stiffeners on the response of extended end-plate joints

Journal of Constructional Steel Research 148 (2018) 669–690 Contents lists available at ScienceDirect Journal of Constructional Steel Research The ...

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Journal of Constructional Steel Research 148 (2018) 669–690

Contents lists available at ScienceDirect

Journal of Constructional Steel Research

The influence of rib stiffeners on the response of extended end-plate joints Roberto Tartaglia, Mario D'Aniello ⁎, Raffaele Landolfo Department of Structures for Engineering and Architecture, University of Naples “Federico II”, Via Forno Vecchio 36, 80134 Naples, Italy

a r t i c l e

i n f o

Article history: Received 11 March 2018 Received in revised form 18 June 2018 Accepted 20 June 2018 Available online xxxx Keywords: Stiffener Bolted joints Moment-rotation response Constructional imperfection Torsional restraint Seismic design

a b s t r a c t The presence of rib stiffeners in extended end-plate joints influences the yield line distribution in the tensile zone of the connection, the depth of internal lever arm as well as the resistance of compression components of the joint. In addition, the stiffeners may affect the plastic rotation capacity of the connected beam in both monotonic and cyclic regime. The current EN1993:1–8 (2005) gives limited recommendations on these issues, while EN1998-1 (2005) does not provide any detailing rules to enforce ductile cyclic response when rib stiffeners are adopted in end-plate connections. In order to investigate these criticisms, extensive parametric finite element simulations were carried out and the obtained results are described and discussed in this paper. The main analyzed parameters are the thickness, the slope (i.e. the depth to width ratio), and the constructional imperfections of the rib stiffeners for different beam-to-column assemblies alternatively designed with full and partial strength connection. The monitored response from monotonic and cyclic analyses allows characterizing the yield line distribution and the variation of internal forces into the rib and the bolt rows. The evolution of the internal lever arm of the connection, the out-of-plane bending and torsional moments developing when the connected beam experiences large plastic rotations as well as the forces acting on lateral torsional restraints are also investigated. © 2018 Elsevier Ltd. All rights reserved.

List of symbols

bCP bEP D db E fy fy,beam fy,Rib hEP hRib iz p1 p2 tCP

Base of the continuity plate Base of the end-plate Bolt diameter beam depth Vertical distance from the bolt to the edge Yielding strength Yielding strength of the beam Yielding strength of the rib End-plate height Height of the rib Radius of gyration about the weak axis of the beam Vertical distance between the first and the second bolt row line Vertical distance between the second and the third bolt row lines Thickness of the continuity plate

⁎ Corresponding author. E-mail addresses: [email protected], (R. Tartaglia), [email protected], (M. D'Aniello), [email protected] (R. Landolfo).

https://doi.org/10.1016/j.jcsr.2018.06.025 0143-974X/© 2018 Elsevier Ltd. All rights reserved.

tEP tf tRib tSWP tw,beam W C0 C1–4 CFlange CRib E Lbeam LRib Lstable M0.035 My Mpl,rd Mt Mwa Nf,Ed

Thickness of the end-plate Thickness of beam flange Thickness of the rib Thickness of the supplementary web panel Thickness of the beam web Horizontal distance between two bolts Joint without constructional defect Joints with constructional defects Resultant of forces acting in the beam flange Resultant of forces acting in the rib Elastic modulus of the steel Length of the beam Length of the rib Stable length among the restraining braces Moment at 0.035 of plastic rotation Yielding moment Beam plastic bending resistance Torsional moment Bending moment around the weak axis Axial force in the compressed flange of the stabilized member at the plastic hinge location Qm Horizontal transverse reaction forces of the braces Qm, EN1993–1-1 Design forces of the torsional bracing according to the EN1993–1-1

670

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Qm, AISC 341 Design forces of the torsional bracing according to the AISC 341 Sini Joint elastic stiffness ε Elongation δ Displacement at the beam end γov Material overstrength factor θy Yielding rotation θu Ultimate rotation ξ Normalized position of the center of compression ψ Ratio between the bending moments at the beam end of the stable length

List of acronyms CPRESS ESEP FE FEA FEM MRF PEEQ RFEM USA

Contact forces Extended Stiffened End-Plate Finite Element Finite Element Analysis Finite Element Model Moment Resisting Frames Equivalent plastic deformations Research Finite Element Model United States of America

1. Introduction Steel rib plates and haunches are commonly used to increase the strength and the stiffness of steel beam-to-column joints. Experimental evidence demonstrated that the detailing of stiffeners influences the monotonic and cyclic ductility of connection and beam, respectively in partial and full strength joints [1–15]. Among the wide variety of stiffened beam-to-column connections, extended end-plate stiffened by rib plates on both tension and compression are commonly adopted for seismic applications because they are characterized by symmetric hogging and sagging behavior and they are less expensive than haunched end-plate connections [16]. Notwithstanding the key role of the stiffeners, their design, verification and fabrication is considered troublesome by European engineers and constructors due to the limited guidance given by the current Eurocodes and the increase of constructional costs as respect to unstiffened connections [16, 17]. The nonlinear monotonic and cyclic behavior of stiffened connections can be predicted using experimental tests, analytical approaches and sophisticated finite element models, which can be impractical and inconvenient in current design practice. With this regard, Kurejková and Wald [18] recently presented a promising method to predict the response of steel joints with different types of stiffeners (i.e. rib plates and haunches) based on the “research finite element model” (RFEM). However, as highlighted by the same Authors, the RFEM is still less applicable in current practice owing to the difficulties in setting the geometrical and mechanical imperfections in advanced numerical models as well as the time-consuming calculation. Based on finite element analysis (FEAs) validated against experimental data, several studies were carried out to investigate the influence of the rib stiffeners on joint response and to develop consistent design rules. In particular, Lee [8] and Lee et al. [9, 10] validated an equivalent strut model of the rib with the relevant equations to calculate the required strength and stiffness. More recently, Abidellah et al. [14] provided a conservative estimation of the position of compression center in rib-stiffened end-plate connections. Based on the findings given by Zoetemeijer [19, 20], the current EN1993:1-8 (2005) [21] provides some design rules for haunches, which should be detailed using (i) plates for web and flanges with thickness and steel grade equal or larger than those of the beam; and (ii)

slope no larger than 45°. EN1993:1-8 (2005) [21] does not give direct specifications to detail the free-edge triangular stiffeners as the rib plates that are usually adopted for extended stiffened end-plate (ESEP) connections, even though it allows estimating the strength and the stiffness of the connection by means of the component method (i. e. the presence of the stiffener is accounted for the evaluation of the effective length of the equivalent T-Stub per bolt row close to the rib). However, it is worth noting that the Eurocodes are currently under updating and the 3rd draft (v.3.1) of the amended EN 1993-1-8 [22], which is still under revision by the CEN/TC 250/SC 3 experts at the time of the submission of this article, gives some specifications for the rib stiffeners of end-plate connections (see clause A.6.1(6)). These rules are based on the North American codes. In United States of America (USA), ESEP joints are seismically prequalified by AISC358-16 [23], which provides a step by step procedure to characterize all features of the joints such as the allowed geometry and the verification checks for strength and stability of the rib stiffeners and their influence on tension side on the basis of the studies carried out by [4–7]. In Europe, the current EN1993:1-8 (2005) [21] and EN1998-1 (2005) [24] provide neither specific requirements nor codified prequalification procedures for seismic resistant extended stiffened end-plate joints. Recently, a European seismic pre-qualification procedure of ESEP joints has been developed within the RFCS EQUALJOINTS research [16, 25] on the basis of both experimental tests and finite element simulations. In the framework of this project, the present paper describes and discusses the results of parametric finite element simulations that have been performed to investigate the role of the rib stiffeners on strength and ductility of ESEP joints in order to propose design requirements to enhance the seismic performance of this type of connection. The examined parameters are the depth-to-width ratio (i.e. the slope), the depth-to-thickness ratio of the rib stiffeners and their constructional imperfections for different beam-to-column assemblies. The yield line distribution and the relevant variation of internal forces into the rib and the bolt rows are monitored, thus allowing to characterize the evolution of the internal lever arm, the out-of-plane bending and torsional moment developing when the connected beam experiences large plastic rotations as well as the forces acting on lateral torsional restraints. The paper is organized in two main parts as follows: the investigated parameters and the design assumptions of the joints are briefly presented in the first part; the results of the FE parametric study are presented and critically discussed in the second part. 2. Parametric study 2.1. Investigated parameters The geometry of the rib stiffeners largely influences the local and global behavior of the joint. In this study the investigated geometrical features of the ribs are the following: - The thickness, which affects the stability of both the stiffener and the beam flange in compression, and the strength of the bolt rows in tension. To cover both the conditions satisfying and violating the prescriptions of AISC 358-16 [23] as well as those recommended by Lee [8] for welded joints with ribs (see Table 3 and Fig. 6) the thickness was varied in range 5 mm to 30 mm. - The slope (i.e. the depth to width ratio), which influences the transmission of the bending effects from the beam to the connection and the relevant stress concentration. Indeed, the smaller is the slope and the larger the distance of the plastic hinge from the column face, namely the larger the forces that the connection should resist although the transmission of the bending effects from the beam to the connection is more gradual, thus limiting stress concentration. In order to analyze these mechanisms, the slope of the stiffener was varied from 20° to 45°.

