Plieninių kabamųjų tiltų su standžiais lynais įtempių ir deformacijų būvis ; Stress And Deformation State Of Suspension Steel Bridges With Rigid Cables

Tatjana.Grigorjeva

Description

TatjanaGRIGORJEVASTRESSANDDEFORMATIONSTATEOFSUSPENSIONSTEELBRIDGESWITHRIGIDCABLESSummaryofDoctoralDissertationTechnologicalSciences,CivilEngineering(02T)1366Vilnius 2007VILNIUSGEDIMINASTECHNICALUNIVERSITYTatjanaGRIGORJEVASTRESSANDDEFORMATIONSTATEOFSUSPENSIONSTEELBRIDGESWITHRIGIDCABLESSummaryofDoctoralDissertationTechnologicalSciences,CivilEngineering(02T)Vilnius 2007DoctoraldissertationwaspreparedatVilniusGediminasTechnicalUniversityin2002–2006.ScientificSupervisorProf Dr Habil Ipolitas Zenonas KAMAITIS (Vilnius GediminasTechnicalUniversity,TechnologicalSciences,CivilEngineering–02T).ThedissertationisbeingdefendedattheCouncilofScientificFieldofCivilEngineeringatVilniusGediminasTechnicalUniversity:ChairmanProfDrHabilGintarisKAKLAUSKAS(VilniusGediminasTechnicalUniversity,TechnologicalSciences,CivilEngineering–02T).

Sujets

• Suspension bridge

Informations

• Publié par: vilnius_gediminas_technical_university
• Publié le: 01 janvier 2007
• Nombre de lectures: 29

Extrait

 

 

        Tatjana GRIGORJEVA       STRESS AND DEFORMATION STATE OF SUSPENSION STEEL BRIDGES WITH RIGID CABLES               Summary of Doctoral Dissertation Technological Sciences, Civil Engineering (02T)                

Vilnius    

 2007

1366

 

 

  VILNIUS GEDIMINAS TECHNICAL UNIVERSITY                     Tatjana GRIGORJEVA       STRESS AND DEFORMATION STATE OF SUSPENSION STEEL BRIDGES WITH RIGID CABLES               Summary of Doctoral Dissertation Technological Sciences, Civil Engineering (02T)                

Vilnius

 2007

 

Doctoral dissertation was prepared at Vilnius Gediminas Technical University in 2002–2006.   Scientific Supervisor Prof Dr Habil Ipolitas Zenonas KAMAITIS  (Vilnius Gediminas Technical University, Technological Sciences, Civil Engineering – 02T).   The dissertation is being defended at the Council of Scientific Field of Civil Engineering at Vilnius Gediminas Technical University: Chairman Prof Dr Habil Gintaris KAKLAUSKAS  (Vilnius Gediminas Technical University, Technological Sciences, Civil Engineering – 02T).   Members: Prof Dr Habil Jonas BAREIŠIS  (Kaunas University of Technology, Technological Sciences, Mechanical Engineering – 09T),   Prof Dr Habil Audronis Kazimieras KVEDARAS  (Vilnius Gediminas Technical University, Technological Sciences, Civil Engineering – 02T), Assoc Prof Dr Žymantas RUDŽIONIS  (Kaunas University of Technology, Technological Sciences, Civil Engineering – 02T), Prof Dr Habil Edmundas Kazimieras ZAVADSKAS  (Vilnius Gediminas Technical University, Technological Sciences, Civil Engineering – 02T).   Opponents: Assoc Prof Dr Virgaudas PUODŽIUKAS  (Lithuanian Road Administration under the Ministry of Transport and Communications, Technological Sciences, Civil Engineering – 02T), Assoc Prof Dr Antanas ŠAPALAS  (Vilnius Gediminas Technical University, Technological Sciences, Civil Engineering – 02T).   The dissertation will be defended at the public meeting of the Council of Scientific Field of Civil Engineering in the Senate Hall of Vilnius Gediminas Technical University at 2 p. m. on 26 March 2007. Address: Saul÷tekio al. 11, LT810223 Vilnius, Lithuania. Tel.: [phone], fax [phone], e8mail [e-mail] The summary of the doctoral dissertation was distributed on 26 February 2007. A copy of the doctoral dissertation is available for review at the Library of Vilnius Gediminas Technical University (Saul÷tekio al. 14, Vilnius, Lithuania).   © Tatjana Grigorjeva, 2007

