Numerical Models on Innovative Steel Hollow Section Joints for

Truss Girders using Laser Cut Technology

Bernardo Segurado Correia Pita DiasInstituto Superior Tecnico, Lisboa, Portugal

October 2017

Abstract

This thesis is framed by LASTEICON EU research project on the development of steel joints usinglaser cut technology aimed at enhancing the economy and sustainability of I-beam-to-CHS-columnconnections fabrication, by eliminating stiffener plates and reducing the amount of welding. Theextendibility of laser cut technology to steel truss girder applications is the kick-off for this dissertation.Based on numerical and parametric analysis of different steel truss girder joint typologies using lasercut technology, the main goal is to retrieve conclusions about its feasibility and give indication to itsexperimental work package. Taking advantage of laser cut and the possibility of opening precise slotson the face of the chord, the joint typologies studied consisted on the prolongation of the bracingelements of the truss girder to the inside of the chord. These were analysed and stress distributionon the connection was evaluated. Global rigidity of the truss girder is also under interest. Numericalanalysis suggests an increase of performance in laser cut joints, in some cases up to 10% reductionof maximum Von Mises stress. Local study shows that it is possible to have similar behaviour oftraditional joints with lower values of thickness of the chord if Laser Cut Technologies joints are used.In addition, parametric analysis suggest a higher improvement in structural behaviour for lower valuesof chord thickness.Keywords: Laser cut; Steel truss girders; Numerical analysis; Steel joints

1. Introduction

1.1. Framework

The aesthetic reasons and their inherently excel-lent properties in terms of structural behaviour anddurability has contributed to the increase of use oftubular sections since the 60s [1].

This structural behaviour is highly dependent onthe connection technology and the possibility of tak-ing full advantage of tubular section properties maybe compromised by its complex connections [2]. Itis known that connections are a critical step in thedesign and represent many times the weak pointin steel structures [1] [3]. In fact, the number ofstructural collapses caused by the inadequate con-nections (mainly in extreme phenomena) is veryhigh [4].

The fact that erection and fabrication togethercan represent about 40-55% of the overall cost ofthe structure (figure 1) show the impact that a highlevel of complexity of the connections (and conse-quent high fabrication costs) could have on the over-all price [5].

Steel is still considered to be an European Indus-try with 500 production sites between 23 MemberStates. Today, EU is responsible for 177 milliontonnes of steel a year, representing 11% of global

output, being the second largest producer of steelafter China [6]. Under this scope, LASTEICON isframed in a green and competitive European strat-egy aimed at developing a sustainable and innova-tive steel connection solution with Laser Cut Tech-nology (LCT), by eliminating stiffener plates andreducing the amount of welding. Main focus is givento I-beam to circular shape column but extendibil-ity of the technology for steel truss girder applica-tion is the kick-off for this dissertation.

In fact, investigation in the field of material cut-ting techniques was performed [7] and indicationsare that LCT advantages include the increase on thequality and financial saving by diminishing humanerror (operations are programmed and done by themachine). In addition, the speed (laser cutting canbe up to 30x faster than traditional cutting meth-ods) and precision cut making use of CAD toolsallow for a cut edge quality with higher precision,reducing tolerances and eccentricities.

This extended abstract is a summary of a Dou-ble Degree master thesis between Instituto SuperiorTecnico (IST) and Politecnico di Milano, with theaim of developing numerical models on innovativehollow section joints for girders using laser cut tech-nology.

The primary goal is to prove the feasibility of

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Figure 1: Proportional factors of steel frame cost [5]

the technology for steel truss girder applications.It is expected that the joints typologies taking ad-vantage of this technology constitute a more rigidalternative to the steel joints today. If so, the pos-sibility of designing lighter and more economicalstructures with the same level of safety and struc-tural behaviour is the main objective. Suggestionsof joint typologies were developed and the numer-ical and parametric analysis is the first part of awork package that contains experimental testing oftruss girders at IST laboratory. Conclusions aboutthe feasibility of the technology and respective de-sign guidelines are the output of this 4-year projectat IST.

1.2. Literature reviewFrom all the non-linear finite element software

packages available, Abaqus seems to be the pre-ferred one for research purposes and has been widelyused in the past for modelling steel structures andin particular hollow section profiles [8–11].

