The Creep Effects On Simply Surported Prestressed Concrete Beams Under Repeated Loads

Simply supported prestressed concrete (PC) beams are widely used with the rapid development of high-speed and heavy-haul railway in recent years. The requirement of smoothness of rail is very high and the limit of long-term deflection or camber after track laying is strict in high-speed railway;heavy-haul rails also require epical smoothness for the reduction of rail smoothness caused by variation of deflection or camber during service will greatly increase the rail wear, and even affect the normal operation of trains. Long-term deformation of simply supported PC beams under dead loads (self-weight and secondary dead loads) so far has been deep studied both at home and abroad, and some research results have already been applied in engineering practice, however, the researches of effects of repeated loads on long-term deformation of beam are less. Based on typical section types and reinforcement characteristics of simply supported PC beams, characteristics of live load and train track time of china railway, this paper presents studies about creep effects of simply supported PC beams under repeated loads.The foundation of further research on creep effects of simply supported beams under repeated loads is accurately analyzing the creep effects of simply supported PC beams under dead loads. Automatically Step-up Method(ASUM) which is based on concrete time-dependent constitute relation of TB equation, cross section internal force equilibrium equations and deformation coordination conditions, is a method for computing creep effects of simply supported PC beams under single load(constant load). It can be used for full variable computing methods with any section types, reinforcement layout and random creep characteristics, whose precision is improved with the subdivision of time. In this paper, calculation formula of creep effects of beams under single live load is again deduced relying on ASUM, which is then extended to creep effects analysis of beams under repeated loads(multiple live loads). A computer program was developed to implement the extended ASUM using Fortran90, and it is used for creep effects analysis of6m simply supported PC T-beams and32m simply supported PC box-beams, and some of the computed results are compared with the test results or MIDAS results. Analysis shows that the again deduced formula can accurately calculate creep effects of beams under single loading. Qualitative analysis of the influence live load frequency and sustain time of train make on creep effects of beams under repeated loads is carried out in the example. Some conclusion are obtained, for example, at the same frequency, the long-term camber of mid-span decreases with the number of times of repeated loads; on the same calculate time point, the camber of mid-span decreases with the time accumulation. At the same time, the variation law of camber of PC beams under repeated loads is similar to creep development law.