hysteretic behaviour of tubular joints under cyclic 老师/07/hysteretic behavior... ·...

Journal of Constructional Steel Research 63 (2007) 1384–1395www.elsevier.com/locate/jcsr

Hysteretic behaviour of tubular joints under cyclic loading

Wei Wang∗, Yi-Yi Chen

Department of Building Engineering, Tongji University, Shanghai, 200092, China

Received 11 July 2006; accepted 4 December 2006

Abstract

This paper examines the cyclic performance of CHS joints used in steel tubular structures. Quasi-static experimental study into the responseof eight T -joint specimens is described. Four of them are subjected to cyclic axial load, and the other four are subjected to cyclic in-planebending. The general test arrangement, specimen details, and most relevant results (failure modes and load-relative deformation hystereticalcurves) are presented. Some indexes to assess the seismic performance of tubular joints, including strength, ductility and energy dissipation, aresynthetically analyzed and compared. Test results show that failure modes of axially loaded joints mainly contain weld cracking in tension andchord plastification in compression. But for joints under cyclic in-plane bending, both punching shear and chord plastification become regularfailure modes accompanied by ductile fracture of the welds. Hysteretic curves take on a plump form in general. Ultimate strengths of joints arealso compared with equation values for monotonic loading from various design codes. Results indicate the strength at a certain deformation limitcan be regarded as the ultimate strength of a T -joint under cyclic loading and existing codes can be used to check it. It is also found that thereis a significant distinction in the energy dissipation mechanism for tubular joints under different loading conditions. Finite element analyses areperformed by taking into account weld geometry to facilitate the interpretation of the test results. It is identified that high tensile stress triaxialitycan be one primary cause of weld cracking which happened under low cyclic load level.c© 2006 Elsevier Ltd. All rights reserved.

Keywords: Tubular connection; Cyclic loading; Hysteretic behaviour; Seismic resistance; Experiment; FE analysis

1. Introduction

Steel tubular structures have been widely used all overthe world for their pleasing appearance, light weight, easyfabrication and rapid erection. Many successful large-spantubular truss applications now exist in regions of high seismicrisk because it is assumed that their strength and ductility allowsthem to dissipate energy through hysteretic behaviour, thusreducing their response. However, the Northridge earthquakeand the Kobe earthquake exposed weaknesses in steelstructures, causing serious damage of some high-rise apartmentbuildings with trussed frames in addition to widespreaddamage of moment connections in steel moment resistingframes. This prompted research into the behaviour of steelconnections under seismic loading. Up to now that researchhas principally considered moment resisting frames and littlework has been done on connections in tubular trussedstructures, which are widely used offshore and in architecturally

∗ Corresponding author. Tel.: +86 21 65982926; fax: +86 21 65984976.E-mail address: [email protected] (W. Wang).

0143-974X/$ - see front matter c© 2006 Elsevier Ltd. All rights reserved.doi:10.1016/j.jcsr.2006.12.002

adventurous structures onshore. Previous research has shownthat unstiffened tubular joints may usually have lower capacitycompared with adjacent members so that the plasticity can notbe fully developed in connecting braces. This feature, differingfrom that of other type joints, makes yielding and bucklingof steel tubular joints become the main contributors to theinelastic behaviour of pipe trusses under seismic loadings [3,7–9]. Based on the recovery characteristic model of tubular joints,proper numerical methodology can be modified to predict theresponses under severe earthquake excitations [16]. Therefore,the hysteretic behaviour study of tubular connections forms abasis for a rational aseismic design of such tubular structures aslarge-span lattice girders, space frames and towers.

Existing research concerned with tubular joints focused onultimate static capacity of tubular connections as their maintarget. A few studies on cyclic behaviour of tubular connectionswere almost limited to the case under axial loads, which can besummarized as follows. Kurobane accomplished 23 completetubular truss tests, in which four specimens have concrete filledchords, four specimens are composite trusses with concreteslabs and two specimens are space trusses [7–9]. All of the

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W. Wang, Y.-Y. Chen / Journal of Constructional Steel Research 63 (2007) 1384–1395 1385

(a) Vierendeeltrussedcolumn.

