Finite element modelling for static behaviour analysis of suspension bridges with varying rigidity...

THE BALTIC JOURNAL OF ROAD AND BRIDGE ENGINEERING

2008 3(3): 121–128

ISSN 1822-427X print / ISSN 1822-4288 online

http://www.bjrbe.vgtu.lt

1. Introduction

Suspension bridges are very attractive structures possess-ing a number of technical, economical and aesthetic advan-tages. The main problem of them is their excessive deform-ability, especially under action of traffic loads, changes in environmental temperature and the wind effects. Deform-ability of suspension systems depends on the kinematical character of displacements of a flexible suspension cable. Various structural measures are taken to improve the stiff-ness and stability of suspension structures (Juozapaitis et al. 2006, 2007; Krishna 2001; Palkowski 2006).

As is shown in our previous investigations, one of the ways to increase the rigidity of a bridge suspension sys-tem is to transfer a part of stiffening girder’s rigidity to a suspension cable (Grigorjeva et al. 2004; 2006). The cables can be made of standard steel profiles or have a compos-ite section. The steel hollow sections filled with concrete can be an attractive solution (Kuranovas, Kvedaras 2007; Soundararajan et al. 2008). By changing the cable to stiff-ening girder bending stiffness ratio it is possible to reduce considerably the vertical displacements of the loaded sus-pension system and to retain its original geometric form. The stabilization of the deformability of the suspension bridges by giving a certain bending stiffness to the sus-

pension cables are also known in practice. The examples of suspension bridge in Pittsburgh (Качурин et al. 1971) and famous Tower Bridge in London (Bennett 1997) can be mentioned.

The analysis of suspension bridges with flexible cables is based on the deflection theory and solution of the dif-ferential equations. In all cases, the existing well-known theories of suspension system’s analysis are tedious and in-volve several operations and approximations with complex numbers. In an analysis of suspension bridges, main cables are generally assumed to have no flexural stiffness and to be subject to axial tension only (Gimsing 1997).

Although several research papers focus on the bend-ing problem of suspension or stay cables (Furst et al. 2001; Prato, Ceballos 2003), to the best of the author’s knowl-edge little information on theoretical analysis of suspen-sion bridges with rigid cables is available. Some results of influence of the main cable stiffness on the deformabili-ty of suspension bridge decks are presented in referenc-es (Качурин et al. 1971; Ladret et al. 2002). A simplified engineering analytical method and design of suspension bridges with varying rigidity of cables is proposed by the authors (Grigorjeva et al. 2006). An analysis shows that there is a close relationship between the rigidity of the main cable, its layout, the character of applied load, and

FInITE ELEMEnT MODELLInG FOR STATIC BEHAVIOUR AnALYSIS OF SUSPEnSIOn BRIDGES WITH VARYInG RIGIDITY OF MAIn CABLES

Tatjana Grigorjeva1, Algirdas Juozapaitis2, Zenonas Kamaitis3, Ainars Paeglitis4

1 Dept of Architectural Engineering, Vilnius Gediminas Technical University,Saulėtekio al. 11, 10223 Vilnius, Lithuania, e-mail: [email protected]

2, 3 Dept of Bridges and Special Structures, Vilnius Gediminas Technical University,Saulėtekio al. 11, 10223 Vilnius, Lithuania, e-mails: 2 [email protected]; 3 [email protected]

4 Dept of Roads and Bridges, Riga Technical University, Azenas st. 20, 1048 Latvija, e-mail: [email protected]

Abstract. The paper presents a summary of numerical analysis on static behaviour of suspension bridges with varying rigidity of cables. The primary purpose of this study was to compare suspension systems with flexible and rigid cables and to determine the influence of varying rigidity of cables on the response of bridge members under the action of uni-formly distributed symmetrical and unsymmetrical static loading. The finite element analysis of a three-dimensional bridge model was performed. In the first model, the cable is modelled as TRUSS3D element, in the second model as BEAM3D element. In both models, the hangers and backstays are TRUSS3D elements and stiffening girder as BEAM3D element. It is shown that a suitable increase of main cable’s bending stiffness can effectively reduce the displacements, internal forces and stresses of suspension systems. Recommendations for appropriate stiffness are given.

Keywords: suspension bridges, flexible cables, rigid cables, FEM, displacements, moments and stresses.

DOI: 10.3846/1822-427X.2008.3.121-128

122 T. Grigorjeva et al. Finite element modelling for static behaviour analysis of suspension bridges...

the displacements of the stiffening girder. It is possible to reduce deformability of suspension systems substantially by variation of the flexural stiffness of the main cables.

From a mechanics standpoint, suspension systems present a complex hyperstatic behaviour. It was clear that there was a need to use more refined method of analysis based on finite element modelling (FEM) as the only way to confirm fully the structural concept and to check the overall behaviour of the suspension system with rigid ca-bles. Two models were developed: the first one with flexu-ral cable and the other with cables of varying rigidity. Two and three-hinged rigid cables were considered. In this pa-per, the results of such analysis are presented.

