Truss girder joint with a large diameter mechanical fastener

Transcription

1 UDK : Građevinar 0/03 Primljen / Reeived: Ispravljen / Correted: Prihvaćen / Aepted: Dostupno online / Available online: Truss girder joint with a large diameter mehanial fastener Authors: Krunoslav Pavković PhD. CE Polytehni of Zagreb Building department krunoslav.pavkovi@tvz.hr Krunoslav Pavković Miljenko Haiman Mladen Meštrović Vlatka Rajčić Truss girder joint with a large diameter mehanial fastener Original sientifi paper A joint with a large diameter fastener for onneting large span truss girder nodes is presented in the paper. The joint strength and slip modulus were analysed by means of experimental testing and the finite element method. The experimental testing was onduted on four truss girders with the proposed joint. The nonlinear truss girder model analysis was onduted using the Abaqus/CAE software with the UMAT subroutine. The results obtained and analysed aording to EN 5 show that the proposed joint has a large strength and slip modulus and that it an be used for large-span truss girders. The results also show that the equation for embedding ompression strength aording to EC5 should be modified. Key words: truss girder joint non-linear analysis large diameter fastener glued-in rods UMAT subroutine Krunoslav Pavković Miljenko Haiman Mladen Meštrović Vlatka Rajčić Izvorni znanstveni rad Prof. Miljenko Haiman PhD. CE University of Zagreb Faulty of Arhiteture miljenko.haiman@arhitekt.hr Rješenje čvora rešetke spajalom velikog promjera U radu je prikazan priključak spajalom velikog promjera za čvorove rešetkastih nosača velikih raspona. Eksperimentalnim istraživanjima i metodom konačnih elemenata provedena je analiza otpornosti i modula popustljivosti priključka. Eksperimentalna ispitivanja provedena su na četiri rešetkasta nosača s predloženim priključkom. U programskom paketu Abaqus/CAE s UMAT podrutinom prikazana je nelinearna analiza modela rešetke. Dobiveni rezultati prikazani u radu obrađeni su prema EN 5 a pokazuju da predloženi priključak ima veliku otpornost i modul popustljivosti primjenjiv za rešetke velikih raspona te da izraz dan u EC5 za karakteristični pritisak po omotaču rupe treba mijenjati. Ključne riječi: čvor rešetke nelinearna analiza spajalo velikog promjera ulijepljene šipke UMAT podrutina Prof. Mladen Meštrović PhD. CE University of Zagreb Faulty of Civil Engineering mestar@grad.hr Prof. Vlatka Rajčić PhD. CE University of Zagreb Faulty of Civil Engineering vraji@grad.hr Wissenshaftliher Originalbeitrag Krunoslav Pavković Miljenko Haiman Mladen Meštrović Vlatka Rajčić Fahwerkträgerknoten mit Befestigungselementen großen Durhmessers Fahwerkträgerknoten mit Befestigungselementen großen Durhmessers Zusammenfassung In dieser Arbeit ist ein Knotenpunkt mit Befestigungselementen großen Durhmessers für Fahwerkträger bedeutender Spannweiten dargestellt. Festigkeit und Steifigkeit der Verbindung sind durh experimentelle Versuhe und numerishe FEM-Analysen ermittelt. Die Versuhe sind an vier Trägern mit der vorgeshlagenen Verbindung abgeshlossen während nihtlineare Analysen mit dem Programm Abaqus/CAE im UMAT Unterprogramm durhgeführt sind. Die erhaltenen Resultate zeigen dass der Knoten ausreihende Festigkeit und Steifigkeit vorweist und für Träger großer Spannweiten angewandt werden kann. Außerdem wird auf die notwendige Modifizierung der Gleihung für Einbettungsdruk nah EC5 hingewiesen. Shlüsselwörter: eingeklebte Stäbe Verbindung großen Durhmessers nihtlineare Analyse Fahwerkträgerknoten UMAT Unterpogramm GRAĐEVINAR 65 (03)

2 Građevinar 0/03 Krunoslav Pavković Miljenko Haiman Mladen Meštrović Vlatka Rajčić. Introdution In the design of large-span strutures the truss girder system due to its small onsumption of material and simpliity is a logial and eonomially more ost-effetive system when ompared to glulam girders. However timber truss girders are very rarely used in our onditions for rossing large spans i.e. the alternative solution involving the use of glulam girders is almost always adopted. Main reasons for suh situation inlude the problem of truss node solving wood industry lobby and the negative attitude of arhitets toward truss girders. The usual and most frequently used solution for onneting timber truss girders is the onnetion by steel node plates and mehanial fasteners whih requires