Non-linear Analysis Of Simple-Supported Concrete Beams Externally Prestressed With Tendons

To the analysis of externally prestressed concrete beams, besides adopting experimental study, the most believable method is numerical simulation. But with the response of externally prestressed concrete beams under loads having double non-linear characteristics: the non-linear with geometry and the non-linear with material, we are encountered with two troubles, one is how to get the curvature and the strain of the point of specified height of the section under a combination of axial force and moment, the other trouble is that the procession of the integral analysis of externally prestressed concrete beams is very apt to go in to die circulation. To the above two troubles, after deeply investigation, new methods were put forward in this dissertation accordingly. To the fist trouble, a new method---Equivalent secant rigidity method was put forward. According to the real-time stressstrain state, the Equivalent secant rigidity of the section is calculated, adopting iterative algorithm, from the zero stressstrain state, the true stressstrain state of the section is approached step by step .This method is of clear physics meaning, compared with other methods, it is of relatively higher precision and cost less time. In adopting this method, there is a problem that this method can't promise absolutely a result be received, the procession of the calculation goes dispersed sometimes in dealing with combination of large moment or large axial force. To solve this new problem, rigidity rebound method was put forward to improve Equivalent secant rigidity method, this method inherits the characteristics of high precision and high efficiency of Equivalent secant rigidity method, at the same time, it solves the problem that the iterative goes dispersed under large internal force. To the second trouble, after careful analysis on the iterative procession of the stress and the deflection, the cause of the unconvergence was found that the calculation goes into die circulation. To solve the problem, perturbation method was used to eliminate the unconvergence. About the optimization of perturbation method, a general discussion was carried on about how to choose variable to be adjusted. Against the two kinds of vibration die circulations could occur in the two stages of non-linear analysis of externally prestressed concrete beams—camber stage and positive deflection stage, concrete advice about how to choose variable to be adjusted was given. Finally, in this dissertation, computer codes were composed on nonlinear analysis of section and nonlinear analysis of externally prestressed concrete beams.