(b) Vierendeel open web truss girder.

Fig. 1. Engineering application of T type tubular joints.

trusses were tested under a reverse load so that specimensreach a complete failure after two to four cycles of reverseloading. The emphasis was laid on the interacting behaviourof connections and trusses. In the test of 15 steel trusses, thecapacities observed in truss tests coincided accurately withthose predicted by the ultimate capacity formulas derivedfrom the results of isolated joint tests. No significant effectsdue to different boundary conditions between actual joints intrusses and isolated joints (e.g. secondary moments and endrestraint) were found. The ultimate capacity of the K -jointwas governed, unless tensile fracture occurs, either by localizedshell bending deflection of the chord wall or by local bucklingof the compression brace in the region adjacent to the joint. Sohinvestigated the behaviour of completely overlapped tubularjoints used in the eccentrically braced offshore jackets [13,15]. Two full-scale specimens are tested, where one for staticstrength with monotonic compressive loadings and the other forseismic behaviour under cyclic quasi-static loading. The energyanalysis indicated that the local buckling at the intersection areawas the main energy-dissipating mechanism. Finite elementanalysis showed that the completely overlapped joint performedbetter than N -joints under seismic loadings. Four multi-planarKK tubular joints were experimentally researched both undermonotonic and repeated loads [3]. A special loading device wasdesigned to perform the cyclic loading test in order to producegreater internal forces in truss members and the joints. Theresearch reveals the characteristics of the joints that the plasticdeformation accumulates in one direction in which the plasticdeformation occurs first, and the monotonic load-deformationcurves can generally envelop those under repeated loadingconditions.

Because of the lack of test and analytical evidence, thecurrent design approach for tubular connections is limited tostatic and fatigue strength [1,2,12]. Hence an experimentalprogram has been set up to investigate the hystereticalbehaviour of CHS connections under quasi-static cyclicloading. Typical T -joints of a Vierendeel lattice girder withoutdiagonals in which shear forces are resisted by the verticalbraces and chords are selected as an objective to be tested. Fig. 1shows two examples of practical engineering applications of

T type pipe joints. In total eight tubular joint tests have beenconducted. Four of them were subjected to cyclic axial loadon brace, and the other four were subjected to cyclic bendingmoment on brace, with the results being analyzed and reportedin this paper. The seismic performance of the joints wasevaluated in terms of strength, ductility and energy dissipation.A finite element analysis was performed to facilitate theinterpretation of the test results.

2. Experimental program

2.1. Test specimen

The schematic view of the T -joint specimen is shown inFig. 2. The geometrical characteristics and details of all thespecimens are listed in Table 1. The chord length betweensupports is lc = 1500 mm (with α = 2lc/D = 12.2) whilethe brace length lb is approximately 5 times the brace diameterd. The chosen geometrical parameters (with γ = D/(2T ) =

10.2 and 15.3; β = d/D = 0.49 and 0.79; τ = t/T =

0.75) correspond to typical values for T -joints in steel tubularstructures. The chord and brace members are jointed togetherby combinations of fillet weld and butt weld. Fillet welds areused for connecting parts where the fusion faces form an angleof no more than 120◦. For angles greater than 120◦, groovedbutt welds are adopted. The throat thickness of the fillet, h f isshown in Table 1. Inspection on at least 20% of the intersectionwelds by ultrasonic testing is required. Table 2 summarizes themeasured material properties of the chord and brace.

2.2. Test setup

Fig. 3 shows the general arrangement for the T -joint tests.The chord was placed horizontally with brace placed in anupright position. The two ends of the chord were bolted to thesupports that extended to the base of the laboratory floor. Foraxially loaded joints, a 1000 kN capacity actuator was bolted tothe free end of the brace to apply the force. For joints loadedby in-plane bending, the vertical jack was first used to apply

1386 W. Wang, Y.-Y. Chen / Journal of Constructional Steel Research 63 (2007) 1384–1395

(a) Under axial load.

