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79 Several critical issues relative to the design of concrete box- girder bridges were identified at the beginning of the project. Methods exercised in this study that were intended to address these issues consisted of a survey of the state of practice, a re- view of published literature, analytical studies of global and local response, discussions of the experienced research team that attempted to reach a consensus on critical design re- quirements, and a review by an advisory panel with expertise in this area of study. Several conclusions were drawn from the research conducted in this project. In many cases, these conclusions have trans- lated into recommended AASHTO LRFD Specification pro- visions as presented in Appendix A. Analysis guidelines were also developed to assist designers in performing response analysis. These are provided in Appendix C. Other conclu- sions found that current design practice was adequate and did not require a change. The following paragraphs discuss con- clusions relative to the critical issues defined at the beginning of the project. ⢠Applicability. Curved concrete box-girder bridges are used throughout the United States. Most modern bridges of this type are prestressed. A review of the state of practice in the United States found that both single- and multi-cell box-girder bridges are widely used. The predominate construction type in some West Coast states is multi-cell box-girder bridges cast-in-place on falsework. This type is also widely used throughout the United States. Single-cell box-girder bridges are also common, but tend to dominate the type of box-girder construction used on the East Coast. East Coast construction also uses more precast segmental construction than is used on the West Coast where cast- in-place construction is more dominant, even when seg- mental methods are used. Some states do not use this type of bridge on a regular basis. Curved spread box beams are an emerging structure type, but are not widely used at this time. Both single- and multi-cell concrete box-girder bridges are covered by this project. They may be cast-in-place or precast and may be constructed segmentally or on falsework. ⢠Appropriate levels of analysis and design. Selecting the type of global analysis that should be used for curved con- crete box-girder bridges is one of the most important issues addressed by this project. Published research shows that these types of bridges are most accurately analyzed using 3-D finite element or similar techniques. Unfortunately, these analysis methods are tedious and in general not prac- tical for production design work. Also, in many cases, more simplified analysis methods will produce acceptable results. To determine the range of applicability of various analysis methods, a detailed global analysis study was undertaken. The first step was to identify a more simplified 3-D analy- sis approach that would yield results comparable to the more detailed finite element technique. This was accom- plished with the grillage analogy approach. In this method, the bridge is simulated as a grillage of beam elements in the longitudinal and transverse direction. Guidelines for preparing the computer model, performing the analysis, and interpreting results were developed and are included in Appendix C. From the designerâs point of view, this analysis method has advantages over the finite element approach. Besides being a smaller and less computationally intense analytical model, the grillage analogy produces results in terms of the structural members commonly con- sidered by the designer. This makes it easier to design these elements, whereas the finite element approach would in- volve considerable post processing of analytical results to accomplish the same goal. Second, the limits of applicability of three analytical ap- proaches were assessed. The three methods considered were 1. Plane Frame Analysis. This allows the bridge to be ana- lyzed as if it were straight. 2. Spine Beam Analysis. This is a space frame analysis in which the superstructure is modeled as a series of C H A P T E R 6 Conclusions
straight, chorded beam elements located along the cen- terline of the superstructure. 3. Full 3-D Analysis. This includes several different sophis- ticated approaches that include the grillage analogy de- scribed above as well as the finite element and other sophisticated approaches. Extensive parameter studies were performed that in- cluded the effects of structural framing (simply supported or continuous), span lengths, radius of curvature, cross section (including bridge width), and bearing configura- tion on the response of bridges. These studies included both grillage analysis and spine beam analysis for which plane frame analysis constituted the case of a bridge with a very large radius. These studies showed that the radius-to- span length ratio as represented by the central angle be- tween two adjacent supports was the dominant parameter that determined the accuracy of the various analysis meth- ods. The span length-to-width ratio (aspect ratio) of the superstructure also had a minor effect. Based on these pa- rameter studies, the following limits for the various types of analysis are recommended: 1. For central angles less than or equal to 12 degrees, plane frame analysis is acceptable. 