All in here (if using Euler Bernoulli beam theory)

http://sci-toys.com/bent_paper_problem.pdf

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(*Added by Joseph O'Rourke*).  Here is Fig.1 from the paper by Antoni Colom,
 "Analysis of the shape of a sheet of paper when two opposite edges are joined," PDF link above.
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![Tear Drop][1]


  [1]: https://i.sstatic.net/N0OW1.jpg