2. FE model

Analysis of suspension bridges was performed with a rela-tively simple FE model using commercial finite element programs CosmosM and Midas/Civil. The three-dimen-sional models, consisting of beam and bar elements, were constructed to examine the overall behaviour of the bridge system (Fig. 1). The models were developed using the fol-lowing assumptions:

Bar elements TRUSS3D were used to represent the flexible cable (Model 1), the hangers and backstays;Beam elements BEAM3D were used for the rigid cables (Model 2) and stiffening beam;The girder deck and the cables are hinged at the tower footings and tower saddles, respectively;The deck ties (if any) are excluded from analysis;The main rigid cable, stiffening girder, backstays are steel box profiles with the Young’s modulus E = 2,1×105 N/mm2 and Poisson’s ratio v = 0,3; suspend-ers are steel circular rods with the tension rigidity EI = 412 125 kN; pylons are wide-flange shapes with compression rigidity EApyl = 1 274 280 kN;The cable possesses geometrical non-linearity.

Fig. 1. Finite element space model of the bridge

•

•

•

••

•

The model studies had several objectives:Investigate the deflections, internal forces and stress-es caused by uniformly distributed static loads;Study the influence of cable to girder stiffness ratio and live to dead load ratio on behaviour of suspen-sion system;Compare the behaviour of suspension system with flexible and two- and three-hinged rigid cables.

Tables 1 and 2 summarize the geometric and loading characteristics of bridge models used in analysis. The basic structural system is shown in Fig. 2.

Table 2. Loading characteristics

γ = v/g Live load v, kN/m2 Permanent load g, kN/m2

1.01.52.02.53.0

5.05.05.05.05.0

5.03.332.52.0

1.66

3. Structural behaviour

The suspension bridge models with flexible and rigid ca-bles were analyzed through the comparison of vertical dis-placements, bending moments and normal stresses under the action of symmetrical and unsymmetrical static dis-tributed loadings. These parameters were done, when the flexural stiffness is imposed on the cables from the very beginning of bridge erection, i.e. before it is loaded by the permanent and variable loads.

3.1. Symmetrical loadingIn Figs 3 and 4 the main parameters are shown for the two studied system cases.

The vertical displacements, moments and stresses in the stiffening girder are reduced due to participation of the rigid cable, as part of the suspension system. The magni-tude of reduction will depend on the bending stiffness of the main cables. The main reduction of displacements and moments at mid-span by about 30 and 70%, respectively, is observed when the stiffness ratio ξ is up to 0.5−0.6. It seems that the bending stiffness of the stiffening girder should be about two times higher than the flexural stiff-ness of the rigid cables. On the other hand, the moments

•

•

•

Table 1. Geometric characteristics of cable and stiffening girder

ξ = EIc/EIgCable section,

b×h×t, mmCable tension

rigidity, EAc, kNCable flexural

rigidity, EIc, kNm2Stiffening girder

section b×h×t, mmStiffening girder

rigidity EIg, kN/m2Amount of

steel, kg0

0.10.20.40.60.81.0

100×400×25100×480×25120×560×25120×620×25120×650×25120×670×25

4 725 0005 565 0006 615 0007 245 0007 560 0007 770 000

74 484123 967206 296273 627312 112339 650

400×700×25400×660×25400×610×25400×580×25400×540×25400×510×25

718 922622 213513 219453 912381 647332 374

117 750120 890124 815127 170126 385125 600

The Baltic Journal of Road and Bridge Engineering, 2008, 3(3): 121–128 123

Fig. 2. Structural system of a bridge model and loading configuration

a b

Fig. 3. Vertical displacement curves (a) and mid-span deflection (b) of the stiffening girder under symmetrical loading (γ = 1): 1 − two-hinged cable; 2 − three-hinged cable

a b

Fig. 4. Max moments (a) and stresses (b) in the midspan of the stiffening girder and cable under symmetrical loading (γ = 1): 1 − two-hinged cable; 2 − three-hinged cable


and bending stresses are increasing in the cables, when the stiffness ratio ξ is increased. However, these moments and stresses are relatively small. The main action effect in the rigid cable remains its axial force.

Comparison of the suspension system with two and three-hinged cables shows that displacements follow the same pattern. Max displacements and bending moments in the stiffening girder for the system with three-hinged cable are up to 10% lower (Figs 3, 4). The max moment in the three-hinged cable is in the quarter point of the span

and is up to 30% (depending of the values of ζ) lower, than that in the mid-span of the two-hinged cable (Fig. 4).

Fig. 5 shows the finite element results for one of the models of suspension bridge.

3.2. Unsymmetrical loadingFig. 6 shows the displacements of stiffening girder under the action of unsymmetrical live loading as a function of the ratio ξ and γ. Under the action of unsymmetrical load-ing, deflection curves become S-shaped. Such a stiffening girder is found to be essential lack of suspension bridges.