a large truss girder element area to adequately transfer fore to the node plates and to ensure suffiient dutility. This frequently results in a bigger size of truss elements so that an appropriate number of fasteners an be distributed along an appropriate area whih leads to a greater onsumption in wood and steel and the struture beomes eonomially ineffiient. Some other reasons why truss girders are avoided for rossing large spans inlude: redued fire resistane at joints and diffiulties with the preamber whih is indispensable in strutural systems whih are exeeding 300 m in span. In response to the belief that it is easier to use more than 50% of additional laminated timber for a glulam girder rather than to solve the truss girders joints and fire-resistane problems various possibilities have been investigated to see whether the situation an be hanged through introdution of new onnetion systems. The objetive of this paper is to find an appropriate solution for joints of large span trusses in order to enable fast assembly proper definition of preamber during assembly and a greater fire resistane. In this respet it should be noted that an another solution based on a large diameter mehanial fastener urrently at the researh stage has been developed by SP-Trätek Boras Sweden []. The authors of this onept also onsider that presentday solutions are overly ompliated and ostly and that a new solution appliable to large-span trusses should be developed... Conept of the joint The onept of the joint studied in this paper is presented in Figure. It has been oneived through the use of a large-diameter fastener. The timber element into whih the fore is introdued (truss girder ord) is 0.0 mm in width f. Figure but its width is defined based on the required truss girder ord resistane. The truss girder ord is oneived in suh a way that its width an easily be hanged via the number of lamellas depending on the required resistane while the height is defined based on the width of lamellas. The main onnetion element is a large-diameter mehanial fastener whose diameter is defined depending on the required resistane of the joint. It is installed in the hole drilled in the zone perpendiular to the element axis. Bolts are onnetion elements that link the fasteners with the element that introdues the fore into the joint and the diameter and number of bolts depends on the size of the fore to be transfer by the joint. The seond half of the joint onsists of an element that introdues the fore into the joint. The introdution of the fore into the joint an be solved via a timber element with a glued-in rod (as shown in Figure ) [] or diretly by steel rod. The end of the rod (regardless of whether it is glued-in or independent) is inserted into the onnetion bush. Figure. View of the truss joint.. Dutility yield fore and resistane of joint Dutility is a material property whih indiates the level of material deformation in a plasti region prior to failure. It may rightfully be stated that it is an indispensable property of strutures situated in seismially ative areas. The dutility (D) is expressed as the ratio of slip at yield fore (d y ) and max. fore (d max ) [3]: D = δ max δ y When subjeted to earthquake load timber strutures have to exhibit a suffiient level of dutility so that the deformation in the plasti region would lead to the dissipation of energy in the stati system. CEN (European Committee for Standardisation) defines the test protool for determining mehanial properties of onnetions/joints in timber strutures through the following standards: -- for testing joints by stati load EN for testing joints by yli load EN 5 However these standards do not provide speifi guidelines for determining dutility of joints subjeted to stati load [4]. As the joint subjeted to stati load is being tested guidelines given in EN 5 will be used for the determination of dutility. Eah joint has the following signifiant properties: initial joint slip modulus K u and joint slip modulus K s. The slip modulus an be determined from the line defined with 0 % and 40 % of the maximum load and orresponding slips at the 0 % of () 870 GRAĐEVINAR 65 (03)