For an accurate description of the structural be-haviour, past analysis suggest that Finite Element(FE) truss girder models should include both globaland local behaviour of members and joints [12].With this in mind, the authors have listed and com-pared the type of models that can be built depend-ing on the requested accuracy (and on the power-fulness of the software):

• Beam model - truss is represented by linear ele-ments, is the simplest model and it is generallypossible to perform linear or nonlinear analy-sis, with both hinged (most common) or rigidnodes. However, it is not possible to considerlocal effects at the joints;

• Truss space model - all of the truss is mod-elled with planar type elements, it is more pre-cise and can include both global and local be-haviour but due to its heaviness and complex-ity of creation it is generally used only for re-search purposes;

• Combination of beam and shell type space ele-ments - submodeling technique in which braceand chord elements are modelled as beam andjoint detail is modelled with planar elements.In this way, both local and global behaviourcan be captured, as the same time, reducingthe model creation complexity and calculationduration;

• Isolated truss girder joints - often used to studythe behaviour of joints but dealing many timeswith the problematic of including the actual in-fluences and the correct set of Boundary Con-ditions in the numerical model.

The work of Radic et al. [12], concludes that thereis no significant difference between space modelsand space combined beam space model, which in-dicated that the last one gives sufficient accurateresults without further complexity.

Figure 2: Modelling procedure combining linearand planar elements [13]

The effect of boundary conditions and restrainsof brace and chord on the axial capacity of K-jointswas studied by Dexter et al. [14] and posterior workof Bjornoy [15] have revealed the strong effect ofboundary conditions on the ultimate strength, es-pecially for the cases of eccentric overlapped joints.Similar findings to previous researchers were foundon the work of Liu et al. [16] [17] with the investi-gations of multiplanar and uniplanar RHS gap K-joints. More recently, Van Der Vegte [18] conclu-sions are in line with previous research that is notnegligible the influence of boundary conditions onthe ultimate capacity of K-joints. Jurkova and Ros-manit [13] also address this problem and suggestcombination of modelling methods (figure 2) wherethe boundary conditions and load would be relatedto the entire structure behaviour. Future work onthis topic is asked for correctness of the hypothesis.

For truss girder applications, and hollow sectionprofiles in particular, Eurocode [19] suggest a designcriteria based on semi-empirical formulae valid onlyin limited conditions. Eurocode and CIDECT [20]allow the design of truss girders under the assump-tion that members are connected by pinned joints.In any case, bending moments can arise and shouldbe accounted for, depending on: the structure de-sign; to which component one is referring to (chord,brace or joint); and on the source of bending mo-

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ment itself (secondary moments, transverse loadingor eccentricity at intersections).

In general, the design should be done under thehypothesis that the design axial forces in the bracemembers should not exceed the design resistanceof the joints. This static design resistance of thejoints is expressed in terms of geometric and ma-terial properties and reference is made to the dif-ferent failure modes. When applicable, the staticdesign resistance of the joint is the minimum of de-sign resistances of the appropriate failure modes.This design procedure is under a range of geometri-cal validity that limit the field of application of theformulae for the different failure modes.

2. Numerical Study

With reference to the model types presented insection 1.2, considering that the results can be ac-curate enough without further complexity and thatthe boundary conditions issue could be solved bystudying the joint at its real location, combinationof beam and shell elements is the modelling proce-dure that was used. The modelling phase can bedivided in two different steps. The modelling ofthe truss and the modelling of the detailing of theconnection.

The model was built assuming a bi-linear consti-tutive law of S355 with kinematic strain hardeningof 1% of the Young modulus.The beam elementsused were B31 and the shell elements S4R.

Figure 3: Detail of the interaction between linearand planar elements

The interaction between truss and shell parts isan essential step because it guarantees that theanalysis on the shell detailed connection is beingdone with the right boundary conditions. The con-nection should be able to guarantee the transferof displacement and rotations and also forces andbending moments. Abaqus offers a wide varietyof interaction properties. In this case beam typeMulti Point Constraint (MPC) was used, in whichthe master node is connected to a region of slavenodes making sure that the force resultants andbending moment coming from the linear element

are transmitted to the shell surface in the correctway (Figure 3).

Figure 4: Comparison of load convergence withCPU time when increasing the number of elements

For the particular case of modelling the complex-ity of the connection, it was chosen to model by in-tersecting mid-surfaces of the member walls. Thisprocedure is validated in the work of Lee et al. [21].

As any Finite Element Analysis (FEA) problem,there is the need to find the best trade-off betweenaccuracy of solution and computer time. This meshconvergence study can be achieved by performing ah-refinement or a p-refinement approach. The for-mer means increasing the number of elements andthe last is referred to the use of higher order ele-ments.