0.00000e+000–3.33107e–003–6.66215e–003–9.99322e–003–1.33243e–002–1.66554e–002–1.99864e–002–2.33175e–002–2.66486e–002–2.99797e–002–3.33107e–002–3.66418e–002–3.99729e–002–4.33039e–002–4.66350e–002–4.99661e–002–5.32972e–002–5.66282e–002–5.99593e–002–6.32904e–002–6.66215e–002–6.99525e–002–7.32836e–002–7.66147e–002

Fig. 5. Deformed FEM of the bridge under symmetric loading (ξ = 0.6, γ = 1)

Fig. 6. Vertical displacement curves under unsymmetrical loading of two-hinged system


The largest displacements occur in suspension bridg-es with flexible cable (ξ = 0). If the ratio ξ increases, the vertical displacements of the girder decrease leading to considerable reduction of suspension system’s deformabil-ity. Referring to Fig. 7, the useful limit value of stiffness ratio ξ is somewhat of 0.5–0.6. When the ratio ζ = 0.6, the reduction of the vertical displacements of the left quarter point of the span is on average of 30% and that of right quarter point of 60%. The higher ratio ξ has only a little influence on vertical displacements.

a

b

Fig. 7. Vertical deflection in the left (a) and right (b) quarter points of the span in the stiffening girder under unsymmetrical loading

The rigidity of cables also influences the bending mo-ments and stresses in the stiffening girder and cables as illustrated in Figs 8 and 9.

As can be expected, the bending moments in the stiff-ening girder decrease and in the rigid cable increase with the rigidity ratio, ζ. Referting to Fig. 9, it should be noted that the max stresses change rapidly when ζ increases from 0 to 0.1 but the higher values of ζ appear to have little effect on the stresses.

a

b

Fig. 8. Maximum moments at the quarter point in the stiffening girder (a) and cable (b) under unsymmetrical loading

a

b

Fig. 9. Maximum stresses at the quarter point in the stiffening girder (a) and cable (b) under unsymmetrical loading


Fig. 10 shows the influence of hinges in the rigid cable on the bending moments of the members as a function of the ratio γ (ζ = 0.6). It is seen that internal hinge slightly re-duces the vertical displacements (up to 20%) and max bend-ing moments (up to 10%) in the stiffening girder and cable.

Fig. 10. Comparison between the max bending moments of the stiffening girder and rigid cable in two and three-hinged system vs ratio γ

Fig. 11 shows the deformed FEM of the bridge under unsymmetrical loading.

4. Influence of cable shape

The original outline of the cables of a final bending stiff-ness is very important factor in the behaviour of suspen-sion bridges. It influences the stability of the main cables as well as the structural performance of a whole bridge.

The influence of the initial shape of the axis of the three-hinge cables was analyzed on the bridge’s model with varying initial sag from f1 = 0.25 f0 up to f5 = 0 in a quarter of the bridge span (Fig. 12).

All the cables illustrated in Fig. 12 would deform in a similar way under the action of the load, but the actual displacements of the stiffening girder would be different.

Fig. 13 shows the displacements of a stiffening gird-er with various initial shapes of the main cable under the action of symmetrical and unsymmetrical uniformly dis-tributed loading. There is a close relationship between the rigidity of main cable, the original shape of the rigid cable, and the displacements of the stiffening girder.

For a uniformly loaded bridge deck, the shape of the rigid cable is ideally parabolic. Min displacements are de-veloped in the stiffening girder.

Under action of unsymmetrical loading the efficien-cy of the initial shape of the cables becomes obvious. The displacements of stiffening girder form S-shape curve. By changing the initial shape or curve of a cable, it is possible to reduce or almost eliminate the upward displacement curve. For example, if initial sag of a suspension cable in a quarter span is f4 = 0.0625 f0, then the shape of deflections in the loaded part of stiffening girder is similar to a pa-rabola. At the part of stiffening girder free of loading very small deflections are observed.

It should be pointed out that the shape of the cable axis may be governed by the distribution and magnitude of the superimposed loads. On the other hand, curved cable can be replaced by a combination of straight members.

5. Conclusions

The main behaviour problem of suspension bridges is their excessive deformability, especially under the action of traf-fic loads, changes in environmental temperature and the effects of wind. The use of cables with finite bending stiff-ness is proposed by the authors of the present paper with the aim to increase the rigidity of suspension bridges.

1.39333e–0011.23046e–0011.06759e–0019.04712e–0027.41837e–0025.78963e–0024.16089e–0022.53214e–0029.03398e–0030.00000e+000

–2.35409e–002–3.98283e–002–5.61158e–002–7.24032e–002–8.86906e–002–1.04978e–001–1.21265e–001–1.37553e–001–1.53840e–001–1.70128e–001–1.85415e–001

Fig. 11. Deformed finite element model of the bridge under unsymmetrical loading (ξ = 0.6, γ = 1)


Fig. 12. Geometrical shapes of a rigid cable in a half of bridge span: 1 – f1 = 0.25 f0; 2 – f2 = 0.1875 f0; 3 – f3 = 0.125 f0; 4 – f4 = 0.0625 f0; 5 – f5 = 0

Fig. 13. Displacements of stiffening girder of suspension bridge with various initial shapes of the main cable under action of symmetrical (top) and unsymmetrical (bottom) loading


Finite element analysis using commercial finite ele-ment programs CosmosM and Midas/Civil of the suspen-sion bridge models was performed. Two finite element space models were developed to simulate suspension sys-tem with flexible and rigid two and three-hinged main ca-bles. The suspension bridge models were analyzed through the comparison of vertical displacements, bending mo-ments and normal stresses under the action of symmetri-cal and unsymmetrical static uniformly distributed loads.