3 Truss girder joint with a large diameter mehanial fastener Građevinar 0/03 the maximum load (d 0 ) and 40 % of the maximum load (d 04 ) aording to the following expression: F F K = 04 max 0 S δ δ 04 0 max The initial joint slip modulus is determined from the inlination of line defined with the initial slip and slip at the load of 40% of the maximum load F max (d 04 ). The differene between these two slip modulus is determined by unreoverable deformations aused by beading of a fastener. As in this ase we are dealing with the fastener haraterized by a large diameter the relevant failure mode ours after ompressive strength exeeds embedment strength of the timber element. At that the fastener remains undeformed. The design resistane (R d ) for the embedment strength is given by the expression [5]: R d = f had t d (3) where: f had - design embedment strength for the load under the angle α with respet to grain t - is the thikness of the timber element for whih the design resistane is determined d - is the diameter of the fastener. The typial fastener embedment strength resistane is determined via experimental testing in aordane with EN 383 [6]. Aording to this standard the harateristi embedment strength is obtained by driving the fastener of a speified diameter into a timber element in whih the hole of an appropriate diameter is previously made. The fastener is inserted at a speified angle with respet to the grain and the harateristi embedment fore is obtained from the load (F max5 ) whih orresponds to a 50 mm slip value.. Preparations for experimental study.. Geometry and truss girder materials used in experimental study In the sope of this experimental study four truss girder models were made using the new onept of the joint. They measure 6.0 m in axial span with.0 m of axial distane between ords. Trusses are made with three ells i.e. with four vertial ompression web elements and tension web elements in the first and the last ell (Figure ). Truss girder elements were made of lamellas 4.0 mm in thikness and eah element onsisted of five lamellas whih after planing resulted in elements with the ross setion measuring.0 x 0.0 [m]. The melamine glue "Caso adhesives MUF system 47/56" manufatured in Caso Adhesives AB Stokholm Sweden was used to glue the lamellas. Aording to mehanial properties of the timber () used in lamellas prodution the produed laminated elements an be lassified as GL4h aording to the EC5 standard. To gain insight into the entire onept of this joint glued-in rods with the gluing-in depth of 35.0 m were installed in to vertial ompression web elements of the truss girder. A hole with the diameter exeeding by.0 mm the nominal diameter of the threaded rod was drilled in the entre of the timber element as shown in paper [7]. Threaded rods quality grade 8.8 were seleted and the epoxy universal glue manufatured by KGK d.o.o. Karlova was used for the gluing. The glue is marketed under the ommerial name "Epoon 88". The quality of the materials used for steel elements was seleted based on stresses obtained by preliminary finite element models (FEM). The steel quality 4CrMo4 f u =600 N/mm aording to EN-007- was seleted for the fabriation of washers onnetion pipe and fasteners. The steel quality S35JRCu aording to EN 007- was used for onnetion elements that are less exposed to stresses (rings). Allen bolts DIN 9 steel quality.9 were used for bolts in onnetions while two bolts type M0 quality.9 were used for introduing fore into the onnetion from steel diagonals. One bolt type M quality.9 was used to ensure strutural onnetion between the vertial and the truss girder ord. Steel rods.0 mm in diameter were used for tensile diagonals instead of timber elements with glued-in rods as shown in Figure. The reason why timber diagonals were replaed with steel ones lies in greater simpliity of measurement easier ontrol of stress in steel diagonals and smaller manufaturing prie of rods for experimental testing. Tensile diagonals were made of steel quality 4CrMo4 f u =600 N/mm... Experimental testing proedure The girder supportes were provided by steel plates 0 x 00 [mm] positioned on 600 m axially spaed distane. These steel plates were laid on steel setions rounded on top and in this way hinged supports were simulated. During the testing the top ored of the truss girder was laterally supported by a struture omposed of steel pipes (Figure ) to prevent loss of global stability of the girder. The testing proedure onsisted of applying onentrated load in eah third of the span with a ontrolled onstant load rate. The load