R. Tartaglia et al. / Journal of Constructional Steel Research 148 (2018) 669–690

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In the light of these assumptions, nine joints were considered as reference configuration for the parametric investigation, i.e. three full strength joints (ES1-F, ES2-F, ES3-F), three equal strength joints (ES1E, ES2-E, ES3-E) and three partial strength joints (ES1-P, ES2-P, ES3-P). The geometric details of these joints are depicted in Fig. 2 and summarized in Table 1 and the investigated variations of the rib geometry are reported in Table 2. The forces in each bolt row were extracted to investigate the role of the stiffener on their evolution and distribution into the connection. In addition, the equivalent plastic deformations (PEEQ) were measured to identify the most suitable detail reducing the stress concentration in the beam flange to rib welds at the tip of the rib.

- The constructive imperfections of the stiffeners, namely misalignment of the rib as respect to the beam and the connection (see Fig. 1). These constructional faults can easily occur in ordinary production conditions and when recognized during the quality control of the execution should be rectified with increase of unitary costs. Therefore, in order to understand how this type of defect can compromise both the global and the local joint behavior, four configurations of constructional faults were investigated. As shown in Fig. 1, the stiffeners (both on tension and compression side) were shifted from the vertical symmetry axis of a distance equal to ± their thickness.

The influence of the geometry of the stiffeners on the joint performance can also vary with both dimensions and shapes of the connected beams as well as with the expected performance of the connection (i.e. if the connection is full or partial strength). Hence, three single sided beam-to-column assemblies were selected to cover both shallow, intermediate and deep girders. These joints were extracted from Moment Resisting Frames (MRFs) designed according to EN1993-1-1 [27] and EN 1998-1 [24] (more details on the design of the reference frames can be found in [16]). The considered assemblies were identified as follows:

2.2. Verification checks of the investigated rib stiffeners The rib stiffeners should behave elastically in tension as well as in compression without buckling mode to restrain the deformation LRib tSWP

bCP

tRib

• ES1: with IPE360 for beam and HEB 280 for column; • ES2: with IPE450 for beam and HEB 340 for column; • ES3: with IPE600 for beam and HEB 500 for column.

Beam

tEP Column

w

p1

tCP

In addition, each beam-to-column assembly was alternatively designed three times to comply with three different performance objectives, namely full, equal and partial strength connection as established within EQUALJOINTS project (more details can be found in [16, 25]). For the sake of clarity, full strength joints should guarantee the formation of plastic hinge at the unrestrained end of the beam. Equal strength joints are characterized by balanced plastic deformations in both the end-plate of the connection and the beam, while in partial strength joints the plastic deformations and the energy dissipation mostly occur in the end-plate.

p2 Supplementary Web Plate

End-Plate hRib

Continuity Plate

bEP Fig. 2. Features of extended stiffened end-plate joints.

hRib

c tRib

LRib

arctan hRib / LRib t Rib Constructional defect type 2 (C2)

d

LRib

c

Constructional defect type 1 (C1)

e

Rib

20 , 25 ,30 ,35 , 40 , 45

5,10,15, 20, 25,30 mm Constructional defect type 3 (C3)

Constructional defect type 4 (C4)

Fig. 1. Investigated geometries and constructional faults of the rib stiffeners.

hEP

672

R. Tartaglia et al. / Journal of Constructional Steel Research 148 (2018) 669–690

Table 1 Geometrical features of the reference joints. Joint ID

Performance level

ES1-Fa ES1-E ES1-P

Full strength (F) Equal strength (E) Partial strength (P) Full strength (F) Equal strength (E) Partial strength (P) Full strength (F) Equal strength (E) Partial strength (P)

ES2-Fa ES2-E ES2-P ES3-Fa ES3-E ES3-P a

End-Plate

Rib

Bolts

Continuity plates

Supplementary web plate

hEP

bEP

tEP

hRib

LRib

d

e

W

p1

p2

bCP

tCP

Side

tSWP

mm

mm

mm

mm

mm

mm

mm

mm

mm

mm

mm

mm



mm

760 600 600

260 280 280

25 18 16

200 120 120

235 140 140

30 27 27

50 50 50

150 160 140

75 160 160

160 180 180

222 222 222

14 14 14

2 1 –

8 8 –

870 770 770

280 300 300

25 20 18

210 160 160

250 190 190

30 30 30

50 55 55

150 160 160

75 200 200

180 260 260

234 234 234

15 15 15

2 1 –

10 8 –

1100 1100 900

280 300 300

30 22 22

250 250 170

295 295 200

36 36 36

55 55 55

160 160 160

95 95 220

210 210 390

232 232 232

20 20 20

2 1 –

15 15 –

The constructional imperfections of rib stiffeners were investigated for these models.

pattern of the end-plate under both sagging and hogging moment. As previously discussed, the current EN1993:1-8 [21] provides limited requirements to guarantee this response, while AISC358-16 [23] provides more detailed requirements and verification formulas to check the strength and the stability of the rib that are summarized hereinafter. The minimum rib length on the beam side LRib should satisfy the following condition: LRib ¼

hRib tan30

ð1Þ

Å

where hRib is the height of the stiffener, equal to the height of the end-plate from the outside face of the beam flange to the end of the end-plate. It should be noted that EN1993:1-8 [21] does not give this strict requirement, but the maximum allowed angle between the edge of the stiffener and the beam flange should not be N45°. Besides, several studies [8–10, 25] suggest assuming the slope of the stiffener in the range 30°–40°. In line with AISC358-16 [23], the recent 3rd draft of the amended EN1993:1-8 [22] recommends using Eq. (1). Analogously with EN1993:1-8 [21], AISC358-16 [23] recommends that the strength of the stiffener is deemed adequate if the thickness of the rib (tRib) satisfies the following condition: t Rib ≥t w;beam

f y;beam f y;Rib

! ð2Þ

where tw,beam is the thickness of the beam web; fy,beam and fy,Rib are the yield strength of the beam and the stiffener, respectively.

To prevent buckling of the stiffener plate, AISC358-16 [23] recommends that the slenderness of the rib (i.e. its width-to-thickness ratio) should comply with the following criterion: hRib ≤0:56 t Rib

sffiffiffiffiffiffiffiffiffiffiffi E f y;Rib

ð3Þ

where E is elastic modulus of the steel. This requirement is not incorporated in both EN1993:1-8 [21] and the 3rd draft of the amended EN1993:1-8 [22]. Table 3 summarizes the strength and stability verification checks for the range of variation of the rib geometry of all investigated joint assemblies (i.e. ES1, ES2 and ES3). As it can be noted, the examined range of thickness covers both cases that do not comply with the strength and stability criteria of AISC 358 and cases that largely satisfy both Eqs. (2) and (3). 3. Finite element modelling 3.1. Modelling assumptions The finite element models (FEMs) were developed using ABAQUS 6.14 [28]. All modelling assumptions and their validation against experimental tests carried out within EQUALJOINTS project are the same as described by the Authors in previous publications [16, 25, 38, 40]. Therefore, for the sake of brevity only the main features of the models are summarized hereinafter. The beam-to-column joints were modelled considering a sub-assemblage obtained by extracting the beam and the column at the inflection points of the bending moment diagram induced by shear type

Table 2 Investigated variations of the rib geometry. Joint ID

Performance level

Rib thickness (tRib) [mm]

ES1-F ES1-E ES1-P ES2-F ES2-E ES2-P ES3-F ES3-E ES3-P

Full strength (F) Equal strength (E) Partial strength (P) Full strength (F) Equal strength (E) Partial strength (P) Full strength (F) Equal strength (E) Partial strength (P)

