UIC+774-3R(track-bridge interaction)

 

 

      

                 

            

                       

      

  

   

 

            

 

            

                       

      

  

   

 

            

 

                                                                                                                                 

           

 

  



      

        

           

 

           

 

    

      

   

 

   

        

  

 

     

 

      

          

  

 

       

 

       

 

       

            

     

 

           

 

     

 

      

 

  

 

    

        

   

 

          

          

      

 

     

 

       

 



       

                    

   

 

     

 

      

 

             

      

     

 

    

      



 

         

 

             

 

       

   

                  

   

 

      

 

     

                                                                                                                      

 

                                                                                                                                               

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                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   

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 

         

   

                                                                                                                                                                                                

 

          

                                                                                                                                                             



 

    

    

 



  



  

             





     





            





         

 



      





     

                  

      

          

         

                                                                      

                           



                       



 

                  

 

   

           

 

 

 

 

                                                                                                                                                                                                      



 

    

 

 

                         

 

 

                                                                                            

 

    

                                 

 

   

                                          

 

 

 

 

                                                                                 



 

 

     

           

 

  

                                                        

 

 

         

                             



                                    

                

 

     

                                                            

Resistance of the track, k

    

Scatter range of curves Theoretical relationship (bilinear)

Longitudinal displacement of the rail u

                            



 

                                   

 

    

                                               

Resistance of the rail in sleeper (loaded track) (frozen ballasttrack without ballast)

Resistance k of the track

Resistance of sleeper in ballast only (loaded track) Resistance of rail in sleeper (unloaded track) (frozen ballast or track without ballast)

Resistance of sleeper in ballast (unloaded track)

Displacement ⇒

u0

u

⇒

                                                                            

          

           

    

        

 

               



 



            

        

   

        

   

        

 

                      

 

 

                                                                            

               

 

               

 

   

                    

     



    



    



   



     

 

 

                                                          



 

a) Simply-supported deck / no rail expansion device

Simply-supported deck / with rail expansion device

b) Continuous deck / no rail expansion device fixed support at one end

Continuous deck / with rail expansion device fixed support at one end

c) Continuous deck / no rail expansion device fixed intermediate support

Continuous deck / with rail expansion device fixed intermediate support

d) Series of simply-supported or continuous decks / no rail expansion device

Series of simply-supported or continuous deck / with rail expansion device

         

   

       

                                                                                      

 

      

                                 



 

           





           





                





            





           

                                  

        

 

 

                                                          

 

  

                                                                                                   



 

                                       

 

    

                                                                                                                                                        

          

   

      

                                                                                            



 

                                                           

 

     

         

                  



                 

                                                                                                            

 

     

                                 



                

        





                

        



           

                                                                                                                          



 

 

      

                                                                                                          

 

       

                             

 

    

                                   

                  

      

                  

 

      

         

                                                                                                      

 

   

                                                        



 

     

                   



                                



                          

 

    

                                                     

                                                                                        



      

                                

                                

 

 

                                   

 

  

                                                                  



 

                             

                  



                         

                                                                                                                                                       

 

   

                                                         

 

 

                                                                                                                                        

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 

                        

 

    



   

   

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

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

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                                                                           

   

              

                                                                                      

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 

                 

                                                                                                            

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                                                                                                 



                                                          

 

    

                                                       

   

         

                                                                  

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 

                                                                                                                                                                 

 

   

                  

                                                                                                                                              

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                                                                                                                                    

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                                                                          



 

 

     

                                                                                                                               

                                            



                              



                                            



 

    



  

 

                                                                                                                   



 

                                                                                                              

   

 

      

    

                                                                                                                                             



 



 

    



        

       

                                                                                                                                                                                                                                                                                                                                                                                        

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                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       

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 

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     

 

 

                

                                                                                                                                                                                                                                                                                                                                                                                                         

 

   

                                  

 

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  



 

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     

 

                

                                                           

           



        



    

        

                                                                                                                                                            

 

            

                                                     

                 



                 

                   



 

                                                   

  



     

  

  



   

  

  

  

                                               

 

    

 

    

                            

  

                                                



 







        

        

 

 

  



 







        

        

 

 

   



 



 





   

    

 



 

                              



 

                                         





      





          

 





          

    



   

      

                                        

 

   

                                                               