This technique is applied to the truss girders(beam model only) in order to find a reasonabletrade-off between accuracy and computer time, byperforming limit load analysis, in different modelswith increasing number of elements, until the re-sult tends to a certain value. The computer time(referred here as CPU time - dashed line) used toperform this analysis is the indicator that measuresthe heaviness of the mesh (Figure 4).

From the plot it is clear that it is possible toidentity the number of elements (320) that give suf-ficient accurate results without further complexityof the mesh.

For the case of shell elements similar approachwas performed. Due to the geometrical shape of themembers, only quad type elements were considered.

2.1. Joint typologiesThe main goal of this work is the numerical anal-

ysis of joint typologies, making use of LCT. Thesejoint typologies are modelled in substructures inwhich they will be experimentally tested, in futurework.

The comparative and parametric analysis thatwill be performed aim at identifying the behaviourof the different joint typologies using LCT technol-ogy for hollow section profiles. Taking advantage oflaser cut technology, different joint typologies can

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be suggested- base, cut1 and cut2.

• Base - joint configuration in which the brac-ing elements are laser cutted at their ends sothat they can be fully welded to the outer faceof the chord. No prolongation to the inside ofthe connecting elements is done. This is thesimplest joint configuration and it can be com-pared to the traditional method of joint design(Figure 5a).

(a) Base

(b) Cut1

(c) Cut2

Figure 5: Detail of joint typologies

Cut - taking advantage of the possibility of open-ing slots in the chord face for the bracing profilesto enter (due to precise laser cut technology), twocombinations of these type of configurations are pre-sented:

• Cut1 - in which one of the bracings enters theinside of the hollow section through an openingon the upper face of the chord and it is weldedto lower face. In this case one of the bracingelements is extended and the other one stops atthe surface of the chord. This solution has as aside consequence the elimination of part of thechord by creating a hole when passing through,both at the upper face and at the lower faceof the chord. The other(s) bracing element(s)converging in the node are cutted and weldedto the upper face of the chord (Figure 5b).

• Cut2 - in which both bracing elements are pro-longed in half of the original cross sections(dashed line), so that they can cross each otherand be welded at the bottom of the chord. This

alternative solution allows for the extension ofboth bracing members without the creation ofthe holes in the chord. Instead, only a slot isneeded so that the profiles are welded at theupper face and lower face of the chord (Figure5c).

Due to its precise cut LCT allows for zero eccen-tricity at the joint.

2.2. The studyThe parameters that are going to be evaluated for

the comparison of the solutions are:

• Maximum Von Mises stress (σmaxVM )

• Global behaviour P − δ

This evaluation will be done by comparing themaximum value of maximum Von Mises stressfound in the node of interest, ie , in the modelled setof elements composed by chord and bracing mem-bers at a specific location, with different joint ty-pologies (Figure 6).

Figure 6: Substructure A modelled with shell ele-ments on NA-2

Figure 7: Nodes of interest in substructure A

Figure 8: Nodes of interest in substructure B

The joint typologies are studied on one locationat a time to ensure that they all have the sameBoundary Conditions (BC) and that the only dif-ference between the numerical models is the jointtypology. With this in mind, the connections that

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are going to be studied for substructure A and forsubstructure B and the nodes of interest (NA-1 andNA-2 for substructure A and NB-1 and NB-2 forsubstructure B) are shown in Figure 7 and 8, re-spectively.

On the other hand, for a comparison of the globalbehaviour of a structure with the different joint ty-pologies, it makes sense that all of the joints aremodelled with one typology at a time (Figure 9)and that the results in terms of P − δ are comparedto a structure modelled with beam model (no detail-ing of the connection) considering rigid and pinnednodes at a time. In this way, not only it is possibleto compare the different joint typologies with eachother and with the case of rigid and pinned nodes,but also to make sure that the combined beam andplanar model is built in a correct way.

Figure 9: Substructure A modelled with shell ele-ments at the nodes

Substructures are modelled with SHS hollow sec-tions and are going to be experimentally tested un-der increasing monotonic load.

3. Results and discussion

3.1. Numerical analysis

The load considered for this phase of the analysisis P=100kN (after yielding), so that results can beanalysed after the spread of plasticity. The resultsfrom the non-linear numerical analysis for NA-1 andNA-2 are showed in Figures 10 and 11, in which isclear the Von Mises stress distribution on the jointtypology and its respective maximum value foundin the analysis (σmax

VM ).

There are some clear differences between the jointtypologies both for the maximum stress value andfor the stress distribution at the top and bottomfaces of the chord.