(b) Under in-plane bending.

Fig. 2. Joint specimen and loading rig.

Table 1Geometrical characteristics of specimens

Specimen D × T d × t lb h f β γ τ Load on brace

A1 245 × 8 121 × 6 600 12 0.49 15.3 0.75 Cyclic axial loading, with a larger magnitude fortension than compression in each displacementamplitude

A2 245 × 8 121 × 6 600 12 0.49 15.3 0.75 Cyclic axial loading, with a smaller magnitude fortension than compression in each displacementamplitude



B1 245 × 8 121 × 6 600 12 0.49 15.3 0.75 Cyclic in-plane bending, with no axial loadB2 245 × 8 121 × 6 600 12 0.49 15.3 0.75 Cyclic in-plane bending, keeping the brace member

with 20% of plastic axial resistanceB3 245 × 12 121 × 8 600 12 0.49 10.2 0.75 Cyclic in-plane bending, with no axial loadB4 245 × 8 194 × 6 1000 8 0.79 15.3 0.75 Cyclic in-plane bending, with no axial load

Notes: D= outer diameter of the chord, d= outer diameter of the brace, T = wall thickness of chord, t= wall thickness of brace. All dimensions are expressed inmm.


Table 2Material properties of specimens

Section size (mm) Yield strength fy (MPa) Tensile strength fu (MPa) Elongation ζ (%) fy/ fu

121 × 6 CHS 345 485 26 0.71194 × 6 CHS 344 482 27 0.71121 × 8 CHS 392 601 25 0.65245 × 8 CHS 398 564 28 0.71245 × 12 CHS 356 583 26 0.61

Fig. 3. Arrangement of measuring instruments.

compressive load on the brace. Keeping this load constant, in-plane bending moment was then produced by two horizontaljacks to apply cyclic lateral forces to the brace end.

2.3. Instrumentation arrangement

For each specimen, the instrumentation includes straingauges around the crown and saddle points to measure the straindistributions at the hot spots, and transducers to measure thedisplacements at selected key points. The general arrangementof displacement transducers and strain gauges is shown inFig. 3. The local deformation of the chord wall can be obtainedby measuring the brace displacement around the brace-chordintersection and the mid-span deflection of the chord as a beamelement.

2.4. Loading history

Axially loaded joints were tested by applying cycles ofalternated load with tip vertical displacement ∆v as shown inTable 3. Due to the difference in the performance of CHS jointsunder tension and compression, different loading programmesare set for the four specimens, which made the correspondingloading properties of the brace as shown in Table 1. Forjoints loaded by in-plane bending, a typical tip horizontaldisplacement-controlled loading programme is shown in Fig. 4.But for B2, a compressive preload shown in Table 1 is firstapplied and kept constant during the whole testing process.

Before the actual test, one complete cyclic load of ±2 mmwas applied to check the working conditions of the strain

Fig. 4. Loading program for joints loaded by in-plane bending.

gauges and other equipment and to loosen the friction andremove any lock-in forces within the test setup.

3. Experimental results

3.1. Observations and failure modes

Under axial loads, for the test of specimen A1, it wasobserved that at the tension phase of the second loading cycle,a small crack initiated at the weld toe between the chord andthe brace. In the next cycles, the crack extended and expandedgradually until the applied load dropped quickly with thedisplacement greatly increased at the tension phase of the ninthloading cycle. The large crack almost cut through the chord wall


Table 3Loading history for axially loaded joints

Specimen A1 Specimen A2 Specimen A3 Specimen A4 Number of cycles∆v (mm) ∆v (mm) ∆v (mm) ∆v (mm)

±6.6, −1.8 ±1.0, −2.0 ±1.6, −1.4 ±1.1, −1.5 1±14.9, −2.8 ±2.0, −3.6 ±6.7, −5.2 ±2.0, −3.6 1±19.3, −3.5 ±6.1, −8.1 ±9.0, −8.2 ±4.4, −8.1 3±22.6, −5.7 ±8.1, −10.5 ±15.3, −11.3 ±7.2, −10.2 3±30.3, −8.2 ±9.5, −12.6 ±26.9, −14.0 ±11.8, −13.0 3

±10.2, −14.3 ±12.2, −16.7 3

Fig. 5. Typical failure modes of specimen A1.

