Increasing load capacity of steel space trusses with end-flattened connections

Journal of Constructional Steel Research 65 (2009) 2197–2206

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Journal of Constructional Steel Research

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Increasing load capacity of steel space trusses with end-flattened connectionsLuciano Mendes Bezerra ∗, Cleirton André Silva de Freitas, William Taylor Matias, Yosiaki NagatoDepartment of Civil Engineering, University of Brasilia, PECC/ENC/FT, Brazil

a r t i c l e i n f o

Article history:Received 24 July 2008Accepted 12 June 2009

Keywords:Space trussesEnd-flattened connectionsTruss load capacity

a b s t r a c t

Steel space trusses are generally made of tubular section members. There are several types of linksto connect these members. The most popular is the end-flattened connection. The advantages of suchconnections are reduced costs and fast assemblage of the truss. However, they present disadvantages suchas eccentricities and stiffness reduction ofmembers. In thiswork, based on computer simulations andnineexperimental lab tests on space truss prototypes, small changes on the end-flattened connections such asreinforcement and eccentricity correction are evaluated. The results show a 68% increase for local collapseand a 17% increase for global collapse in the truss load carrying capacity. Global and local collapses are,respectively, associated with the ultimate limit state and serviceability limit state.

© 2009 Elsevier Ltd. All rights reserved.

1. Introduction

Steel space trusses are generally made of linear bars connectedby their ends forming three-dimensional structures that are atthe same time light weighted and load resistant. The linear barsare made of standard rolled shapes or cold-formed steel sections,connected by their ends. The first choice is generally to make trussmembers of steel angles or tubes. Fig. 1a shows the elements of athree-dimensional (3D) truss. Connections or nodes are thepoint ofintersection of bars (chords and diagonals). Rigidity of the linkingsystem, chord and diagonal arrangements, support conditions andloading directly influence the relationship between truss height(H) and span (L). In references [1–8], recommendations on therelationship between H and L are given. In Fig. 1a, the calculationmodels usually consider the truss connections as hinged nodesunder axial centered loads. However, the implementation of jointsto ensure a perfect hinge is very difficult and costly.Steel space trusses are frequently used as roof structures (see

Fig. 1b) in industrial, residential and sport facility buildings tocover large open areas with few or no internal supports [3,4].Due to their economy and versatility, space trusses are becomingmore common nowadays. These structural systems, made ofbars connected at nodes, make possible the construction of veryefficient 3D meshes of various shapes [9].Engineers and architects report major advantages in the use of

space steel trusses, such as: (a) ease to expand, (b) uncomplicateddismantling and transportation for assembling in other site, (c)empty space between chords to accommodate service facilities, (d)capacity to easily incorporate cladding and finishing surfaces, (e)

∗ Corresponding author. Tel.: +55 61 31070998.E-mail address: [email protected] (L.M. Bezerra).

0143-974X/$ – see front matter© 2009 Elsevier Ltd. All rights reserved.doi:10.1016/j.jcsr.2009.06.011

ability to cover large open areas with few or no internal supports,(f)mass production, (g) easy transportation, (h) fast assemblage, (i)light weight and (j) pleasant appearance, among others [9,10].The truss type depends, essentially, on the range of geometries

associated with the truss system and on the type of connectionused. Among others, geometries like square on square and diagonalon square are common. Fig. 1a shows a square on square geometrywhich is the most common geometry found in practice. However,the complexity of the different types of connections is the mainfactor for the cost difference between the various truss systems.Between welded or bolted connections, the latter is preferred

due to fast assemblage, reduced costs, uncomplicated dismantling,transportation and expansion and workforce availability amongother advantages. For medium and large span trusses, boltedconnections are usually recommended. Truss members are joinedwith bolts and screws, or using multiple pressed jointed or‘‘rosette’’ type connections. There are examples [11] of steeltrusses, joined only by bolts, that able to cover spans up to60 m. Among bolted connections for trusses there are the highquality ones, generally patented joints, and there are those inthe public domain. When patented connections are employed, itis understood that the quality and strength of the space trusses,generally, increase — although the truss system becomes moreexpensive. Due to costs, there are even situations in which thesteel space truss use is limited to applications where a pleasingappearance is the highest priority [12]. Despite the continuousdevelopment during the last decades, the use of space trusses inthe markets of large-span structures is still small. The main reasonfor this restricted use is their relative high cost due to specialconnections required for space truss assembly [10].For many practitioners, manufacturing costs and fast assem-

blage are themain factors in the decisionmaking process to choosethe type of connection to be used. In light of this, one of the most