 

 

   

 

VILNIAUS GEDIMINO TECHNIKOS UNIVERSITETAS                   Tatjana GRIGORJEVA       PLIENINIŲ KABAMŲJŲ TILTŲ SU STANDŽIAIS LYNAIS ĮTEMPIŲ IR DEFORMACIJŲ BŪVIS             Daktaro disertacijos santrauka Technologijos mokslai, statybos inžinerija (02T)                

Vilnius

 2007

 

Disertacija rengta 2002–2006 metais Vilniaus Gedimino technikos universitete.   Mokslinis vadovas prof. habil. dr. Ipolitas Zenonas KAMAITIS  (Vilniaus Gedimino technikos universitetas, technologijos mokslai, statybos inžinerija – 02T).   Disertacija ginama Vilniaus Gedimino technikos universiteto Statybos inžinerijos mokslo krypties taryboje: Pirmininkas prof. habil. dr. Gintaris KAKLAUSKAS (Vilniaus Gedimino technikos universitetas, technologijos mokslai, statybos inžinerija – 02T). Nariai: prof. habil. dr. Jonas BAREIŠIS  (Kauno technologijos universitetas, technologijos mokslai, mechanikos inžinerija – 09T), prof. habil. dr. Audronis Kazimieras KVEDARAS (Vilniaus Gedimino technikos universitetas, technologijos mokslai, statybos inžinerija – 02T), doc. dr. Žymantas RUDŽIONIS  (Kauno technologijos universitetas, technologijos mokslai, statybos inžinerija – 02T), prof. habil. dr. Edmundas Kazimieras ZAVADSKAS  (Vilniaus Gedimino technikos universitetas, technologijos mokslai, statybos inžinerija – 02T). Oponentai: doc. dr. Virgaudas PUODŽIUKAS  (Lietuvos automobilių kelių direkcija prie Susisiekimo ministerijos, technologijos mokslai, statybos inžinerija – 02T), doc. dr. Antanas ŠAPALAS (Vilniaus Gedimino technikos universitetas, technologijos mokslai, statybos inžinerija – 02T).   Disertacija bus ginama viešame Statybos inžinerijos mokslo krypties tarybos pos÷dyje 2007 m. kovo 26 d. 14 val. Vilniaus Gedimino technikos universiteto senato pos÷džių sal÷je. Adresas: Saul÷tekio al. 11, LT810223 Vilnius, Lietuva. Tel. [phone], faksas [phone], el. paštas [e-mail] Disertacijos santrauka išsiuntin÷ta 2007 m. vasario 26 d. Disertaciją galima peržiūr÷ti Vilniaus Gedimino technikos universiteto bibliotekoje (Saul÷tekio al. 14, Vilnius, Lietuva). VGTU leidyklos „Technika“ 1366 mokslo literatūros knyga.   © Tatjana Grigorjeva, 2007

 

 

General Characteristic of the Dissertation Need for research in the field. Suspension bridges possess a number of advantages, allowing overlapping average and large spans. The basic disadvantage of suspension bridges can be considered their increased deformability, particularly under the action of non8symmetrical and local loads. Deformability depends, in general, on the kinematical character of displacements of a flexible suspension cable. Required rigidity of suspension bridges is achieved, by increasing the height, and consequently the weight of a stiffening girder, by diagonal suspenders or two8cable or combined prestressed systems. Reduction of kinematical displacements of the main cable can also be achieved by a reduction of the sag8to8span ratio, but the smaller the sag of a cable, the greater are the cable thrust forces and the required cross8sectional areas of the cables. One of the ways of suspension systems stabilization is giving certain bending stiffness to the suspension cables. Such structural solution with success is used in suspension roofs. With the aim to increase the stability of suspension bridges the author proposes to use the finite bending stiffness cables. The cables can be made of standard steel profiles or have composite sections. Conventionally, they are called as “rigid cables”. To verify this solution, the investigation on behavior of suspension bridges with rigid cables under loading has to be undertaken. Subject of research. The main subject of this work is the steel suspension bridges with rigid cables under uniformly distributed symmetrical and unsymmetrical static loading. Methodology of research. This thesis deals with analytical and numerical research methods. Main objective. The main objective of this work was to carry out the investigation on the suspension bridges with rigid cables and to propose an analytical method for the analyzing and determining the internal forces in cables and stiffening girder under static loading to provide recommendations for design of suspension bridges with rigid cables. Main task 1.   To review structural solutions and behaviour features of suspension bridges. 2.   To review analysis and design methods of suspension bridges. 3.   To propose a method for the analyzing and determining the internal forces in cables and stiffening girder of suspension bridges with rigid cables under static loading. 4.   To execute the numerical investigation on the suspension bridges with rigid cables.