was applied by two hydrauli jaks onneted to one another so that the pressure in both jaks was always the same. Truss girders were tested with the relaxation at total load of 600 kn after the fore was brought down to 00 kn load was ontinuously inreased until truss girder failure. The applied load was measured via measuring devies plaed between hydrauli ylinders and the top ord of the truss girder as shown in Figure. During the testing stresses in the steel diagonals were measured via tensometers marked T to T4. Measuring of truss girder deformation was onduted in the thirds of the span using measuring devies marked L500/03 and L500/04. Loal deformation was measured for joints situated at GRAĐEVINAR 65 (03)

4 Građevinar 0/03 Krunoslav Pavković Miljenko Haiman Mladen Meštrović Vlatka Rajčić the bottom ord of the truss girder i.e. the displaement of the bolts end whih are entering into the diagonals was measured with respet to the point situated in the bolt axis 00 mm away from the entre of the fastener. The total of four measuring devies marked L00/0 to L00/05 were plaed on two measured joints at the bottom ord of the truss girder i.e. one measuring devie per bolt by whih the fore from the tensile diagonal is introdued into the joint. Deformation and displaement were monitored and reords at one seond intervals via personal omputer. Figure. Experimental testing of trusses It should be noted that during truss girder assembly in the laboratory all bolts at joints were mounted using the ontrolled fore of 4.5 kn i.e. the fastening moment of 7.0 Nm. This bolt tightening resulted in a.0 mm preamber at the entre of the span. During the testing the moisture of truss girder elements varied from.8 to 3.7 perent. The temperature in the room during the testing of the seond truss girder was 30 C and during other tests was 8 C..3. Analysis by finite element method.3.. Geometry and materials for numerial modelling of the truss The FEM of the truss girder was made using the program pakage Abaqus/CAE ver The nonlinear analysis was onduted. The FEM geometry fully oinided with the truss girder geometry used in laboratory testing. Volume finite elements C3D3 defined with six nodes [8] were used for modelling of timber elements. All steel elements of the onnetion as well as tensile ties were modelled with the volume finite elements C3D8 defined with eight nodes. The FEM of the truss girder was fully defined with finite elements and onsidering the great number of finite elements only one half of the truss girder was modelled with boundary onditions whih simulate symmetry as shown in Figure 3. The load was modelled in two steps; in the first one the bolt and tie prestressing load were applied whih orresponded to the methodology used in the experimental testing and in the seond step external load was applied on upper ord of truss girder. As this was a nonlinear analysis with geometrial and material nonlinearity the load values were set related to time. The bolt prestressing load was defined as "bolt load" and inreasing of load was related to time - amplitude urve as is presented in Figure 3. A linear inrease of prestressing load was modelled in eah bolt in the time period varying from 0 t to 0 t. After full prestressing Figure 3. Presentation of FEM with boundary onditions and applied load 87 GRAĐEVINAR 65 (03)

5 Truss girder joint with a large diameter mehanial fastener Građevinar 0/03 load was applied the load ontinued with the seond step in whih the external load was applied onto the truss girder set as the pressure on the steel plate above the ompression web elements as shown in Figure 3. The load inreasing rate was set by a time -dependent amplitude. The graphial presentation of time-related load amplitudes is given for both loading steps in Figure 3. Modelling of mehanial properties of steel parts was onduted elasto - plasti aording to diagrams presented in Figure 4. The plasti region was modelled aross 5 points whih were obtained as an average value from atual stress - strain diagram while elasti modulus and yield strength were set aording to values given in Table. Bolts were modelled bi-linearly with the yield strength and elasti modulus as given in Table while the tangential elasti modulus was defined as being equal to 0 perent of the elasti modulus. Figure 4. Atual stress - strain steel diagrams used for onnetion