The toppling of hanging beams

This paper considers the behaviour of beams hanging from cables. If heavy, these beams can topple sideways in a mode which can be idealised as a rigid body rotation, combined with a minor axis de¯ection. This simpli®cation allows an analytical treatment of the toppling mode, which in turn allows a stability analysis of heavy beams, such as prestressed precast concrete bridge beams. A detailed analysis is presented for beams with inclined or vertical cables, with inclined or vertical lifting yokes, with lateral loads (as from wind or inertia e€ects), and with initial imperfections. Examples are given of the various e€ects that can be analysed in this way, and the validity of the initial assumption, about rotation without variation in twist, is checked. It is shown that this type of analysis is particularly suited to concrete beams.