The figures suggest that the presence of the brac-ing part inside the chord in cut1 absorbs the stressand redistributes it to the lower face (the evidenceof this can be seen in NA-1 views and in the lateralview NA-2). In this last case, a reduction of 9.6%was determined for cut1, compared to the base case.

The presence of the hole due to the prolonga-tion of the vertical bracing member is increasingthe magnitude of stress distribution at the top faceof the chord. This can be problematic if the bracingis big enough.

Cut2 shows a similar stress distribution with re-spect to cut1 for the vertical element of the bracingbut not for the diagonal one. The main difference isin the interface between the chord and the bracingelements. In fact, it is clear in the figure the higherconcentration of stresses around this area in cut1case, while in cut2, where the diagonal element isprolonged (in half of its original cross section) thestress distribution magnitude is lower. In quantita-tive terms, it is possible to calculate a 8% reductionfor cut2 compared to base case.

(a) NA-1 (b) NA-2

(c) NB-1 (d) NB-2

Table 1: Comparing results for the different jointtypologies

Table 2: Comparing results for the different jointtypologies: NB-2 (P=110 kN)

A more detailed analysis of the results [22] sug-gest a redistribution of stresses in the joint due tothe extension of the bracing element, and althoughthere is a slight difference at the outer face of thechord, this is compensated by the reduction at thelower face, leading to a more uniform stress distri-bution at the joint.

The collection of σmaxVM results for NA-1 and NA-2

can be found in Table 1a and 1b. Same procedureis applied to the other nodes of interest and the col-lection of results for all nodes of interest are showedin Table 1.

For the case of substructure B, no significantchange is verified by changing joint typology. Con-sidering that substructure B has bracing elementswith different width and thicknesses, the questionof which member to extend (in cut 1 joint typology)can be raised. To consider this, cut1 joint typology

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(a) Base (b) Cut1 (c) Cut2

Figure 10: Comparison of joint typologies for NA-1 in terms of Von Mises Stress

(a) Base (b) Cut1 (c) Cut2

Figure 11: Comparison of joint typologies for NA-2 in terms of Von Mises Stress

is replaced by cut1-a and cut1-b in which the pro-longation of the element is done in the bigger or thesmaller one, respectively. This is done in NB-2 andresults are showed in Table 1d.

Considering that, unlike for substructure A, theprevious results do not show expressive improve-ments, and also due to the fact that the magnitudeof stresses is lower in comparison with substructureA, a tentative higher load (P=110kN) was assumedand the results are shown in Table 2.

The difference of 10% for cut1-b (compared to4% of cut1-a) suggests that the choice of extendingthe smaller element instead of the bigger one has animpact on the behaviour of the connection. Thisimpact could be explained by the size of the holethat inevitably weakens the face of the chord.

The global rigidity evaluation results are showedin Figure 12 and load-displacement curves show avery similar behaviour for the different joint typolo-gies and for the case of pinned and rigid nodes. Thisbehaviour suggests that the modelling of the nodesof interest is being done correctly and the use ofLCT joints is not modifying the overall behaviourof the structure. Results for substructure B are sim-ilar and can be read in the full thesis document [22].

Figure 12: Load-displacement diagram for the dif-ferent joint typologies in substructure A

3.2. Parametric analysis

The goal of the parametric analysis is to investi-gate the effect of the thickness of the bracing andchord members on the comparison results of thejoint typologies using laser cut technology.

To be coherent with the numerical analysis theevaluation of the behaviour was done again, usingthe maximum Von Mises stress (σmax

VM ) found at thejoint. The thicknesses used for the parametric anal-ysis were: for the bracings tb = {3.2; 4; 5; 6.3} andfor the chord tc ={4; 5; 6.3; 8; 10} (mm).

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(a) Base (b) Cut1 (c) Cut2

Figure 13: Deformation of joint typologies for tb = 4mm

The analysis was performed for base, cut1 andcut2 for every thickness and the comparison of thelast two was done with the first in terms of percent-age reduction of the σmax

VM at the connection level.The comparison was done between joint typologies.The node chosen for this sensibility analysis wasnode NA-2.

The results suggest a high sensibility to defor-mation for lower values of thickness of the chordand improvements in the joint behaviour when us-ing LCT in the joint typologies (Figure 14).

Figure 14: Evolution of the difference in terms ofσmaxVM from cut1 and cut2 to base case

The σmaxVM parameter was evaluated and to con-

firm this suggestion a simple study of the local be-haviour is performed. In fact, the local behaviourof the different joint typology for brace thicknessequal to 4mm is shown and it is clear on the de-formed configuration the effects of the prolongationof the profiles (the figures are under an amplifica-tion factor of 3 so that the representations are ex-plicit) (Figure 13).

