Concreting of span by span construction with travelling scaffolding is typically made in two phases. In the first phase, webs and bottom flange of the box girder are concreted. In the second phase, top flange is concreted. Once the cross section is self-supporting, this is to say, once the concrete of the top flange is hardened, the segment can be prestressed and the scaffolding can be shifted to the next span. This procedure takes usually two weeks per span. In order to shorten the critical path, it would be advisable to look for self-supporting cross sections after the concreting of the first phase, prestressing and shifting the scaffolding subsequently and pouring the second phase out of the critical path. First phase would include the concreting of webs, bottom flange and the overhung top flanges. The trade-off of this procedure will imply some structural problems to be studied, such are the connection between different phases and the transverse bending moments to appear until the cross section is closed. The paper will provide an insight into the modification of the traditional construction methods and into the associated structural problems and potential solutions.