elements Mehanial properties of timber were modelled elasto - plasti and orthotropi. As due to its orthotropi nature modelling Table. Mehanial properties of materials proedures is muh more omplex than steel modelling and hene impratiable with the basi program pakage Abaqus/ CAE the UMAT subroutine had to be used to define the timber. Two timber yield riteria were defined via this subroutine: the Tsai-Wu riterion for the onnetion zone and a yield riterion derivative from the Hill s yield riterion for other parts of the timber. The oordinate system by whih mehanial properties of timber were desribed is marked with R T and L axes (whih stands for radial transverse and longitudinal diretions respetivelly). Elasti modulus and shear modulus for eah diretion were obtained as average values of timber having the bulk density (ρ = kg/m 3 ) similar to the timber used in truss girger manufature as found in available literature [9-4]. The values from these soures are presented in Table. Main wood strength values for eah diretion were adopted from literature [5 6]. The testing onduted in the seleted literature was made on the same timber quality the bulk density of wood was almost idential and the wood type and weather onditions in whih the tree has grown are quite similar..3.. UMAT subroutine and wood yield riteria The UMAT subroutine was used for the definition of yield riteria and mehanial properties of wood. Prior to its inorporation in the program pakage ABAQUS as the "userdefined material" the UMAT subroutine had to be written in the programming language FORTRAN [7]. One of main problems enountered during FEM of timber resulting from the orthotropi nature and in homogeneity of this material lies in the definition of yield riteria. In this respet a derivative of the Hill s riterion for homogeneous materials was used in the UMAT subroutine as the basi yield riterion. The Hill s yield riterion for orthotropi homogeneous materials [8] is expressed as: Material Meh. properties Modulus of elastiity [N/mm ] Shear modulus [N/mm ] Poisson ratio Compressive strength [N/mm ] Tensile strength [N/mm ] E L =.340 G LR = 6770 ν LR = 04 f ul = -86 ft ul = 98 Glulam timber GL 4h E T = 4690 G RT = 500 ν RT = 057 f ut = -330 N ft ut = 038 E R = 7460 G LT = 6580 ν LT = 05 f ur = -330 ft ur = f us = 33 f us = 33 Steel 4CrMo4 E = G = ν = 03 f y =.450 f u =.6350 Steel S 35JRCu E = G = ν = 03 f y = 5350 f u = 5958 Bolt quality.9. (modelled bi-linearly) E = G = ν = 03 f y = GRAĐEVINAR 65 (03)

6 Građevinar 0/03 Krunoslav Pavković Miljenko Haiman Mladen Meštrović Vlatka Rajčić ( ) ( ) ( ) = A σr σt B σt σl C σl σr D τrt E τtl F τ LR A = ; B = ; ( fur) ( fut ) ( ful ) ( fut ) ( ful ) ( f ) ur C = ; D = ; ( ful ) ( fur ) ( fut ) ( furt ) = ; F = ( futl ) ( fu LR E ) where s is the normal stress t is the shear stress and f u is the stress in the orresponding diretion. As the above expression does not take into aount the brittle failure of wood in tension i.e. if the above ondition is not satisfied mehanial properties for all diretions are alulated in a plasti area. For this reason the above ondition does not give a suffiiently aurate desription of the wood behaviour in ompression and its brittle failure. The behaviour would be muh more aurate if the expression is separated and if a separate riterion is set for eah diretion [9 0]: σl τrt σr τlr σt = ; TL = ; τ = t t t f f f f f ul ush ur ush ut f ush where f u t is the tensile strength and f ush is the shear strength equal for eah diretions. This riterion for tension takes into aount interation between the normal stress and shear stress for a given plane and their separation ensures independene of three mutually orthogonal planes. The riterion of yield in ompression is defined via a simple maximum stress riterion. If maximum stresses exeed the yield limit for one diretion then a plasti region is assumed for all three diretions. (4) (5) The seond timber yield riterion in the onnetion zone is the Tsai-Wu riterion whih is defined with: FσL FσR F3σT FσLσR F3σLσT F3σTσR F σl Fσ R F3 3 σt 44τLR 55τLT 66τRT F F F = If the values F F 3 F 3 are negleted beause of the small influene the expression (7) an be adopted in an abbreviated form: F σ F σ F σ F σ L R 3 T L F σ R F σ 33 T F τ 44 LR F τ 55 LT F τ = 66 RT F = ; F = ; F3 = ; F = ; F t t = ; t f t f f t f fut fut ful ful fur fur ul ul ur