Keywords: movable scaffolding system, RC bridge, construction sequence, creep, dead load moment, tendon moment.

The design and analysis of bridges constructed by the movable scaffolding system (MSS) requires consideration of the internal moment redistribution because of the time-dependent deformations of concrete, stress relaxation of tendons and changes in the structural system repeated during construction. Hence, an analysis that considers the construction sequence must be performed. All the related bridge design codes [1,2] have also noted the need to consider the internal moment redistribution due to the time-dependent deformations of materials when the structural system is changed during construction.

In this paper, simple but effective formulae that can calculate the internal moment redistribution in concrete bridges after completion of construction by MSS are introduced. With the previously developed computer programs [3], many parametric studies for bridges erected by a movable scaffolding system are conducted, and correlation studies between the numerical results obtained with those determined by the introduced formulas are included to verify the applicability of the formulae. Finally, a reasonable guideline to determine the internal design moments, which are essential in selecting a proper initial section, is proposed.

Movable scaffolding construction refers to a step-by-step construction technique for a bridge superstructure sequentially from the first to the end span using a movable scaffolding system, wherein each span of the superstructure is tied to the previous one by sequential post-tensioning of tendons. The same erection process is repeated until the structure is completed; consequently the internal moment is continuously changed according to the construction sequence and the changing structural system during construction. This means that the tendon force and the dead load dominantly affect the internal moment variation because these two force components accompany the secondary moments caused by concrete creep deformation with the changing structural system.

The sequential applications of the dead load by the self-weight of the following span with the concentrated loads of P_g and P_c introduce repeated increases and decreases in the moment distribution along the span. However, the dead load moment distribution is not greatly affected by the time-dependent deformations of the concrete because of the relatively short duration of construction sequences and the subsequent application of the concentrated load P_g and P_c. That is, the dead load design moment in a bridge constructed by MSS can be determined on the basis of an elastic analysis considering the construction sequence only.

The tendon moment distribution at time t represents a difference from that of the total structure (TS) because of the changes in the structural system and the accompanying time-dependent effects of concrete and the tendons at each construction step. In time, the positive moments at the interior supports do not display a large variation while the negative moments at the mid-spans show definite decreases with time. This variation can be explained by following: (1) the creep moments represent the positive moment distributions along the entire spans; and (2) since the stress relaxation represents the reduction of the tendon forces with time, the moment reduction occurs along the entire span.

In this paper, a simple but effective relation that can simulate the internal tendon moment variation due to the creep deformation of concrete, relaxation of tendons, and changes in the structural system during construction is proposed, and a new guideline to determine the design moments is introduced. The design moments for a dead load at any construction step can be determined on the basis of an elastic analysis considering the construction sequence only. The design moments after construction can also be determined from the elastic moment for the total structure without considering any effect. When the longitudinal tendons, which may affect the internal moment redistribution during construction, need to be considered in calculating the internal moments and the corresponding normal stresses at an arbitrary section, Eq.(4) can be suitable employed. In advance, the moment envelop curves for the dead load, longitudinal tendons, and the superposition of both loads also show that the design moments by the proposed method can effectively be used in determining an initial section of the bridge at the preliminary design stage.

1

AASHTO, Standard specifications for highway bridges.15th ed. Washington, DC, 1992.

2

British Standards Institution, Part 4. Code of practice for design of concrete bridges, Milton Keynes, United Kingdom, 1984.

3

H.G. Kwak and Y.J. Seo, "Numerical analysis of time-dependent behavior of pre-cast pre-stressed concrete girder bridges", Construction and Building Materials, 16, 49-63, 2002. doi:10.1016/S0950-0618(01)00027-7

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