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2198 L.M. Bezerra et al. / Journal of Constructional Steel Research 65 (2009) 2197–2206

a b

Fig. 1. (a) Truss elements: square on square. (b) Part of a soccer stadium roof.

a b

Fig. 2. (a) End-flattened node system. (b) Collapse detail of nodes and bars.

common connections used for steel space trusses are the connec-tions obtained by end-flattened tubes later to be joined with a sin-gle bolt. In Brazil, due to economic reasons, this is themost adoptedconnection in trusses used in sports gymnasiums, soccer stadiums,churches, large textile industries, and in infra-structure such asairports, warehouses for grain storage, railway and bus stations,among other applications along the vast Brazilian territory — seeFig. 2a. However, structural collapses, mainly associatedwithwith,are not uncommon to such space truss solutions — Fig. 2b.The end-flattened node is the simplest and therefore cheaper

connection in the manufacture of 3D trusses, but it has two maindisadvantages [9]: the generated eccentricity bendingmoment andthe reduction of stiffness in the tubes due to the end-flatteningprocess. It is important to notice that themost traditional methodsused for structural analysis of steel space trusses presupposethat all the designed connections are hinged. The eccentricalconnections which modify the assumption of pinned joints,generally, are not considered in the calculation. Therefore, usuallyonly traction and compression forces are considered. No bendingmoment is expected at the truss connections. However, in practice,the joints are not ideal and show eccentricities and loss of stiffness.This article does not encourage the use of low quality conn-

ections, but it studies specifically the end-flattened connectionwhich is very popular in many developing countries. The researchpoints out the weaknesses of such connection andmakes attemptsto improve it with simple and cheap changes. The investigationsfocus on modifications to the end-flattened node with the aimto improve the load carrying capacity of space trusses and,therefore, to make it safer for the construction industry. Theproposed modifications were first numerically simulated and thenexperimentally tested at the University of Brasilia’s StructuralLaboratory.

2. Main space truss systems

This section presents a brief overview of space truss systems.Several authors [10,13–15] contributed with investigations for

the development of space truss systems. In general, according toEl-Sheikh [10], the available space systems can be categorizedinto two main groups: (a) systems with short chord membersjoined together by nodes (also called connectors); and (b) systemswith continuous chord members that do not need nodes for theirassembly. The first group system includes the most space trusssystem available today while only a small number of systemsbelong to the second group.The first group is characterized by short length bars connected

at the joints with similar nodes. The main systems belongingto this group are: (a) The Mero system (Fig. 3a), widely usedaround the world. This system comprises nodes made of a steelsphere with eighteen screw thread holes where the truss barsmay be screwed. The similarity of members and nodes in suchsystems allowmass productionmaking the assembly fast, easy andpleasant in appearance. (b) The Nodus system (Fig. 3b) has a verysophisticated node created by the superposition of two steel platesto hold the chord and connect the diagonals with bolts. (c) TheTriodetic truss system (Fig. 4a) uses a solid cylindrical body nodeto hold the bars inserted in special slots without the use of boltsor welds. (d) The End-flattened truss system is the most popularand is very cheap to manufacture (see Fig. 4b). It is assembledwith tubular steel members with the ends of chords and diagonalsflattened in order to be connect by a single large diameter bolt. Inthis system no special gadget is used to hold the tubular membersand, consequently, the fabrication cost is very much reduced.The second group is characterized by a continuity of the chord

member across the joints, and the members are not similar inlength. The main systems belonging to this group are: (a) TheSchmidt system [16] that uses no special node and the diagonalsare connected to the chord by bolts — Fig. 5a. (b) The Harleysystem is the most known system of this group and was firstdeveloped by Codd [10,12]. Fig. 5b depicts the Haley’s connectionsystem. No special gadget is used in this system, and, consequently,manufacturing is cheap.Adetailed study of each truss system from the first or the second

group is not within the scope of this research. More information

L.M. Bezerra et al. / Journal of Constructional Steel Research 65 (2009) 2197–2206 2199

Fig. 3. (a) Mero node. (b) Nodus node ([10] — modified).