ur F33 = ; F = F = F = t fut fut f ush In order to obtain regions in the working diagram the yield riterion presented in expression (8) is adopted in suh a way that the first yield strength is defined if the expression reahes the value 0.0 the seond when the value of 0.7 is reahed and the third when the value of.0 is reahed. This is presented graphially in Figure 5. (7) (8) σl σr σt = ; = ; = (6) f f f ul ur ut where f u is the ompressive strength. It should be noted that there is a onsiderable similarity between the above yield riterion and the Hasin (980) yield riterion [] whih is destined for materials with the pronouned differene in mehanial properties in the diretion of fibres and perpendiular to these fibres. Figure 5. Tsai-Wu yield riterion Figure 6. Stress - strain diagram for timber Hill s yield riterion Figure 7. Stress - strain diagram for timber Tsai-Wu yield riterion 874 GRAĐEVINAR 65 (03)

7 Truss girder joint with a large diameter mehanial fastener Građevinar 0/03 These yield riteria and their onditions are defined so as to obtain regions in the stress - strain diagram for timber as shown in Figures 6 and Finite element method in the UMAT subroutine After the yield riterion was defined the subroutine for the elasti orthotropi material was formulated by means of the finite element method. Due to omplexity of the subroutine that would desribe the elasto - plasti behaviour of materials the formulation of finite elements was adopted for the elasti behaviour of materials. The modifiation made to the subroutine so that it an provide highly aurate results same as elasto- plasti analysis is that the seond (plasti) elasti modulus is adopted for the stresses if one of riteria is not met. Suh a simplifiation is possible in this ase beause the load inreasing rate is onstant and residual plasti deformations are not observed. Elasti stresses aording to the finite element method [] are alulated aording to the expression (9): 3. Analysis of results Stress - strain diagrams of onnetions were obtained from the data olleted by stresses measurements in all four diagonals and by measuring displaement of bolts that form an integral part of the onnetion. The applied load and the displaement of onnetion devie was obtained for eah onnetion through analysis of results as shown in graph presented in Figure 8. The yield fore slip modulus and dutility of joints an be determined aording to method /6 from load - slip diagrams obtained from truss girder joints. In addition as in these joints the failure prinipally ours beause the ompressive embedment strength is exeeded. Embedment strength an be determined in aordane with EN 383 [6]. {s} t = {s} t [M]{e} Dt (9) where: {s} t - stress vetor in time t {s} t - stress vetor in time t [M] - orthotropi matrix of elasti onstants {e} Dt - deformation vetor in time t D D D DRRRR D [ M]= D sim LLLL LLRR LLTT RRTT TTTT DLRLR 0 0 D 0. LTLT {e} = {e L e R e T g RT g LT g LR } T {s} = {s L s R s T t RT t LT t LR } T D RTRT where e is the normal deformation and g is the shear deformation. Component matries for elasti onstants are alulated aording to: D LLLL = E L (-(n RT n TR ))g D RRRR = E R (-(n LT n TL ))g D TTTT = E T (-(n LR n RL ))g D LLRR = D RRLL = E L (n RL (n TL n RT ))g D LLTT = D TTLL = E L (n RL (n RL n TR ))g D RRTT = D TTRR = E R (n TR (n LR n TL ))g D LRLR = G LR D LTLT = G LT D RTRT = G RT γ = ν ν ν ν ν ν ν ν ν LR RL RT TR TL LT RL TR LT Figure 8. Average values of experimental results for truss girders In order to avoid wrong definition of arateristi values the average value of all truss joint results was defined as shown in Figure 8 (blak line). The maximum fore aording to EN 5 was adopted as the smaller value of three onditions: maximum load at the moment of total joint failure maximum load until the moment the 80 % of load drop was registered and maximum load at 300 mm slip value. In the analysis of results the assumption of joint behaviour in plasti region until 300 mm slip value was added to the average value. In fat the analysis of experimental tests revealed that it an be assumed with a great amount of ertainty that the onnetion will attain 300 mm slip value before failure of any of its elements or before load drop in the load - slip diagram. It should be noted that the load for all joints and for the average load value was inreased for 90 kn in the graph given in Figure 8 whih is the prestressing load aplied before the start of experimental testing. Carateristi load values were defined aording to the graph given in Figure 8 and based on the maximum load defined aording to the above desribed proedure. The failure load F y = 8 kn and maximum load F max = 344 kn were obtained through analysis of results. In addition the maximum fore at GRAĐEVINAR 65 (03)