5 5 5 5 5 5 5 5 5

10 10 10 10 10 10 10 10 10

15 15 15 15 15 15 15 15 15

Rib slope 20 20 20 20 20 20 20 20 20

25 25 25 25 25 25 25 25 25

30 30 30 30 30 30 30 30 30

20° 20° 20° 20° 20° 20° 20° 20° 20°

25° 25° 25° 25° 25° 25° 25° 25° 25°

30° 30° 30° 30° 30° 30° 30° 30° 30°

35° 35° 35° 35° 35° 35° 35° 35° 35°

40° 40° 40° 40° 40° 40° 40° 40° 40°

45° 45° 45° 45° 45° 45° 45° 45° 45°

R. Tartaglia et al. / Journal of Constructional Steel Research 148 (2018) 669–690

ES1

Design performance level

Rib Rib Verification checks thickness slenderness tRib [mm] hRib/tRib [−] Strength check according to Eq. (2)

Buckling check according to Eq. (3)

Full strength

5 10 15 20 25 30 5 10 15 20 25 30 5 10 15 20 25 30 5 10 15 20 25 30 5 10 15 20 25 30 5 10 15 20 25 30

Not satisfied Not satisfied Satisfied Satisfied Satisfied Satisfied Not satisfied Satisfied Satisfied Satisfied Satisfied Satisfied Not satisfied Not satisfied Not satisfied Satisfied Satisfied Satisfied Not satisfied Not satisfied Satisfied Satisfied Satisfied Satisfied Not satisfied Not satisfied Not satisfied Satisfied Satisfied Satisfied Not satisfied Not satisfied Satisfied Satisfied Satisfied Satisfied

Equal and partial strength

ES2

Full strength

Equal and partial strength

ES3

Full strength

Equal and partial strength

40.00 20.00 13.33 10.00 8.00 6.67 24.00 12.00 8.00 6.00 4.80 4.00 42.00 21.00 14.00 10.50 8.40 7.00 32.00 16.00 10.67 8.00 6.40 5.33 50.00 25.00 16.67 12.50 10.00 8.33 34.00 17.00 11.33 8.50 6.80 5.66

Not satisfied Satisfied Satisfied Satisfied Satisfied Satisfied Not satisfied Satisfied Satisfied Satisfied Satisfied Satisfied Not satisfied Satisfied Satisfied Satisfied Satisfied Satisfied Not satisfied Satisfied Satisfied Satisfied Satisfied Satisfied Not satisfied Not satisfied Satisfied Satisfied Satisfied Satisfied Not satisfied Not satisfied Satisfied Satisfied Satisfied Satisfied

The accuracy of the modelling assumptions were validate against the experimental tests performed within the EQUALJOINTs research project [16]. Fig. 4 shows the comparison between the experimental results and the corresponding simulated response of a test performed on an equal strength joint having the same geometry of the ES1 assemblies investigated in the present article. As it can be observed the FE simulation satisfactory mimics both the moment-rotation response curve and the damage pattern. Further details about the validation of the adopted modelling assumptions can be found in [16, 38, 40, 42]. 4. Results from finite element analyses 4.1. Influence of rib thickness Fig. 5 depicts the moment vs joint rotation (which is the rotation due to connection and column web panel only, the beam contribution is kept out) response curves of the full strength joints. The last point of all curves corresponds to an overall chord rotation (i.e. the rotation taken as the ratio between the displacement at the tip of beam δ and its length Lbeam/2, see Fig. 3) equal to 0.06 rad. It can be observed that the joint resistance is strongly influenced by the rib thickness. Indeed, the thicker ribs keep the connection in elastic range, while those that do not comply with the AISC 358 checks (see Table 3) show plastic deformations that increases reducing the rib thickness, as also confirmed by the evolution of the yielding lines with the rib thickness shown in

Hcolumn / 2

Joint ID

3.2. Validation of FE models

Lateral-Torsional Restraint

F

Hcolumn / 2

Table 3 Verification checks of the rib stiffeners.

corresponds to an electrode grade A46 (as given by EN ISO 2560, [34]). The geometrical imperfections of beam profiles due to mill tolerances given by EN 10034 [35] were accounted for. To this end, the outof-square of the flange tips with respect to the nominal mid-axis of the flange was modelled by imposing the shape of the relevant buckling Eigen modes properly scaled to reproduce the maxima allowed imperfections, as also shown in [38, 41, 42]. Contacts were modelled considering both the normal and the tangential behavior [39]. Augmented Lagrangian Formulation was considered for the normal contact behavior. The penalty function with the friction coefficient equal to 0.30 was used to model the tangential behavior. “Surface-to-surface” interactions were used to model the contacts between (i) end-plate and column flange, (ii) bolt head and endplate and nut and column flange, (iii) shank and the corresponding surface of the holes. The surfaces belonging to the more rigid portions of the model were set as master surface. Therefore, in the case (i) the column flange was set as master surface, while in the cases (ii) and (iii) the relevant surfaces of the bolts were denoted as a master surface. Both fillet and full penetration welds were connected to the corresponding parts by means of “Tie” constraints. Both monotonic and cyclic displacement histories were used and applied at the tip of the beam as shown in Fig. 3. The loading protocol of AISC 341 [26] was adopted for cyclic analyses.

Hcolumn = 3500 mm

lateral loads on the reference MRFs [25, 29, 30]. The boundary conditions and assumed length of the members are reported in Fig. 3. Except where specified differently, the spacing of lateral torsional restraints is assumed equal to the lateral-torsional stable length segment according to clause 6.3.5.3 of EN 1993-1 [27]. All elements were discretized using C3D8I solid element type (i.e. 8node linear brick, incompatible mode), while the mesh dimension change in function of the model parts. Based on preliminary sensitivity analysis, the adopted mesh dimensions are 12.5, 10 and 15 mm respectively for bolt, end-plate and steel profiles (beam and column) with at least three elements through the thickness. The beam, the column and all the plates have a European S355 steel with the average yield strength equal to γov × fy. The Von Mises yield criterion was adopted to model steel yielding. Both isotropic and kinematic hardening were modelled by means the Chaboche model implemented in ABAQUS. The isotropic hardening material parameters b and Q as well as the kinematic parameters C and γ (for stabilized cycle) were derived from the data provided by Dutta et al. [31]. The non-linear response of the adopted high-strength pre-loadable bolts was modelled according to D'Aniello et al. [32, 33]. The pre-tensioning was modelled using the “Bolt load” option available in ABAQUS and the clamping force was set equal to the values recommended by EN1993:1-8 [21]. The material of the welds was modelled with an elastic perfectly plastic constitutive law, with yield stress set equal to 460 MPa, which

673

δ

Lbeam / 2 = 3500 mm

Fig. 3. Geometrical dimensions and boundary condition of the sub-assemblage.

R. Tartaglia et al. / Journal of Constructional Steel Research 148 (2018) 669–690 600

600

400

500

Moment [kNm]

Moment [kNm]

674

200 0 -200 -400 -600 -0.08

400 300 200 ES1-E-TEST ES1-E-FEM

100

ES1-E-TEST ES1-E-FEM

0 -0.04 0.00 0.04 Chord rotation [rad]

0.08

0

0.04 Chord rotation [rad]

0.08

Fig. 4. Validation of the FE modelling assumptions: experimental vs simulated response.

of the rib is verified. Indeed, as shown in Fig. 7a and b, the case with rib thickness equal to 5 mm (which does not satisfy the strength check) behave as unstiffened joint. On the basis of the obtained results, the requirement given by Eq. (2) suffices to restrain the connection and the beam flange under monotonic loading. This finding clarifies why both the EN1993:1-8 (which is a non-seismic code) and its recent revised draft [22] do not give additional requirements for the stability of the rib stiffener. It is also worth noting that for full strength joints the plastic demand mostly concentrates in the beam and after the formation of plastic hinge up to its capping rotation (i.e. the rotation corresponding to the peak bending moment) the deformation pattern in the ribs is almost

1000

2500

500

800

2000

400 300 200 100 0 0.00

tRib= 0 tRib= 5 tRib= 10 tRib= 15 tRib= 20 tRib= 25 tRib= 30

0.02 0.04 0.06 Joint Rotation [rad] a) ES1 beam-to-column joints

600 400

200 0 0.00

tRib= 0 tRib= 5 tRib= 10 tRib= 15 tRib= 20 tRib= 25 tRib= 30

0.02 0.04 0.06 Joint Rotation [rad] b) ES2 beam-to-column joints

Moment [kNm]

600

Moment [kNm]

Moment [kNm]

Fig. 6 (for the sake of brevity, the figures are given only for the ES2-F joints, but the trend is similar for all beam-to-column assemblies). Although the slenderness limit given by Eq. (3) is equal to 13.62 in the examined cases, it is interesting to observe that, under monotonic loading condition, only the cases with rib slenderness larger than 21 exhibit the buckling of the stiffener (e.g. ES2-F joints with rib slenderness larger than AISC limit are shown in Fig. 7a,c and e). However, all cases subjected to cyclic loading confirmed the validity of the AISC limit, experiencing out-of-plane deformations of the rib only for slenderness larger than 13.62 (e.g. shown in Fig. 7b, d and f). These findings suggest that the requirement given by Eq. (3) can be relaxed if the joints are designed for non-seismic applications, provided that the tensile strength

1500 1000 500

0 0.00

tRib= 0 tRib= 5 tRib= 10 tRib= 15 tRib= 20 tRib= 25 tRib= 30

0.02 0.04 0.06 Joint Rotation [rad] c) ES3 beam-to-column joints

Fig. 5. Moment vs. joint rotation response curves of full strength joints.