By the results of the simulation analysis performed it has been shown that vertical displacements, moments and stresses in the stiffening girder are reduced due to par-ticipation of the rigid cable as a part of the suspension sys-tem. The magnitude of reduction varies with the bending stiffness and shape of the cable, loading characteristics and presence of internal hinge in the cable. Loading effects de-pend to a large extent on the cable to girder stiffness ratio, ζ. The rational cable to girder stiffness ratio is somewhat 0.5−0.6. The vertical deflections can be reduced up to 30% and the bending moments up to 70%.

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mas Telford Ltd. 198 p. ISBN 0727725297.Furst, A.; Marti, P.; Ganz, H. R. 2001. Bending of stay cables,

Structural Engineering International 11(1): 42–46.Gimsing, N. J. 1997. Cable supported bridges: concept and de-

sign. 2nd edition. Chichester: John Wiley & Sons, 480 p. ISBN 0471969397.

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Grigorjeva, T.; Juozapaitis, A.; Kamaitis, Z. 2006. Simplified en-gineering design method of suspension bridges with rigid ca-

bles under action of symmetrical and asymmetrical loads, The Baltic Journal of Road and Bridge Engineering 1(1): 11–20.

Juozapaitis, A.; Norkus, A. 2007. Determination of rational pa-rameters for the advanced structure of a pedestrian suspen-sion steel bridge, The Baltic Journal of Road and Bridge Engi-neering 2(4): 173−181.

Juozapaitis, A.; Vainiūnas, P.; Kaklauskas, G. 2006. A new steel structural system of a suspension pedestrian bridge, Journal of Constructional Steel Research 62(12): 1257−1263.

Krishna, P. 2001. Tension roofs and bridges, Journal of Construc-tional Steel Research 57(11): 1123−1140.

Kuranovas, A.; Kvedaras A. K. 2007. Behavior of concrete-filled steel tubular composite elements, Journal of Civil Engineering and Management 13(2): 131−141.

Ladret, P.; Marquez, M.; Joan, R.; Rius, C. 2002. Inspection of ca-ble forces of cable-stayed bridges using a modified taut string method, in Proc of the First International Conference on Bridge Maintenance, Safety and Management (IABMAS’02) selected papers. Ed. by Casas, J. R.; Frangopol, D. M.; Nowak, A. S. July 14–17, 2002, Barcelona, Spain. Barcelona: CIMNE, 310–318.

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Prato, C. A.; Ceballos, M. A. 2003. Dynamic bending stresses near the ends of parallel bundle stay cables, Structural Engi-neering International 13(1): 42–46.

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Received 5 March 2008; accepted 12 June 2008


2008 3(3): I a–I c



ABSTRACTS In LITHUAnIAn

Eugedijus Juozas Dulinskas, Viktor Gribniak, Gintaris Kaklauskas. Šutinimo įtaka cikliškai apkrautų įtemptųjų gelžbetoninių tiltų elementų elgsenai, The Baltic Journal of Road and Bridge Engineering 3(3): 115–120.

Santrauka. Aprašoma kietėjimo sąlygų (šutinimo ir kietėjimo normaliomis sąlygomis) įtaka įtemptųjų gelžbetoninių tiltų elementų cikliniam valkšnumui bei atsparumui nuovargiui. Analizėje panaudoti pirmojo au-toriaus atliktų nuovargio eksperimentinių tyrimų duomenys. Cikline apkrova (iki 2 milijonų ciklų) išbandytos 46 betoninės prizmės bei 13 įtemptos gelžbetoninės sijos. Gniuždomojo betono atsparumas nuovargiui, t. y. apkrovimo ciklų skaičiaus priklausomybė nuo apkrovos intensyvumo (S-N santykis), tirta, taikant regresinės analizės metodus. Atlikta analizė parodė, kad šutinimas turi nedidelę įtaką gniuždomojo betono atsparumui nuovargiui. Kita vertus, kietėjimo sąlygos turi reikšmingą įtaką cikliniam betono valkšnumui. Šutintam betonui gautos vidutiniškai 30–80 % didesnės valkšnumo deformacijos. Šutinto ir normaliomis sąlygomis kietėjusio betono valkšnumo deformacijų skir-tumas didėjo didėjant apkrovimo ciklų skaičiui.

Reikšminiai žodžiai: kietėjimo sąlygos, nuovargio bandymai, ciklinis valkšnumas, įtemptojo gelžbetoninio tiltai.

Tatjana Grigorjeva, Algirdas Juozapaitis, Zenonas Kamaitis, Ainars Paeglitis. Baigtinių elementų metodo taikymas, siekiant įvertinti kabamojo tilto su skirtingo standžio lynais statinę elgseną, The Baltic Journal of Road and Bridge Engineering 3(3): 121–128.