          

 



   

           





                                   

                                                                              

 

         

                                                                             



             

       

        



 



            

 

                                                              

 

    

                                

                           



                       



       

  

                  

    

              

     

              

      

                                     

 

                        

 

           

                                                                                                    



 

 

 

 

   

                                                                                      

                 





 

       

 

     

 

 

 

         



 

    

   

 

 

 

         



 

 

   

 



 

 

   

 

     

     



 

        

     

    





                     

 

  

                                                                                                              



 

 

  

 

        

 

   

                                                    

 

  

                                                                                                                                                   

ΘH

ΘH

 

 

                    

 

 

               

                               



 

                                                               

L1

L

L

L1







                                    

        

 





                           

                 

σrail

(L1 + L, K, k)

K

L1

L

                                    

k K  K

L

                      



 

  

             

                                                                                                                                              

 ΘH

ΘH

 ΘH

ΘH



ΘH

ΘH

 

 

                    

 

          

                                               



 

         

     

                                                                                              

 

    

                                                                                                                                                         

    

               

                                           

                             

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              

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                                   



 

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                  

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                                                             

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                     

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                                  

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                                 

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                 

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                                 



                       



                                      



                                        

  

      

                              



 

 

    

                                          

  

   









 

   

 















  

  

 



  

  







 

  





  

 



                    

                               



                                                      



             

  

              

       

                      

                                                    



 

 

   

                                                                                                                                                                                                                



 

 

                            

  100 90 80 70

     ] 60

   2

    m 50     m      /      N      [

K2k60 K2k40

40 K5k60

30

K5k40

20

K20k60 K20k40

10 0 10

20

30

40

50

60

70

80

90

100

110

 

       



 

 

 

 

       



 

       



 

 

  100 90 80 70

     ] 60

   2

    m 50     m      /      N      [ 40 K20k40

30

K20k20

20

K5k20 K2k20 K5k40

10

K2k40

0 10

20

30

40

50

60

70

80

90

100

110

 

       

   

 

 

       



   

 

 



 

       



   

 

       

 8000 K20k40 K20k60

7000

K2k40

6000

K2k60

5000

   ]    N4000    k    [ 3000 2000 1000 0 50

100

150

200

250

300

350

400

 

          

  100 90 K2k60

80 70

K2k40

   ] 60

   2

  m   m50    /    N    [ 40 30 K20k60

20

K20k40

10 0 50

100

150

200

250

300

350

400

 

       



 

 



 

       



   

 

 

 

                

100.0

gamma=0.5 / K2

RAIL STRESS AT THE FIXED DECK END

gamma=0.0 / K2

ENVELOPE,

Θ

H = 8 m m , A 60

gamma=0.5 / K5 gamma=0.0 / K5

90.0

gamma=0.5 / K20 gamma=0.0 / K20

80.0

70.0

   )   a    P    M    (    F  ,    l    i   a   r

60.0

50.0

40.0

30.0

20.0

10.0

0.0 0

15

30

45

60

75

90

10 5

1 20

13 5

15 0

SPAN LENGTH (m )



 

         

gamma=-5 / K2

RAIL STRESS AT THE FIXED DECK END

gamma=0.0 / K2

ENVELOPE,

Θ

H=1mm, A

60

gamma=-5 / K5

100.0

gamma=0.0 / K5 gamma=-5 / K20 gamma=0.0 / K20

80.0

60.0

(MPa)40.0 rail,F

20.0

0.0

-20.0 0

15

30

45

60

75

90

105

120

135

150

SPAN LENGTH

      

gamma=0.5 / K2

RAIL STRESS AT THE MOVABLE DECK END

gamma=0.0 / K2

ENVELOPE,

Θ

H = 8m m , A 60

gamma=0.5 / K5

20.0

gamma=0.0 / K5 gamma=0.5 / K20

10.0

gamma=0.0 / K20 0.0

-10.0

   )   a    P    M    (    M  ,    l    i   a   r

-20.0

-30.0

-40.0

-50.0

-60.0

-70.0

-80.0 0

15

30

45

60

75

90

105

120

135

150

SPA N LENGTH (m )



 

         