R. Tartaglia et al. / Journal of Constructional Steel Research 148 (2018) 669–690

675

Fig. 6. ES2-F yielding line distribution in function of the rib thickness variation.

constant. However, in line with the findings by Cermelj et al. [36] for welded stiffened joints, large concentration of plastic deformations occurs at the rib-to-beam welds that can consequentially lead to potential brittle failure. With this regard, Fig. 8 shows the evolution of the PEEQ index at 0.06 rad of monotonic chord rotation evaluated in the ribs (both tension and compression) and the beam flanges (both tension and compression) varying the thickness of the stiffener with slope set equal to 40°. As it can be trivially recognized, for the rib in tension (see Fig. 8a) the larger the PEEQ index the smaller the rib thickness, due to the yielding of the stiffener when its thickness is thinner than the thickness of beam web. The trend of the PEEQ index on the compression side is similar to that developing on tension side if the rib buckling does not occur (see Fig. 8b). In the cases with slender rib (i.e. tRib equal to 5 and 10 for the ES3 assemblies) the buckling of the stiffener occurs before the formation of the plastic hinge in the beam; this phenomenon occurs for both the ES2 and ES3 configuration and it is evidenced by the discontinuities in the curves. In the beam the PEEQ index both in tension and in compression (see Fig. 8c,d) is almost constant with the variation of the rib thickness. In the cases experiencing the rib buckling before the formation of the plastic hinge in the beam, the values of the PEEQ in the beam flange tends to zero.

In the beam flanges (see Fig. 8c and d) the normalized PEEQ indexes are almost constant (i.e. the ratios between the monitored peak PEEQ as respect to the maximum value is close to 1) if the stiffeners are in elastic range and without buckling. Fig. 9 shows that the global performance in equal and partial strength joints is more sensitive to the thickness of the rib as respect to the case of full strength joints, since the connection is involved in the plastic deformation and the thickness of the rib influences the resistance and ductility of the connection from the initial to the ultimate state. Indeed, the joints with thicker ribs exhibit the larger strength and the plastic deformations that move from the connection to the beam (see Figs. 10 and 11), even though the amount of rotation due to the connection prevails in all cases. Figs. 10 and 11 show also the contact forces (CPRESS) at the interface between the end-plate and column flange corresponding to 0.06 rad of chord rotation. It can be observed that the increase of the rib thickness corresponds to an increase of the contact forces around the bolt lines on the tension side of the connections, thus an increase of strength and stiffness of the equivalent T-stub per bolt row belonging to the rib in tension. This effect is more significant for partial strength joints where the opening of the end-plate is the main source of joint rotation, and the yield pattern corresponds to plastic mode type 2 at each bolt

676

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Fig. 7. Influence of loading protocol on buckling of rib with non-compliant slenderness.

R. Tartaglia et al. / Journal of Constructional Steel Research 148 (2018) 669–690 1.2 ES1-Rib Tension

1

ES2-Rib Tension

0.8

ES3-Rib Tension

0.6 0.4 0.2

PEEQ/PEEQMax [-]

PEEQ/PEEQMax [-]

PEEQ on ribs

1.2

0

1 0.8 0.6

0.4 0.2

0 t=5

t=10

t=15

t=20

t=25

t=30

ES1-Rib Compression ES2-Rib Compression ES3-Rib Compression

t=5

Rib Thickness [mm]

t=10

a)

t=20

t=25

t=30

b) 1.2

1 0.8 0.6

ES1-Flange Tension

0.4

ES2-Flange Tension

0.2

ES3-Flange Tension

0

PEEQ/PEEQMax [-]

PEEQ/PEEQMax [-]

t=15

Rib Thickness [mm]

1.2

PEEQ on beam flanges

677

1

0.8 0.6

ES1-Flange Compression

0.4

ES2-Flange Compression ES3-Flange Compression

0.2 0

t=5

t=10

t=15

t=20

t=25

t=30

t=5

Rib Thickness [mm]

t=10

t=15

t=20

t=25

t=30

Rib Thickness [mm]

c)

d)

Fig. 8. Max PEEQ vs rib thickness: rib in tension (a) and in compression (b); beam flange in tension (c) and in compression (d).

row in tension. On the compression side of the connection, the distribution of contact forces is clearly influenced by the rib thickness. Indeed, once the rib buckling is avoided, increasing the thickness of the stiffener the distribution of compression forces moves from the beam flange to the tip of the rib, thus modifying the position of the compression center. Fig. 12 shows the evolution with the chord rotation of the position of the compression center at column face, which is evaluated as its distance (ξ∙hRib) from the base of the rib stiffener (i.e. above the beam

2500

800

2000

400

tRib= 0 tRib= 5 tRib= 10 tRib= 15 tRib= 20 tRib= 25 tRib= 30

300 200 100

Moment [kNm]

Moment [kNm]

500

500

800

tRib= 0 tRib= 5 tRib= 10 tRib= 15 tRib= 20 tRib= 25 tRib= 30

300 200

100 0 0.00

0.02 0.04 Joint Rotation [rad] ES1- Partial Strength

0.06

Moment [kNm]

1000

1000

0 0.00

0.02 0.04 0.06 Joint Rotation [rad] ES3- Equal Strength

0.02 0.04 0.06 Joint Rotation [rad] ES2- Equal Strength

600

tRib= 0 tRib= 5 tRib= 10 tRib= 15 tRib= 20 tRib= 25 tRib= 30

1500

500

0 0.00

0.02 0.04 0.06 Joint Rotation [rad] ES1- Equal Strength

Moment [kNm]

400 200

0 0.00

400

tRib= 0 tRib= 5 tRib= 10 tRib= 15 tRib= 20 tRib= 25 tRib= 30

600

Moment [kNm]

1000

2500

tRib= 0 tRib= 5 tRib= 10 tRib= 15 tRib= 20 tRib= 25 tRib= 30

600 400 200 0 0.00

0.02 0.04 0.06 Joint Rotation [rad] ES2- Partial Strength

Moment [kNm]

600

flange, as shown in Fig. 12a). This assumption explains the negative value of the position of the center of compression in the case without rib (i.e. tRib = 0 mm) that is in the mid-thickness of the beam flange. In all examined cases the distance of the center of compression from the beam flange increases with the rib thickness except for the cases affected by out of plane deformations of the stiffener where the curves in Fig. 12 drop to zero (i.e. the compression center moves to the beam flange). In full strength joints without buckling of the

2000

1500 1000 500 0 0.00

tRib=0 tRib=5 tRib=10 tRib=15 tRib=20 tRib=25 tRib=30

0.02 0.04 0.06 Joint Rotation [rad] ES3- Partial Strength

Fig. 9. Moment vs. joint rotation response curves of equal and partial strength joints.

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Fig. 10. Influence of rib thickness for equal strength joints: a) Yielding lines and b) CPRESS distribution.

stiffeners, the center of compression ranges within 0.3 and 0.4 times the rib depth and its position is almost constant after the formation of the plastic hinge in the beam (see Fig. 12b). The center of compression of equal strength joints is slightly deeper, but its position is still almost constant with the imposed rotation when plastic deformations occur also in the beam (e.g. after 0.022 rad for ES2 assemblies as shown in Fig. 12c). Even for partial strength joints the distance of the center of compression from the beam flange increases with the rib thickness, but this distance increases with the rotation (see Fig. 12d). Indeed, with the connection opening that occurs after the end-plate yielding, the compression forces are transferred by the rib with an equivalent strut mechanism, thus modifying the distribution of the internal forces that migrate from the beam flange to the tip of the rib, as shown in Fig. 11.