8 Građevinar 0/03 Krunoslav Pavković Miljenko Haiman Mladen Meštrović Vlatka Rajčić 5.0 mm displaement is F max5 = 8563 kn the slip modulus is K S = 5489 kn/mm while the dutility is D = 808. Stress values obtained at the 400 kn load are presented for the diretion parallel to grain S in Figure 4 and perpendiular to grain S33 (tangential diretion if related to truss girder model for experimental testing) in Figure 5. Stress values are presented in suh a way that the legend is limited to the tensile strength and ompression strength so that the zones in whih stress values exeed strength of the timber lass GL 4h an easier be identified. Figure 9. Deformation of entral joint in the seond truss Figure. Displaements in eah third of the truss girder as obtained by experimental testing and FEM Figure 0. Deformation of edge joint in the seond truss Values reorded in eah third of the loally reinfored truss girders monitored by devies L500/4 and L500/3 are presented below. Deformations obtained by FEM of the truss are presented in Figure for the time when full bolt prestressing load is applied. Displaements obtained by FEM show maximum displaement of 50 mm at truss ord near boundary onditions. The displaements obtained by FEM show good orrelation with the preamber obtained during preparation of truss girder for experimental testing. FEM analysis of the truss girder model was onduted to the load of 400 kn. As these are very large deformations espeially in the onnetion zone the onvergene of analysis was interrupted due to exessive deformation of finite elements before the speified load of 4500 kn was reahed. Displaements at the load of 400 kn was presented in Figure 3. The entire load - slip diagram is presented together with diagrams of experimental testing in Figure (red line). For stress values parallel to grain it an be onluded that they do not exeed the timber strength in large areas whih is why they are not of big signifiane for the truss girder resistane and stiffness. Signifiant stress values for the resistane of joints and truss girders were obtained in the S33 diretion. As shown in Figure 3 great zones in whih stress exeed the strength in the diretion perpendiular to grain appear in zones around the fasteners. This stress auses great slip of the joint i.e. the steel pipe penetrates into the timber. A similar ourrene (pipe penetration) was noted during experimental testing. The greatest onentration of the stress that exeeds the strength was obtained in the onnetion (joint) above the hinged support. During experimental testing a big penetration of steel support into the timber ourred at this very joint and the laminas separated due to exessive ompression perpendiular to the grain. The harateristi embedment strength in the diretion parallel to grain was derived based on experimental results. This strength value is presented in the graph (Figure 6) together with some other harateristi embedment strength proposed by other authors depending on the diameter of the fastener. It an be seen from the graph that the expression in EC5 has an exessive stress redution with respet to the inrease of the fastener diameter. Better design equations are presented by S. Franke and P. Quenneville [3] and K. Sawata and M. Yasumura [4]. 876 GRAĐEVINAR 65 (03)

9 Truss girder joint with a large diameter mehanial fastener Građevinar 0/03 Figure. Truss girder displaements after prestressing Figure 3. Truss girder displaements at the load of 400 kn Figure 4. Stress in the S diretion parallel to the fibres Figure 5. Stress in the S33 diretion perpendiular to the fibres 4. Conlusion Figure 6. Comparison of harateristi embedment strength parallel to grain The harateristi embedment strength in the diretion parallel to grain as shown in graph form (Figure 6) was derived based on experimental tests results. It an be onluded that the expression given in regulations EC5 should be modified and extended to enable dimensioning of joints with fasteners that exeed 30 mm in diameter. In addition FEM based on the program pakage Abaqus/CAE and UMAT subroutine with the mentioned Hill and Tsai-Wu yield riterion show a very good orrespondene overlapping with experimental results. Suh omplex FEM analyses enable to ondut joint parametri analyses in the sope of whih the behaviour of fasteners with other diameters ould be monitored. GRAĐEVINAR 65 (03)