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5.  To compare the results that are obtained by the analytical method with the results of numerical simulation by finite element method. 6.   To execute the numerical simulation of layout parameters (two or three8 hinged cables, cable initial form, cable’s initial sag8to8span ratio) of suspension bridges with rigid cables and their influence on suspension systems deformability. 7.   To evaluate the technical and economical effectiveness of suspension bridges with rigid cables and the rational fields of their application.        Scientific novelty   1.   With the aim to increase the suspension bridge’s stability, it’s proposed to use the cables of varying bending stiffness. 2.   The suspension bridge models with flexible and rigid cables is analyzed through the comparison of vertical displacements, bending moments and normal stresses under the action of symmetrical and unsymmetrical static distributed loadings. 3.   The analytical method for the analyzing and determining the internal forces in cables and stiffening girder under static loading is proposed. 4.   An analysis of layout parameters (two or three8hinged cable, cable initial form, and cable initial sag8to8span ratio) of suspension bridges with rigid cables and their influence on structural system’s deformability is performed. 5.   The technical and economical effectiveness of suspension bridges with rigid cables is evaluated.  Approbation and publication. The main results of this work were submitted in four scientific technical conferences. Eight papers were published on the topic of the dissertation and two of them were published in the journals from the list approved by the Department of Science and Higher Education (see 15–16 p.). The scope of the thesis. The thesis consist of general characteristics, list of notations,  pictures, 15 tables, four main chapters, general conclusions, appendices and list of references. The total scope of the dissertation is 133 pages.   The Content of the Dissertation 1. Conception of research topic and objective of investigations In this chapter historical review of suspension bridges, their structural systems and analysis methods were briefly outlined. The main problem of suspension bridges is their increased deformability, especially under action of traffic loads, changes in environmental temperature and the effects of wind. Required rigidity of suspension bridges is achieved, by increasing the height, and consequently the weight of a stiffening girder. In

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addition, various structural solutions on stabilization of the initial form of suspension bridges are applied. Such as inclined suspenders, the two8cable or combined prestressed systems. For reduction of the kinematical displacements of the main cable, reduction of cable‘s initial sag8to8span ratio can be used, but it leads to increase of cable thrust. One of the ways on stabilization of the initial form of suspension systems is application of rigid cables. The analysis of suspension bridges with flexible cables is based on the deflection theory and solution of the differential equations. In all cases, the existing well8known theories of suspension system’s analysis are tedious and involve 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. As the author knows, the investigation on the suspension bridge behavior with rigid cables until now was not carried out.   2. Analytical method of analysis of suspension bridges with rigid cables This chapter presents an analytical method for the analyzing and determining the internal forces in cables and stiffening girder under static loading to provide recommendations for design of suspension bridges with rigid cables (Fig 3).   The method is based on the following assumptions: •   Deflections of the stiffening girder and rigid cable are strictly elastic; •   The stiffening beam is loaded only by live load and is stressless under the dead load; •   The stiffening beam of constant moment of inertia is simply supported at the ends; •   The suspenders are subject to tension only; their elongation under loading is neglected; •   The suspenders are uniformly stressed along the whole length of span for any given imposed loading; •   The loads are uniformly distributed to the main cable through the discrete suspenders. The model was developed from a simple equation of compatibility of deformations by considering the initial length of cable axis S 0  and cable axis elongation S H  due to cable thrust force H :   S = S 0 +  S H ,  (1) where S is the length of cable axis after elongation.