Fig. 6. Typical failure modes of specimen A3.

near the saddle point. No obvious plastic deformation of thechord wall was found during the whole process of the test. Thefailure modes of A1 are shown in Fig. 5.

For the test of specimen A2, A3 and A4, cracking of the weldat the saddle point under tension happened after the maximumVon Mises stress at the intersection area reached the yieldstress of the steel. When reverse load was applied, the crackclosed up and plastic deformation developed continuously.After a number of cycles like this, the peak compressiveload was reached and obvious chord ovalization and concavedeformation was noticed at the end of the test. Fig. 6 showsthe failure modes of specimen A3. It is worthy to be noted thatthe difference in fracture modes between A1 and the other 3specimens mainly resulted from different loading programmeson them in Table 3.

Under in-plane bending loads, for all specimens, thefollowing observations were made: (1) In the first twodisplacement amplitude, there was no weld cracking. But afterintersection area between the chord and the brace steppedinto plastic phase, small cracks formed at the tension sideof the weld toe along the chord. (2) Weld cracking didnot occur in the first loading cycle of certain displacementamplitude but in the second or third cycle. (3) In the followingtesting process, small cracks extended with the chord wallsustaining plastic deflection. Two typical failure modes of jointsloaded by bending are graphically illustrated in Fig. 7. Amongthem, B2 and B4 can be attributed to the combination ofpunching shear fracture and plastic bending of the chord wall(Fig. 7(a)), while B1 and B3 belong to ductile fracture of welds(Fig. 7(b)).


(a) Specimen B2. (b) Specimen B3.

Fig. 7. Typical failure modes of joints loaded by in-plane bending.

(a) Specimen A1. (b) Specimen A2.

(c) Specimen A3. (d) Specimen A4.

Fig. 8. Load–displacement curves of axially loaded joints.

3.2. Hysteretical curves

The load–displacement hysteretical loops obtained foraxially loaded joint tests are presented in Fig. 8. Dimensionlessaxial load N/Nbp has been plotted against the intersection linedisplacement δ, which is defined as the average displacementof the crown points and saddle points minus that of the chordcentreline, thus effectively excluding the displacement dueto chord beam bending. Nbp is the plastic axial resistance

of the brace. Tensile forces are represented in positive signswhile compressive forces in negative signs. The deformationlimit used to determine the ultimate strength of a jointhas been investigated and suggested by different researchers:Mouty [11], Yura et al. [17], Korol and Mirza [5], Zhao [18].However, these deformation limits are only valid for certaincases. A more general deformation limit based on the localindentation of the chord face was proposed by Lu et al. [10]to cover all types of welded tubular joints. The proposal was


(a) Specimen B1. (b) Specimen B2.

(c) Specimen B3. (d) Specimen B4.

Fig. 9. Moment–rotation curves of joints loaded by in-plane bending.

mainly based on static tests. There is a need to verify theproposed deformation limit for welded T -joints under cyclicloading. So Yura’s limit and Lu’s limit has been plotted in eachcurve respectively.

The moment–rotation hysteretical loops obtained for jointtests loaded by in-plane bending are presented in Fig. 9. Thedimensionless moment M/Mbp has been plotted against therotation of the brace θ , which is acquired by dividing the sumof relative concave and convex at the crown points by bracediameter. The moment M is taken at the chord surface at thecrown point. For B2, additional moment due to second ordereffect of axial loading is taken into account. Mbp is the plasticmoment capacity of the brace member.

In addition, the first weld cracking occurrences are markedin these figures.