In order to investigate how the rib thickness influences the transmission of compression forces in the connection, the resultant of forces (which were obtained integrating the longitudinal normal stress) acting in both the rib (CRib) and the beam flange (CFlange) at the end-plate interface were monitored. The distributions of their values normalized to the total compression force (C) are depicted in Fig. 13 in function of the chord rotation. For the sake of brevity, solely the curves corresponding to ES2 joints are shown in Fig. 13, being similar the trends for the other beam-column assemblies. Fig. 13 a and b depict the evolution of compression forces in full strength joints transferred by the rib and the beam flange, respectively. It can be noted that the distribution between the rib and the beam is almost constant, once the buckling is avoided (e.g. thickness larger than 5 mm for ES2-F joints under monotonic loading). However, for the stockiest stiffener (e.g. 20 mm ≤ tRib

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679

Fig. 11. Influence of rib thickness for partial strength joints: a) Yielding lines and b) CPRESS distribution.

≤ 30 mm) the beam flange and the rib transfer almost the same amount of compression forces. On the contrary, in case of partial strength (see Fig. 13c and d) increasing the rib thickness the compression forces are mostly transferred by the stiffener. Indeed, due to the connection opening the resistance of outer bolt rows decreases and the inner bolt rows are activated, thus modifying the transfer mechanism of bending moment from the beam to the connection. In particular, when the rib thickness is equal to or larger than twice the thickness of the beam web, plastic deformation develops in the beam and localizes at the rib-beam flange interface at about 0.02 rad of imposed chord rotation. Following this phenomenon, the most of compression forces are entirely transferred by the rib stiffener, thus explaining the shifting of the compression center for equal and partial strength joints (see Fig. 12c,d).

4.2. Influence of rib slope Fig. 14 shows the moment-rotation response curves of ES2 assemblies with rib thickness equal to 20 mm, which satisfies the AISC requirements for strength and stability of the stiffener, varying the rib slope. As it can be observed, the shape of the curves does not appreciably differ varying the slope of the stiffener, but both strength and stiffness of the joints change. All full strength joints are characterized by a post-capping response with similar softening due to the deterioration of plastic hinge. However, the strength and stiffness decrease with the slope of the rib (e.g. for ES2-F assemblies in Fig. 14a the strength and stiffness with rib slope set equal to 20° are about 20% larger than those of joints with rib slope equal to 45°). Equal strength joints with rib slope ranging from 20° to 30° show a post-capping response with

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Fig. 12. Compression center vs. chord rotation.

The differences of global response curves correspond to different local behavior in both tension and compression zones of the connections. It was observed that the variation of rib slope has negligible influence on the internal distribution of tensile forces in the connection. However, the steeper ribs bring on tensile force demand slightly larger in the second and third bolt rows, which are the lines close to the beam flange (i.e. the second line is out of the beam section and the third row is immediately inside the beam depth). On the contrary, the most significant effect can be observed on the compression side. Indeed, the steeper the rib the closer to the beam flange is the position of the center of compression (see Fig. 15), but this tendency differs with the

1.0

1.0

0.8

0.8

0.4 0.2 0.0 0.00

0.04

0.6 0.4 t =30 mm

0.2

t =5 mm 0.02

t = 0 mm

tRib

CFlange / C [-]

t =30 mm

0.6

tRib

CRib / C [-]

degradation similarly to full strength joints, while no degradation can be observed for the cases with steeper rib. The influence of the rib slope on strength and stiffness of equal strength joints is slightly lower, but still significant (e.g. for ES2-E assemblies in Fig. 14b the strength and stiffness with rib slope set equal to 20° are respectively about 14% and 10% larger than those of joints with rib slope equal to 45°). The slope of the rib influences the partial strength joints less than the other types of joints. Indeed, all partial strength assemblies do not exhibit degradation of the response curves and the variations of strength and stiffness are lower than 10% and 6%, respectively, at 0.06 rad of chord rotation (see Fig. 14c).

0.0 0.00

0.06

0.02

Chord Rotation [rad]

0.04

0.06

Chord Rotation [rad]

a) compression forces transferred by the rib

b) compression forces transferred by the beam flange ES2-F joints

0.6

0.4 t =5mm

0.2 0.0 0.00

0.02

0.04

t =0 mm

tRib

0.8 CFlange / C [-]

0.8

1.0 t =30 mm

tRib

CRib / C [-]

1.0

0.6

0.4 0.2

0.06

Chord rotation [rad]

0.0 0.00

t =30 mm

0.02

0.04

0.06

Chord rotation [rad]

c) compression forces transferred by the rib

d) compression forces transferred by the beam flange ES2-P joints

Fig. 13. Evolution of compression forces transferred by the rib and the beam flange for different thicknesses of the rib stiffeners.

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Fig. 14. Moment-rotation response curves varying the slope of the rib stiffener.

Fig. 15. Evolution of the compression center for different slopes of the rib stiffener.

design level of the joints. Table 4 summarizes the position of the compression center for different slopes of the rib stiffener, and in Fig. 15 the curves of the normalized position of the center of compression (ξ) are compared to the centroid of the equivalent T-area made of the rib web and beam flange, which is the value proposed to calculate the resistance of extended end-plate joints according to [14, 25]. As it can be noted, assuming the center of compression in the centroid of the Tarea is conservative for equal and partial strength joints for every slope of the rib stiffener, while it can be unconservative for full strength joints if the slope of the rib is set equal to 45° (see Fig. 15a). This result depends on the deterioration of plastic hinge due to the out-of-plane deformation of the beam flange in compression that increases for the steeper ribs. As a general remark, for a given slope of the rib stiffener, the position of the compression center of both full and partial strength joints is almost constant up to 6% of chord rotation, see Fig. 15 and Fig. 15c respectively. Despite the fact that partial strength joints have deeper normalized position of the compression center (ξ) as respect to full strength assemblies, negligible variations with chord rotation can be recognized for each value of the slope of the rib. Contrariwise, for full strength joints the position of the compression center decreases with the rotation for steeper stiffeners due to the degradation of plastic hinge. Equal strength joints exhibit different local response due to peculiarity of their failure modes. Indeed, the assemblies with rib slope in the range 20°–30° exhibit first the plastic deformation of the end-plate connection (i.e. gap opening between the end-plate and column face), which corresponds to the initial horizontal branch in Fig. 15b.

Table 4 Position of the compression center for different slopes of the rib stiffener. Design criteria

Full Strength Equal Strength Partial Strength

Rib slope

Max variation

20°

25°

30°

35°

45°

ξ [−]

ξ [−]

ξ [−]

ξ [−]

ξ [−]

[%]

0.520 0.418 0.577

0.452 0.396 0.553

0.407 0.362 0.508

0.378 0.343 0.487

0.233 0.261 0.381

226 105 151

Afterwards, due to the strain hardening occurring in the connection, plastic deformations develop into the beam and the position center of compression drops to the beam flange. The cases with steeper ribs show a more gradual transition with almost constant position of the center of compression for a given rib slope. This finding is consistent with their failure modes, which tend to those experienced by partial strength joints (i.e. the most of plastic deformation concentrates into the end-plate). The variation of the compression center depends on the distribution of the compression forces in the beam flange and the rib. Fig. 16 shows that the amount of compression force transferred by the stiffener decreases with its slope. In particular, for full strength joints the resultant of compression forces in the rib varies from 80% to 40% of the total compression force if the rib slope change from 20° to 45° (see Fig. 16a,b). In equal and partial strength joints the range of variation of the compression forces transferred by the rib is smaller and it falls within 60% to 40% the total compression force varying the rib slope from 20° to 45° (see Fig. 16c,d,e,f). The rib slope can also influence the stress concentration in the ribto-beam zone. Similarly to what previously described in Section 4.1 (see Fig. 8), also in this case the evolution of PEEQ index normalized to the peak value of the joint at 6% of rotation is monitored in both beam flanges and rib of full strength joints (see Fig. 17, where the data for ES2 assemblies are depicted). The plastic strain demand of the beam flange decreases for steeper ribs (see Fig. 17a). However, the evolution of PEEQ index in beam flange on tension side is almost constant with the rib slope, while in beam flange on compression side it largely decreases varying the rib angle from 20° to 45°. On the contrary, the normalized PEEQ index in the rib stiffener increases for both tension and compression side at the tip of the stiffener, even though the plastic strain concentration is more pronounced for the rib in compression where the normalized PEEQ index varies from 30% to 60% more than the corresponding values of the rib in tension for rib slope ranging from 30° to 45°. These findings highlight that increasing the slope of the stiffener increases the plastic strain demand in the rib and its welds to the beam flange, thus potentially inducing the failure at the toe of the weld. The plots depicted in Fig.17a also infer that the rib slope can also influence the degradation of hysteretic response of plastic hinge in the

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Fig. 16. Evolution of compression forces transferred by the rib and the beam flange for different slopes of the rib stiffener.

