The camber, or total net upward deflection, of prestressed concrete bridge girders is the result of the eccentric axial compression force provided by prestressing strands which counteract the deflections due to gravity loads. At the time of strand release, the deflection behavior of prestressed concrete girders is considered to be elastic, and it is common for bridge designers to use elastic camber calculations to predict the camber at release. To estimate the girder camber at bridge erection, a multiplier method is typically used which amplifies the camber at release to roughly account for the time-dependent effects (e.g., creep and shrinkage) that occur between release and erection. Additionally, there are numerous factors which affect the camber at erection and are not known at the time of design, including the girder storage condition in the precasting yard (i.e., bunking) and the age of the girder at erection, that further lead to potential errors in the estimates of the girder camber at erection. The Minnesota Department of Transportation (MnDOT) uses the release camber calculations, based on gross section properties and elastic shortening losses, and a multiplier method to predict the camber at release and erection, respectively.
An accurate estimate of camber at erection is important, because if the girders that arrive at a bridge site have cambers that are much lower or much higher than the expected design erection camber, it causes significant problems related to the formation of the bridge deck profile, the composite behavior of the girders and bridge deck, negative or very high stool height requirements, delays in construction and increased costs. It was recently observed that girders were being erected at bridge sites in Minnesota with cambers that were often much lower than predicted. The main side effect of this problem is required stool heights that are too high, especially at midspan. If the required stool heights approach the height of the protruding top flange shear reinforcement, the composite action needed between the girders and the bridge deck cannot be achieved, thus requiring the use of additional reinforcement or changing the entire bridge deck profile, which adds cost and creates delays. To account for this issue, MnDOT switched in late 2007 from the multiplier method recommended by Leslie A. Martin (1977) and PCI (2010), to a universal multiplier of 1.5. However, the problem persisted and added costs and delays continued to occur.
The primary objective of this study was to investigate and determine the cause of low girder camber at both release and bridge erection, which was observed by MnDOT, and to create an improved method for camber prediction, through modified calculations (if necessary) and a new set of multipliers. This objective was achieved through examination of extensive camber records from precasting plants and from in-situ measurements during erection of Minnesota I-girders, instrumentation and camber monitoring of fourteen girders from release to erection, concrete material testing, an analysis of prestress losses due to thermal effects, and PBEAM time-dependent camber modeling to investigate various effects including creep and shrinkage, girder support conditions during storage and age at erection. Extensive historical fabrication data was collected from two precasting plants (referred to as Plant A and B) for 1067 girders produced between 2006 and 2010. Camber at erection data was collected from the counties for 768 of those girders. On average, it was found that the measured camber at release for those 1067 girders was only 74% of the design value. Furthermore, it was found that the measured camber at erection for the 768 girders was only 83.5%, on average, of the design value; and that girders erected at early ages almost always had cambers that were significantly lower than the design value. Because the predicted camber at erection is obtained by amplifying the elastic camber at release, inaccurate estimates of the camber at release can compound the problems of estimating the camber at erection.
Various factors that affect the release camber were investigated, including concrete strength and modulus of elasticity, and variation in the strand prestress force. It was found that the increased concrete strengths achieved at the precasting plants (15.5% over the specified design value, on average) decrease camber due to the increased elastic modulus. Multiple concrete cylinder samples from both precasting plants were tested to investigate the concrete strength and elastic modulus over time. It was found that the ACI363R-10 expression used by MnDOT to estimate the concrete modulus of elasticity from the specified concrete compressive strength greatly underestimates the elastic modulus of concrete produced at both precasting plants. The Pauw (ACI 318-08, AASHTO LRFD 2010) equation was determined to be the best predictor of the concrete elastic modulus, and when used to recalculate the release camber predictions for the 1067 historical girders, yielded significantly more accurate results.
