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576 This appendix provides methods of estimating the restraining moment developed in prestressed girders when girders are made continuous over supports, as well as meth- ods to mitigate the problem. D.1 bAckground In simple-span noncomposite bridges, time-dependent deformations result in little or no change in the distribution of forces and moments within the structure. However, continuous multispan composite bridges are statically indeterminate. As a result, in- elastic deformations that occur after construction will generally induce statically inde- terminate forces and restraining moments in the girders. Sources of inelastic deformation include concrete creep and shrinkage and temper- ature gradients. For example, a common type of jointless bridge construction consists of precast, prestressed girders connected with a continuous cast-in-place deck slab, as illustrated in Figure D.1. The girders are simply supported for dead load but may be considered continuous for live load. Continuity is established with deck steel as nega- tive moment reinforcement over the piers. Commonly, a positive moment connection is also provided in the diaphragms. It has long been recognized that positive secondary moments develop in the con- nection at piers of continuous prestressed concrete bridges when the deck is cast at a relatively young girder age (Freyermuth 1969). Creep of the girder concrete under the net effects of prestressing and self-weight will tend to produce additional upward camber with time. The piers prevent this upward movement. When girders are made continuous at a relatively young age, it is possible that positive moments will develop at the supports over time, as shown in Figure D.2. D RESTRAiNT MOMENTS
577 Appendix D. RESTRAiNT MOMENTS Deck Reinforcement M M = Positive Restraint Moment Positive Reinforcement M M Figure D.1. A typical precast prestressed bridge simply supported for dead load and made continuous for live load. Conversely, differential shrinkage, with the newer deck slab concrete shrinking more than the girder concrete, causes the continuous structure to bow download. Dif- ferential shrinkage has a tendency to reduce the positive moment due to creep or result in negative secondary moments at the supports. In addition to creep and shrinkage of concrete, temperature gradients can play a major role if the girders are made continuous. Solar heating of the top deck will tend to produce upward camber, adding to the positive restraint moment caused by creep. Large restraining positive moment can cause cracking in the bottom flange near the pier locations. Heat of hydration in the cast-in-place deck concrete can have a miti- gating effect on the development of positive restraint moment. The cast-in-place deck may be heated to a temperature that is higher than the supporting girder temperature by heat of hydration during the initial hydration when the concrete is still plastic. Contraction of the deck concrete with subsequent cooling after the concrete has hard- ened results in a downward deflection, thereby reducing the positive restraint moment caused by creep and solar heating. NCHRP and FHWA funded an experimental and analytical research program on the behavior of continuous and jointless integral abutment prestressed concrete bridges with cast-in-place deck slab (Oesterle et al. 1989, 2004a, 2004b). Results of the analytical studies (Oesterle et al. 2004a) showed that the age of the girder when the deck was cast was the most significant factor in determining whether positive or negative restraint moments occurred at the interior transverse joints over the piers in response to the interaction of creep and shrinkage. Results of analytical and experimen- tal research (Oesterle et al. 1989, 2004a, 2004b) indicated that the live load continuity Figure D.2. Restraint against upward movement, positive secondary moment.
578 DESiGN GUiDE FOR BRiDGES FOR SERviCE LiFE of the bridge may be reduced significantly with long-term and time-dependent loading effects and with thermal effects. In the experimental part of the jointless bridge research (Oesterle et al. 2004a, 2004b), testing of materials, bridge components, and a full-scale girder indicated that 1. Expected shrinkage of the deck concrete did not occur in the concrete in the out- door environment of Skokie, Illinois. Thus, the effects of deck shrinkage to miti- gate the effects of girder creep did not occur. 2. Heat of hydration effects in the cast-in-place deck concrete can have a mitigating effect on the development of positive restraint moment. 3. Daily temperature effects of heating and cooling of the deck with respect to the girder have a significant effect on restraint moments. Solar heating of the deck causes positive restraint moments of the same order of magnitude as the moments caused by girder creep and are additive to the moments caused by creep. 4. Tests on a full-scale girder that was monitored and loaded periodically with simu- lated live load on sunny days and cloudy days during different seasons over an 18-month time frame demonstrated that positive restraint moment and the re- sulting cracking at the transverse connection significantly reduced continuity for live load. Using change in beam reactions under application of live load to assess continuity, the lowest measured percentage of full live load continuity was 48% measured on a cloudy day in summer. 