1.2 1 0.8 0.6 0.4 0.2 0

Beam flange in tension Beam flange in compression

20°

25°

30° 35° Rib slope a)

40°

the slope of the rib stiffeners. Fig. 19 shows that the amount of compression force transferred by the stiffener decreases with its slope, while the resultant of tensile force is almost insensitive (see Fig. 19b). On the contrary the contribution transferred by the beam flange increases both in tension and in compression if the rib angle changes from 20° to 40°. Under both monotonic and cyclic loading conditions, the localized forces transferred by rib stiffener on the beam flange modify the deformation pattern under large plastic strains, magnifying the out of plane deformations of the flanges and web and leading to a lateral-torsional deformed shape of the plastic segment of the beam that should be properly restrained to avoid the overall buckling of the member. Therefore, both European and North American codes recommend adopting bracings to restrain the beam where plastic hinge forms. However, out-ofplane deformations of the plastic hinge induces secondary effects on the connection, namely bending in the weak axis of the connection and torsional moments. These effects are generally disregarded by

PEEQ / PEEQMax

PEEQ / PEEQMax

beam of full strength joints, being the deterioration of plastic hinge related to the plastic buckling of the beam flanges that are restrained by the stiffener. Therefore, cyclic analyses have been carried out on full strength joints to investigate the flexural response of the connected beams. Fig. 18 shows the hysteretic response curves (i.e. moment at the tip of the rib vs. rotation) of the beams of ES2-F assemblies with rib slope equal to 20°, 30 and 40°, where it can be observed a moderate influence of this parameter on the beam degradation. Indeed, the residual bending resistance at a plastic rotation (which has been evaluated according to ECCS-45 [37] procedure) equal to 0.035 rad varies from 78% to 81% the yield bending strength increasing the slope from 20° to 40°. This finding is also confirmed by the variation of maximum PEEQ index that occurs on the beam flange close to rib tip (see. Fig. 18d,e,f). Analogously to the results observed under monotonic loading, the distribution of internal forces and their resultants are influenced by

45°

1.2 1 0.8 0.6 0.4 0.2 0

Rib in tension Rib in compression

20°

25°

30° 35° Rib slope b)

Fig. 17. Max PEEQ vs rib slope in beam flange (a) and rib (b).

40°

45°

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Fig. 18. Cyclic response of the beam of full strength joints varying the rib slope.

design codes, although potentially responsible of unexpected plastic deformations in either end-plate or bolts, or even in both components of the connection when plastic hinge in the beam experience large rotation under cyclic loading. Both torsional and weak axis moments trivially depend on the cumulated damage in the plastic hinge, but they are also affected by the spacing of bracings (i.e. the lateral restraints), the shape of beam and column (i.e. their second moment of area in both strong and weak axis, as well as the torsional inertia). Therefore, the secondary effects on the connection as well as the transverse reactions of the restraints of the beam flanges at plastic rotation equal to 0.035 rad are monitored for the examined beam-to-column assemblies (i.e. ES1, ES2 and ES3) considering alternatively the spacing of bracings recommended by EN1993–1 [27] and AISC341–16 [26]. The former code specifies that the stable length Lstable among the restraining braces for uniform beam segments with I or H cross sections with db/tf ≤ 40ε (being db the beam depth and tf the thickness of beam flange) under linear moment should be assumed as follows: Lstable ¼ 35  ε  iz

for 0:625 ≤ψ≤1

Lstable ¼ ð60−40ψÞ  ε  iz

for

ð4Þ

−1 ≤ψ≤0:625

ð5Þ

-0.05 0.00 0.05 Chord rotation [rad]

a)

for

−1≤ψ≤0:625

ð6Þ

ð7Þ

where Nf,Ed is the axial force in the compressed flange of the stabilized member at the plastic hinge location; db is the beam depth and tf the thickness of the beam flange. The design force required by AISC341-16 [26] is given as follows:   Q m;AISC341 ¼ 0:06N f ;Ed ¼ 0:06  γov  Mpl;Rd = db −t f

ð8Þ

As it can be recognized Eq. (8) leads to larger forces because it was derived for seismic condition, while Eq. (7) was determined for monotonic loading conditions.

0.0 R20° R30° R40°

-0.5

0.10

is the ratio between

  Q m;EN1993−1 ¼ 0:015  N f ;Ed ¼ 0:015  1:1  γov  Mpl;Rd = db −t f

0.5

-1.0 -0.10

MEd; min Mpl;Rd

The design forces that the bracing should resist are assumed by EN1993-1 [27] as follows:

0.5

-0.5

with fy expressed in N/mm2; iz is the radius of gyration

  Lstable ¼ 0:19  iz  E= γ ov  f y

1.0

R20° R30° R40°

235 fy

the bending moments at the beam end of the stable length among the lateral restraints and Mpl,rd is the beam plastic bending resistance. AISC341-16 [26] recommends that the maximum spacing of the bracing should be assumed as follows:

1.0

0.0

qffiffiffiffiffiffi

about the weak axis of the beam; and ψ ¼

CRib / C [-]

CFlange / C [-]

where

ε¼

-1.0 -0.10

-0.05 0.00 0.05 Chord rotation [rad]

0.10

b)

Fig. 19. Cyclic evolution of normal forces in the beam flange (a) and rib (b) for slope of the stiffener equal to 20°, 30° and 40°.

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14

10

8 6

Qm

4

30° 35° Rib slope

40°

45°

Mt

25°

30° 35° Rib slope

40°

Qm

Mt/Mpl,beam [%]

10

20°

10 8 6

2

Qm

0

ES2_EN1993-1 ES2_AISC341

12

4

5

30° 35° Rib slope

40°

20°

25°

30° 35° Rib slope

40°

ES3_AISC341

20 15 Qm

10 5

25°

30° 35° Rib slope

40°

45°

3

2 Mwa

20°

25°

30° 35° Rib slope

40°

45°

40°

45°

14

10

ES3_EN1993-1

8

ES3_AISC341

6

4

12 10 8

ES3_EN1993-1

6

ES3_AISC341

Mwa

4 2

Mt

0

0 20°

4

f)

2

Qm

0

45°

ES2_EN1993-1 ES2_AISC341

45°

Mwa/Mpl,beam [%]

25

Mt/Mpl,beam [%]

ES3_EN1993-1

40°

0

12

30

30° 35° Rib slope

5

1

e) 35

25°

6

Mt

20°

45°

d)

5 Mwa

0

25°

10

c) 14

ES2_EN1993-1 ES2_AISC341

ES1_AISC341 15

45°

b) 15

ES1_EN1993-1

20

0 20°

20

Qm/Nf,Ed [%]

4

Mwa/Mpl,beam [%]

25°

a)

Qm/Nf,Ed [%]

6

0 20°

ES2

ES1_AISC341

2

Qm

0

ES3

8

Mwa/Mpl,beam [%]

ES1_AISC341

10

Mt/Mpl,beam [%]

Qm/Nf,Ed [%]

ES1

ES1_EN1993-1

2

g)

25

ES1_EN1993-1

12

20°

25°

h)

30° 35° Rib slope

40°

20°

45°

25°

30° 35° Rib slope

i)

Fig. 20. Reaction forces of the lateral torsional restraints and secondary effects on the connection.

The horizontal transverse reaction forces of the braces (Qm) were measured in the theoretical location of the lateral bracing that were simulated by fixing the transverse translational degree of freedom of the reference points connected to the centroid of each beam flange of the FE model. In addition, both the torsional (Mt) and weak axis bending (Mwa) moments were measured in the connection (i.e. at column face). Fig. 20 shows that the reaction forces and internal moments due to the formation of plastic hinge are highly influenced by the stable length Lstable. It is interesting to observe that spacing the braces according to EN1993-1 [27] corresponds to larger effects than the cases compliant to AISC341-16 [26]. This finding is consistent with the examined assumptions. Indeed, both Eqs. (4) and (5) calculate a stable length smaller than Eq. (6), thus shorter restrained beam segments have larger lateral stiffness and consequently larger reaction forces although the EC8 compliant braces would be theoretically designed for the smaller forces. It is also interesting to note that both Eqs. (7) and (8) unconservatively estimate the brace reaction forces in the most of cases. Fig. 20a,d,g, also show that the influence of the rib slope on Qm differs with the joint assembly. In particular, for ES1 joints the reaction force of

the braces increases with the rib slope, while decreasing for ES2 and ES3 assemblies. The different tendency of the smaller beam-to-column assemblies can be explained considering that the torsional stiffness of the column as well as the out-of-plane stiffness of the beam play an important role when plastic hinge forms in the beam and out of plane deformations occur. In ES1 assembly the ratio between the column torsional stiffness and the weak axis bending stiffness of the beam is smaller of about 15% than ES2 and ES3. This difference is also confirmed by the twisting of the column and it can be the reason why increasing the rib slope the reaction forces increase. In the light of the obtained results, it seems that the braces should be designed to resist forces larger than 2.5–3 times those predicted by Eq. (8) to restrain effectively the beam under cyclic loading up to 4% of chord rotation. The trend of torsional and out-of-plane bending moments at column face is similar to that of the brace reaction forces, showing considerable values. Indeed, the torsional moments vary from 5% to 13% of the inplane bending strength of the beams, while the out-of-plane bending moments vary within 2% to 22% of the corresponding in-plane bending strength.