Fig. 4. (a) Triodetic node — ([2] — modified). (b) End-flattened node.

Fig. 5. (a) Schimidt’s node system. (b) Harley’s node system ([10,12] — modified).

on other types of systems can be found in [2,9,10,12,17,18]. Thiswork concentrates efforts in a cheap alternative way to increasethe resistance of the end-flattened system — Fig. 4b. Trusses withthis system connection are widely used in Brazil and in manydeveloping countries. The aims of this research are outlined in thefollowing section.

3. Research objective

The stacked end-flattened connection behavior is very popularbut its behavior is not yet fully understood. Such a connectionbelongs to the public domain and is the simplest and cheapestto manufacture. The two main disadvantages of the stacked end-flattened connection are: (a) nodal eccentricities E1 and E2 (seeFig. 6) and (b) section flattening. Nodal eccentricity generatesbending moments at the tube ends, and the end-flattening processreduces the bending stiffness of the bar cross section. Thesetwo major disadvantages are believed to reduce the resistanceof the bars and consequently decrease the truss load carryingcapacity. The main purpose of this research is to find an easy and

cheap alternative to increase the load carrying capacity for three-dimensional trusses made of steel tubes jointed by stacked end-flattened tubes crossed by a single bolt — as can be seen in Fig. 6.The research is carried out in two fronts: (a) numerical modelingusing finite elements in a chosen geometry, and (b) experimentalinvestigation in 3D truss. The experimental tests will be performedin prototypes at the Structural Laboratory of the Department ofCivil Engineering at the University of Brasilia (UnB).To increase the truss loading capacity, this research proposes

corrections to the eccentricity and the inclusion of additionalreinforcements to the bar ends. These two initiatives shouldreduce, at least in part, the disadvantages outlined above and,consequently, increase the truss load carrying capacity. Cuencareported [19] using nuts, bolts andwashers to reduce eccentricities— see Fig. 6c. However, he does not present any preliminary studieson the determination of the nut size nor on the effectiveness ofthe adopted node. In effect, to correct the eccentricities E1 andE2 the diagonals must be lifted in order to make point A coincidewith point B, see Fig. 6b. No research was found dealing with thedetermination of the nut size and on how much more load a trusswith such node corrections can get. In this article such studies willbe carried out numerically and experimentally.At first, computational models will show the advantages of

correcting the connection eccentricities, and then experimentallab tests will confirm the computational results and expectations.Therefore, to correct the eccentricity, a steel washer serving as aspacer is placed in-between the diagonal bars and the chord (topand bottom chords) — see Fig. 7. This washer, made of steel, iscalled spacers to follow. To overcome part of the reduction of thebar stiffness, reinforcement plates are placed over the ends of thediagonal, but opposite the chords reaching a node or connection.Fig. 7 outlines these two changes suggested for the stacked end-flattened connections. The effectiveness of these changes will bestudied in truss prototypes discretized in finite elements and usinglab tests as described in the following section.

4. Space truss prototypes

To understand how the load carrying capacity of space trussesincreases, according to modifications at the end-flattened joints


Fig. 6. (a) Eccentricities and flattened ends. (b) Correcting eccentricity. (c) Cuencas’ node with nuts and washers — ([19] — modified).