5. Continuity induces restraint moments, and effective continuity requires assessment considering all loads. Effective continuity in the test girder was assessed using the distribution of total reactions supporting the test girder, which included the ef- fects of dead load, live load, and restraint moments. Effective continuity is defined as 100% if the distribution of total reactions corresponds to the combination of simply supported dead load reactions plus fully continuous live load reactions. Effective continuity is 0% if the distribution of total reactions corresponds to the combination of simply supported dead load reactions and simply supported live load reactions. The measured effective continuity in two of the live load tests in the jointless bridge study was negative (i.e., less than 0%). That is, the total midspan positive moment in the tested âcontinuousâ girder was slightly higher than the anticipated positive moment if the girder were a simply supported girder for both dead load and live load. 6. The positive moment due to combined creep and temperature effects in the test girder resulted in stresses in the positive moment reinforcement in the connection over the pier that reached or exceeded yield stress. The results of this research indicated that use of a positive moment connection in the diaphragms is not beneficial in determining the net resultant midspan service-level stresses under dead, live, and restraint loads. Without a positive moment connection at the supports, effects that would tend to produce a positive restraint moment (creep in the prestressed girders and solar heating of the deck) will likely cause a crack to form at the bottom of the diaphragm concrete between the ends of the girders. With
579 Appendix D. RESTRAiNT MOMENTS application of live load that would tend to produce a negative moment at the sup- port, the crack at the bottom of the diaphragm concrete has to close before full nega- tive moment develops. The net effect is the loss of some live load continuity, which, depending on the parameters, can range from 0% to 100% of live load continuity. If effects that would tend to produce a positive restraint moment are large enough, the crack at the bottom of the diaphragm can remain open under live load, and the girder acts as if it is simply supported. If a positive moment connection is provided, a crack will still likely form at the bottom of the diaphragm concrete from effects that tend to cause positive restraint moment. The positive moment connection will decrease the crack width, but a positive restraint moment will develop. The positive restraint moment superimposed on the live load negative moment will negate, at least in part, the beneficial effects of the nega- tive moment continuity connection over the piers (for service load stresses). Studies (Oesterle et al. 1989, 2004a, 2004b; Mirmiran et al. 2001) have shown that the effect of the crack at the bottom of the diaphragm that would form without the positive moment connection is essentially equivalent to superposition of a positive restraint moment that would form if a positive moment connection were provided (assuming the amount of positive moment reinforced provided was not excessive). If effects that tend to cause negative restraint moments in the connection over the supports predominate, positive moment reinforcement is not needed. Therefore, these studies indicated that there is no net benefit, in terms of service-level stresses in the prestressed girder, by providing positive moment reinforcement in the transverse connections. It is understood, however, that there may be benefit in terms of structural integrity for providing the positive moment reinforcement. The results of recently completed NCHRP Project 12-53 are included in NCHRP Report 519 (Miller et al. 2004). This project was carried out to further examine the behavior of simple-span precast, prestressed girders made continuous by connections at the transverse joints over the piers. The focus was on the effectiveness of the posi- tive moment connection and on design criteria for this connection. Results of ana- lytical studies (Mirmiran et al. 2001) were similar to those reported in the previous NCHRP study (Oesterle et al. 1989). That is, if positive restraint moments develop, these restraint moments must be added to the moments caused by dead and live load, and the net positive moment at the midspan is essentially independent of the amount of positive moment reinforcement provided in the transverse connection (assuming the amount of positive moment reinforcement provided is not excessive). In addition, analytical studies indicated that cracking in the transverse joint decreases live load continuity. NCHRP Project 12-53 also included experimental studies. Live load testing indi- cated that, contrary to analyses results, the continuity with application of live load was near 100% unless the positive moment crack at the connection became very large. The full-scale testing result in the NCHRP 12-53 study, with essentially no live load continuity lost due to positive moment cracking, differed from the analytical results in the NCHRP studies (Oesterle et al. 1989; Mirmiran et al. 2001) and the result of full-scale testing in the jointless bridge study (Oesterle et al. 2004a, 2004b). However,
580 DESiGN GUiDE FOR BRiDGES FOR SERviCE LiFE live load continuity in the NCHRP 12-53 study was assessed using change in reactions with application of live load. It is not clear how restraint moment present in the test specimen connection was considered. A reason provided in NCHRP Report 519 for the difference between the analytical studies and the experimental studies was that the observed positive moment cracks did not extend into the top flange until the crack was very large, but that in the analytical model, the crack extends into the top flange as soon as it forms. In the NCHRP 12-53 experimental beams, however, the effects of concrete creep were simulated by apply- ing posttensioning near the bottom flanges after the diaphragm concrete was cast. Posttensioning rods were dead-headed at the ends of the girders on each side of the diaphragm and used to apply a relatively concentrated load near the bottom flanges at the end of the girders. The additional compressive strain due to the posttensioning was intended to simulate the creep strain in the girders due to the pretensioned prestress and produce