For most joints, hysteretical curves behave stably withoutexhibiting “pinching” at higher load level. Pinching ischaracterized by an increase in deformation without asignificant increase in load, thus resulting in a loss in stiffness ofthe connection. The hysteretical plots were observed to becomeplump as the load was enhanced.

From the results for specimen A1 and A3, it can be foundthat after small cracks formed in weld toe, the joint can sustaina further increase in load with stiffness descending gradually in

the next cycles until the joint failed. The displacement valuesof hysteretical curves under tension seem very large by theend of the test, because they contained displacements due tocrack expansion. From the results for specimen A2, A3 and A4,peak compressive forces are all clearly shown, accompanied bydeterioration in capacity and stiffness at the compressive phasenear the end of test.

For specimen B1 and B2 with the same geometry, it wouldbe of interest to investigate the effect of the brace axial loadon cyclic joint behaviour under in-plane bending. From thehysteretical curves, initial elastic rigidities are very close. Thefirst cracking moment of B2 is a little higher than that of B1.However, a significant difference can be noted between them:After first cracking the bending load could still be increased forB1, whereas there appeared significant strength and stiffnessdeteriorations for B2. This may be caused by enhanced plasticbending of the chord wall under brace axial load due topunching shear crack initiation. For specimen B3 and B4, thefirst crack did not emerge until the maximum loads had beenachieved. Afterwards, the strength and the stiffness began todecrease. Moreover, a little pinching was observed to occur forB2 and B4.

For axially loaded joints, the peak compressive loads agreewell with the load at the Lu’s deformation limit 3%D. Yura’s


Table 4Comparison between test resistance of axially loaded joints and the predicted strengths

No. Joint test resistance (kN) Joint strength predictions (kN)a Brace strength (kN)Ny Nwcr Nu N pj

uc,GB N pjut,GB N pj

u,EC3 Nbp Nwcr /N pjut,GB Nu/N pj

u,GBb Nu/Nbp

A1 330 400 447 −305 427 273 745 0.94 1.05 0.60A2 −396 327 −418 −305 427 −273 −745 0.77 1.37 0.56A3 −670 480 −707 −566 792 −507 −1105 0.61 1.25 0.64A4 −520 438 −693 −523 633 −513 −1216 0.69 1.33 0.57

a Superscript pj shows failure mode for the joint is chord plastification; subscript uc or ut denotes compressive or tensile resistance.b For A1, N pj

u,G B denotes N pjut,G B ; For A2, A3 and A4, N pj

u,G B denotes N pjuc,G B .

Table 5Comparison between test capacities of in-plane bending loaded joints and the predicted strengths

No. Joint test resistance (kN m) Joint strength predictions(kN m)a

Brace strength (kN m)

My Mwcr Mu M pju,EC3 Ms j

u,EC3 Mbp Mwcr /Ms ju,EC3 Mu/Ms j

u,EC3 Mu/Mbp

B1 21.0 23.4 27.7 28.65 26.91 26.04 0.87 1.03 1.06B2 23.0 26.0 26.5 28.65 26.91 26.04 0.97 0.98 1.02B3 31.8 38.6 39.0 47.08 36.11 37.47 1.07 1.08 1.04B4 67.5 76.1 81.7 74.06 69.19 70.74 1.10 1.18 1.15

a Superscript pj or s j shows failure mode for the joint is chord plastification or punching shear.

deformation limit is much larger than Lu’s limit and thedeformation at the peak compression. For in-plane bendingloaded joints, the rotations at the peak moments are allconsiderably smaller than Yura’s rotation limit 80 fy/E (=0.13rad). It can be concluded that the 3%D deformation limit for theultimate strength proposed by Lu et al. [10] applies to T -jointsin CHS sections under cyclic axial loading.

