An arrangement for projecting cantilever sections of multi-sectional bridge supporting structures of steel and concrete and/or prestressed concrete forming a superstructure which is supported on bridge piles, comprising at least one traveling auxiliary beam movably carried on and arranged above said superstructure for spanning between superstructure sections, two concreting scaffolds each comprising a supporting part having crossbeams and rollers arranged above said superstructure, said rollers riding on rails positioned above said superstructure, a platform suspended from said supporting part of said scaffolds and arranged below said superstructure for carrying casings for extending said projecting superstructure sections, a transport device movably carried on said auxiliary beam so as to support therefrom said concreting scaffolds for transporting said scaffolds between superstructure sections, and from completed sections to a bridge pile for beginning construction of the next section, said supporting part of each concreting scaffold having longitudinal girders arranged adjacent said auxiliary beam, said crossbeams of said supporting part being connected to said longitudinal girders and arranged below said auxiliary beam, a pair of retractable supporting blocks supporting said auxiliary beam on a pile next succeeding a completed superstructure section, said supporting blocks being alternately retractable to allow passage of said crossbeams of said supporting part when said scaffold is transported to said next succeeding bridge pile, and said platform of said scaffolds comprising a bending resistant lattice formed by a plurality of longitudinally extending platform girders and a plurality of platform crossbeams extending transverse to said platform girders, each of said platform crossbeams having inner and outer parts, said inner parts being movable with respect to said outer parts between an opened and a closed position, said outer parts being supported in a stationary position, said inner parts of said crossbeams being mounted on hinges so that said inner parts may be swung about said hinges for movement to the open position to permit formation of opening in said platform corresponding to the width of a bridge pile to allow said platform to pass said pile as it is transported to the next section.