Fig. 7. (a) Traditional end-flattened node and (b) modified node.

suggested, a prototype truss geometry is chosen. Numericalmodels of this prototype are built with bars and nodes with samegeometry, span, height, tube shape, diameter and thickness, andalso the same steel material and bolt. However, the models differonly in the configuration of the nodes/connections. The chosengeometry is shown in Fig. 8. It is noted that the truss prototypeis made of pyramidal units (Fig. 8a) connected at nodes (pyramidvertices). As indicated in Fig. 8b, the connections of the prototypesmay be modified. Each pyramid has a square base with ` =1000 mm and height H = 707 mm. The diagonal inclinationangles are, therefore, 45◦ with respect to the base plane of thepyramid. The steel tubes of the truss have 25.4 mm (1′′) as theexternal diameter and 1.59 mm (5/8′′) of thickness. Details ofthe dimensions of the truss chords and diagonals may be seen inFigs. 8 and 9a and b. Due to the flattening process of the diagonaltube ends, the inclination angle 47.5◦ corresponds with 45◦ in theideal truss case in which the diagonal is defined by the line AB inFig. 9c. The tubes are made of Brazilian steel known in industry asMR250 [20] which is equivalent to the A36 [21]. This steel has thefollowing material properties: Yielding Stress, 250 MPa; UltimateStress, 400 MPa; Modulus of Elasticity, 205000 MPa and Poisson’sratio, 0.3.Fig. 10 shows the types of connections considered for evalua-

tions. The first connection in Fig. 10a is named ‘‘Ideal Link’’ andreferred to as IL. The second in Fig. 10b is referred to as TL (mean-ing the Typical Link or the end-flattened node). The third is pre-sented in Fig. 10c and is denoted by TLS. In fact TLS is a TL con-nection with a Spacer (thick steel washer separating the diagonalsand the chords) in order to reduce the eccentricity. The last one,named TLSR (for Typical Link with Spacer and Reinforcement) cor-responds to two reinforcement plates encapsulating a TLS connec-tion (Fig. 10d). The spacers and the reinforcement plates may becircular or squared.The thickness of the spacer (d) in Fig. 6b is a geometry problem.

Consider first that the lines of the centers of gravity of all thetubes (arriving at a node) converge to a single point. Then, todeduce the thickness (d), take into account the pyramid unit withits base length (`) and height (H), the thickness (t) of the tube wall(flattened) and the eccentricities E1 and E2. Eq. (1) presents theformula for the calculation of the spacer size (d). It is important

to observe that for tubes with different diameters and thicknesses,Eq. (1) changes [22,23].

d = 2HE1/(`√2− 4E1

)− 8t. (1)

The spacer thickness is fixed but its diameter has a range ofacceptable solutions that fits in-between the diagonals. Taking intoaccount the truss prototype dimensions and tube thickness, thespacer is found to be 20 mm thick. The adopted diameter of thespacer was 50 mm (2′′) while plates of 1.91 mm (3/4′′) thicknesswill reinforce the connections.Fig. 8 illustrates the prototype truss. It has a total of 32 tubular

members (12 bottom chords, 4 top chords, and 16 diagonals) and13 nodes or connections, four nodes at the upper part and 9 nodesat the lower part. At the node in the middle of the truss located atthe lower part of the truss a downward and vertical load ‘‘Q’’ will beapplied (see Fig. 8). Q produces tension forces at the bottom chordsand diagonals of the middle pyramid (upside down pyramid) andcompression forces at the upper chords and other diagonals. Thecritical bars, under the largest compression forces, are the fourupper chord bars.The maximum compressive load at those bars can be deter-

mined from the Brazilian Standard [20] or using similar recom-mendations from the AISC-LRFD [21]. The critical compressive barstrength (Nc), based on the limit state of flexural buckling, can becalculated as Nc = 13 kN, which corresponds to an approximateload Q ≈ 37 kN applied at the middle node, as illustrated in Fig. 8.

5. Numerical models and preliminary results

The scope of this section is to investigate the stress distributionat the truss bars under a vertical load Q equal to 37 kN acting atnode9 (Fig. 8)while considering themodifications suggested to theend-flattened connections. For this purpose, three-dimensionalfinite element models of the prototype trusses are here conceived.The finite element (FE) program SAP2000 (Structural AnalysisProgram) [24] is here used to discretize the 3D standard truss withits different node/connection configurations — (see Fig. 10). Twotypes of finite elements from the SAP element library are usedfor the numerical modeling: the FRAME element and the SHELL


Fig. 8. (a) Pyramid units. (b) The prototype truss.

Fig. 9. Details and dimensions of (a) chords, (b) diagonals, and (c) angles.