Santrauka. Straipsnyje pateikta tilto su skirtingo standžio lynais elgsenos skaitinė analizė. Atliktas tilto konstrukcijų su lanksčiaisiais ir standžiaisiais lynais palyginimas bei įvertinta lyno standžio įtaka tilto įtempių ir deformacijų būviui veikiant tolygiai paskirstytoms simetrinėms ir nesimetrinėms apkrovoms. Sukurti du tilto su trijų lankstų lynais modeliai. Pirmame modelyje lynas aprašytas kaip TRUSS3D elementas, antrame – kaip BEAM3D. Abiejuose modeliuose pakabos sumodeliuotos kaip TRUSS3D, standumo sija kaip BEAM3D elementai. Atlikta tilto elgsenos analizė parodė, kad taikant pagrindiniam lynui tam tikro lenkiamojo standžio elementus galima labai padi-dinti bendrąjį tilto konstrukcijos standumą bei sumažinti standumo sijos įrąžas ir įtempius. Pateiktos rekomendaci-jos, kaip parinkti lyno ir sijos standumų santykį.

Reikšminiai žodžiai: kabamieji tiltai, lankstusis lynas, standusis lynas, BE modelis, poslinkiai, lenkimo momen-tai, įtempiai.

Dmitrijs Serdjuks, Kārlis Rocēns, Leonīds Pakrastiņš. Tempiamųjų konstrukcijų padidėjusio santykinio stiprumo mišrieji kompozitiniai lynai, The Baltic Journal of Road and Bridge Engineering 3(3): 129–136.

Santrauka. Didelio stiprumo mišrieji kompozitiniai lynai, sudaryti iš tokių padidėjusio santykinio stiprumo medžiagų kaip stiklo pluoštu armuoti plastikai (GFRP) ir Vectran, yra plačiai vartojami statyboje. Naudojant plie-ninius komponentus, galima pagerinti didelio stiprumo mišriųjų kompozitinių lynų plastines savybes ir išplėsti jų taikymo sritį. Tiriamas plienas derinyje su tokiomis medžiagomis kaip anglies ir stiklo pluoštas bei Vectran. Atlikti mišriųjų kompozitinių lynų elgsenos analiziniai ir eksperimentiniai tyrimai. Mišrieji kompozitiniai padidėjusio san-tykinio stiprumo lynai nagrinėti juos taikant iš anksto įtemptuose 50×50 m balno formos kabamuosiuose stoguose. Buvo siekta sumažinti stogų poslinkius naudojant kabamąsias konstrukcijas, sukonstruotas iš mišriųjų kompozitinių padidinto santykinio stiprumo lynų. Racionalūs kabamųjų santvarų geometriniai parametrai nustatyti skaitiniu eks-perimentu. Parodyta, kad taikant mišriuosius kompozitinius lynus jų santykinis stipris gali padidėti iki 2,4 karto. Taikant skaitinį eksperimentą, parinkti racionalūs kompozitinių padidėjusio stiprumo lynų komponentai.

Reikšminiai žodžiai: mišrieji kompozitiniai lynai, racionalūs komponentai, balno formos stogas, kabamosios santvaros, didžiausi vertikalieji poslinkiai, lynų tinklo medžiagų efektyvumas.


2008 3(3): II a–II c



ABSTRACTS In LATVIAn

Eugedijus Juozas Dulinskas, Viktor Gribniak, Gintaris Kaklauskas. Betona tvaicēšanas ietekme ciklisku iedarbju pretestībai spriegbetona tilta elementos, The Baltic Journal of Road and Bridge Engineering 3(3): 115–120.

Kopsavilkums. Darbā pētīta betona kopšanas tehnoloģijas (tvaicēšana un parasta betona kopšana) ietekme uz ciklisku šļūdes un noguruma pretestību dzelzsbetona tilta elementos. Pielietotā analīze balstās uz raksta pirmā autora veiktajiem eksperimentālajiem pētījumiem, kuros 46 nestiegrota betona prizmas un 13 spriegbetona sijas tika pakļautas cikliskai slodzei (līdz 4 miljoniem ciklu). Spiesta betona noguruma pretestībai veikta salīdzinošā regresijas analīze, slogojuma ciklu izteiksmē, pie noteiktā maksimālā sprieguma līmeņa (S-N attiecībai). Iegūtie rezultāti rāda, ka betona kopšanas veidam nav būtiskas ietekmes uz S-N attiecību. Turpretim betona kopšana būtiski ietekmē spies-ta betona ciklisko šļūdi. Caurmērā, tvaicētajiem elementiem bija par 30% līdz 80% lielākas deformācijas, kā betonam ar tradicionālām kopšanas metodēm. Lielākas atšķirības ir elementiem ar lielāku slodzes ciklu skaitu.

Atslēgvārdi: kopšanas apstākļi, noguruma pārbaude, cikliskā šļūde, spriegbetona tilti

Tatjana Grigorjeva, Algirdas Juozapaitis, Zenonas Kamaitis. Iekārto tiltu, ar mainīgu galveno kabeļu stingumu, statisko īpašību analīze izmantojot galīgo elementu modeli, The Baltic Journal of Road and Bridge Engineering 3(3): 121–128.