RAIL STRESS AT THE MOVABLE DECK END ENVELOPE,

Θ

H=1mm, A

60

0.0

-20.0

-40.0

-60.0 (MPa) rail,M

-80.0 gamma=-5 / K2 gamma=0.0 / K2 gamma=-5 / K5

-100.0

gamma=0.0 / K5 gamma=-5 / K20 gamma=0.0 / K20

-120.0 0

15

30

45

60

75

90

105

120

135

150

SPAN LENGTH

     

gamma=0.5 / K2

SUPPORT REACTION

gamma=0.0 / K2

ENVELOPE,

Θ

H = 8m m , A 60

gamma=0.5 / K5

2500.0

gamma=0.0 / K5 gamma=0.5 / K20 gamma=0.0 / K20 2000.0

   ) 1500.0    N    K    (    t   r   o   p   p   u   s

   F

1000.0

500.0

0.0 0

15

30

45

60

75

90

105

120

135

150

SPA N LENGTH (m )



 

        

2500.0

gamma=-5 / K2

SUPPORT REACTION

gamma=0.0 / K2

ENVELOPE,

Θ

H=1mm, A

60

gamma=-5 / K5 gamma=0.0 / K5 gamma=-5 / K20 gamma=0.0 / K20

2000.0

1500.0 (KN) F

support

1000.0

500.0

0.0 0

15

30

45

60

75

90

105

120

135

150

SPAN LENGTH



 

 

                                         

   

             

                                  

                                                                          

    

    



  

    



  

     

 

                              

       

                      

 



                 



 

                                          

                  

                 



    

     



     



    



    

                                        



        



         

         



   



     

  

                          



                         

     

                                                                                                              



 

                            

   

     

       

        

                                    

                                                                          

    

    



  

    



  

   

 

    





                                                     

               

                



     



     



    



    

    

    

                                                 



       



 

  

         

         



   



     

  

      



  

   

   

  

 

               

         

                

       



     

                                 

  





      

         

   

          

   



   



   



   

   

   



         

   



 

                          

   

     

      

        

                                      

                                                                          

    

    



  

    



  

   

 

  

 



                                                      

                

                



     



     



    



    

    

    

                                               



 

  

       



        

         



        



          

      



  

          

 

                        



                         

     

                                    





      

         

   

             

   



   



   



   



   

   

   





 

                            

        

   

      

        

                                          

                                                                          

    

    



 

    



 

     

                         

  

 



                                            



                     



           



             



            



        



     



   

     

    

  

      



 

                                               



          



                   



            

                                      



     



      

  



       

  

    

   

  

             

  

                                    

   

                                               

                                        

 



  



       

   

      



 

 

                            



                       



         

    



          



            



       



     

   

    

  

      

 

        

                                     

     



       

  



       

  



   

   

        

   



        

                            

        

   

     

        

                                    



 

                                                                                

    

    



    



     

            

     

               

 

                             



                

           



    

               





     



     



         



    

                                                 



       



     

         



   



    



 

                  

   

           

                                   

   

                       



           

 

 

     

      

   

                                                 

    

         

    



           



          



        

                                             

    



  

   

  

                            



  



 

 

                                                                                                            

0.30 H

H

H

0.50 DECK TYPE 1

DECK TYPE 2



DECK TYPE 3

 

 

                                      

        

                                    



 

                                                                                                 

90 m 300 m

var.

300 m

                                                                                                                                                                                                                                                                                                                                                                     



 

            

60 m 60 m

100 m

60 m

60 m

60 m

60 m

100 m

                   

  

 

 

 

  

  

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



  

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

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











                                                                                                                                       

                                       



           



 

  

                            



                                                         



 

 

     6      2      7  ,      0  ,      5  ,      2      8      3      1      1      9         2    -      1    -

  s   s   e   r    t    l   r   s   a   o    l   a   m   b   r    t   o   r   e    l   u   o    t    S   G   %

     4      4      2  ,      0  ,      1  ,      4      7      9      3      2      6         2    -      1    -

  s   s   e   r    t    l   r   s   a   o    l   a   m   b   r    t   o   r   e    l   u   o    t    S   G   %

