D3. The different construction phases

Studying the phases of construction has two objectives:

to ensure the stability of the structure in the various transitional states leading to the final state,

to calculate the effects that have the assembly on the force distribution and the deformation of the structure.

There are various effects related to assembling. They are due to:

the evolution of the static state during construction. For example, a bridge span built by two cantilevered bridge spans and finally clamped/keyed in its center will present, just after the clamping, a moment diagram under permanent loads that cancels out in the middle of the span, which is quite different from the one that would have been obtained without taking into account the assembly method (Figure 5),

the interaction of the delayed effects with the evolution of the static state. In the above example, after keying, the moment in the middle of the span will increase due to creep,

the evolution of the sections over time. For example, in the case of composite steel-concrete structures, if the structure does not rest on arches when the concrete is poured, the weight of the slab is supported by the steel structure alone,

voluntary adjustments of the structure: support elevations, adjustments of the bracings, keystone actuators, ...

Taking these effects into account can be relatively complex and, in the most difficult cases, it may be essential to use software that can model the evolution of the structure step by step.

However, it is often possible to proceed by superimposing various linear analyses.

Effect of the construction phases in the case of the keying of a cantilevered bridge span

The main issues are related to the effects of the delayed deformation of concrete. Indeed, how can one evaluate the final state midspan moment in the above example? In the case of a single keying point, it is possible to use the method known as the "coefficients method" (Figure 6). This approach is based on the following arguments:

Final state = (E(t₀, t₁)/E(t₀, t_∞)) x Final state not keyed + (1-(E(t₀, t₁)/E(t₀, t_∞))) x Final state without phasing.

with t₀ the duration of load application, t₁ the duration of the keying, t_∞ the time considered for the final state, and E(t₀, t₁) the concrete modulus for obtaining the deformation of the concrete at time t₁ for a load applied at t₀.

This method, in the case of a single keying point, outputs the exact theoretical final state. However, it is difficult to extend it to the case of multiple keying points and can lead to absurd results.

The unitary case used for the coefficients method

It is best to externalize the effects of changes in the static state as follows (Figure 7) :

case 1: calculation of the final state, if the keying was not carried out ;

case 2: calculation just before keying, with the adequate concrete modulus;

case 3: calculation of the effect of keying: apply an imposed displacement to the structure at the keying point returning the value of the discontinuity (for this example, in rotation) to the value fixed by the keying process,

the final state is the sum of cases 1 and 3.

This technique can be extended more easily to cases where the static configuration of the structures is modified many times.

Unitary cases used for the superposition method

It is worth remembering that, under the effects of delayed deformation, concrete reacts with an apparent deformation modulus called relaxation modulus, which is lower than the corresponding creep modulus. If the classical ratio between the moduli of steel and concrete, including creep effects, is about 18, in the case of an imposed displacement, this ratio increases up to 24. This tends to make the adjustments by support elevation and actuators less efficient when the latter leads to imposing a deformation on the structure.

From the point of view of FE simulations, the large number of intermediate states that need to be processed multiplies the risk of errors. The verifications must concern:

the respect of the boundary conditions in the intermediate phases;

the respect of the displacements fixed by the construction phases in the structure (for example, discontinuity of slope at the keying point).

In construction studies, one must also remember that the actual creep of concrete can deviate strongly from the theoretical formulations. The model must therefore be constructed such that it is easily adaptable to restore the deformations appearing in the first phases, and thus improve the prediction of the following ones.