The most characteristic aspect of the design of an incrementally launched bridge is the need to resist transient flexural and shear stresses due to the movement of the deck during launch. Every cross-section of the deck passes cyclically in midspan and above the piers. When in midspan, the cross-section is subject to positive self-weight bending and minimal shear. When over a pier, the same cross-section is subject to negative self-weight bending and maximum shear. Each cross-section must therefore resist transient launch stresses that are substantially different from the service stresses. Thermal stresses and the hyperstatic effects of geometry irregularities in the deck, the time-dependent deformations of a prestressed-concrete (PC) deck, and misaligned launch bearings further complicate the situation.
Although transient in nature, the launch stresses of a PC deck can damage the deck and accelerate deterioration with time, and must therefore be analyzed with care and controlled with appropriate levels of launch post-tensioning.
The steel girders of composite bridges are almost always launched without the concrete slab, and self-weight during launch is only 20-30% of the weight of the final composite section; however, the cross-sections of a built-up girder typically vary throughout the bridge, with different distributions of flange areas and thicker web panels in the final support regions. In a steel girder, prevention of web buckling due to migrating support reactions and structural detailing are the critical aspects of launch design. In both cases, in other words, bridge launching is not as simple as it might appear and leads to high-quality products only if the bridge is designed and constructed properly.
The stress distribution in the deck evolves between two limit conditions. Considering two consecutive piers and a typical span of the deck, the first condition is the final position, with the pier diaphragms located over the piers. The second condition is with the deck advanced by half a span and supported on cross-sections that on launch completion will be midspan sections.
In both positions, the cross-sections temporarily in midspan are rarely overloaded in a PC deck. Self-weight shear is minimal, and positive bending is smaller than in service conditions that also include superimposed dead and live loads. Moreover, most PC launched bridges have box section, and a box girder is well suited to positive bending. The wide top slab provides large compression area and lifts the center of gravity of the cross-section, and longitudinal launch prestressing designed to control tensile stresses at the lower edge is particularly effective due to the long lever arm from the gravity axis.
With regard to the support sections, negative bending in the first support configuration is smaller than negative bending in service conditions, and the deck can be designed for the latter. Longitudinal launch post-tensioning is still needed to cover tensile axial stresses at the upper edge, but launch tendons designed for positive bending at midspan are often adequate for negative bending in the support regions due to the raised location of the deck gravity axis and the greater section modulus at the upper edge. In the absence of draped tendons during launch, the webs may be designed for the launch shear, and integrative draped tendons are applied at the end of launch to resist the additional shear forces generated by superimposed dead and service loads.
When the deck is supported on the final midspan sections, sections that on launch completion will resist positive bending and minimal shear are subject to peak negative bending and shear. They will often have to be designed for these transient load conditions, and since every cross-section of the deck is a support section during launch, moment of inertia and web thickness have to be constant throughout the deck length.
Uniform axial post-tensioning is provided during launch to alternately resist tensile axial stresses at the opposite edges of the cross-section. The deck region far from the leading end is subject to uniform envelopes of self-weight bending and shear, the peak negative bending is about twice the peak positive bending, the distance of the gravity axis of a PC box girder from the upper edge is about one-third of the section depth, the section modulus at the upper edge is about twice the section modulus at the lower edge, and a box girder is therefore perfectly balanced for resisting launch self-weight bending with axial post-tensioning. Internal or external draped tendons are added on launch completion to resist the additional tensile stresses due to superimposed dead and live loads.
Ribbed slabs with double-T section are also compatible with incremental launching construction, provided that the lower edge of the cross-section is designed to resist the longitudinal compressive stress due to negative self-weight bending and axial launch post-tensioning in the support regions of the deck. Because of this reason, ribbed slabs are rarely launched on spans longer than 30-40m. If all the post-tensioning tendons cannot be lodged within the cross-section, internal launch tendons are combined with external draped tendons fabricated and tensioned on launch completion. Solid and voided slabs are launched on short 20-25m spans; in this case the launch tendons are designed for service conditions because of the impossibility of applying integrative post-tensioning on launch completion.
The behavior of a prestressed composite box girder with steel corrugated-plate webs is more complex during launching. Compared with a PC box girder, higher flexural efficiency and lighter self-weight reduce the edge stresses during launch and require less launch post-tensioning. The launch tendons are mostly located within the concrete slabs, aligning the resultant prestressing force with the gravity axis of the cross-section is difficult when only internal tendons are used, and some external tendons are often necessary. This results in a more efficient final design of prestressing, as the external tendons can be released and repositioned on launch completion.