2. For central angles between 12 and 46 degrees and an aspect ratio above 2.0, spine beam analysis is required. 3. For central angles between 12 and 46 degrees and an aspect ratio less than 2.0, sophisticated 3-D analysis is required. 4. For central angles greater than 46 degrees, sophisticated 3-D analysis is required. 5. For all bridges with otherwise unusual plan geometry, sophisticated 3-D analysis is recommended. ⢠Section properties and member stiffness. The section properties and member stiffnesses that should be used in the spine beam analysis and the grillage analogy analysis are critical and are discussed in the analysis guidelines pre- sented in Appendix C. For the spine beam analysis, the cross-sectional area and the three rotational moments of inertia are important. In the case of the grillage analogy, all six section properties of each beam member are required. Special formulae for some of these section properties are used to simulate various aspects of the behavior of a curved concrete box-girder bridge. This in turn requires special interpretation of some of the results. ⢠Critical position of live loads. The number and position of the live load lanes in the transverse direction as well as their position along the longitudinal axis of the bridge are critical for curved concrete box-girder bridges. Given the number of possible load positions, it will be desirable to use the live load generating capabilities of sophisticated commercially available software to rigorously envelope the live load response. This can be a daunting task if such software is not used. Fortunately, the whole-width design approach as described in the LRFD specifications was shown to yield conservative results when used in conjunction with the plane or spine beam approaches. This will greatly simplify the effort of the designer in determining live load response. When using this approach, it is important to distinguish between the longitudinal response along each of the webs and the effect of torsion across the whole section. When torsional response is being assessed by the whole-width design approach, the number of live load lanes should be reduced to the actual number of lanes that can fit on the cross-section and adjusted by the multiple presence factor and dynamic load factor (for truck loading only). When a 3-D model of the bridge (either a spine beam or grillage analogy model) is being used, it is important to consider the transverse position of prestress tendons. The length of the various tendons will have an effect on friction losses and tendons will also produce a transverse response in the bridge superstructure. Vehicular effect may be assessed using the method pre- scribed in the LRFD Bridge Design Specifications. Other load conditions such as centrifugal forces, breaking or acceleration forces, wind, etc. should be determined according to the LRFD Specifications and then applied to the spine beam model. If the plane frame approach is being used, these loads may be analyzed in the same manner as if the bridge were straight. The effect of bridge supereleva- tion can usually be ignored. ⢠Torsion design. The design of concrete box sections for torsion is covered in the current AASHTO LRFD Specifi- cations. However, some clarification of these requirements is in order. These were discussed in the review of published literature included in Chapter 3. Torsion demands usually translate to additional lateral shear demands in the webs of concrete box-girders. These may be determined from both the spine beam and grillage analogy methods. In the case of the spine beam analysis, the torsion de- mands are taken directly from the torsion forces generated in the spine beam. These forces must be transformed into shear flow around the perimeter of the box section. This shear flow will increase the effective shear in one web while decreasing it in another. Webs should be designed for the combined flexural and torsional shear. In the case of the grillage analogy, the effects of torsion on web shear are partially accounted for because each web is explicitly included in the analytical model. However, be- cause of the way torsional stiffness of the superstructure is distributed to the individual longitudinal members of the grillage model, the total effect of torsion on the entire cross section is not completely accounted for by the longitudinal member shear demands. To correct for this deficiency, it is 80
