Study On Creep Behavior Of Prestressed Concrete Beams With Pretensioned Bent-up Tendons

Accurate prediction model of creep behavior has considerable influence to many aspects of prestressed concrete bridges, such as pre-camber setting during bridge design or construction, estimating long-term deformation and the safety at high speed driving during operation period of bridges. The prestressed concrete beam with pretensioned bent-up tendons would have a wide application prospect in bridge engineering. It not only combines many advantages of the straight-line pretensioned prestressed beams and the curvilinear posttensioned beams, but also avoids the uncompacted grout in reserved pipes. Therefore, it has important significance to research the creep behavior of the prestressed concrete beams with pretensioned bent-up tendons.Three prestressed concrete beams with pretensioned bent-up tendons (XPB1, XPB2, XPB3) and one post-tensioned concrete beam (HPB1) respectively were researched. XPB1 and XPB3 were put in standard curing room, and XPB2 and HPB1 were put in outdoor environment. All the experimental beams were simple supported under long-term loads, whose Partial Prestressing Ratios (or PPR) are different but their span lengths are 7.5m.The prestress loss of four beams were monitored during the course of construction, and their deformation in mid-span section were observed about 600 days after second loading. By studying the test data, several researches have been accomplished as following:1) By analyzing the prestress loss during the course of construction, calculation method was suggested for the prestress loss of the prestressed concrete beams with pretensioned bent-up tendons. The results show that the friction loss?n can be calculated by the equation obtained in previous research, and the other prestress losses in construction stage can be caculated according to Code for Design of Highway Reinforced Concrete and Prestressed Concrete Bridge and Culverts (JTGD62-2004).2) Through studying the time-history curves of Creep Strain, Creep Degree, Creep Function, and Creep Coefficient of four test beams, it was demonstrated that surrounding conditions and PPR have great impact on creep property, but the strand line shape only has a little effect on it. Combined the former research results of concrete creep behavior, "Multiple coefficient method" model of creep coefficient was put forward. This model considers the effect of PPR, loading-age, component section size, environment conditions, concrete strength and holding time of stress, and it can be adapt to calculate creep coefficient of the prestressed concrete beams with pretensioned bent-up tendons. Compared this model with the code models such as ACI209R-92, CEB-FIP MC90 and'86 model'proposed by China Academy of Building Research, which the±10% margin error of this model was pointed out, and it can be referred to design or construct the prestressed concrete beams with pretensioned bent-up tendons.3) Based on the creep strain measured at different height in midspan section, the Assumption of Plane Section is demonstrated true to beams under long-term loads. Moreover, the displacement of beams neutral axis was characterized, and the creep strain geometry model was established. Selecting the creep strain geometry model to study, using analytic method, and combining the creep curvature, the numerical relationship between creep coefficient and creep deflection coefficient of prestressed concrete beams was demonstrated. For full-prestressed concrete beams, the creep deflection coefficient is greater than the creep strain coefficient, while the opposite is true for partial-prestressed beams. Moreover, this conclusion was further proven by analyzing creep deflection of 3 test beams with pretensioned bent-up tendons in nonlinear Finite Element Method.4) The expression of the ratio k between creep deflection coefficient and creep coefficient was established, and the formula for creep deflection calculation was further demonstrated. It is to note that this expression is determined by Creep Coefficient, PPR, the axial compressive force and the moment resulting from prestress, component equivalent sectional area and the module of bending section,etc. Through sensitivity analyzing the k's influencing factor respectively, it was pointed out that k is determined by PPR, but the other factors have little impact on k. Then the simplified formulas on the ratio between k and the creep deflection was established. 5) By studying four test beams'time-history curves of long-term deflection coefficient, it's demonstrated that work environment and loading statuses have some impact on this coefficient, but holding time of stress is the main factor. Based on "geneogenous theory" about concrete creep, "single factor" model was established, which can be used to calculate long-term deflection coefficient of the prestressed concrete beam with pretensioned bent-up tendons. Moreover, the end value of long-term deflection coefficient??can be considered to be 2.15.6) By studying the numerical relationship between long-term deflection coefficient and creep deflection coefficient of the prestressed concrete beams with pretensioned bent-up tendons, the "multiple factors" method model was established, which can be used to calculate long-term deflection coefficient, this model is determined by concrete shrinkage, creep and PPR, etc. Moreover, "multiple factors" method and "single factor" method were put forward to calculate long-term deflection, and the proper scope of these methods was suggested respectively, all these conclusions can be referred and applied in engineering design.