simulated positive moment cracks in the bottom of the diaphragm con- crete. Applying the posttensioning forces concentrated near the bottom at the ends of the girders, however, may have distorted the plane of the ends of the girders so that the change in crack width over girder depth did not simulate an expected positive moment crack in an actual bridge. Experimental tests in the jointless bridge study (Oesterle et al. 2004a, 2004b) were carried out with full-scale girders with positive moment cracks in the diaphragm that were primarily the result of actual long-term creep in the girders due to the original pretensioned prestress combined with temperature gradient caused by actual solar heating. Several results from the NCHRP 12-53 full-scale tests were similar to those observed in the jointless bridge study, including 1. The shrinkage strains in the deck concrete were significantly less than expected. 2. The effects of heat of hydration in the deck concrete were significant. 3. Daily thermal effects were significant. On the basis of the analyses and testing, recommendations for the positive moment connection in NCHRP Report 519 included 1. The positive moment connection should be provided and designed for the cal- culated moment due to dead, live, and restraint moment. At least minimum re- inforcement should be provided for a moment equal to 0.6 M cr, where Mcr is the cracking moment of the connection. Also, the design moment should not exceed 1.2 Mcr because providing additional reinforcement is not effective. If the design moment exceeds 1.2 Mcr, the design parameters should be changed. The easiest change to reduce the positive moment is to specify a minimum age of the girder at the time of making the continuity connection. 2. If the contract documents specify that the girders are a minimum age of 90 days when continuity is established, the restraint moment does not have to be calcu- lated. This is based on the observation from surveys and analytical work that if the girders are more than 90 days old when continuity is formed, it is unlikely that time- dependent positive restraint moments from concrete creep and shrinkage will form.
581 Appendix D. RESTRAiNT MOMENTS 3. The transverse connection can be considered fully effective if âthe calculated stress at the bottom of the continuity diaphragm for the combination of superimposed permanent loads, settlement, creep, shrinkage, 50% live load and temperature gradient, if applicable, is compressive.â Results presented in NCHRP Report 519 were used to provide extensive and comprehensive revisions and additions to Article 5.14.1.4 (Bridges Composed of Simple Span Precast Girders Made Continuous) in the fourth edition of the LRFD Bridge Design Specifications (LRFD specifications) (AASHTO 2007). Based on Article 5.14.1.4.1, the connections between girders should be designed for all effects that cause moments at the connections, including restraint moments from time-dependent effects. Note that although restraint moment due to thermal gradient is not specifi- cally mentioned in Article 5.14.1.4.1, it should be included. However, Article 5.14.1.4 includes the following two exceptions regarding the need to design for the restraint moments: 1. Per Article 5.14.1.4.1, multispan bridges composed of precast girders with conti- nuity diaphragms at interior supports that are designed as a series of simple spans are not required to satisfy Article 5.14.1.4. 2. Per Article 5.14.1.4.4, if contract documents require a minimum girder age of at least 90 days when continuity is established, then a. Positive restraint moments caused by girder creep and shrinkage and deck slab shrinkage may be taken as zero, b. Computation of restraint moments shall not be required, and c. A positive moment connection shall be provided as specified in Article 5.14.1.4.9. D.2 deSign recommendAtionS This section provides various alternatives for handling the positive moment developed in continuous prestress girders. D.2.1 Restraint moments in Prestressed Concrete girders In general, it is recommended that LRFD specifications Article 5.14.1.4 should be followed in the design of jointless bridges constructed with precast prestressed girders made continuous for live load. However, the further considerations discussed in this section should be taken into account. D.2.1.1 Thermal Effects Calculated thermal gradient stress caused by the combined internal restraint and sec- ondary continuity moments can be very high, particularly when combined with other secondary effects (Oesterle et al. 2004a, 2004b). NCHRP Report 519 states that daily thermal effects were significant and mentions that they should be considered in de- sign. However, results of analyses and example calculations included in the report
582 DESiGN GUiDE FOR BRiDGES FOR SERviCE LiFE to demonstrate that restraint moment is near zero if the girder age is at least 90 days when continuity is established did not include the effects of thermal gradient. Also, although the commentary to LRFD specifications Article 5.14.1.4.2 mentions temper- ature variation as a cause of restraint moments, Article 5.14.1.4 does not specifically address design considerations for thermal effects. It is commonly considered that ther- mal effects are self-limiting for strength limit states and can generally be disregarded. However, prestressed girders also have to be designed for service-level and thermal stresses in continuous prestressed concrete bridges. D.2.1.2 Differential Shrinkage Effects The results of the FHWA jointless bridge project indicated that expected shrinkage based on theoretical shrinkage models and on laboratory shrinkage tests did not occur in the outside environment. NCHRP Report 519 (Miller et al. 2004) included a similar observation; however, analyses and example calculations included in NCHRP Report 519 to demonstrate that restraint moment is near zero if the girder age is at least 90 days when continuity