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By substituting the values of S , S 0 ,  and  S H  in Eq (1), the following equation is obtained:    2  2 L + f 0 +  f 0 = + f 0 + H ⋅ L (2) 3 L L 3 L EA cab , where f 0 is the initial cable sag;  f 0 is the vertical deflection of the cable at mid8 span; The cable thrust H is given by the expression:   2 4 0 (3) = H ( f p cab L f ) −  f 5 L 2 EI cab . 0 +  0 The load p cab taken by the cable:   EI rd  f (4) p cab = p − 0 gi 0 , L 4 where p = g + q = p cab + p gird is total load. Substituting in Eq (2) the values for H  and p cab   from Eq (3) and (5) and assuming that  f 02 ≈ 0 the equation for the increment of initial sag or the vertical deflection at mid8span of the bridge will be:    0,375 L 4 (5) f 0 = 16 f 02 k 1 + 2, p f 0 k 2 + 30 k 3 , where k 1 = EA cab  is tension stiffness of the cable; k 2 = EI cab  is bending stiffness of the cable; k 3 = EI gird is bending stiffness of the stiffening girder. The vertical deflection calculated on the basis of Eq (5) taking into consideration ambient temperature variations  t and horizontal movements of tower saddles δ h can be determined according to following expression:   0,375 4 + 6 δ 0 k 1 + 3  S L 0 k 1 (6)  f 0 = 16 f 0 k 1 + 2 p  L ,( k 2 + L k f 3 ) − 6 δ Lk 1 T − 3 f  S T Lk 1 . 2 The systems with three8hinged cables or inclined cable supports (e.g., three span suspension bridges) are analyzed in the same manner.

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Having thus obtained the vertical deflection, the next step required is the computing the parts of the load that are taken by the main cable through the suspenders and that by the stiffening beam. Note that the unsymmetrical loading can be thought of as the sum of two full8span loadings: a symmetrical loading p 1 = g + q /2 and an unsymmetrical loading of q /2 . This redistribution of loads is influenced by appropriate method of bridge erection. After the loads taken by the main members of a bridge are obtained, bending moments, tension and shearing forces and stresses can be easily computed using well8known expressions. For dead load g the rigid cable is designed to create axial and bending stresses. Bending of cable and stiffening girder is caused by live load q .   Proposed analytical method results in considerably simpler mathematical computations and it was used in all instances to compare the results obtained with the numerical simulation. q cab g

δ h

EI l, EA l q gird

δ h

EI s a l a   Fig 1 . Basic structural system   3. FE analysis of suspension bridges with rigid cables In order to check the proposed theoretical method and to determine vertical deflections, internal forces and stresses of a suspension bridge under the distributed static loading, the FEM was used. Analysis was performed with relatively simple FE model using commercial finite element software CosmosM   and Midas/Civil . The three8dimensional models are constructed to examine the overall behavior of the bridge system. The elements TRUSS3D were used to represent the flexible cable (Model 1), the suspenders and backstays. Beam elements BEAM3D were used for the rigid cables (Model 2), stiffening girder

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and towers. The girder deck and the cables are hinged to the tower footings and tower saddles, respectively. The principal scheme is shown in Fig 2. The main rigid cables, stiffening girder and back stays are steel box profiles with the Young’s modulus E = 2,1×10 5 N/mm 2 and Poisson’s ratio v =   0,3. Suspenders are steel circular rods with the tension rigidity EI = 412125 kN . The towers are 2Η cross8sections with rigidity EA = 127420 kN. The cable to     girder bending stiffness ratio ξ = EI cab / EI gird   = 0−1. Live to dead load ratio γ = q / g = 1−3. Analysis was performed considering geometrical nonlinearity of cables by ten analytical steps of iteration. Some results of analysis are given in Fig 3. q g Unsymmetrical  loading

q l S o y a m di m n e g trical  g

EI cab ,   EA cab 1 21 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 EI gird a l a   Fig 2. Structural system of a bridge model and loading configuration   The predicted displacements, moments and stresses of 3D model were compared to the results from proposed analytical method using the values ξ  = 0,6 and γ = 1,0. Table 1 shows a comparison of computed and predicted maximum vertical displacements and bending moments for the symmetrical and unsymmetrical loading. As expected, the proposed analytical approach is slightly conservative, as indicated by values of the ratio presented in the last column of the table (computed/predicted) of more than unity. The highest value of this ratio is 1,1. Detailed analysis showed that ratio ξ and γ have no influence on this ratio.    

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