Fig. 10. Types of nodal connections studied (a) IL, (b) TL, (c) TLS, and (d) TLSR.

element. FRAME elements are employed to discretize the trusstubular members (diagonals and chords) and SHELL elements,when necessary, are used to discretize the connections. Thematerial properties (Modulus of Elasticity and Poisson’s ratio) ofsteel and the geometry of the tubes (diameters, thicknesses andlengths) described in the previous section were used in the SAPinput files.To investigate the distribution of normal forces (tractions and

compressions) and bending moments along the bars of the spacetrusses, three 3D finite element models were built correspondingto trusses with connections IL, TL and TLS (defined in section

four and in Fig. 10). No FE model is necessary for the truss withTLSR connection, since there is no significant change in the force& moment distribution with respect to the truss with TLS node.For the TLS connection model, all the FE nodes were completelycoupled between chords and diagonals, making the TLS connectionsufficiently rigid. The truss with IL nodes (Ideal Link nodes), issimply represented in a FE model by just using FRAME elements.In this case, the bars show no eccentricity and, therefore, the endsof the bars match perfectly to the FE nodal points. The TL (TypicalLink or end-flattened node) is modeled with FRAME elements, butthe flattened tube ends are modeled with SHELL (plate) elements.The ends are bent to make the diagonals match with the chords.The TLS node has a washer serving as a spacer to correct theTL eccentricity. The FE modeling is straightforward, employingagain FRAME and SHELL elements — placing a thick (20 mm) plateelement in-between the diagonals and chords. In the FE models,nodes are numbered from 1 to 13, and elements from 1 to 32 — seeFig. 11. The connection details for the threemodels for connectionsIL, TL, and TLS are represented in Fig. 12.Restrictions for displacement and rotations are applied to nodes

at the supports of the truss located at the corner— representing thesupport conditions to be replicated in the experimental tests. Node9 in Fig. 11 is the middle node where the concentrated load ‘‘Q’’ isapplied. Note that in linear elastic analysis, any load valuewould besuitable for obtaining the force & moment distributions along thetruss bars. However, in this research, the downward and verticalload value was representatively chosen to be Q equal to 37 kN andwas applied at node 9, Fig. 11. The elastic linear distributions of theaxial forces and bending moments along the bars, are representedin Figs. 13–15. Figs. 16 and 17 review these distributions in amore practical approach so that changes among the trusses with


Fig. 11. (a) Finite element node numbers. (b) Finite element connectivities.

Fig. 12. (a) FE for IL, (b) for connections TL, and (c) for TLS.

-13,02kN

-13,00kN

13,05kN 13,05kN

-13,00kN

0,39kN.cm0,39kN.cm

1,18kN.cm -1,18kN.cm-1,18kN.cm

-0,75kN.cm -0,75kN.cm

b

a

Fig. 13. For Ideal Link (IL). (a) Axial force and (b) bending moment.

different connections are noticed in a more instantaneous andremarkable way.In effect, examining Figs. 16 and 17, it is clear that the normal

force distribution shows minor changes among trusses with IL, TL,and TLS connections. In contrast, the bendingmoment distributionvaries considerably from one FE model to the other. The presenceof a spacer in the truss with TLS produces a significant decreasein the bending moment values presented in the truss with TL(end-flattened connections). Actually, the moment distributionsof the trusses with TLS connections move toward the ideal trusswith IL. This is an important conclusion, since due to eccentricityat TL connections and the combination of axial compression andbending; the bars may have their strength capacity reduced.From the point of view of displacement, along the bottom

middle chord formed by the FE nodes 2, 6 and 4 (in Fig. 11a), thetrusswith TLS connections has a tendency to present displacementvalues similar to the truss with the Ideal Link (IL) — see Fig. 18.On the contrary, the truss with the end-flattened connections (TLnodes) is less rigid and consequently shows a greater verticaldisplacement of the bottom middle chord — see Fig. 18. The

-12,73kN

12,83kN 12,83kN

-12,82kN -12,82kN

-18,29kN.cm -18,29kN.cm

3,15kN.cm

13,33kN.cm 13,33kN.cm

a

b

Fig. 14. For Typical Link (TL). (a) Axial force and (b) bending moment.