3.3. Load-carrying capacity and comparison with codeestimation

One way of presenting extreme values of connectionload–displacement curves is to plot the skeleton curves.Skeleton curves of the cyclic response of connections havebeen shown experimentally to be a reasonable estimate of theprobable monotonic response. For specimen A2, A3 and A4,they all exhibited a peak compressive load. Therefore, themaximum load on the skeleton curve is defined as the ultimatestrength of the joint (Nu). But for specimen A1, no peak loadis shown. So Lu’s deformation limit [10] is used to define theultimate tensile resistance of A1, although it should be basedon the local deformation of the chord face at the intersectionunder monotonic loads. Following the same principle, theultimate bending strength (Mu) of specimens loaded by in-plane bending can be determined. The yield strength observedon load-deformation curves can be used as another measurefor the capacities of the joints. The yield strength (Ny or My)defined by Kurobane et al. [6] is determined by secant modulusof 0.779KN or 0.779KM . Where, KN or KM refers to initialjoint rigidity under axial force or bending moment.

Test values of Ny , Nu , My , Mu are presented in Tables 4 and5. Furthermore, the first weld cracking load (Nwcr or Mwcr ) forthese joints are also listed in the tables. They are compared with

design strength calculated from Chinese (N pjuc,GB, N pj

ut,GB) [12]

and European (N pju,EC3, M pj

u,EC3, Ms ju,EC3) structural steelwork

design specifications [2]. Predicted values of strengths werecalculated using material properties obtained from the tensilecoupon tests described previously. In Table 4, tensile loads arerepresented in positive signs with compressive loads in negativesigns.

For axially loaded joints, strength predictions based onfailure modes of chord plastification under monotonic loadingin general underestimate the actual joint resistances undercyclic loading conditions. It also can be found that the bracemember efficiency (Nu/Nbp) is less than one for these jointspecimens. This means they dissipated energy mainly by plasticdeformation of chord wall.

For joints in-plane bent, it can be noticed that predictedstrengths based on failure modes of chord plastification arehigher than that based on failure modes of punching shear,which tend to agree with the actual joint resistances undercyclic loading conditions reasonably. The brace memberefficiency (Mu/Mbp) is larger than one for these jointspecimens. This feature is different from the joints under axialload, meaning they have enough strength to make plastic hingeformed in the connecting brace.

Whether for axially loaded joints or for in-plane bendingloaded joints, weld cracking sometimes happened under lowerload level compared with design resistance specified by thecodes. Early development of cracks may be caused by localmaterial deterioration due to reversals of inelastic strain andtriaxial tensile stress distribution around intersection lines.

3.4. Ductility ratio

The ductility ratio is an important index to assessdeformability. The ductility ratio is defined as µ = δu/δy for


Table 6Ductility ratio of axially loaded joints

No. δy (mm) δu (mm) µ = δu/δy

A1 3.80 12.16 3.2A2 −3.32 −4.40 1.4A3 −4.20 −7.42 1.8A4 −1.00 −4.66 4.7

Table 7Ductility ratio of joints loaded by in-plane bending

No. θy (mm) θu (mm) µ = θu/θy

B1 0.017 0.048 2.8B2 0.016 0.027 1.7B3 0.012 0.047 3.9B4 0.017 0.051 3.0

axially loaded joints and θu/θy for joints loaded by in-planebending, where δu or θu is assumed to be local deformation ofthe chord face corresponding to ultimate strength and δy or θyis the yield deformation. From the hysteretical curve shown inFigs. 6 and 7, the ductility ratios under axial load and underin-plane bending are determined and listed in Tables 6 and 7respectively. From Table 7, θu of B2 is obviously smaller thanthat of B1 due to the compressive preload on the brace.

It is important to consider if cyclic loadings woulddeteriorate the ductility of unstiffened tubular joints. Accordingto test results of four multi-planar KK tubular joints [3], theductility ratio under cyclic axial loadings would be smallerthan that under monotonic loadings. Weld cracking or punchingshear cracking of tubular T -joints, which happened at certainload level in this study, may lead to the same result.

