Approximate Method For Analyzing Of Cable-stayed Bridge

The modern cable-stayed bridge has made remarkable achievements after 60 years of development;it also ushered in new challenges and difficulties after a cycle of sixty years.Cable-stayed bridges need to have a larger span and more bridge spans to cope with the demands of the people.Bridge engineers can solve this problem from two aspects: increasing the span of cable-stayed bridges,increasing the number of the span of the cable-stayed bridges.The traditional cable-stayed bridge main span increases will encounter many limiting factors,the most important is the girder axial force is too large on the root of tower;the most important problem of multi-tower cable-stayed bridges is insufficient stiffness of the non side tower and difference for overall stability.In view of the above problems,the main research results are included in this paper:(1)Through the analysis of the literature,it is concluded that the axial stress is the main factor affecting the growth of the span of the bridge,in order to explore the limit span of cable stayed bridge,calculate out axial force of the girder of long-span cable-stayed bridge with different cable arrangement type quickly,based on cable-membrane assumption of cable-stayed bridge with multiply cable,solved the position equation of the cable in the main tower,the axial force of girder formula of fan system cable-stayed bridge under the live load and dead load was derived based on the modified cable-membrane method,and simplify the main beam axial force formula type of radiation and harp arrangement of cable-stayed bridge,and compared with the axial force formula from Danish scholar Gimsing and the Chinese scholar Wang Bo-hui and verified with examples.The results show that when calculating the axial force of main girder of long span cable stayed bridge,it is needed to consider the length of cable free zone of tower root and the length of cable free zone of middle span,the presented theoretical can meet the requirements of the conceptual design,and it is suitable for the axial force calculation of large span cable-stayed bridges.(2)On the premise that ultimate tensile and compress strength are equal for steel girder,that is,tension of steel girder at cross anchor and end of tower are equal,withcable-membrane theory of cable-stayed bridge to solve ultimate span length of partially earth-anchored and ratio of ultimate anchor-span ratio,aiming that exploring the extreme span length of partially earth-anchored cable-stayed bridges more deeply.Key dynamic responses are derived and calculating outcomes are compared with solution attained from one finite element model.The results show that ultimate span length of partially earth-anchored cable-stayed bridges based on axial force of the girder is 1.4 times as that of conventional cable-stayed bridge,and the ultimate anchor-span ratio about 0.293.In this paper,the key derived dynamic responses are consistent with that of the finite element model.The error is due to the fact that the cable arrangement system is usually fan-shaped rather than a radiation pattern in the real bridge structure.(3)In order to explore the extreme span length of partially earth-anchored cable-stayed bridges,Make for axial force of the girder of four types of cable-stayed system,the superiority of the girder of the cable stayed bridge and partially cable stayed bridge is verified.Making full use of the ultimate strength of steel,for partially earth-anchored cable-stayed bridges with cross stays,the pressure of Mid span cable section is equal to the pressure of tower section,based on cable-membrane method of cable-stayed bridge with multiply cable,solved extreme span length of the partially earth-anchored cable-stayed bridges,and get the ultimate anchor-span ratio.A series of estimating formula of the key structural responses are provided and calculating outcomes are compared with are compared with that of a finite element model.The results show that extreme span length of partially earth-anchored cable-stayed bridges with cross stays is 1.5 times as the conventional cable-stayed bridge,and the ultimate anchor-span ratio about 0.333.The presented theoretical can meet the requirements of the conceptual design,and it is suitable for the key structural responses and mechanical analysis of partially earth-anchored cable-stayed bridges with cross stays.(4)The cable-stayed bridges with three tower was taken as research object,frequency formula for vibration mode of cable-stayed bridges was induced by the Rayleigh method and vibration mode function of vertical free vibration of main beam and vibration type function of longitudinal free vibration of main tower were introduced,and practical vertical frequencyformula for vibration of cable-stayed bridges with three tower considering tower stiffness influence was derived.Finally,the presented theoretical formula of fundamental frequency was validated by the engineering and the frequency formula for vibration was discussed therein.The results indicate that section types of the girder,tower and cable has no influence on the vertical frequency formula for vibration of cable-stayed bridges,but the tower stiffness has a great influence to vertical frequency of cable-stayed bridges,it must carefully consider the constrain condition and tower stiffness when it calculation frequency.(5)In order to explore the stiffness characteristic of multi-tower cable-stayed bridge,the three tower cable-stayed bridge was taken as research object,based on the principle of deformation coordination,longitudinal restraint stiffness of the non side tower and the side tower for multi-tower cable-stayed bridge was solved out,a series of estimating formula provided and calculating outcomes were compared with that of a finite element model,and analyzes the influence of main structure parameters for longitudinal restraint stiffness of the non side tower and the side tower and combined with domestic and foreign famous several practical engineering of cable-stayed bridge to lifting tower longitudinal anti push rigidity.(6)Explore the stiffness characteristic of multi-tower cable-stayed bridge,analysis the structure features of them,the three tower cable-stayed bridge was taken as research object,derived analytic formula of cable-stayed bridges cable elastic support rigidity under unit load based on the principle of deformation coordination,a series of estimating formula provided and calculating outcomes were compared with that of a finite element model,and analyzes the influence of main structure parameters for cable support vertical stiffness.In the calculation of horizontal force of cable elongation and provide horizontal force pylon deviation of weight distribution calculation instead of the default for unit force.The presented theoretical can meet the requirements of the conceptual design,and it is suitable for the stiffness characteristic of multi-tower cable-stayed bridge.(7)Explore the action mechanism of crossed cables,ignore the small level displacement of the side tower,an analytic formula for calculating the longitudinal restraint stiffness of themiddle tower of multi-tower cable-stayed bridge with cross stays considering the effect of tower and beam based on the principle of deformation coordination was deduced,and carried out a numerical example.The results show that crossed cables can make the beam deflection decreases,thus increasing the overall stiffness of the cable-stayed bridge.The overall stiffness of multi-tower cable-stayed bridge rises as the number of crossed cables increasing,the displacement of middle tower reduction up to 51% after set 10 pairs crossed cables,but the stiffness increased gradually slowed down.The change of the stiffness of the tower’s effect on longitudinal restraint stiffness of the middle tower for multi-tower cable-stayed bridge is greater than the main beam,but the crossed cables play more important roles in increasing the stiffness of the structure.