Analysis Of Friction Effect And Second Order Dynamic Performancein Externally Prestressed Beam

Theexternal prestressing technology,as one of the most important part and thebranch of post tensioning system,has a rapid development in the field of building and bridge with the advantage such as constructionspeed,convenient for maintenance and replacementand so on.In recent years,external prestressing technology is widely used in the new structure andstructuralreinforcement.Nowadays,the research about external prestressed structure mainly focus on simply supported beam and static performance,there are less research about continuous beam and dynamic performance,especially about the friction effect between external tendons and deviator.Second order dynamic performance and friction effect in externally prestressed beam is analyzed.The current study about the external prestress increment calculation method is reviewed,and theircharacters and range of application are discussed.Then,a concise friction element locating at angle bisector between two sides of external tendon at deviator is constructed to simulate the slip with or without friction between the external tendon and deviator.The continuous beam and simply supported beam is calculated with various factors including different friction coefficient,externaltendon areas,eccentricities,load value,symmetric loading and asymmetric loading.The results show that eccentricity influence external prestress increment obviously,the friction decrease the maximum bending moment and deflection.For simply suuported beam and continuous beam under symmetric loading,the friction effect of bending moment and deflection is negligible,but friction effect is obvious to prestress increment.For continuous beam under asymmetric loading,the friction effect of bending moment and deflection can't negligible,and the effect to prestress increment is more obvious..The natural frequency is analyzed by equivalent stiffness method,energy method and lumped mass method.In the equivalent stiffness method,in order to find the natural frequency,we put forward the concept of equivalent stiffness which consider the external tendon's contribution to beam stiffness,then the external prestressedbeam is transformed into compressed beam with higher stiffness.Recently research show that prestress force does not affect the natural frequencies of bonded or unbonded prestressed beams.But we don't find any research prove whether the prestress force affects the flexural natural frequencies of beams.So in the energy method,we mainly focus on the second order effects of external prestress on frequencies of continuous beam,put forward the concept of compression softening effect,obtain the influence coefficient of external prestress related to the number of deviator.As the number of contact increase,the loss of eccentricity decrease,the external tendon is gradually close to unbonded prestress tendon.The influence coefficient is reduced to close to zero,and the external prestress hardly produces the compression softening effect,which hardly affects natural frequency of the beam.For lumped mass method,put forward the stiffness matrix of the beam after consider the influence coefficient of external prestress.Then,the results of the three methods are compared and analyzed.The results show that the energy method is more accurate.