C15. More about phased calculations

C15. More about phased calculations

The reader may also refer to Part 1 - D.3 Construction Phases.

Structural phasing can lead to modification:

• resistant sections,

• support conditions,

• internal continuity conditions of the structure.

It can concern both elevation and linear structures, longitudinally or transversely, and of course, a combination of all these cases is possible.

C.15.1 How to make a phased calculation with non-phased software?

Case A - Modification of the net cross-section

This is the case for the implementation of self-supporting collaborative pre-slabs.

During the implementation phase, it is the pre-slab that must resist the weight of the structure (pre-slab weight + compression slab). Then, it is the complex [pre-slab + compression slab] which will take up the loads later implemented (superstructure, overloads, ...).

At the SLS (Service Limit State), there is an accumulation of stresses in the tensioned reinforcement, but there is no direct accumulation of compressive stresses in the concrete.

At the ULS (Unlimited Limit State), the verification must be conducted for the concreting phase and the service phase, but without considering the phasing.

Case B - Modification of support conditions

This is the case for a structure with temporary supports.

It can be associated with a modification of the resisting structure (example: supported collaborative pre-slabs).

Accumulation of the loadings

Phase 1: Loading the structure with a temporary support

Phase 2: Removal of the temporary support

Phase 1 + Phase 2: The final stress is identical to a non-phased structure.

This method enables dealing with the installation and removal of temporary supports.

It is always necessary to pay attention to the conditions of deformation of the structures during the installation of temporary supports (placing the temporary support in contact with a deformed structure).

Case C - Modification of structural continuity

This is the case for a structure that is clamped during construction.

The stresses generated by the loads associated with a static diagram are calculated, then the stresses are summed up (if there has been no evolution of the net cross-section) or the stresses are accumulated (if there has been an evolution of the net cross-section).

Accumulation of the loadings

Example:

Phase 1: Self-weight sustained by isostatic spans

Phase 2: Accidental loads sustained by a continuous structure

Particular attention should be paid to the evolution of materials over time. In the case of reinforced or prestressed concrete or mixed concrete-steel structures, creep (quantifiable by the difference between instantaneous and delayed deformation) must be considered.

In the above example, before clamping, the deformation of the structure corresponds to a quasi-instantaneous deformation. After clamping, the concrete creeps and tries to increase its deformation under long-term load, but the structure is now continuous. The clamping of the creep deformations will here generate a moment of continuity on the support that stretches the upper fiber.

Creep behavior can be considered approximately (see the CEREMA documents on the subject) or with the help of an FE calculation with so-called scientific creep.

C.15.2 Pushing of a concrete bridge and launching of a steel bridge

The one thing these two models have in common is that during their installation phases, they will witness a shift in the position of the support nodes according to the advancement of the pushing or launching phenomena. Potentially, any node of the structure can be, at a given moment, a support node. Software that accept a pseudo-language of programming may, in this case, have an advantage in creating incremental loops to simulate the advancement (by incrementing the numbers of support nodes). Whenever possible, having bars of the same length facilitates the regular motion of the supports.

Modeling the cutwaters, in both cases, does not pose any problem: they are steel bars, usually I-beams, embedded at the extremity of the final structure.

Pushed concrete bridges: The calculation is almost a classical phased calculation. The sections casted over concrete beams behind the bridge are modeled using bars resting on non-linear Z-shaped narrowed supports (possible lifting). The bars with their casting dates and the prestressing, temporary or definitive are activated throughout time. Finally, the cutwater and part of the prestressing are deactivated.

Launched steel frame: models can represent classical bi or multi-beams, but also boxes. The main differences with the pushed concrete bridge model lie in the facts:

• that the structure is very flexible,

• that in the design phase, the added sections (of the order of 30m in length) rest on punctual supports, generally two supports per section, instead of a continuous ground beam,

• that the structure has a camber, determined beforehand by the calculation of the framework on its final supports. The junction of the steel sections must be made by taking the necessary measures to guarantee the continuity of the rotations of the edges of the sections. The two possible types of modeling to describe the phenomenon are detailed below.

During modeling, when a section is added to the rear of the already reassembled construction frame, the set of bars must be deactivated and reactivated after the new section is added. Otherwise, there is no continuity of rotation at the connection (figure below) and the structure would not be compatible with the 3rd bullet point above.

Modeling can also be done by classical phasing, provided that a prior "presentation" of the joints is carried out, which consists of finding the altimetric offset of the two supports 1 and 2 that enables having the same rotation and the same altimetry at each end E1 and E2, schematically (following figures) :

Vertical translation for the Z-correspondence of the lips

Displacement of supports 1 and 2 to generate a rotation of the section

Once these operations are performed in the model, continuity is ensured.

For the launching, practice consists of modeling the neutral axes of the framework and the cutwater according to a geometry algebraically accumulating the shape of the intrados (rectilinear or parabolic, for example), the longitudinal profile, and the counter-axis, at an arbitrarily chosen altitude. During the assembling of the structure, especially during the launching process, the nodes located in front of the provisional supports are given a difference in elevation corresponding to the altimetric offset between the geometry described above and the altitude of the provisional supports. It will be verified that the structure is in contact with the launching supports thanks to the sign of the support reaction. A support in tension means that the structure is no longer in contact and that the support must be released. Finally, for landings, there are always two cases to be studied, one right before and the other just after.

C.15.3 Phasing Affecting the Straight Sections

Since the construction phasing of a structure has an impact on the stress distribution on the straight sections of the structure, it must be considered.

This is the case for structures built with transverse phasing, where only certain parts of the structure see the first loads: such as for composite bridges with coated girders, or ribbed girders, or cast slabs in a second phase, and for compound slabs ...

C.15.4 Expanding a Structure - Delayed Connections

To expand a structure, when a new structure (metallic or concrete) is connected to an older structure, the modeling of the transverse phasing and the apprehension of the relative stiffness of the different elements is essential to correctly determine the deformations of the structure and especially the connecting forces between the structures.

The case of delayed connections between several new structures is similar: the consideration of creep and shrinkage is essential for a good dimensioning of the forces developing in the elements.

C.15.5 Cast-in-place or prefabricated structure - Deflection - Effect on the calculation

Please refer to § 2.1 and 2.2 of the Cerema Guide "Conception des ponts à haubans".