necessary to consider the torsional forces in each of the lon- gitudinal members at a given longitudinal location in the grillage model and apply the sum of these torsions to the entire cross section to obtain residual shear flow about the perimeter of the section. This is done in a manner similar to that used for the spine beam. When this residual shear flow is combined with the flexural shear in the extreme longitudinal members, the correct demands to be used for web shear design are obtained. The procedures to be used for torsion design for both the spine beam and grillage analogy analysis methods are illus- trated in the example problem included in Appendix B. ⢠Tendon breakout. Extensive analytical studies were per- formed to investigate lateral bursting stresses in curved concrete box-girder bridges with internal prestress tendons. The first step in these studies was to verify that the nonlin- ear finite element models used could accurately predict lat- eral tendon breakout behavior observed in experimental studies performed at the University of Texas. The results of the analyses compared well with the experimental results so that there is confidence that both the experimental and analytical results have yielded accurate results. Based on parameter studies conducted using these veri- fied nonlinear finite element techniques and the results of the University of Texas studies, modifications to the spec- ifications for considering in-plane force are recommended. These include 1. A method for assessing the local lateral shear resistance to pullout. These provisions are the recommendations from the University of Texas, which were further veri- fied by the nonlinear finite element parameter studies conducted as part of this study. They also include pro- visions for considering the effect of construction toler- ances, which have been shown by past failures to have a significant effect on web performance and are discussed in Chapter 5. 2. A method for checking flexural cracking of the unreinforced concrete cover over the inside of the prestress tendons. This is a new requirement that applies only to vertically stacked tendons. It is included to prevent maintenance, architectural, and structural problems that can arise due to longitudinal cracking of the web. The results are used to determine the need for web and duct tie reinforce- ment. Vertical duct stacks are limited to three tendons high and concrete cover over the inside of the ducts should be maximized. Generic web and duct tie rein- forcement details are included in the commentary. 3. A method for calculating the regional transverse bending moments within a web. These moments result from the regional transverse bending of a web between the top and bottom slab of the bridge due to lateral prestress forces. When combined with global forces such as flexural shear and torsion, regional transverse bending can re- sult in the need for more stirrup reinforcement in the webs. Regional transverse bending also exacerbates flex- ural cracking of the concrete cover as described in Item 2 above. ⢠Consideration of stresses at critical locations. Several critical stresses should be considered in the design of curved concrete box-girder bridges. These include 1. Axial stresses in the top and bottom slabs and the webs. These stresses result from vertical flexure of the bridge between supports and the primary and secondary effects of longitudinal prestressing. Regional transverse bend- ing of the superstructure may also occur and should be considered when determining these stresses. Because the web lengths vary in a curved bridge, moments and flexural shears in each web may also vary. This effect is best captured in the grillage analogy approach. To best capture it with the spine beam approach, prestress ten- dons should be located at their correct transverse posi- tions with respect to the bridge centerline. 2. Shear stresses in the webs. These stresses result from the flexural and torsional behavior of the superstructure. Torsion results in shear flow around the perimeter of the cross section that should be combined with the flex- ural shear. In continuous superstructures or between the joints in precast superstructures, these shear forces result in diagonal tension stresses that can combine with the flexural tensile stresses resulting from regional trans- verse bending. Stirrup design may be accomplished by combining the reinforcing requirements for each of these actions. At the joints in precast bridges, the shear is carried by a shear friction mechanism. 3. Transverse stresses in the cross section. These stresses can generally be determined using the same methods used for a straight bridge. They govern the design of the deck and soffit. The transverse deck and soffit reinforcing must also participate in carrying the shear flow gener- ated by torsion, but because concrete is often sufficient for this purpose, this is often not a significant consider- ation in design. 4. Flexural and lateral shear stresses in the vicinity of pre- stress tendons. Complex stresses are developed in the webs of curved concrete box-girders due to the lateral forces developed by the curvature of prestress tendons. Simplified methods for assessing these effects have been developed and are included in the recommended LRFD specifications and commentary. Because design for the above forces is often optimized, it is prudent to evaluate these forces at several longitudinal locations along the length of the bridge. Prestress forces and path location, web and slab thicknesses, and the size and spacing of stirrups can be designed accordingly. 81