-12,25kN

12,64kN

-12,64kN -12,64kN

12,64kN

-6,80kN.cm -6,80kN.cm

4.82kN.cm 4.82kN.cm

a

b

Fig. 15. For TLS. (a) Axial force and (b) bending moment.


15,00

10,00

5,00

0,00

-5,00

-10,00

-15,00

Axi

al F

orce

(kN

)

IL

TL

TLS

Bar FE number

Fig. 16. Axial force distribution for IL, TL and TLS.

15,00

20,00

10,00

5,00

0,00

-5,00

-10,00

-20,00

-15,00Ben

ding

Mom

ent (

kN.c

m) IL

TL

TLS

Bar FE number

Fig. 17. Bending moment distribution for IL, TL and TLS.

Fig. 18. Displacements — chord with nodes 2-9-4 for IL, TL and TLS.

numerical analyses demonstrate the changes in the momentpattern and in the stiffness of trusses with IL, TL and TLSconnections. They show that trusses with TLS connection tend towork as ideal trusses with insignificant moment, and presumably,higher loading capacity.Finally, we notice that the numerical analyses in this section

were not intended for comparison with experimental results butjust to provide guidance on how to increase the strength oftrusses with stacked end-flattened nodes. The numerical analysesperformed here point out that trusses with TLS connections couldbe an easy and cheap alternative. The experimental tests in the nextsection investigate this conclusion.

6. The experimental program and results

This section investigates by means of experimental tests thedistribution of normal forces and bending moments along thebars of the trusses with links TL, TLS and TLSR. This experimentalprogram seeks to collect simple quantitative and qualitativeinformation on the standard space truss taking into accountdifferent nodal types. To achieve this goal, static tests are carried

Node TL TLS, TLSR

Diagonal Chord

Rigid steel base

Fig. 19. General assembly of a truss prototype for test.

out on truss prototypes under an increasing vertical load applied atthe middle node (node-9 in Fig. 11). The load is gradually applieduntil truss collapse is reached. For each specific connection system,three experimental truss prototypes were constructed. Prototypeswith IL nodes (Ideal Link) were not built since the goal is to observehow much load capacity can be gained with simple modificationson trusses with the common TL nodes (the end-flattened nodes).Therefore, considering the three links under analyses (TL, TLS andTLSR) a total of nine prototypes were manufactured.The nine experimental prototypes (TLEn, TLSEn, and TLSREn,

n = 1, 2, 3) were tested in the Structural Laboratory at theDepartment of Civil Engineering in the University of Brasilia (UnB).The corners of the prototype trusses were fixed on a very stiff steelbase available in the laboratory. A downward and vertical load isapplied at themiddle node (node 9) through a strong cable passingthrough a hole in the laboratory resistant floor. Fig. 19 shows thecomplete assembly for the lab tests. Each prototype measures incm 200 × 200 in base and 70.7 in height; and has the geometryas outlined in Figs. 8–11 with 32 tubes and 13 nodes. The tubedimensions and material properties were previously described insection four of this article. At themiddle node, the loadwas appliedby a cable attached to a hydraulic jack. Load values are controlledwith a load cell. The hydraulic jack has a 300 kN load capacityand the load cell reads up to 500 kN with a 0.1 kN precision.Displacements of all bottom nodes (nodes 1, 2, 3, 4, 9, 10, 11, 12and 13)weremeasured using analog deflectometers as can be seenFigs. 19 and 20.Two strain gages (as indicated in Fig. 20), were positioned,

respectively, at the upper and lower part of the top chordperimeter (tube 10 in Fig. 11) to measure variations of bendingmoment stresses at that tube. With these strain gages the momentassociated to the different types of connections tested can beevaluated. At node 9, the cable pulls the prototype downward inload-steps of 1.0 kN and after every given load-step readings ofthe total load, displacements, and strains were taken. For the dataacquisition from the strain gages, the system Spyder-8 connectedto a computer and controlled by the Catman-4.5 software wasused. For node 9, Fig. 21 shows the loads-displacement curves forthe 9 prototypes tested. These curves generate polynomial curveswhich are also plotted in Fig. 21 and in Fig. 22. Such polynomialscorrespond to the average of the three lab tests performed foreach prototype with its respective connection. Therefore, thepolynomial TLE is the average of the tests performed on prototypesTLE1, TLE2 and TLE3. The polynomial TLSE is the average of thetests on TLSE1, TLSE2 and TLSE3; finally, the polynomial TLSRE isthe average of tests TLSRE1, TLSRE2 and TLSRE3. The plots go up tothe points where global collapse is achieved — points 1, 2 and 3 inFig. 22.