Fig. 21. Variation of the compression center with the thickness and the slope of the rib: ES2-F (a), ES2-E (b) and ES2-P (c).

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Fig. 22. Position of the compression center of ES-2-F assemblies: rib slope equal to 30° and 40° varying the thickness.

These results suggest that some ductility requirements may be conservatively used also for full strength joints to avoid potential brittle failure of the bolts that might be subjected to these secondary effects when large rotation demand cumulates in the beam plastic hinge. It is also interesting to note that for joints with Eurocode-compliant restrained length the torsional and out-of-plane bending moments are larger than those occurring in the cases with AISC-compliant restrained length. 4.3. Thickness vs. slope This section describes and discusses the mutual interaction of both thickness and slope on the joint response. For the sake of brevity only the cases with rib slope equal to 30° and 40° are shown hereinafter, being representative of the detail adopted by AISC358-16 [23] and the forthcoming European pre-qualification [16], respectively. As general remark, the moment-rotation response curves are almost overlapped varying the thickness of the stiffeners for both rib slopes for all

examined beam-to-column assemblies (i.e. ES1, ES2 and ES3). However, the response of the joints differs at local level. As shown in Section 4.1, increasing the rib thickness, the compression center moves from the beam flange to the web of the stiffener, but this effect differs with its slope. With reference to ES2 assemblies, Fig. 21 shows that the center of compression is closer to the beam flange in the cases with the steeper rib (e.g. those with slope equal to 40°). However, for all cases with the stiffener compliant to Eq. (3) the results confirm that assuming the center of compression in the centroid of the T section made of the beam flange and the rib web at 4% of rotation is satisfactory (see Fig. 22 with reference to ES2 full strength assemblies). The distribution of the internal compression forces in both the beam flange (CFlange) and the rib web (CRib) clarifies the findings as show in Figs. 21 and 22. Indeed, as depicted in Fig. 23, the cases with a rib slope equal to 30° develop larger compression forces in the rib web than those with rib slope equal to 40° for all examined values of the rib thickness. The resultants of compression forces in the beam flange are almost independent of the rib slope for the cases with thin stiffener,

Fig. 23. Compression forces in the rib web and the beam flange for 30° and 40° rib slope varying the rib thickness: 5 mm (a and d), 20 mm (b and e) and 30 mm (c and f).

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Fig. 24. Bolt-row forces for ES2-F assemblies with rib slope equal to 30° and 40° at 2% and 4% of rotation: rib thickness equal to 5 mm (a and d), 20 mm (b and e) and 30 mm (c and f).

whose response tends to be similar to that of unstiffened connection due to rib buckling (Fig. 23d). Contrariwise, CFlange increases with the rib thickness, but decreases with the rib slope (Fig. 23e,f). Since the bending strength of the joints is similar at the same beamcolumn assembly, the differences of the distribution of compression forces are counterbalanced by slight differences of the distribution of tensile forces in the bolt rows. Fig. 24 depicts the distribution of boltrow forces in ES2-F assemblies (i.e. full strength with six bolt rows) at 2% and 4% of chord rotation. It is interesting to note that at 2% of rotation the cases with a rib slope equal to 40° exhibit larger forces per bolt row than the cases with 30°, thus compensating the differences in the distribution of the compression forces. At 4% of rotation the differences of bolt-row forces become negligible, although small differences of corresponding moment can be observed (see Table 5) due to the different positions of the center of compression. As a general remark, the tensile forces increase in the first bolt row and decrease in the third line (which is the inner bolt row below the beam flange) if steeper ribs are used. It is also important to highlight that the forces of inner bolt rows increase with the imposed rotation for the cases with thin rib web, whichever the rib slope is considered. This effect is due to the rib buckling that modifies the response of the assembly, which tends to behave as an unstiffened end-plate joint. For thick stiffener (i.e. thickness compliant with Eq. (3)), the forces of the inner bolt rows under the symmetry axis of the connection are quite small, thus neglecting their contribution to calculate the design resistance of the joint seems justifiable.

4.4. Constructional imperfections Both monotonic and cyclic analyses were performed in order to investigate the influence of constructional imperfections on the global and local response of the joints. The FE results are very similar for all examined joint assemblies. For the sake of brevity, the obtained findings are discussed with reference to ES2-F assemblies with rib slope equal to 45° and thickness equal to 20 mm, which is also referred as configuration “C0” hereinafter. Fig. 25a depicts the monotonic moment-rotation curves that are almost overlapped up to 3.5% of chord rotation. For larger imposed rotation, the results are apparently surprising. Indeed, the constructional imperfections C3 and C4 exhibit larger capping rotation than the reference “perfect” configuration C0. The local behavior of the connection is more affected by the imperfections, which induce non-symmetrical distribution of internal forces and deformations. Indeed, except for the configuration C1, all other types of constructional defects have the compression center closer to the beam flange than the reference assembly C0 (see Fig. 25b), with a consequent decrease of the internal level arm. This result is also confirmed by the distribution of compression forces in the beam flange and rib web (see Fig. 25c and d, respectively). The different types of behavior mostly depend on the position of the stiffener on the compression side. Indeed, only the constructional imperfection type C1 has the rib in compression perfectly aligned with the beam web, thus being effective to transfer the compression forces. In addition, the eccentricity of the rib on tension side provides a

Table 5 Bolt-row forces and corresponding moment at 4% of rotation (ES2-F assemblies). tRib = 5 mm

Line 1 Line 2 Line 3 Line 4 Moment [kNm]

tRib = 20 mm

tRib = 30 mm

Rib slope = 30°

Rib slope = 40°

Rib slope = 30°

Rib slope = 40°

Rib slope = 30°

Rib slope = 40°

Bolt-row force

Level arm

Bolt-row force

Level arm

Bolt-row force

Level arm

Bolt-row force

Level arm

Bolt-row force

Level arm

Bolt-row force

Level arm

[kN]

[mm]

[kN]

[mm]

[kN]

[mm]

[kN]

[mm]

[kN]

[mm]

[kN]

[mm]

296 910 855 292 1060

626 551 371 191

236 911 856 308 1020

623 548 368 188

651 720 617 42 1187

698 623 443 263

610 744 682 16 1143

672 597 417 237

624 733 649 13 1203

708 633 453 273

671 7193 583 40 1145

678 603 423 243

R. Tartaglia et al. / Journal of Constructional Steel Research 148 (2018) 669–690

687

Fig. 25. Influence of constructional imperfections: moment-rotation curve (a), position of the compression center (b) and distribution of the compression forces in the beam flange (c) and the rib web (d).

beneficial effect because it restrains the beam flange of the plastic hinge. In all the other cases, the eccentricity of the rib on compression side impairs the effectiveness of the transfer mechanism of compression forces, thus the compression center moves from the rib web to the beam flange. However, some differences can be recognized between the types of imperfection C2, C3 and C4. The latter cases show a similar variation of the compression as respect to the reference joint C0, while C2 configuration is the closer to the C0 joint. These differences are due to the position of the stiffener on the tension side. In the C3 and C4 configurations both the ribs on tension and compression sides are not aligned

with the beam web; contrariwise in C2 configuration the rib on tension is perfectly centered with the beam. The misaligned stiffeners restrain the buckling of the beam flange more effectively than the cases with aligned ribs, thus providing larger bending strength and rotation capacity to the plastic hinge of the beam of C3 and C4 configurations (see Fig. 28), despite the smaller internal lever arm of the connection (see Fig. 26). This latter consideration is better clarified analyzing the distribution of contact forces (CPREES) between the end-plate and the column (see Fig. 26). For C1, the CPREES distribution shows that the rib web can

Fig. 26. Distribution of contact forces (CPRESS) for the joints with constructional imperfections: C1 (a), C2 (b), C3 (c), C4 (d).

