1. The problem statement, all variables and given/known data A beam (e.g. a steel liner) of a length L is bent between two supports, as shown in fig (a). According to the Euler column, the shape is a half period of a sine. Now, a force P is applied at the axis of symmetry - fig (b). What is the shape of the liner? y=f(x) Instead of the general case, let's choose P so weak that the liner remains always convex (h1=0.9*h or so ...). 3. The attempt at a solution I followed the "Strength of Materials and Structures" of Case-Chilver-Ross (ISBN:0340719206) and tried to modify the 18.9 - "Strut with uniformly distributed lateral loading" to a "... with concentrated lateral load" . How to apply the boundary conditions so that the length of the liner (arc length) L remains constant?