Support Support

Support Support

Node 2

Node 6

Node 9

Node 8

Node 4

Node 7

Node 5

Nod

e

Nod

e

1 3

StrainGages

a b

Fig. 20. (a) Prototype view, nodes for displacement readings and strain gages. (b) Portable analog deflectometers fixed to the steel base with a magnetic device.

4540353025201510

50

0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50

Load

(kN

)

Test TLE1

Test TLE2

Test TLE3

Average - TLE

Displacement (mm) - node 9

4540353025201510

50

0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50

Load

(kN

)

Test TLSRE1

Test TLSRE2

Test TLSRE3

Average - TLSR


4540353025201510

50

0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50

Load

(kN

)

Test TLSE1

Test TLSE2

Test TLSE3

Average - TLS


a

b

c

Fig. 21. Load-displacement curves for TLEn, TLSEn and TLSREn prototypes.

We understand ’’global collapse’’ as the moment in which anysmall load increment is no longer bearable to the prototypes.Global collapse is directly related to the ultimate limit state,imminent risk of failure. It is characterized by the buckling ofcritical members under combined axial compression and bending.For the same load level, it is clear that the trusses with TL nodes(end-flattened nodes) showed the largest final displacement.

45

40

35

30

25

20

15

10

5

00,0 2,0 4,0 6,0 8,0 10,0 12,0 14,0 16,0 18,0 20,0 22,0 24,0 26,0 28,0 30,0 32,0 34,0 36,0 38,0 40,0 42,0 44,0 46,0

Load

(kN

)


Average-TLEAverage-TLSEAverage-TLSRE

12

3

4

9

Fig. 22. Load-displacement averaged curves for TLEn, TLSEn and TLSREnprototypes.

Actually, in Fig. 22, point 1 corresponds to coordinates (36 kN;46 mm), point 2 (38 kN; 36 mm) and point 3 (42 kN; 33 mm).However, the global collapse of a truss does not reflect theexcessive deformation (local collapse) observed at the prototypeconnections.The so called ‘‘local collapse’’ is here related to the serviceability

limit state since the prototypes can still bear load increments.Local collapse is basically characterized by an excessive rotationof a node or connection but not necessarily buckling of a member.Actually, in Fig. 22, at point 4 (25 kN), the corresponding prototypes(TLE1, TLE2 and TLE3) show excessive rotation of few connections— as shown in Fig. 23a. Fig. 23b illustrates the global collapsetypical for TLEn prototypes. However, examining Fig. 23c ande, respectively, for prototypes TLSEn and TLSREn, less excessivedeformation is observed for the same 25 kN load, when comparedto TLEn in Fig. 23a. Therefore, for 25 kN, TLEn prototypes (with end-flattened connections) show local collapse and quite the oppositemay be observed in the other prototypes (TLSEn and TLSREn).At this point, it is useful to observe that the connections

of the prototypes TLSEn have spacers, and the connections ofprototypes TLSREn have spacers and reinforcements. Excessiverotation deformations at connections is immediately followed byglobal collapse and reached for the prototypes TLSEn and TLSREn,respectively, at loads of 38 kN and 42 kN — see Fig. 23d andf. Therefore, on average, and considering only the local collapse(excessive rotation of connections), TLEn prototypes collapse at25 kN, TLSEn at 38.5 kN (53% more) and TLSREn at 42 kN (68%more). For global collapse, compared to TLEn prototypes, TLESnincreased 2.5 kN (7% more) while TLSREn increased 6 kN (17%


(a) Local collapse for TLE at 25 kN. (b) Global collapse for truss TLE at 36 kN. (c) No local collapse for TLSE at 25 kN.