Kopsavilkums. Darbā apkopoti iekārto tiltu, ar mainīgu galveno kabeļu stigumu, statisko īpašību analīzes rezultāti izmantojot galīgo elementu modeli. Šī pētījuma galvenais mērķis ir salīdzināt iekārtās sistēmas ar lokaniem un stingiem kabeļiem reakciju uz vienmērīgi izkliedētu simetrisku un nesimetrisku slodzi. Izpētei tika izmantots tilta trīsdimensiju galīgo elementu modelis. Pirmajā modelī kabelis tiek modelēts kā TRUSS3D elements, bet otrajā modelī kā BEAM3D modelis. Abos modeļos piekari un atsaites ir pieņemti kā TRUSS3D elementi, bet stinguma sija, kā BEAM3D elements. Ir parādīts, ka adekvāts galvenā kabeļa stinguma pieaugums var efektīvi samazināt pārvietojumus, piepūles un spriegumus iekārtās sistēmas elementos. Izstrādātas rekomendācijas galvenā kabeļa stin-guma raksturojumam.

Atslēgvārdi: iekārtie tilti, lokanie kabeļi, stingie kabeļi, galīgo elementu modelis, pārvietojumi, momenti un piepūles

Dmitrijs Serdjuks, Kārlis Rocēns, Leonīds Pakrastiņš. Hibrīdie kompozītie kabeļi ar paaugstinātu stiprību stieptām konstrukcijām, The Baltic Journal of Road and Bridge Engineering 3(3): 129–136.

Kopsavilkums. Būvniecība plaši tiek pielietoti augstas stiprības hibrīdie kompozītie kabeļi ar lielu speciālo stiprību, kas izgatavoti no stiegrotiem oglekļa plastikātiem (CFRP), stiegrotiem stikla plastikātiem (GFRP) un Vectran materiāla. Tērauda komponentes pielietojums šādos materiālos ļauj palielināt mazo relatīvo pagarinājumu, samazināt trauslumu un palielināt augstas stiprības hibrīdo kompozīto kabeļu pielietojumu. Tērauds tika pētīts kombinācijā ar CFRP, GFRP un Vectran. Hibrīdo kompozīto kabeļu īpašības tika pētītas gan analītiski, gan eksperimentāli. Augstas stiprības hibrīdie kompozītie kabeļi ar lielu speciālo stiprību tika pētīti kā dažādu grupu kabeļi, kas paredzēti sedlu tipa jumta konstrukcijai ar izmēru 50 × 50 m. Darbā ir pētīta iespēja samazināt pārvietojumus spriegotu kabeļu sedlu veida jumta konstrukcijā, pielietojot hibrīdos kompozītos kabeļus ar palielinātu specifisko stiprību. Skaitlisku eksperimentu rezultātā ir noteikti racionālie kabeļu kopnes ģeometriskie raksturojumi. Darbā iegūtie rezultāti rāda, ka izmantojot hibrīdos kompozītos kabeļus ir iespējams palielināt specifisko stingumu līdz 2.4 reizēm. Ar iepriekš minētajiem kabeļiem ir veikti skaitliskie eksperimenti.

Atslēgvārdi: hibrīdie kompozītie kabeļi, racionālie komponenti, sedlu tipa jumts, kabeļu kopne, maksimālie vertikālie pārvietojumi, kabeļu tīkla materiālu efektivitāte.

Algirdas Juozapaitis, Arnoldas norkus, Povilas Vainiūnas. Tērauda iekārto tiltu formas stabilizācija, The Baltic Journal of Road and Bridge Engineering 3(3): 137–144.

Kopsavilkums. Viena no galvenajām iekārto tiltu projektēšanas problēmām ir nodrošināt to sākotnējo formu. Iekārto tiltu formas izmaiņas asimetriskam slogojumam ir aprakstītas ar elastīgiem un kinemātiskiem pārvietojumiem. Vislielāko ietekmi uz tilta formas maiņu atstāj kabeļa, kā galvenais tilta nesošais elementa, spēja


2008 3(3): III a–III b



ABSTRACTS In ESTOnIAn

Eugedijus Juozas Dulinskas, Viktor Gribniak, Gintaris Kaklauskas. Auruga tardumiskeskkonna mõju eelpingestatud betoonsilla elementide käitumisele korduvkoormuse all, The Baltic Journal of Road and Bridge Engineering 3(3): 115–120.

Kokkuvõte. Artikkel käsitleb tardumistingimuste (auruga ja normaalne) mõju armeeritud eelpingestatud be-toonsilla elementide roomavust ja väsimustugevust korduvkoormuse all. Analüüs põhineb esimese autori poolt te-ostatud eksperimentaalsel uuringul: 46 betoonprismat ja 13 eelpingestatud betoontala allutati korduvkoormusele (kuni 4 milj tsüklit). Teostati betooni väsimustugevuse ja koormustsüklite regressioonanalüüs tuginedes koormu-stsüklite arvule ja antud maksimaalsele pingetasemele (S-N seos). Analüüs näitas, et tardumistingimused ei mõjuta oluliselt S-N seost. Vastupidiselt mõjutasid tardumistingimuselt märkimisväärselt betooni roomavust. Keskmiselt omasid auruga tardumisel proovikehad 30 kuni 80% suuremaid deformatsioone, kui proovikehad tardumisel nor-maalses keskkonnas. Erinevus oli suurem suurema korduskoormuse tsüklite arvu puhul.