⢠Bearing load and bearing movement considerations. Both the spine beam and grillage analogy methods of analysis will accurately predict elastic bearing forces if used accord- ing to the criteria outlined in the proposed AASHTO LRFD Bridge Design Specifications and Commentary and the Analysis Guidelines included in Appendix C. Because of the curvature of the structure, the bearing forces at any longitudinal position along the bridge will vary across the width of the bridge. In addition to this, both field experience and time- dependent analysis show that the bearing forces will change over time. The extent of this change is not accu- rately determined by currently available time-dependent software because of the treatment of torsion creep in these programs, but software that takes into account axial creep is thought to give conservative results. In lieu of a time- dependent analysis, elastically determined abutment dead load torsions should be increased by 20%. It is recommended that bearing force capacities be designed to accommodate both initial and long-term conditions. Methods for addressing bearing design when bearing forces are excessive (i.e., either too high or too low) may in- clude, but not be limited to, one or more of the following: 1. Size individual bearings to accommodate the calculated range of bearing forces. 2. Specially design bearings so that they will not be dis- placed if the applied load goes into tension or very low compression. 3. Provide ballast in the superstructure to ensure that the envelope of bearing forces is within an acceptable range. 4. Reshore the structure at its bearing locations prior to setting the bearings and then release the shoring after the bearings are set. 5. Use an outrigger diaphragm to increase the eccentricity of the individual bearings. 6. Place the bearing group eccentric to the centerline of the superstructure in order to make the individual bearing forces more equal. 7. Select bridge framing to better control bearing forces. Balancing the center and end span lengths can mitigate bearing problems. Considering the curvature of long bridges in a spine beam analysis can mitigate excessive design movements at the bearings due to temperature change and possibly elim- inate the need for interior expansion joints. Care should be taken that bearing travel is through the center of movement so that binding of the shear keys does not occur. Prestress shortening may occur along a slightly different orientation. ⢠Diaphragms. Current AASHTO LRFD provisions require that diaphragms be used for curved box-girder bridges with a radius of less than 800 feet, but also allows that they be omitted if justified by analysis or tests. Analytical grillage analogy and finite element studies performed as part of this project demonstrated that interior diaphragms have a min- imal effect on the global response of a curved concrete box- girder bridge with a 400-ft radius and 300-ft span lengths. Therefore, it is proposed that the requirement that interior diaphragms be included in bridges with a radius less than or equal to 800 feet be eliminated. It is recommended that end diaphragms still be used at all supports. ⢠Post-tensioning sequence. Because the curvature of tendons can increase the transverse bending of the super structure and result in tensions on the inside of the curve and com- pression on the outside of the curve, it is recommended that at least one tendon on the inside of the curve be stressed first. With respect to varying the final distribution of prestress forces across the width of the bridge, there does not seem to be any significant advantage in doing this. Although webs to the inside of the curve are shorter and thus theo- retically subject to less dead load and live load bending forces, decreasing prestress forces for this web will be over- come by the transverse bending of the bridge that will put the inside web in tension. Thus it is thought to be impor- tant to model tendons in their correct transverse position for analysis, but a relatively even distribution of prestress forces is desirable. It is theoretically more important for the designer to consider the incidental distribution of prestress forces as allowed by some construction specifications. ⢠Skew effects. Analytical studies were performed to consider the effect of skew at the abutments on the overall response of the bridge. It is commonly known that skew will affect the shears in the web near the obtuse corner of a skewed abutment support. The point of the study was to determine if bridge curvature altered the relationship between the rel- ative response of a skewed and non-skewed abutment. Two skew cases were studied. One case was where the skew occurred at only one of the abutments and the other case was where both abutments were skewed but in opposite directions. The second case is the likely orientation of a curved bridge that crosses over an obstruction that is lin- ear in orientation. In both cases, it was found that the rela- tionship between the response of a non-skewed support and the skewed support followed the same relationship as for a straight bridge. Thus, it was concluded that existing skew correction factors apply to curved concrete box-girder bridges analyzed by the spine beam method. The effect of skew on interior supports was not studied nor were the effects of different abutment skew configura- tions. In all cases, a grillage analogy analysis would capture any effect of skew. This method should be used to analyze any curved concrete box-girder bridges with large skew an- gles at the interior supports or abutment skew configura- tions that vary significantly from those studied. 82