(d) Global collapse for truss TLSE at 38.5 kN (e) No local collapse for TLSE at 25 kN.

(f) Global collapse for truss TLSRE 42 kN.

Fig. 23. Local and global collapses for TLEn, TLSEn and TLSREn prototypes.

more). It is noted that these results may change for prototypesof different sizes [25]; however, the small scale here used for theprototypes does not compromise the qualitative conclusion of thisinvestigation.Data from the two strain gages were collected to enable a

qualitative idea of the bendingmoment changes at the connectionsof each truss prototype tested. They were averaged and plottedin Fig. 24. It was possible to conclude that as the differencebetween the upper and lower strains increases, the bendingmoment at that truss connection also increases. Therefore, byexamining Fig. 24, it is obvious that the bendingmoment is greaterfor TLEn prototypes, and decreases successively for TLSEn andTLSRE prototypes substantiating the numerical results obtainedpreliminarily in Section 6.It is important to notice that the lab tests in this section were

carried out until ultimate load capacity; and since the start of load-ing, the trusses exhibit nonlinearities such as connection accom-modation and local plasticity at the end-flattened connections. Dueto these nonlinearities, deflections in Fig. 22 are larger than inFig. 18 obtained from linear elastic analyses. For a fair comparison

45

40

35

30

25

20

15

10

5

00,00 -100,00

Load

(kN

)

Strain Difference (µm/m)

Average-TLAverage-TLSAverage-TLSR

12

3

4

-200,00 -300,00 -400,00 -500,00 -600,00 -700,00 -800,00 -900,00

Fig. 24. Strain gage differences for TLEn, TLSEn and TLSREn prototypes.

between numerical and experimental data, complex finite elementmodels taking into account physical and geometrical nonlineari-ties and also gap elements could be used. However, such complex


modeling was out of the scope of this article but will be the objectof future investigations and publications.Essentially, the results of this section show that the strengths

of the prototypes TLSEn (with spacers correcting eccentricities)and TLSREn (with spacers and reinforcement plates) increasewhen compared to the strength of the prototypes TLEn (withend-flattened connections). This is an interesting conclusion,since with simple and cheap devices correcting eccentricityand providing more reinforcement; the popular truss withend-flattened connections can have its load carrying capacitysubstantially increased.

7. Conclusion

This research presented numerical and experimental studies onsteel space trusses made of tubes with end-flattened connections.This type of truss is very popular inmany countries but its behaviorhas not yet been completely understood. End-flattened tubeslinked with one bolt form trusses which are easy to manufacture,fast to build, inexpensive and aesthetically acceptable. However,they present disadvantages at the connections: nodal eccentricitiesand flattening of the tube section. These disadvantages produce asubstantial increase in the bending moment and loss of rigidityin the connections thus decreasing the efficiency of this type oftruss. The goal of the research was to improve the load carryingcapacity of such trusses with simple constructive alternativesthat could be used by practitioners. The use of spacers andreinforcement plates were suggested to increase the load carryingcapacity of this type of truss. Spacers and the reinforcement platesmay be circular or squared, and the article also presented anequation to calculate the size of the spacers. In this research, totest the effectiveness of using spacers and reinforcement plates,nine finite element models and nine prototypes made of steeltubes, under a central point load were considered. Different typesof connections on the prototypes were analyzed. The resultsshowed that correcting the eccentricities with spacers and usingreinforcement plates on the connections increase substantially thestrength of the prototypes. Just using spacers on the end-flattenedconnections, the experimental tests showed that the local collapsestrength of the prototypes increased in 53%, and using spacers andreinforcement plates the increasewas 68%. For global collapse, justusing spacers the increase in strength was 7% and when spacersand reinforcement plates are utilized, the increase in strength was17%. This alternative can be easily applied to a new truss designor in strengthening actual trusses. This investigation will proceedwith the tests of different types of materials to manufactureinexpensive spacers.

Acknowledgements

The authors wish to express their acknowledgements to theUniversity of Brasilia (UnB) where all the experimental tests took

place and also to CNPq for its financial support in the developmentof this research.

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Increasing load capacity of steel space trusses with end-flattened connections