is established did include the effects of differential shrinkage as determined from a theoretical shrinkage model. Results of the analyses presented in the report show that early negative moment due to differential shrinkage between the deck and the girder essentially offset the longer-term positive moment that developed due to creep in the prestressed girder. D.2.1.3 Combined Creep, Shrinkage, and Thermal Effects The effects of creep in the prestressed girders and solar heating of the deck are additive with respect to inducing positive moment at the connection over the supports. When creep and solar heating are combined with an absence of differential shrinkage, it is not clear, even in bridges constructed with 90-day-old girders, that positive moments will not be significant. D.2.1.4 Potential Negative Moment Limiting construction to the use of girders with a minimum age of 90 days will in- crease the potential that factors that induce negative restraint moments over the sup- ports may predominate. Increasing the potential for negative moment increases the risk of cracking in the deck over the support regions. Deck cracking over the support regions may have a more detrimental effect on long-term durability of a bridge than positive moment cracking in the diaphragm. D.2.1.5 Uncertainties in Determining Restraint Moments In addition to concrete creep, shrinkage, and solar heating of the deck, various other effects can contribute significantly to restraint moments. These effects include differen- tial settlement of supports; heat of hydration of the deck concrete during construction; variation of the coefficient of thermal expansion between the girder and the deck; and seasonal moisture changes in the concrete that cause shrinkage reversals. In addition, in jointless bridges with integral abutments, additional forces may be imparted on the
583 Appendix D. RESTRAiNT MOMENTS positive moment connection by the restraint of the abutment to longitudinal tempera- ture movements. All of these factors contribute to restraint forces within a continuous jointless bridge structure. In some instances, these factors are additive, but in others, they oppose one another. The magnitudes of these effects to be considered in design and the critical combinations are uncertain. Although methods are available to esti- mate restraint moments due to all of these effects, the moments that actually occur may be significantly different from the estimated values. D.2.1.6 Effects of Excessive Positive Moment Reinforcement In spite of all the uncertainties regarding magnitudes and combinations of restraint moments, there have been few cases of distress related to these secondary stresses. In general, concrete cracking and reinforcement yielding will diminish the stresses caused by the secondary effects. However, an overly strong connection combined with the effects of creep and thermal gradient may result in excessive positive restraint moment (ENR 1994; Alabama DOT 1994; Telang and Mehrabi 2003). A strong posi- tive moment connection increases the positive moment along the span and in some cases may result in cracking in the beams. Figure D.3 shows an example bridge (Telang and Mehrabi 2003) with significant flexural cracking of this type. The flexural crack occurred at the end of the embedment of the positive moment connection bars near the ends of the prestressed girders with a large quantity of positive moment reinforcement. In contrast, Figure D.4 shows the end region of another girder in the same example bridge where cracking and spalling occurred within the diaphragm. The diaphragm cracking and spalling were associated with positive moment connection bars bent out of place during erection (because of constructability issues) for several girders in the bridge such that the connection bars became ineffective. However, no flexural cracking occurred within the span of these girders. Figure D.3. Cracks near girder supports.
584 DESiGN GUiDE FOR BRiDGES FOR SERviCE LiFE Because of the uncertainty associated with calculations of positive continuity moments resulting from the variability of the creep and shrinkage effects, tempera- ture gradient, differential coefficient of expansion effects, locked-in heat of hydration effects, settlement, and cracking, calculations to determine restraint moments are com- plex and probably unreliable. To eliminate the need to attempt to calculate restraint moments and to simplify the design, the following recommendations (Options 1 and 2 below) for positive moment connections were developed on the basis of the work in the NCHRP projects (Oesterle et at. 1989; Mirmiran et al. 2001; Miller et al. 2004), the FHWA jointless bridge project (Oesterle et al. 2004a, 2004b), and the LRFD speci- fications (AASHTO 2007). D.2.1.6.1 Option 1 for Positive Moment Connections Positive moment connection reinforcement at the piers should not be provided. This approach prevents the development of significant positive restraint moments in the pier diaphragms (and eliminates constructability issues with the overlapping reinforce- ment). The girders should be analyzed as simply supported for dead plus live loads at service levels. This practice is allowed by LRFD specifications Article 5.14.1.4.1; it eliminates the requirement to calculate restraint moments (without the need to age girders prior to construction); and, as stated in the commentary of the LRFD specifi- cations, it has been used successfully by several state departments of transportation. D.2.1.6.2 Option 2 for Positive Moment Connections If positive moment connections are used to improve structural integrity and to pro- vide some crack control, as recommended in the commentary of LRFD specifications Article 5.14.1.4.1, it is suggested that the positive moment capacity (fMn) be limited to the minimum moment of 0.6 Mcr recommended in the LRFD specifications. Note Figure D.4. Crack and spall at diaphragm over pier support.
