In a continuous beam, vertical misalignment of the support points generates hyperstatic stresses in the longitudinal and transverse directions. The steel girders of composite bridges are launched without the concrete slab, and the girder is so flexible that longitudinal and transverse stresses due to misaligned launch bearings are rarely a major issue (local effects apart, of course). A prestressed-concrete (PC) deck is much stiffer, as the cross-section is cast in its entirety before launch. Ribbed slabs with double-T section and solid and voided slabs are relatively flexible, but in most cases a PC launched deck has single-cell box section; the high moment of inertia increases the longitudinal effects of bearing misalignment, and the high constant of torsion increases the transverse effects.
At long term, vertical bearing misalignment may often be tolerated in the longitudinal direction, as the time-dependent behavior of concrete diminishes and redistributes the hyperstatic stresses with time. Some extent of vertical misalignment may also be tolerated in the transverse direction, between the two bearings on a pier-cap, as the pier diaphragm avoids distortion of the deck cross-section, and the torsional stiffness of a box girder diminishes the tangential stresses in the webs and slabs due to primary torsion. These load conditions are also relatively rare, as the upper bearing seats are cast along with the rest of the deck or after placing precast segments or units.
During launch, a PC box girder is devoid of diaphragms at the launch supports. When the pier diaphragms are cast along with the rest of the segment, they move with the deck during launch and cannot control cross-section distortion effectively. The launch bearings may be misaligned from the very beginning or may become misaligned with time, the stresses due to misaligned supports are not mitigated by the time-dependent behavior of concrete, and they may cause deck cracking, uplift from the launch bearings, and stress redistribution in the longitudinal and transverse direction. Several causes may generate this type of problems in a launched bridge:
- Elevation errors in the launch bearings due to inaccurate initial positioning, settlement of foundations or the axial flexibility of steel temporary piers under the support reactions applied by the deck. Shimming of the launch bearings may easily correct these errors. The launch bearings are surveyed frequently during launch; topographic targets glued to the front and rear sides of the launch saddles allow visual access from both abutments and control of longitudinal inclination according to the local alignment of the launch cone.
- Geometry imperfections in the deck. These errors are more difficult to detect and may be due to multiple causes. In a PC deck, irregular alignment of the launch surfaces is mostly due to irregular vertical alignment of the extraction rails of the casting cell; when these errors are discovered, the extraction rails are realigned and the geometry irregularities in the deck portion already built cannot be corrected. Because of the repetitiveness of segmental construction, these errors affect all deck segments at the same location and may occur in the longitudinal and transverse direction. In a PC deck, geometry inaccuracies may also derive from irreversible time-dependent deflections accumulated by the deck during the launch stoppages for casting of new segments; these geometry irregularities cannot be corrected but can be controlled with proper design of the launch sequence and post-tensioning, and they typically occur only in the longitudinal direction. In a steel girder, longitudinal and transverse geometry imperfections may derive from fabrication and assembly tolerances in built-up girders and cross diaphragms; primary geometry irregularities are frequently due to the cambered profile of the steel girder, which is rarely a launchable line. Since the cambered profile is attained by assembling rectilinear segments to shape, angle brakes at the field splices also cause local stress concentrations in webs and bottom flanges when passing over the launch bearings.
- Unforeseen events such as breaking of a bearing pad or the expulsion of a neo-flon pad during launch. Such events can be avoided with proper design of launch bearings and training of personnel. Breaking of bearing pads and expulsion of neo-flon pads may occur on only one side of the pier, and therefore their effects mostly develop in the transverse direction.
The effects of the vertical misalignment of launch bearings are different in the longitudinal and transverse direction. The deck is post-tensioned longitudinally, and the launch tendons are designed to allow jacking at every support to replace worn neo-flon pads in case of need. A few design standards specify the bearing misalignment to be considered for the design of launch post-tensioning. For instance, AASHTO specifies that the effects of 5mm elevation tolerances in two adjacent bearings in the longitudinal direction, and of 2.5mm tolerances in the transverse direction, shall be superimposed upon the effects of gravity loads.
Other industry standards are more demanding. In the longitudinal direction, a ±10mm vertical misalignment may be assumed at every launch bearing with the other bearings assumed to be aligned, and the stresses may be enveloped. The 10mm misalignment derives from the assumption of 7mm misplacement and 7mm settlement combined with SRSS rule, and may therefore be diminished in case of stiff foundations and simple deck geometry, or increased in case of a curved deck and flexible foundations. A +10mm uplift may be considered at a launch abutment equipped with Eberspächer launchers, and a ±5mm displacement may be applied to the leading end of the casting cell to consider the flexibility of the extraction rails.
Launch prestressing is often designed for the lower-edge tensile stress at midspan, which is not much affected by misaligned launch bearings. Therefore, different provisions of design standards in relation to the entity of bearing misalignment do not have an immediate impact on the construction cost of a launched bridge. In a continuous beam, the span length diminishes negative bending with quadratic ratio, and launch post-tensioning typically exceeds the minimum demand due to technological constraints related to tendon symmetry, location of the resultant force in relation to the center of gravity of the cross-section, and number of consecutive segments crossed by the launch tendons. For all of these reasons, the longitudinal axial stress due to launch bearing misalignment is often tolerable without immediate increases in launch post-tensioning.
The situation is more complex in the transverse direction, as bottom slab and webs of a single-cell box girder are not prestressed, and transverse spacing of the launch bearings is one order-of-magnitude smaller than longitudinal spacing. Launch bearing misalignment causes torsion and cross-sectional distortion, and the high torsional stiffness of a PC box girder may lead to bearing decompression and deck uplift, which doubles the support reaction on the other bearing and causes transverse bending in the deck, piers and foundations.
During the service life of a PC bridge, the torsional stiffness of the hollow section controls the tangential stress due to eccentric live loads, and the frame stiffness of the cross-section along with the in-plane flexural stiffness of slabs and webs rapidly reduce distortion. In most cases, therefore, important torsional and distortional effects arise only in the presence of eccentric localized loads.
Although the highest localized loads applied to a bridge deck are the support reactions, their transverse eccentricity is generally neglected in the deck design. Fracture of a bearing is a highly improbable event, in-place casting of the deck or the bearing seats avoids significant support eccentricity in the transverse direction, and the pier diaphragms prevent distortion of the cross-section.
In a launched bridge, the cross-sections temporarily over the piers are devoid of diaphragms. A few-millimeter difference in elevation between the two launch bearings may cause torsion, distortion and severe overloading, and the expulsion of a neo-flon pad may cause serious damage to the deck. Without specific design tools, finite-element analysis of 3D models is necessary, which is impractical, requires experience, and involves long modelling time.
In 11 pages, Launch Bearing Misalignment in Launched Bridges explains how to analyze the effects of misaligned launch bearings with a parametric spreadsheet and closed-form equations. The approach is discussed for the general case of a box girder and can be easily extended to steel U-girders, braced I-girders and prestressed composite box girders with steel corrugated-plate webs.
The eManual explores the analytical approach and includes the Excel spreadsheet and its validation by finite-element analysis with SAP-2000. The spreadsheet will help you to analyze the effects of torsion and distortion without a shell-element model, to optimize rebar design for control of transverse bending and deck cracking, and to streamline and accelerate the design of launched bridges.
Spreadsheet and eManual are fundamental productivity tools for the preliminary and final design of incrementally launched bridges and the neo-flon pads and launch bearings used for their construction.