10 Građevinar 0/03 Krunoslav Pavković Miljenko Haiman Mladen Meštrović Vlatka Rajčić Finally it an be onluded from first results presented in this paper that in addition to further researh regarding large-diameter fasteners this type of joint an also be used to design truss girders from 30.0 to 50.0 m in span. This joint has been registered and proteted with the State International Property Offie of the Republi of Croatia under No. P0049A. Aknowledgement Authors are thankful to the Polytehni of Zagreb on their finanial support without whih the testing presented in the paper would not be possible and for the material support and servies provided by the following ompanies: Hoja d.d. Slovenia and Stolarija Grčić Karlova. REFERENCES [] Kobel P.: Modelling of Strengthened Connetions for Large Span Truss Strutures in Department of Strutural Engineering 0 Lund Institute of Tehnology: Sweden. [] Rajčić V. Bjelanović A. Rak M.: Nosivost ulijepljenih navijenih čeličnih šipki u elementima od hrastovine. Građevinar (3) p [3] J oahim H. Shadle P.: Dutility aspets of reinfored and nonreinfored timber joints. Engineering Strutures 0 33() p [4] Piazza M. Polastri A. Tomasi R.: Dutility of timber joints under stati and yli loads. Strutures and Buildings 0. 64(sb) p [5] CEN E.C.f.S. Euroode 5: Design of timber strutures. EN Part -: General - Common rules and rules for buildings 004 Brussels: European ommittee for standardization. [6] CEN E.C.f.S. EN 383:007. Timber Strutures-Test methods- Determination of embedment strength and foundation values for dowel type fasteners 007. [7] Tlustohowiz G. Serrano E. Steiger R.: State-of-the-art review on timber onnetions with glued-in steel rods. Materials and Strutures 0. 44(5) p [8] Abaqus Analysis User s Manual in Volume IV: Elamants6.0. [9] Bodig J. Jayne A.B.: Mehanis of Wood and Wood Composites 98 New York: Van Nostrand Reinhold Company. p 7. [0] Carrington H.: The elasti onstants of sprue. Philosophial Magazine p [] Jenkin C.F.: Report on materials used in the onstrution of airraft and airraft engines 90 Her Majesty s Stationery Offie: London. p [] Doyle D.V. Drow J.T. MBurney R.S.: Elasti properties of wood. The Young s Moduli Moduli of Rigidity and Poisson s Ratios of Balsa and Quipo (58). The Elasti Properties of Wood. The Moduli of Rigidity of Sitka Sprue and heir Relations to Moisture Content (58-A). The Elasti roperties of Wood. Young s Moduli and Poisson s Ratio of Sitka Sprue and Their Relations to Moisture Content (58-B). Forest Produts Laboratory [3] CEN E.C.f.S. EN 94:999 Timber strutures - Glued laminated timber - Strength lasses and determination of harateristi values 999. [4] CEN E.C.f.S. EN 338:003 Strutural timber - Strength lasses 003. [5] Haiman M.: Analiza sigurnosti lameliranih nosača Građevinski fakultet 00 Sveučilište u Zagrebu: Zagreb. [6] Čizmar D.: Robusnost nosivih sustava drvenih rešetkastih nosača Građevinski fakultet 0 Sveučilište u Zagrebu: Zagreb. [7] Abaqus User Subroutines in Referene Manual6.0. [8] Hill R.: A Theory of the yielding and plasti flow of anisotropi metals. Proeedings the royal soiety A p [9] Xu B.H. et al.: Numerial and experimental analyses of multipledowel steel-to-timber joints in tension perpendiular to grain. Engineering Strutures p [0] Xu B.H. Bouhair A. Taazount M.: 3D non-linear finite element modelling of traditional timber onnetions. in World onferene on timber engineering 00. Riva de Garda. [] Hashin Z.: Failure Criteria for Unidiretional Fiber Composites. Journal of Applied Mehanis () p. 6. [] Abaqus Analysis User s Manual in Volume 3: Materials6.0. [3] Franke S. Quenneville S.: Bolted and dowelled onnetions in Radiata pine and laminated veneer lumber using the European yield model. 0 Institution of Engineers Australia Australian Journal of Strutural Engineering. [4] Sawata K. Yasumura M.: Determination of embedding strength of wood for dowel-type fasteners The Japan Wood Researh Soiet p GRAĐEVINAR 65 (03)