Võtmesõnad: tardumistingimused, väsimuskatsetused, roomavus, eelpingestatud betoonsillad.

Tatjana Grigorjeva, Algirdas Juozapaitis, Zenonas Kamaitis, Ainars Paeglitis. Varieeruva jäikusega peakaablitega rippsildade staatilise käitumise modelleerimine lõplike elementide meetodil, The Baltic Journal of Road and Bridge Engineering 3(3): 121–128.

Kokkuvõte. Artiklis esitatakse kokkuvõte varieeruva jäikusega peakaablitega rippsildade staatilise käitumise arvanalüüs. Uuringu peamiseks eesmärgiks oli võrrelda elastsete ja jäikade kaablitega rippsüsteeme ja määrata kaab-lite jäikuse mõju sillaelementidele ühtlaselt jaotatud sümmeetrilise ja ebasümmeetrilise koormuse all. Lõplike el-ementide analüüs teostati kolmemõõtmelisele sillamudelile. Esimeses mudelis modelleeriti kaablit nagu TROSS3D (TRUSS3D) elementi, teises mudelis nagu TALA3D (BEAM3D) elementi. Mõlemas mudelis on rippelemendid ja toetused TROSS3D elemendid ja jäikustala nagu TALA3D element. On näidatud, et peakaablite paindejäikuse sobiv suurendamine võimaldab efektiivselt vähendada rippsüsteemide paigutisi, sisejõude ja pingeid. Antakse soovitused sobiva jäikuse valikuks.

Võtmesõnad: rippsillad, elastsed kaablid, jäigad kaablid, lõplike elementide meetod, paigutised, momendid ja pinged.

Dmitrijs Serdjuks, Kārlis Rocēns, Leonīds Pakrastiņš. Suurendatud eritugevusega hübriidkomposiitkaablid tõmbe all olevatele konstruktsioonidele, The Baltic Journal of Road and Bridge Engineering 3(3): 129–136.

Kokkuvõte. Kõrgtugevusega hübriidkomposiitkaableid, mille eritugevust on suurendatud selliste materjalidega nagu süsinikukiududega armeeritud plastikud (CFRP), klaaskiududega armeeritud plastikud ja Vectran, kasutatakse ehituspraktikas laialdaselt. Aga teraskomponendi kasutamine võimaldab suurendada väikest suhtelist pikenemist, vähendada haprust ja suurendada kõrgtugevate hübriidkomposiitkaablite kasutusala. Terast uuriti kombinatsioo-nides selliste materjalidega nagu CFRP, GFRP ja Vectran. Hübriidkomposiitkaablite käitumist uuriti analüütiliselt ja eksperimentaalselt. Suurendatud eritugevusega hübriidkomposiitkaableid käsitleti materjalina, mis koosneb erine-vatest kaabligruppidest, mis moodustavad sadulakujulise katuse dimensioonidega 50×50 m. Uuriti komposiitkaabel-trossidest moodustatud sadulakujulise katuse paigutiste vähendamise võimalusi. Arveksperimendiga määrati kind-laks kaabeltrossi ratsionaalsed geomeetrilised karakteristikud. On tõestatud, et hübriidkomposiitkaabli kasutamine võimaldab suurendada selle eritugevust kuni 2,4 korda. Arveksperimendiga valiti suurendatud eritugevusega kom-posiitkaabli ratsionaalsed koostiskomponendid.

Võtmesõnad: hübriidkomposiitkaabel, ratsionaalsed koostiskomponendid, sadulakujuline katus, kaabeltross, maksimaalne vertikaalne paigutis, kaabelvõrgu materjalide efektiivsus.

Algirdas Juozapaitis, Arnoldas norkus, Povilas Vainiūnas. Terasrippsildade kuju stabiliseerimine, The Baltic Journal of Road and Bridge Engineering 3(3): 137–144.

Kokkuvõte. Rippsilla esialgse kuju stabiliseerimine on konstruktsiooni projekteerimisel üheks peamiseks prob-leemiks. Rippterassilla vormi ehk kuju määratakse ette elastsete ja kinemaatiliste paigutistega põhjustatuna asüm-meetrilisest koormusest. Silla kuju peamise tagajaks on silla peakaabel, kui silla peamine kandeelement, mis peab ole-

TURInYS

EUGEDIJUS JUOZAS DULINSKAS, VIKTOR GRIBNIAK, GINTARIS KAKLAUSKASŠutinimo įtaka cikliškai apkrautų įtemptųjų gelžbetoninių tiltų elementų elgsenai ................................................. 115

TATJANA GRIGORJEVA, ALGIRDAS JUOZAPAITIS, ZENONAS KAMAITIS, AINARS PAEGLITIS

Baigtinių elementų metodo taikymas, siekiant įvertinti kabamojo tilto su skirtingo standžio lynais statinę elgseną .......................................................................................................................................... 121

DMITRIJS SERDJUKS, KāRLIS ROCēNS, LEONīDS PAKRASTIņŠTempiamųjų konstrukcijų padidėjusio santykinio stiprumo mišrieji kompozitiniai lynai ..................................... 129