For the base joint typology (Figure 13a), it isclear the deformation on the face of the chord bothat the intersection with the vertical bracing andwith the diagonal one.

On the contrary, for the case of cut1 (Figure 13b),in which there is the prolongation of the verticalelement into the lower face, the deformation is lowerat the intersection between this and the chord. In

this case, the diagonal profile stops and it is weldedto the face, so it is expected (as in base case) tohappen some deformation at this location.

In the case of Cut2 (Figure 13c), the deformedconfiguration shows the lowest values of deforma-tion at the chord upper face level. This is highlysuggestive of what has been presented in the begin-ning of this chapter, and it indicates that it is dueto the prolongation (even though it is only at halfof the original cross sections profile) of the bracingsinto the chord.

To explore this, a simple comparative local be-haviour study of the different joint typologies fordifferent thickness was performed, considering thedisplacement at nj-1 and nj-2, respectively at the in-terface between the vertical bracing and the chordand between the diagonal bracing and chord. Thisout of plane displacement is plotted against the in-creasing load in the substructure.

These results (Figures 15 and 16) are in line withthe previous ones and confirm the parametric anal-ysis. The plots suggest that the presence of materialinside the chord affect the local behaviour, i.e., jointtypologies that are characterized by the prolonga-tion of elements have showed to behave better andhave lower values of displacement at key locations(nj-1 and nj-2), for lower values of thicknesses ofthe chord. With increasing thickness, the behaviourtends to be similar. For a more complete and de-tailed study of the local behaviour for the differentjoint typologies the full master thesis document [22]can be read.

In general, results suggest, for the same thick-ness, an increase in rigidity for joint typologies usingLCT. Considering this, it is possible to find similarbehaviour by comparing base type joints with LCTjoints with lower thickness of the chord

Figure 17 shows this clearly, by comparing load-displacement curves of cut1 and base cases with dif-ferent thicknesses, at nj-1 location. In this case,base (t=4mm) and cut1 (t=3mm) show similar be-haviour. The same is true for base (t=5mm) andcut1 (t=4mm). It can be noted that there is a limit

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(a) t = 3

(b) t = 4

(c) t = 5

Figure 15: Load displacement curve for nj-1

for this and for the exemplificative case of t=2.5mmthe rigidity is lower with respect to base case. Forcut2 case at nj-1, similar results can be found andare shown in figure 17b. This suggest that it is pos-sible to have the same behaviour with lower valuesof thickness of the chord if laser cut technology isused.

4. Conclusions

Comparing all joint typologies, cut1 and cut2show an improvement of behaviour in terms of σmax

VM

at the connection level. In some cases, a reductionover 10% was calculated when using these alterna-tives. This positive results were achieved when thesection was more stressed (higher loads) and only inthe case of substructure A. A more uniform stressdistribution at the joint is possible due to the exten-sion of the bracing element. In fact, higher stressesat the outer face of the chord due to the extensionof the bracing are compensated by the reduction at

(a) t = 3

(b) t = 4

(c) t = 5

Figure 16: Load displacement curve for nj-2

the inner face.

Results from the numerical analysis of the differ-ent joint typologies have not shown differences interms of global rigidity of the structure for highervalues of chord thickness, which indicated thatstructures of this type can still be modelled withhinged nodes as suggested by Eurocode [19] andCIDECT [20]. This is considered to be, also, an in-dication of a good modelling procedure for modelscombining beam and planar elements.

Similar results between cut1 and cut2 also sug-gest prolongation only half of the cross section isenough to achieve the positive results in terms ofimprovement of structural behaviour. The advan-tage is that in this last case only a slot is opened atthe chord face and no hole is needed, which can beeven more problematic in the case of bigger bracingprofiles.

Considering the increase in the rigidity of thejoints by using Laser Cut Technology in compari-

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(a) base and cut1 (b) base and cut2

Figure 17: Load displacement curve at nj-1

son with the traditional method, it is possible tomaintain the same structural behaviour for lowervalues of thickness of the chord. This suggest thatit is possible to design lighter structures, more eco-nomical and aesthetical appealing, with the samelevel of performance.

Due to this results, future studies should includeexperimental testing structures in which the gov-erning mechanism of the truss girder is the collapseof the joint and in particular the chord face failureto which the results indicate the improvement ofbehaviour when using laser cut technology.

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