The external polygonal tendons of the end-of-launch integrative post-tensioning may be designed to resist the shear force due to self-weight and 50% of live loads with tendon deviation forces, and the steel corrugated-plate webs resist the shear fluctuations due to the presence or absence of live loads. During launch, however, the steel webs resist full self-weight shear, and this may led to oversized details, especially when the deck is launched without temporary piers.
Launching a conventional, non-prestressed composite box girder is simpler as the concrete slab is cast in-place segmentally on launch completion to diminish the cost of the launch bearings and to facilitate control of web buckling during launch, and the steel girder is therefore lighter and more flexible during launch.
The self-weight of a PC box girder, a prestressed composite box girder with steel corrugated-plate webs, and a non-prestressed composite deck may be compared for a typical 50m launch span, a 13m-wide top slab, and normal-weight concrete.
- A PC box girder with internal tendons may have an average concrete thickness of about 0.60m and therefore weighs 195kN/m.
- A prestressed composite box girder with steel corrugated-plate webs may have an average concrete thickness of about 0.35m, and the concrete weighs 114kN/m. Adding 6kN/m for two steel webs, the total weight becomes 120kN/m, and weight saving is 38%.
- The average thickness of the concrete slab of a composite box girder is of about 0.28m, which leads to a concrete weight of 91kN/m. A steel U-girder may weigh about 25kN/m, the total weight is 116kN/m, and weight saving is 41%. On 50m spans, a conventional composite box girder is not much lighter than a prestressed composite box girder with steel corrugated-plate webs, as post-tensioning significantly diminishes the weight and cost of the steel webs.
Launching a composite box girder complete of concrete slab would offer significant advantages in terms of logistics, safety, quality and efficiency of the composite behavior. The weight of the U-girder, however, is only 22% of the total weight of the cross-section. Launching the completed cross-section would require expensive launch bearings designed for five-times-greater launch stresses, and would complicate control of buckling of non-stiffened web panels. For these reasons, the concrete slab is typically cast in-place segmentally on launch completion. In-place casting of the concrete slab is the typical solution also for the other types of composite section for launched bridges: twin I-girders, multi-girder systems, girder-substringer systems, and space frames.
During launch, the 25kN/m weight of a U-girder is 13% of the 195kN/m weight of a PC box girder. The launch support reactions are smaller but the open U-girder is more flexible, and large flexural rotations at the supports require expensive articulated launch bearings. The U-girder is also cambered to realign under the weight of the concrete slab on launch completion, and since the concrete slab is 3.6-times heavier than the steel girder, the cambers are substantial. Launching a cambered profile on aligned launch bearings generates hyperstatic effects and longitudinal redistribution of self-weight bending and shear, the center of gravity of the U-girder is located below the mid-depth of the girder, and this may result in oversized top flanges. Finally, the localized weight of the pier diaphragms causes peaks in the envelopes of launch bending and shear. With all types of cross-sections, in other words, control of launch stresses is fundamental in the incremental launching construction of bridges.
Self-weight bending and shear vary continuously during the incremental launching process. The increasing length of the front cantilever and recovery of the elastic deflection at nose landing at the next pier govern the envelopes of self-weight bending and shear, and within those envelopes, the deck cross-sections cyclically migrate from peak negative bending and shear when they are over the piers to peak positive bending when in midspan.
The envelopes of self-weight bending and shear are more demanding in the front deck region and govern deck pre-sizing. Without a launch nose, negative bending at the root of the front cantilever would be 6 times higher than in the rear pier regions, and shear would be double. Launchability criteria require a cylindrical deck geometry, and the launch nose controls self-weight bending and shear and the interaction between cross-sectional moment-of-inertia and the required level of launch post-tensioning.
Structures that present so many load conditions require careful pre-sizing. Optimizing the nose-deck interaction with a parametric spreadsheet shows the effects of the relative length, weight and stiffness of the nose, streamlines and accelerates the design of a launched bridge, and minimizes the risk of remaking the entire launch stress analysis should pre-sizing ultimately turn out inadequate.
In 23 pages, Control of Construction Stresses in Launched Bridges introduces the parameters that govern the nose-deck interaction, explores an analytical model of the nose-deck interaction and a step-by-step procedure for its optimization, and explains the use of parametric design charts for control of self-weight bending and shear in the front region of the deck by means of the relative length, weight and stiffness of the nose.
The spreadsheet enclosed to the eManual draws parametric design charts of positive and negative bending in the front span and at the nose-deck joint and has been time-tested in the design of several launched bridges. Closed-form equations lead to excellent match with the results of the final launch stress analysis with structural analysis programs.
Spreadsheet and eManual will become your productivity tools for value engineering and the pre-award design of incrementally launched bridges, will show you the effects of the relative length, weight and stiffness of the launch nose on deck pre-sizing, and will avoid expensive trial-and-error use of structural software programs during the pre-sizing process.