⢠Lateral restraint issues. Horizontal curvature may result in force demands in the lateral direction at the supports if lateral restraint is present and is modeled as rigid elements for computer analysis. Such may be the case for supports consisting of integrally cast abutments or piers. In these cases, lateral restraint should be modeled as the stiffness of the restraining element under consideration. In the case of bearings, however, steel or concrete shear keys usually pro- vide lateral restraint. These are usually provided with a small transverse gap to prevent binding. This gap is large enough to prevent lateral restraint and, for gravity load purposes, should be modeled as a lateral force release. The key to properly considering lateral restraint is to accurately model the actual condition and to use either spine beam or grillage analogy analysis. ⢠Thermal effects. Thermal movement and prestress shorten- ing will result in movements in different directions at the expansion joints in curved structures. This difference should be reflected in a properly conducted spine beam or grillage analysis. Bearings should be capable of travel through the center of movement, although normal gaps provided in shear keys will allow for slight variations in movement. ⢠Time-dependent effects. Because of the interaction between bending moment and torsion in curved bridges, consider- ation of time-dependent effects is important. However, rigorous 3-D analysis to determine the time-dependent effects of torsion is not present in commercially available software. This requires a reliance on the time-dependent software available. Fortunately, torsion creep is expected to mitigate the effect that has been observed at the bearings, and thus this software will tend to yield conservative results for bearing force redistribution. It can be used for design purposes until improved software is developed. Vertical construction cambers can use the results from currently available time-dependent software. In fact, many design engineers interviewed claim to have had good re- sults from 2-D time-dependent analysis. However the bending of tall columns and twisting of the superstructure had to be approximated using elastic 3-D spine beam analysis. In the case of curved bridges, horizontal cambers may be required for segmental construction. A curved concrete box-girder bridge with relatively tall piers in California that was constructed by the segmental cantilever method re- quired a horizontal camber of approximately 3 inches at the pier. In other words, the pier had to be constructed 3 inches out of plumb. ⢠Construction methods. The effect of construction meth- ods on the behavior of curved box-girder bridges is critical. However, the analysis methods studied apply to staged construction analysis as well as cast-in-place on falsework construction. The same parameters can be used to select the most appropriate analysis method except that time-dependent analysis should be used. Commer- cially available software does not consider torsion creep, but should yield generally conservative results and is adequate for design until more sophisticated software is developed. ⢠External post-tensioning deviators. The use of precast construction results in less weight and quicker onsite assembly and is thus increasing in popularity. Deviation blocks or saddles for external prestress tendons in curved precast concrete box-girder bridges may be designed in the same manner as for straight bridges using strut-and-tie methods or as recommended by an experimental study at the University of Texas (Beaupre et al., 1988). For LRFD design of deviators, a load factor of 1.7 should be used for the prestress deviator force and capacity reduction (Ï) factors should be 0.9 for direct tension and flexure and 0.85 for shear. It is recommended that reinforcing bar sizes in de- viation saddles be limited to #5s to ensure the proper de- velopment of this reinforcement. It is recommended that deviation saddles in tightly curved bridges be continuous across the bottom soffit. An- other consideration for curved bridges is that straight seg- ments of tendons cannot rub against the interior of the webs. If necessary, the designer should include extra devia- tion blocks or saddles to prevent this from happening. A de- viation saddle design example, which is reproduced from the University of Texas report, is included in Appendix B. ⢠Friction loss/wobble. The current formulae for determin- ing prestress losses due to friction and wobble apply to curved bridges if the 3-D effects of angle change and tendon length are considered. It is necessary to explicitly consider the difference in tendon length in individual webs and thus prestress tendons should be modeled in their actual trans- verse location in a 3-D spine beam or grillage analogy analysis. Friction losses should be based on a tendon curved in space when a curved bridge is being designed using 2-D analysis techniques. ⢠Web and flange thickness limits. It is recommended that webs and flanges be designed based on structural and constructability considerations. No minimum thickness requirements are recommended by this study. 83