3.5. Energy dissipation

The capacity of structural connections to dissipate energywhen subjected to seismic loads is as important as theirstrength or stiffness in the evaluation process. The dissipatedenergy is calculated by evaluating the area enclosed by theload–displacement curves. The accumulative energy dissipationratio is used to measure the energy dissipated. The ratio isdefined as ηa =

∑ni=1(E+

i + E−

i )/Ey , where Ey is theenergy absorbed at the first yield displacement δy and is definedas Ey = Pyδy/2. E+

i and E−

i are the energy dissipationin the tension half-cycle and in the compression half-cycle,respectively. These values of the specimens are listed in Table 8.They can be found to be higher than the value of four requiredby the API provision [1]. The similar result has been obtainedfrom the one completely overlapped CHS joint tested in a cyclicexperimental program [15]. Obviously, inelastic deformation atthe intersection area is the main energy-dissipating mechanism.

4. Finite element modeling

To extend the interpretation of the results and observationsobtained in the tests and gain a better understanding of the

Table 8Accumulative energy dissipation ratio of joints

No.∑n

i=1 (E+

i + E−

I ) (kN m) Ey (kN m) ηa

A1 49.32 0.627 78.7A2 29.06 0.657 44.2A3 74.61 1.407 53.0A4 26.62 0.260 102.4B1 16.94 0.179 94.6B2 22.14 0.184 120.3B3 18.69 0.191 97.9B4 48.03 0.608 79.0

behaviour of tubular joints under cyclic loading, a numericalstudy on joint specimens was carried out using the finiteelement analysis programme ANSYS [14].

4.1. Finite element model

Due to symmetry in the geometry and loading conditions,a half of the overall joint specimen is modelled, as shown inFig. 10. A rigid plate is added at the brace tip to keep thebrace prismatic. Tetrahedral ten-node solid elements (elementtype SOLID92 in ANSYS) are used in the FE models, andtwo layers of elements are created through the thickness ofeach member. Finer mesh are used near the intersection regionto get the magnitude of the stress concentration accurately.Symmetric constraints are applied to all nodes lying in theplane of symmetry. Both left and right ends of the chordare fixed to simulate the boundary condition in the test. Theactual geometric definition of the weld is included in all FEmodels. Since the accurate geometry of intersection weldsvaries around the perimeters and is difficult to be obtainedexactly, triangular outlines are used to model the cross-sectionof weld geometry. A bilinear kinematic hardening materialmodel is adopted with material properties taken from tensilecoupon tests. The plasticity model used in the analyses is basedon a von Mises yield surface and an associated flow rule.Considering the immaturity in numerical strategy to predict anunstable crack extension for tubular connections, the damageand fracture mechanisms are not introduced into the finiteelement modeling.

4.2. Comparison with experimental results

To calibrate the finite element model, the numerical resultsare compared with the experimental results. Fig. 11 shows thecorrelation of global monotonic and cyclic responses for axiallyloaded and in-plane moment loaded specimens, respectively.Before cracking occurred, both the initial stiffness and post-yield result correlate reasonably well with the response of thetest results. In addition, the calculated Von Mises stresses arein good agreement with the rosette strain gauge measurementsaround the intersection area for the joint specimens. However,after the cracking, the computed forces are higher than thoseobtained from the experimental results. The main reason is thatthe cracking mechanism had not been involved in the finiteelement modeling. It can be seen that the monotonic FEA curvealmost envelops the corresponding hysteretical loop.


(a) Global view. (b) Local view.

Fig. 10. Finite element model of the tubular joint.

(a) Specimen A2. (b) Specimen A4.

(c) Specimen B1. (d) Specimen B4.

Fig. 11. Hysteresis curves from numerical and experimental results.

4.3. Stress distribution around connection

For a proper understanding of the failure mechanism oftubular joints it is important to execute an analytical study onthe relation of load transfer and stress distribution.

