Stiffness Analysis of Vertical Lift Bridge

Transcription

1 Stiffness Analysis of Vertical Lift Bridge Peter Rosko Abstract The stiffness analysis of vertical lift bridge is presented. The stiffness design has the main importance in real static and dynamic behavior of the bridge. In preliminary design the structural elements are analyzed separately and in the next step the whole system of the movable bridge is analyzed. It is shown, that the stiffness of mechanical equipment guiding of the deck on pylons plays an important role and has influence to system behavior. Keywords Vertical lift bridge, stiffness analysis, substructure system model. T I. INTRODUCTION HE motivation of the presented paper is the project of the new Botlek bridge. The paper provides a part of the vertical lift bridge design. The contribution deals with stiffness analysis of the bridge. The stiffness distribution in the bridge structure has a significant impact on its static and dynamic behavior. Movable bridges in comparison to classical bridges are more complicated because of variable position of the deck and the counterweight there are changes in current stiffness and in mass positions. It will be shown, that the stiffness of mechanical equipment guiding of the deck on pylons plays an important role. In preliminary design it makes sense to analyze separately structural elements of the lift bridge and in the next step to analyze the whole system. The modal analysis shows the shortcomings of the preliminary designed structure. The paper is segmented into following basic parts: Description of the bridge structure, Structural elements of the bridge system, Stiffness analysis and Conclusion. II. DESCRIPTION OF THE BRIDGE STRUCTURE A. System Description Presented vertical lift bridge consists of two independently movable steel decks. Both decks have the same dimensions. Three piers, each with two concrete pylons bears the decks and counterweights. Each end cross beam of deck is connected with cables to the concrete counterweight. Both decks and four counterweights are guided in pylons. B. Decks The finite element model of steel deck is presented. Fig. 2a Finite element model of the deck, view: top Fig. 1 The visualization of the vertical lift bridge Peter Rosko, Vienna University of Technology, Center of Mechanics and Structural Dynamics, Karlsplatz 13/E2063, A-1040 Vienna, Austria, Europe (phone: , pr@allmech.tuwien.ac.at). Fig. 2b Finite element model of the deck, view: bottom 116

2 D. Guidance The bilinear springs model the guiding of the deck and counterweight. 200 F[kN] 60 0,05 0,3 s[m] C. Pylons Fig. 2c Finite element model of the deck: detail Three piers: two end piers and center pier bear the two decks. The concrete pylons enable the vertical movement of decks and counterweights. Fig. 5 Bilinear spring stiffness of the guidance is k= N/m and k= N/m III. STIFFNESS ANALYSIS OF PYLONS The stiffness of each pylon was calculated on the base of virtual force method. Fig. 3 Finite element model of the end pylons of the bridge: pier 30 and pier 50 Fig. 6a Loading: FY = 1 Fig. 4 Finite element model of the central pylons: pier 40 Fig. 6b Loading: FX = 1 End pylons (pier 30 and pier50) 117

3 Fig. 6c Loading: FX = 1 Fig. 7b Loading FX = 1 Fig. 6d Loading: FY = 1 Fig. 7c Loading FY = 1 Central pylon (pier40) Fig. 7a Loading FY = 1 Central pylon (pier40) Fig. 7d Loading FX =

4 TABLE I HORIZONTAL DISPLACEMENTS AND STIFFNESS OF PYLON AT THE TOP POSITION OF THE DECK (Local coordinate system) Deck is at the top (lifted) position Position Load Displacement [m] Stiffness [N/m] 30 North Nd1359 FX=1 UX1359= E-08 KX=1.4427e+008 Nd 1359 FY=1 UY1359= E-07 KY=8.7176e South Nd FX=1 UX 91043= E-08 KX=1.4408e+008 Nd FY=1 UY 91043= E-07 KY=8.6096e North Nd FX=1 UX 15489= E-08 KX=1.4530e+008 Nd FY=1 UY 15489= E-07 KY=8.2467e South Nd 5991 FX=1 UX 5991= E-08 KX=1.4529e+008 Nd 5991 FY=1 UY 5991= E-07 KY=8.2604e North Nd FX =1 UX 91043= E-08 KX=1.4212e+008 Nd FY= 1 UY 91043= E-07 KY=8.1860e South Nd 1359 FX=1 UX 1359= E-08 KX=1.4233e+008 Nd 1359 FY=1 UY 1359= E-07 KY=8.2850e+007 IV. STIFFNESS ANALYSIS OF THE SYSTEM The stiffness of pylons and guiding is applied in 2-D model of the whole system. The extreme positions of decks and counterweights are presented. Fig. 9 2-D schema of the system in horizontal plane, deck: at the top position Deck is at the top (lifted) position Both decks: and are at the top (lifted) position Fig. 8 2-D schema of the system in horizontal plane, both decks: and are at the top position Fig D schema of the system in horizontal plane, deck: at the top position A. Modal Analysis The modal analysis results the natural modes

5 Fig.12 Both decks and are in the top (lifted) position, First natural modes Fig. 13 The deck is at the top position, the counterweight in pylon 40 of the deck is at the top position First natural modes 120

6 V. CONCLUSION The stiffness analysis of the vertical lift bridge was presented. In preliminary design the pylons were analyzed separately and the stiffness of pylons was used for the whole bridge system model. It was shown, that the stiffness of mechanical equipment guiding of the deck on pylons plays an important role and has influence on system behavior. The stiffness design has the main importance in real static and dynamic behavior of the bridge. REFERENCES [1] P. Rosko, Analytical models of structures, PR, Bratislava,