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Fig. 27. Forces in the bolts adjacent to the rib stiffener in ES2-F assemblies.

transfer compression forces increasing the imposed rotation up to 6% of rotation, where the internal distribution of contact forces changes due to the buckling of the beam flange (see Fig. 26a). In the case of C2 (where the rib on the compression is closer to a bolt alignment) the contact forces are almost equally distributed in the beam and in the rib for small rotations (e.g. 2%), but increasing the imposed rotation the compression forces mostly concentrate in the beam (see Fig. 26b) with asymmetric distribution into the beam flange due to its plastic buckling, whose deterioration effects are magnified by the eccentricity of the stiffener on compression side. A similar trend can be also observed for C3 and C4 configurations (see Fig. 26c and d, respectively). Even on the tension side, the constructional imperfections induce non-symmetric distributions of bolt forces, especially in the outer bolt rows adjacent to the rib stiffener. Fig. 27 shows the evolution of bolt forces in the four upper bolts of the ES2-F assemblies with rib slope equal to 45°. As it can be recognized, the larger differences occur in the outer bolt row (i.e. bolts 1 and 2), while the bolt row close to the

Moment [kNm]

500

1000

C0 C1 and C2 C3 C4

Moment [kNm]

1000

0 -500

-1000 -0.08

-0.04

beam flange shows negligible differences. Indeed, the first bolt row is generally subjected to forces smaller than those acting in the second row, which is directly subjected to the larger tensile force transferred by the beam flange that additionally restrains the yield line pattern of the second bolt row. Hence, the additional effects due to the imperfections are more evident in the bolts 1 and 2 (compare Fig. 27a,b to Fig.27c,d). The secondary effects on the bolts differ with the type of imperfection. If the rib on tension is aligned to the beam web (e.g. C2 defect type), the bolt forces are almost symmetrically distributed although the misalignment of the stiffener on compression side. In the cases with misaligned rib on tension side, the equivalent T-Stub per bolt row is non-symmetric and the bolt forces increases in the bolt closer to the stiffener. For instance, in C1 configuration the rib is closer to the bolts on the right side of the connection and, comparing the results of Fig. 27a and b, it can be observed that the force in the relevant bolt 2 is larger of about 30 kN than the paired bolt 1. The same trend can be

0.00

0.04

500 0

-500 -1000 -0.08

0.08

Chord rotation [rad] a) C0 C1 and C2 C3 C4

Moment [kNm]

Moment [kNm]

0.08

1000

0

500

C0 C1 and C2 C3 C4

0 -500

-500

-1000 -0.08

chord rotation = 4%

-0.04 0 0.04 Chord Rotation [rad]

b)

1000

500

C0 C1 and C2 C3 C4

chord rotation = 5% -0.04

0 0.04 Chord Rotation [rad] c)

0.08

-1000 -0.08

chord rotation = 6%

-0.04

0

Chord Rotation [rad] d)

Fig. 28. Hysteretic response curves varying the type of constructional imperfection.

0.04

0.08

R. Tartaglia et al. / Journal of Constructional Steel Research 148 (2018) 669–690

also observed for C3 and C4 configurations where the ribs are closer to the bolt 1 that experiences forces larger than 7% of its paired bolt 2 in both the cases. The constructional imperfections also influence the ductility of the beam in full strength joints under cyclic loading conditions as shown in Fig. 28, where the results of the cyclic analyses are depicted. It is trivial to note that both C1 and C2 configurations exhibit the same hysteretic response curves, since their shapes are antisymmetric (see Fig. 1). The cyclic moment rotation curves are almost overlapped up to 2% of rotation (see Fig. 28a). Increasing the deformation demand in the plastic hinge the differences due to the type of imperfections arise because the stiffener interacts with the buckling waves of the plastic hinge. The configurations C1 and C2 do not show appreciable deterioration of the response curves that are similar to that exhibited by C0 joint. On the contrary, C3 and C4 exhibit an apparently surprising response with less degradation than C0. Indeed, at 4%, 5% and 6% of rotation (see Fig. 28b, c and d) the hysteretic areas and the corresponding energy of C3 and C4 are about 10% larger than C0. This feature can be explained considering the role of the eccentric ribs that contemporary restrains both beam flanges from the buckling and the torsional deformations, thus postponing the degradation of the plastic hinge. This beneficial effect is less pronounced in the configurations C1 and C2 because only a single flange is restrained.





• 5. Conclusions The influence of the rib stiffeners on both global and local behavior of extended stiffened end-plate joints has been investigated by means of parametric finite element simulations. On the basis of the obtained results, the following conclusions can be drawn: • The design rules recommended by AISC 358-16 [23] effectively avoid the buckling of the stiffener under cyclic loading notwithstanding large plastic deformations occur at the tip of the rib. However, the results obtained from finite element simulations show that if the joints are designed for non-seismic applications (i.e. designed to resist solely monotonic loading) it is sufficient to verify only the tensile resistance. This finding confirms the criteria given by the 3rd draft (v.3.1) of the amended EN 1993-1-8 [22]. • The thickness of the stiffener largely influences the moment-rotation response of the joints. The joint response improves increasing the thickness of the ribs and the center of compression moves from the beam flange to the rib web, thus increasing the internal lever arm of the strength of the connection. The results obtained for all examined full strength joints show that assuming the center of compression according to Abidelah et al. [14], namely in the centroid of the equivalent T-area constituted by the beam flange and rib web, is satisfactory consistent with the response of the joint at 0.04 rad of chord rotation provided that the stiffeners do not buckle. The assumption by Abidelah et al. [14] on the center of compression is largely conservative for equal and partial strength joints, which exhibit larger internal lever arm. • Large concentration of plastic deformations occurs at the intersection between the rib tip and the beam flange, which is a weak zone where brittle fracture can occur. The maximum PEEQ index decreases with the rib thickness. Once the rib buckling is avoided, the maximum plastic deformation in the beam is almost constant. • The slope of the rib stiffener in the range 20°–45° does not appreciably modify the overall moment-rotation curve of the joints, but it influences the local behavior at both connection and beam levels where the internal distributions of forces on both tension and compression side change. The internal force regime of full strength joints is more influenced by the rib slope than the cases of equal and partial strength joints, which exhibit the gap opening of the connection. • Increasing the slope of the stiffener increases the plastic strain demand in the rib and its welds to the beam flange, thus potentially



689

inducing the failure at the toe of the weld. In addition, steeper rib slopes (i.e. close to 45°) reduce the beam ductility, because the stockier stiffeners induce additional stress concentration in the beam flange under compression, thus anticipating the buckling of the beam flange and increasing the out-of-plane deformations of the plastic hinge. The out-of-plane deformations of the plastic hinge impose secondary effects on the connections, namely bending moment in the weak axis of the beam as well as torsion of the beam, which vary with the dimensions of the beam-column assemblies. The torsional moments vary from 5% to 13% the in-plane bending strength of the beams, while the out-of-plane bending moments vary within 2% to 22% the corresponding in-plane bending strength. These effects are quite large and should be accounted for in the design stage to avoid premature failure of the bolts. The reaction forces of the lateral-torsional braces vary with their spacing as well as with the torsional stiffness of the column and the out-ofplane stiffness of the beam. Spacing the braces according to EN1993-1 [27] leads to effects larger than those exhibited by the cases compliant to AISC341-16 [26]. In addition, both EN1993-1 [27] and AISC341-16 [26] largely underestimate the brace reaction forces in some cases. In the light of the obtained results, it seems that the braces spaced according to EN1993-1 [27] should be designed to resist forces larger than 2.5–3 times those recommended by AISC341-16 [26] to restrain effectively the beam under cyclic loading up to 4% of chord rotation. The constructional imperfections of the rib stiffener may unexpectedly have beneficial influence on the global response curves of full strength joints. Indeed, the eccentricity of the stiffener allows restraining the buckling of the beam flange and the torsional deformations of the plastic hinge, thus increasing the capping rotation and the overall ductility. However, the bolt forces increase due to the additional secondary effects induced by the rib eccentricity. The influence of this effect on the response of the connections needs further studies. The numerical results suggest that the geometrical requirement of AISC358–16 [23] on the rib slope can be relaxed for full strength joints. Steep ribs (e.g. with slope equal to 40°) can be adopted without modifying the global response curve, thus allowing to reduce the design forces of the connection at column face as early proposed by [25].

Acknowledgment The research activity presented in this paper received funding from the European Union's Research Fund for Coal and Steel (RFCS) research program under the following grant agreements: • n° RFSR-CT-2013-00021- European pre-QUALified steel JOINTS: EQUALJOINTS; • n° 754048 — EQUALJOINTS-PLUS — RFCS-2016.

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