The predicted deformation configurations are shown inFig. 12 with internal force conditions depicted. From theloading directions of axially loaded joints (Fig. 12(a)), it can

be seen triaxial tensile stress fields exist around the crownand saddle points of the intersection region between chordand brace. Similarly, for joints loaded by in-plane bending(Fig. 12(b)), an obvious triaxial tensile stress field also lies onthe tension side of the brace end. This may result in the earlydevelopments of cracks at the weld toes.

As a verified example, Fig. 13 show the stress distributioncomparisons across the brace perimeter at the intersection weld


(a) Axially loaded joints. (b) Joints loaded by in-plane bending.

Fig. 12. Predicted deformed configurations and loading situations.

(a) Specimen A2. (b) Specimen B1.

Fig. 13. Triaxial stress distribution at the intersection weld location.

location of specimen A2 and B1 just before tensile crackingoccurred. The normalized x distance from brace center has beenplotted against the stress ratio, which is defined as the ratio ofthe uniaxial stress to the yield stress of the material, with thereferenced coordinate system shown in Fig. 12. It is found thatweld cracking happened after significant plasticity developedaround the intersection region.

By now no definite criteria to predict tensile crack failure oftubular connections or prevent these cracks are well accepted.In this numerical study, A PEEQ strain index [4], which canbe used as a measure of local ductility, are computed fromANSYS results to assess the performance of the tubular joints.This index is defined as the ratio between the equivalent plasticstrain, PEEQ, and the yield strain, εy :

PEEQ index =PEEQ

εy(1)

where the equivalent plastic strain is defined as:

PEEQ =

√23ε

pi jε

pi j (2)

where εpi j is the plastic strain components in the i and j

directions, i , j = 1, 2, 3.Fig. 14 shows the PEEQ index distribution around the brace

perimeter at the intersection weld location just before tensilecracking occurred. A2 had a maximum PEEQ Index close to 8at the saddle point. While for B1, the maximum PEEQ Indexis a little more than 12 at the crown point on the tension side.This can be partly regarded as the explanation of first crackingobservation at the saddle point for axially loaded joints and atthe crown point for in-plane bending loaded joints.

5. Conclusions

The aim of this paper was to provide informationregarding the cyclic performance of unstiffened tubular joints.Based upon the experimental results of eight tubular T -jointspecimens and the associated analytical study, the followingconclusions can be made.

(1) From the overall deformed shapes of the joint specimens,the T -joints under cyclic axial loading primarily failed byweld cracking in tension and excessive plastic deformation


(a) Specimen A2. (b) Specimen B1.

Fig. 14. PEEQ index at the intersection weld location.

of the chord wall in compression. But for the T -jointsunder cyclic in-plane bending, both punching shear andchord plastification may become regular failure modesaccompanied by ductile fracture of the welds.

(2) For the chord plastification failure mode the 3%Ddeformation limit for the ultimate compressive strengthapplies to T tubular joints under cyclic loading. To acertain extent existing codes including Eurocode 3 [2] andGB50017 [12] can also be used to check the ultimatecapacity of T -joints under cyclic loading.

(3) Hysteretical curves take on a plump form generally. Theenergy analysis showed that the joints have good energydissipating capacity. However, compared with monotonicloads, cyclic reverse loads may reduce the ductility ofunstiffened tubular joints.

(4) For tubular joints under differing loading conditions,there is a significant distinction in the energy dissipationmechanism. The axially loaded joints dissipate energymainly by plastic deformation of the chord wall with bracemember efficiency smaller than one. The in-plane bendingloaded joints dissipate energy mainly by plastic deflectionof the brace with brace member efficiency larger than one.

(5) In cyclic loading conditions, weld cracking sometimeshappened under lower load level compared with designresistance specified by the codes. This may be result frommaterial deterioration owing to repeated cold-working andstress triaxiality around intersection lines.

Acknowledgments

The reported work in this paper was funded by National Nat-ural Science Foundation of China (50578117). The specimenswere contributed by Jiangsu Huning Steel Mechanism Com-pany Ltd. (China). The experimental investigation was con-ducted in the Structural Engineering Laboratory, Departmentof Building Engineering, Tongji University.

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