CONCRETE BRIDGE TECHNOLOGY Camber Variability in Prestressed Conrete Bridge Beams by Dr. Maher Tadros, econstrut Beams ast with extra amber in storage yard at Conrete Tehnology Corporation; amber shown is exeptionally large for illustration purposes. Photo: Conrete Tehnology Corporation. Preast, prestressed onrete girders experiene amber (upward defletion) when the prestressing strands are detensioned and the prestressing fore is transferred from the asting bed to the onrete member. When the girder is stored in the yard of the preast manufaturer, its amber ontinues to hange with time, influened by the ambient air onditions, and even the orientation of the girder as it is exposed to the sun. When the girder is ereted on its seats at the bridge site and just before the dek is plaed, its amber at that time affets the haunh (build up) onrete required to ensure that the top of dek surfae meets the roadway profile requirements. a Strand group debond length plus half transfer length b L Profile of a group of strands (for one point harping, =0) φ φ 1 Initial amber after detensioning is used to indiretly hek the quality of the produt, for example, the level of prestress and other prodution issues. Camber at the time of girder shipping is sometimes required to be heked for ontratual purposes. Camber just before dek plaement and the elasti defletion due to dek weight are used to determine the elevation of the formwork supports at the edges of the top flange. Aurate measurements and alulations at this stage result in minimizing grinding of the dek to bring it to the required profile. a b Curvature diagram (for straight strand profile, urvature is onstant) Figure 1. Beam elevation showing general profile for a group of pretensioned strands. Figures: econstrut. A negative amber (downward defletion or sag) while the bridge is in servie may ause onern for inspetors and the publi and, if exessive, may have strutural and funtional impats as well. A number of state highway authorities (SHA) have speified that the final long-term amber due to all loads, exept live load, must be positive, that is, upward. L/ 38 ASPIRE, Spring 015
beam ends. Speified onrete strength at transfer is 6 ksi and at servie is 8.5 ksi. M e1 L L s M Me Equation 1, applied four times for the four groups of strands, yields a predited prestress-only amber Δip of 5.33 in. The groups are 3 strands that are 137.1-1.5-1.5 = 134.1 ft long, and three groups of four strands that are 1.1, 118.1, and 106.1 ft long. The 1.5 ft quantity used to ompute the length for the 3 strand group is an allowane for averaging the effet of the 3 ft transfer length for the 0.6-in.-diameter strands. Figure. Bending moment diagram for beam in storage, note the onsiderable overhang. Figure: econstrut. At best, amber predition an have ±5% variability, but more realistially it an have ±50% variability. The predition is impated by things that are known within a narrow band of variability suh as the ross-setion dimensions, amount of prestress, and span length, whih are onsidered here to be deterministi variables. It is also impated by random variables, outside of the ontrol of the designer at time of design, suh as soure of aggregates, relative humidity and temperature of the ambient air, method of uring, method of detensioning, onditions of storage, and time elapsed between girder prodution and dek plaement. Calulation of Initial Camber Referene 1 gives a survey of the history of amber predition and proposes a method that an be programmed in a spreadsheet. Only two equations are required. Equation 1 is used to alulate initial amber due to prestress using a general profile of a group of pretensioned strands (Fig. 1). The equation is valid for straight and draped strands and for ases where debonding at the ends is utilized. The equation may be applied to the different types of strand groups, and then superposition used to ombine the individual results to determine the full effet. = φ1 ( b + )(a + b + ) + φ (3ab + b + 6a + 6b 3 ) 6 Eq. 1 ip + The distanes a, b, and are defined in Fig. 1. The urvatures φ 1 and φ are equal to P/ EI for Setions 1 and at the loation at whih prestress is effetive at the end of the girder (dimension a) and at midspan, respetively. The values of P, e, E, and I are the prestress fore, its eentriity, the onrete modulus of elastiity, and the ross setion moment of inertia, respetively, at the setion onsidered for the urvature alulation. The starting setion loation (at dimension a from the end of the girder) is affeted by length of debonding plus an allowane for transfer length. Equation is used to determine defletion due to beam weight (Fig. ). In reent years, long beams have required lifting, storage, and shipping with overhangs as long as 0 ft. The equation aounts for overhang length. gi 5Ls = (0.1M e1 + M + 0.1M e) Eq. 48EI For this equation, the length L s is length between supports during beam storage. Figure defines the moments in Eq. and their loations. The example in Referene 1 is used here for disussion purposes. Not all data are given here. The I-beam is 7 in. deep, 137 ft 1 in. long, and prestressed with forty-four 0.6-in.