We discuss the dynamic behavior of stepped columns subjected to follower forces. In particular, limit cases which correspond to columns with hinges or cracks and concentrated lateral supports are studied for the stability limit. Typically, solutions suffer jumps in certain derivatives, which have to satisfy compatibility conditions. The influence of these interface conditions on the critical force is investigated. The aim is to optimize the location of such singularities and thus to obtain maximum critical loads, respectively worst case estimates for the loss of stability.