585 Appendix D. RESTRAiNT MOMENTS that Mcr should be determined using the properties of the diaphragm concrete. If addi- tional reinforcement is used to increase crack control, the upper limit recommended by the LRFD specifications of fMn = 1.2 Mcr should not be exceeded. To eliminate the need for calculation of restraint moments, the girders should be analyzed as simply supported for dead plus live loads at service levels as allowed by LRFD specifica- tions Article 5.14.1.4.1. However, positive restraint moments are likely to occur. In spite of this, additional stresses in the girders due to positive restraint moment can be minimized by limiting the capacity of the connection fMn so that the connection acts like a fuse that will yield before the development of detrimental stresses. Therefore, the girder service load stresses should be checked along the length of the girder under simple supported dead and live loads plus fMn of the positive moment connections superimposed on the spans, such that the allowable tensile stress in the bottom of the beam of 0.19 fcâ² ksi (6 fcâ² psi) is not exceeded. Particular attention should be paid to the region of termination of the positive moment steel if mild reinforcement is used for the connection. For both Options 1 and 2, the girderâdiaphragm interface should consider details to allow relative movement between the bottom of the girder and diaphragm concrete for girders partially embedded in the diaphragm concrete. For the exterior surface of fascia girders, providing a sealed crack control joint at the beamâdiaphragm interface should be considered. Negative moment reinforcement should be provided over the supports, and dia- phragm concrete should be provided between the ends of the girder bottom flanges. Negative restraint moments may develop, for example when the deck and diaphragms are cast when the concrete girders are older. However, parametric studies carried out in the FHWA jointless bridge project indicate that, with high restraint moments, crack- ing occurs in the deck, and sufficient moment redistribution occurs to prevent the deck reinforcement from becoming overstressed. Therefore, restraint moments do not have to be calculated. Negative moment reinforcement in the deck can be designed for applied dead and live load moments calculated on the basis of uncracked section properties. It can be assumed that the girder is simply supported for dead load and fully continuous for live and superimposed dead loads because of the parapets, barrier walls, wear surface, and so forth. Because the deck in the negative moment region is considered reinforced concrete, the negative moment connection is only designed for strength limit states. D.2.2 Restraint moments in Composite Steel Bridge girders Temperature gradients and differential coefficients of thermal expansion in continu- ous composite steel beams produce both positive and negative restraint moments, but the shrinkage of deck concrete and the heat of hydration locked-in strains produce negative restraint moments. Deck slab cracking partially relieves negative restraint moments.
586 DESiGN GUiDE FOR BRiDGES FOR SERviCE LiFE The parametric studies in the FHWA jointless bridge project indicate that stresses in both the concrete deck slab and steel beams are not excessive under the combination of dead and live load forces combined with positive restraint moments. Consequently, explicit calculations considering positive restraint moments are not necessary. The analyses for effects of negative restraint moments in composite steel beams indicated that, in general, if negative moments are high, deck cracking results in re distribution, and calculated stresses are not excessive. However, analyses also included the effects of a negative temperature gradient, which produces negative restraint moments, combined with dead and live load and restraint of longitudinal expansion provided by passive pressure in backfill and the lateral force in the piles of integral abutments. These analyses indicated that, under certain circumstances, calcu- lated compressive stresses in the bottom flange of the steel beams near interior sup- ports may be excessive, even after allowance for redistribution of the stresses because of deck cracking. On the basis of the parametric studies, the combination of loads described above may become critical for larger beam spacing. Calculations indicate that, for stringer spacing equal to or greater than 7 ft for A36 beams and 9 ft for A572, Grade 50 beams, an explicit check of the effects of the combined load effects of dead and live loads, negative temperature gradient, and restraint of longitudinal expansion may be required to check for lateral torsional buckling of the bottom flange near inte- rior supports.