ALGIRDAS JUOZAPAITIS, ARNOLDAS NORKUS, POVILAS VAINIūNASKabamojo plieninio tilto formos stabilizavimas ............................................................................................................ 137

TOMAS SKUTURNA, JUOZAS VALIVONIS, POVILAS VAINIūNAS, GEDIMINAS MARČIUKAITIS, MYKOLAS DAUGEVIČIUS

Tiltų sijų, sustiprintų anglies pluošto armatūra, įlinkių tyrimas ................................................................................. 145

EDMUNDAS KAZIMIERAS ZAVADSKAS, ROODE LIIAS, ZENONAS TURSKISDaugiatikslių sprendimo priėmimo metodų taikymas tiltų ir kelių statybai vertinti: šiuolaikinių laimėjimų apžvalga ....................................................................................................................................... 152

HENRIKAS SIVILEVIČIUS, EDMUNDAS KAZIMIERAS ZAVADSKAS, ZENONAS TURSKISAsfalto maišyklių kokybiniai rodikliai ir kompleksinė kokybės vertinimo metodika .............................................. 161

ANTANAS KUDZYS, ROMUALDAS KLIUKASRibinių būvių ir tikimybinės sandaros stabilizuojančiųjų žiedinio skerspjūvio taurų skaičiavimui ....................... 167

SATURS

EUGEDIJUS JUOZAS DULINSKAS, VIKTOR GRIBNIAK, GINTARIS KAKLAUSKASBetona tvaicēšanas ietekme ciklisku iedarbju pretestībai spriegbetona tilta elementos ........................................... 115

TATJANA GRIGORJEVA, ALGIRDAS JUOZAPAITIS, ZENONAS KAMAITIS, AINARS PAEGLITISIekārto tiltu, ar mainīgu galveno kabeļu stingumu, statisko īpašību analīze izmantojot galīgo elementu modeli ................................................................................................................................. 121

DMITRIJS SERDJUKS, KāRLIS ROCēNS, LEONīDS PAKRASTIņŠHibrīdie kompozītie kabeļi ar paaugstinātu stiprību stieptām konstrukcijām .......................................................... 129

ALGIRDAS JUOZAPAITIS, ARNOLDAS NORKUS, POVILAS VAINIūNASTērauda iekārto tiltu formas stabilizācija ........................................................................................................................ 137


Ar stiegrotu oglekļaplastu pastiprinātu tiltu siju lieces analīze .................................................................................... 145


2008 3(3)



EDMUNDAS KAZIMIERAS ZAVADSKAS, ROODE LIIAS, ZENONAS TURSKISVairāku parametru metode lēmuma pieņemšanai tiltu un ceļu kvalitātes novērtēšanai: vispārējs apskats ................................................................................................................................................................. 152

HENRIKAS SIVILEVIČIUS, EDMUNDAS KAZIMIERAS ZAVADSKAS, ZENONAS TURSKISKvalitātes parametri un kompleksās novērtēšanas metodoloģija asfaltbetona ražošanas rūpnīcā ......................... 161

ANTANAS KUDZYS, ROMUALDAS KLIUKASRobežstāvokļu un varbūtību pieeju izmantošana tilta starpbalstu, ar gredzenveida šķērsgriezumu, analīzei ...... 167

SISUKORD

EUGEDIJUS JUOZAS DULINSKAS, VIKTOR GRIBNIAK, GINTARIS KAKLAUSKASAuruga tardumiskeskkonna mõju eelpingestatud betoonsilla elementide käitumisele korduvkoormuse all ........................................................................................................................................................... 115

TATJANA GRIGORJEVA, ALGIRDAS JUOZAPAITIS, ZENONAS KAMAITIS, AINARS PAEGLITISVarieeruva jäikusega peakaablitega rippsildade staatilise käitumise modelleerimine lõplike elementide meetodil ............................................................................................................................................. 121

DMITRIJS SERDJUKS, KāRLIS ROCēNS, LEONīDS PAKRASTIņŠSuurendatud eritugevusega hübriidkomposiitkaablid tõmbe all olevatele Konstruktsioonidele ............................ 129

ALGIRDAS JUOZAPAITIS, ARNOLDAS NORKUS, POVILAS VAINIūNASTerasrippsildade kuju stabiliseerimine ............................................................................................................................ 137


Süsinikkiust armeeringuga sillatalade deformatsiooni analüüs .................................................................................. 145

EDMUNDAS KAZIMIERAS ZAVADSKAS, ROODE LIIAS, ZENONAS TURSKISMitmeomaduslikud otsustusmeetodid sildade ja teedeehituse kvaliteedi hindamiseks: kaasaegne lähenemine ....................................................................................................................................................... 152

HENRIKAS SIVILEVIČIUS, EDMUNDAS KAZIMIERAS ZAVADSKAS, ZENONAS TURSKISAsfaldiseguri kvaliteediomadused ja kompleksne hindamismetoodika .................................................................... 161

ANTANAS KUDZYS, ROMUALDAS KLIUKASPiirtingimused ja tõenäosuslik lähenemine rõngakujulise ristlõikega sillasammaste projekteerimisel ................. 167

Finite element modelling for static behaviour analysis of suspension bridges with varying rigidity...

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