-diameter straight strands, 1 of whih are debonded in three equal groups for 6, 8, and 14 ft from the Equation is applied assuming a storage span of 135.5 ft. The orresponding defletion is.3 in. The net predited self-weight amber is therefore 5.33.3 = 3.01 in. Causes of Initial Camber Variability Many fators influene the value of amber at transfer of prestress, some of whih are random variables beyond the ontrol of the designer. Several of the more important fators are listed here: The modulus of elastiity of onrete. The omputed modulus of elastiity of onrete has been shown to vary from the measured value by % for onfidene between 10 and 90 perentiles, aording to the NCHRP study that proposed the aggregate orretion fator, K 1, whih now appears in Equation 5.4..4-1 of the AASHTO LRFD Bridge Design Speifiations. The stiffness of aggregates plays an important role in the modulus variability. Thus, the results are dependent on the aggregate soure. Also, a designer who speifies 6 ksi onrete transfer strength is unlikely to get it mathed during prodution of all the beams in a projet. Curing versus ambient temperature. This fator an be very signifiant in the first 48 hours of onrete age. The onrete temperature may be as muh as 10 F above the ambient temperature beause of uring and ement hydration. This ould derease the tension in the strands by as muh as 0 ksi. This temporary differene may ause signifiant hanges in amber and prestress loss. 3 However, within about 7 hours, this temporary effet seems to dissipate. Loation of lifting inserts and storage supports. The effet of ASPIRE, Spring 015 39
1-1 Figure 3. Initial-amber data olleted by the PCI Fast Team from nine sites in eight states. The red lines show proposed ±50% ½ in. tolerane. Figure: PCI Fast Team with modifiation by econstrut. variation in support loations is illustrated using the example girder. If it is lifted and stored on supports that are 10 ft from the ends, the amber in the example used in the previous setion hanges by about 9%. If prestress is higher than the theoretial value by 5% and selfweight is lower by 5%, both of whih are quite plausible, the net amber in the example in the previous setion would inrease by 13%. Initial Camber Tolerane Limits Beause of the random variability of the influening parameters, it is diffiult to aurately predit initial amber immediately after strand detensioning. If the girder onrete is allowed to ool for 7 hours, predition auray may be most optimistially within ±5%. Aurate formulas, suh as Eq. 1 and, and values of the modulus of elastiity refleting aggregate type and onrete strength would be assumed to be used. However, the designer is not likely to know produer-speifi materials, environmental onditions, and prodution praties in advane. The PCI Tolerane Committee has been debating in reent years how to update the tolerane limits for amber in bridge beams that are given in PCI MNL-116 4, in order to aommodate reent hanges in tehnology. Conrete strengths in the 8 to 1 ksi range, 0.6-in.-diameter strands, and more effiient I-girder shapes have been in ommon use, resulting in pretensioned produts as long as 00 ft. A Fast Team was formed by the PCI Committee on Bridges and the Bridge Produers Committee to reommend adjustments to the urrent MNL-116 toleranes to aount for the reent hanges in pratie. Their reommendation is shown in Fig. 3. It essentially sets the tolerane limits on amber variane from the predited value at 0.1% of the produt length with an upper limit of 1½ in. and no lower limit. Even with this proposed removal of the urrent upper limit of 1 in., the Fast Team report indiated that the perentage of out-of-tolerane girders longer than 80 ft was still 1%, ompared to the urrent 37% level (using the 1 in. upper limit). Aordingly, the Fast Team stated, out of tolerane amber should not be a sole soure for rejetion. While this sentene is well intentioned and justified, it seems to be in onflit with the onept of tolerane enforement that is expeted in a tolerane manual. Proposed Initial Camber Tolerane Beause amber is an important quantity that an be easily measured, amber tolerane limits are expeted to ontinue to be required by most owners. Based on the author s experiene with this topi for nearly 40 years, and on reent disussions by PCI ommittees, produer groups, and state highway agenies, inluding Colorado, Washington, Iowa, and Pennsylvania, the following reommendations are proposed for initial amber of prestressed beams, whih differ from the reommendations of the PCI Fast Team: Initial amber should be measured 7 to 96 hours after beam onrete plaement and after the beam has been set on storage supports. This would allow for the internal onrete temperature to reah equilibrium with the ambient air and for the storage span to be set. Measurements should 40 ASPIRE, Spring 015