A thermal effects analysis was conducted to determine the effect of concrete and ambient temperatures on the strand stress at release. It was found that the combined thermal effects (and strand relaxation) cause a reduction in strand stress at release of approximately 3%, on average. The position of each girder in the bed was also found to cause variations in prestress force through the redistribution of draped strand stress due to the harping sequence (at Plant A) and friction losses (at Plant B). Finally, it was found that high strand density, though often found in long MN-shape girders which had slightly lower release cambers, was not a major cause of reduced release camber. Thus, it was determined that the major causes for the discrepancy in release camber predictions and observed cambers were the increased concrete release strengths, the fact that the ACI 363 equation for concrete elastic modulus underestimated the measured elastic moduli, and strand prestress losses due to thermal effects.
The effects of these primary factors were considered in re-predicting the cambers of a select data set for which detailed fabrication data, including curing and temperature records, were known. The girders included in this data set were those from which the concrete material samples were obtained, the instrumented girders, and selected girders from the historical data set. It was found that the accuracy of the re-predicted cambers was much greater than the original design cambers, and that the amount of variability in the results was reduced. Recommendations for modified camber calculations were made based on average effects (i.e., 15.5% release concrete strength increase, the Pauw equation for estimating concrete elastic modulus, and thermal prestress losses of 3%). These recommendations were then tested against the entire historical girder database, and it was found that the discrepancy between measured and design camber values improved from approximately 74% to 99%, on average. This result confirmed that the revised release camber calculations provided much more accurate camber predictions than the original design equations. It should be noted that the overall scatter was not reduced because the recommendations were implemented in an average sense to all 1067 girders in the historical database.
Once the discrepancy between measured and design release camber values was determined, various factors that affect long-term and erection camber were investigated, including solar radiation, relative humidity, concrete creep and shrinkage, length of cure and bunking/storage conditions. The program PBEAM was also validated for use in release and long-term camber modeling. It was found that solar radiation affects the measurement of camber by as much as 15% during the course of a day, emphasizing that camber is a constantly fluctuating value. Relative humidity was found to cause changes in concrete creep and shrinkage and induce camber variability. High relative humidity during the winter months was also observed to cause slight increases in camber. Through PBEAM validation, it was found that the ACI 209R-92 concrete creep and shrinkage models provided the best results for long-term camber predictions and that the Mokhtarzadeh ACI 209 variation models provided a consistent lower bound. As such, the ACI 209R-92 creep and shrinkage models were used in the time-dependent camber modeling predictions. Weekend curing was found to cause lower erection cambers than weekday-cured girders, even though the camber discrepancy at release was less evident, due to additional stress recovery from cooler curing conditions. Finally, it was found that bunking/storage conditions led to increased cambers, additional camber variability, and possible exceedance of codified stress limits. Bunking limitations were recommended in order to limit these undesirable effects.
These observations and results were used to create PBEAM inputs and ensuing long-term camber predictions for girders of varying depth and length. From these results, four “sets” of multipliers were created by comparing the long-term camber predictions to the current MnDOT and improved release camber predictions. Two of the sets of multipliers were developed to be applied to the MnDOT approach to predict release camber, and the other two were developed to be applied to the improved release camber predictions. For each approach, one set was based on a single multiplier to best predict erection camber and the other set recommended four different multipliers that reflected approximate age ranges for the girders at erection. These four different sets of multipliers were then applied to the historical girder data set and compared to the measured erection camber data. It was found that all four sets of multipliers greatly improved the erection camber predictions, with average measured vs. adjusted design erection camber percent values of 95.6%-97.1%. However, only the “time-dependent” multipliers, which accounted for four potential ranges in girder age at erection, reduced the amount of scatter in the results. In particular, these multipliers alleviated the problem of over-predicted erection cambers for girders erected at early ages. Both the improved release camber predictions and the “Improved Time-Dependent” multipliers are recommended to be used by MnDOT for future camber predictions.
In addition to the recommendations for the modified camber calculations at release and the new set of multipliers, recommendations for girder fabrication were also created to reduce camber variability and improve girder production at the precasting plants. Included in these recommendations are limitations for bunking/storage conditions and a spreadsheet created to produce more accurate temperature corrections (for Plants A and B). It was found that the amount of camber variability that can be expected using the recommended calculations and multipliers is approximately ±15%, or even lower if the girder fabrication recommendations are put into practice.