 ,      2  ,      0  ,      0  ,   r      2  ,      1  ,      6  ,      1  ,   r      3      4      5      0      1   o      6      6      0      0   o   r   r      1   r      3      1   r      3       E    E      1    %    %      3      4    )      1  ,      2      3  ,    )      0  ,      2      3  ,    °      2      0    -      0    -      0    °      1      0    -      0    -      2    T  ,      9      E     E      6    T  ,      0      E     E      6      8      0      1      5      3      2      2      2   m   m      2      7   s   s  ,      1  ,  ,      0  ,    (    (      2      4      2      7   x   x   m   m

  r      3  ,      0  ,      3  ,      9  ,   r      2  ,      1  ,      6  ,      1  ,   o      6      0      7      9   o      4      5      0      1   r   r      3      2      6      6   r   r      3      1    -             E    E      1       %    %    t    2   2   3    3    4   2   3    0  ,    t   c    5   c  ,    0   0    4  ,    0   -    0   -    0   e    1   -   -    0   e    7    f    f    6    E   E    2    f    6   E   E    8    f    3    7   7   e   -    9   3   e    4      6    3    l    l  ,    1  ,  ,    9  ,   a   a    2    2   -    4       -    6    b    b   o   o    l    l    G    G    6   2   3    3    4   2   3    6    0    0  ,    0  ,  ,    0  ,   -    0   -    3   -    3   -    0    9   m   1   E   E    2    E    E   m   2    9    5    0    6    5    5    2    2   u   -    1   3    2   u    1   7   0    0  ,  ,    S    S   -  ,  ,    2    2    2   -    1     -    7    3   3    7    1  .    6  ,  .    3  ,    3   4    7    t  ,    0    8   0   -    0   -    8    t   -    0   -    7    3   o    2   o    2    E    E    E    E   r    8   r      1    4    2    d    0   3    d   -    6    1    6  ,    6  ,  ,    6  ,   n   n    2    1    E    E   -    1   -    9    6   3   3    7    6    3    6  ,    3    0   g    1  ,    0  ,   g  ,   -    0   -    6   -    0   -    0   n    0   n    9    9    i    2    i    E    E    E    E    1      2    3    k    3    k    9    4    2    5   -    1   8    8   a    8   a    1  ,  ,   -   r  ,    8  ,   r    3   3    3    B    B   -    3      4   2   3    3    4   2   3    3  ,  ,    k    1  ,    0  ,    0   -    0   -    0    k    1   -    0   -    0   c    3   E   E    6   c    3   E   E    6   e    4   5   3    8   e    4    5   3    8    d   -    2    d   -    2  ,    1  ,  ,    1  ,    °    °    2    4    2    T   -      T   -    4      l    l    i      6    i      6   a   a   r      2   r      2      0      0      0      0      0      0    °      1    °      1          T    T

                                                                                                    

   t    t    i     a    i     a   n      P     m    m     N   n      P     m    m     N      K      K    U      M    U      M  .  .  .  .  .  .    t    t   c   c   c   c   a   c    t   a   c   y   s   y   s   s    l   s    l   a   l   a   l    t   a   a    i    i   e   e    t   r   p   p   e    t   r   p   p   e   s   r   s   r    t   s   i   n    t    i   s   i  .   n  .   a   s   a   s    i    d   p    d  .   p  .   p    l    d    l    d   u    i   u  .  .    i   p    l    l   s   s   a   a    Q   r   e   b   u    Q   r   e   b   u   r   a   s   r   a   s   n   n   o   o    i    i    t    t   c      1      1      1      1   c      2      2      2      2   e   e   r   r    i    i    d    d  .  .   s   s    i    i    d  .      5      5      5      5    d  .   g   g      5      5      5      5   n   n   o   o    l    l   n      0      0      0      0   n      0      0      0      0   a      9      9      9      9   a      9      9      9      9   p   p   s   s   e   e   p   p   y   y    t    t    k      3      3      3      3    k      3      3      3      3   c   c   e   e    d    d  .  .   o   o    3    3    3    6    N   3    N   -   -   -     -    6   -    6   -    6     e    1   1   1    1   e    4   4   4    4   s    P   P   P    P   s    P   P   P    P   a   a   c   c



 

    

       



 





   





  



                      

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     

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 

 

  

     

 

  

     

 

  

     



     

 

          



 



       

 

     

   

 

     

   

 

     

   



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   



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                  



 

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     

    



           



          



 



   



        



     



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   

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    

 

       

 

          



            

 

           

 

          



              

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 

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   

          

   

          



                       



 