be made early in the morning when the girders should have a neutral thermal gradient. For predited amber 1 in., tolerane is ± ½ in. For predited amber > 1 in., tolerane is ±50% of the predited amber. Out-of-tolerane produts should be further investigated by qualified personnel to identify the presene of possible defiienies. Camber alone should not be the sole ause of rejetion. Camber Variability at Dek Plaement Camber predition at time of dek plaement is needed to establish elevations for beam seats and for formwork for the dek. This is neessary so that the top of road elevation and the overhead learane below the bridge are onsistent with design requirements. Conrete reep and shrinkage ause prestress to be lost. In addition, reep auses the beam to ontinue to amber with time. Creep and shrinkage are funtions of the onrete ingredients, setion dimensions, and environmental onditions. Furthermore, it is not known in advane how muh time will elapse between girder prodution and dek plaement. Camber does not always grow between initial storage onditions and dek plaement. This observation has reently been reported for relatively long beams. The reep multiplier for prestress effets (amber) is not as large as the reep multiplier for beam self-weight beause prestress ontinues to derease with time. For example, a 10 in. initial amber due to prestress multiplied by a 1.7 reep fator is 17 in. An 8 in. defletion due to beam self-weight multiplied by a.0 reep fator is 16 in. The net predited amber at dek plaement is 1 in. This is ompared to an initial amber of 10 8 = in. Methods of aurate predition of amber at time of dek plaement are summarized in the artile by Tadros et al. 1 Several states, in ollaboration with designers and preast produers, have developed their own reep multipliers to aount for amber growth between prestress release and dek plaement. It would seem reasonable to show upper and lower bound amber multipliers, based on loal prevailing onstrution and environmental onditions. For example, Washington State guidelines show a lower bound of 50% of the amber at 40 days, and an upper bound of 100% of the amber at 10 days. The author reommends a multiplier to be determined by eah preaster for the region served by their ompany. For example, Supplier X serving Western State Y would provide the owner with a lower bound and upper bound multipliers of 0.9 and.6 applied to initial amber to predit amber at time of dek plaement. The data presented in Fig. 4, whih has been supplied by Troy Jenkins of Northeast Prestressed Produts, illustrates amber variability at 10 days for girders produed by his ompany in several states in the Northeast. The figure shows that only a few points fall outside the proposed amber toleranes indiated by the red lines. It is suggested that the PCI Committee on Bridges and Bridge Produers Committee should onsider setting up uniform national guidelines for ahieving this important task. Aommodating Differenes There are two options for aommodating differenes between predited and measured amber at dek plaement. Measured amber larger than predited amber Assume for this disussion that 1-1 Figure 4. Measured amber at 10 days. Red lines show proposed ±50% ½ in. tolerane. Data: Northeast Prestressed Produts. ASPIRE, Spring 015 41
predited amber for a 150-ft-span beam is 3 in. while the measured amber is 6 in. The designer had allowed for a ast-in-plae onrete haunh of 1 in. above the top flange of the beam at midspan. The simplest solution is for the owner to allow raising the roadway by to 3 in. Alternatively, the girder seats ould be set to 3 in. lower than previously speified. This option would require appropriate preplanning. Measured amber smaller than predited amber Assume for this disussion that predited amber is 3 in. while the measured amber is 1.5 in. The seats may be raised to avoid infringing on overhead learane below the bridge, if this is a fator, and to avoid exessive haunh onrete. Also, adequate drainage needs to be heked to avoid water ponding on the bridge. Referenes 1. Tadros, Maher K., F. Fawzy, and K. Hanna. 011. Preast, Prestressed Girder Camber Variability, PCI Journal, Vol. 56, No. 1: Preast, Prestressed Conrete Institute (PCI).. Tadros, M. K., N. Al-Omaishi, S. J. Seguirant, and J. Gallt. 003. Prestress Losses in High-Strength Conrete Bridge Girders. Report 496. National Cooperative Highway Researh Program (NCHRP). Washington, DC: Transportation Researh Board. 3. Davison, Bill. 013. Predition of Time-Dependent Stresses and Defletions in Prestressed Conrete Girders from Start of Fabriation to End of Servie Life, M.S. Degree Thesis, University of Washington, Seattle, WA, 013, Advisors John Stanton and Mar Eberhard, 158 pp. 4. PCI. 1999. Manual for Quality Control for Plants and Prodution of Strutural Preast Conrete Produts. MNL-116, 4th edition: PCI. Dr. Maher Tadros is prinipal with econstrut in Omaha, Neb. MOVE THE HEAVYWEIGHTS! 1 Timber Lane Marlboro NJ 07746 USA tel: (73) 46-677 fax: (73) 46-6355 e-mail: sales@hilmanrollers.om 4 ASPIRE, Spring 015