I am currently reading up on the formation of $\beta$-sheets. The following text describes its formation from a free energy point of view:

> The edge of a β-sheet consists of (a) edge β-strands, and (b) bends or
> loops connecting the β-strands [...]. Let the coil free energy be zero
> (i.e., the reference point); $f_{\beta}$ , the free energy of a
> residue in the center of the β-sheet; $f_{\beta}$ + $\Delta f_{\beta}$
> , the free energy of an edge β-strand residue (i.e., 	$f_{\beta}$ is
> the edge effect); and U, the free energy of a bend. Since the β-sheet
> forms, it is stable (i.e., $f_{\beta}$ < 0), and **the edge effects
> prevent it from falling into pieces** (i.e., 	$\Delta f_{\beta}$ > 0
> and U > 0) (Finkelstein, Protein Physics)

Why do $\Delta f_{\beta}$ and U need to be positive? Wouldn't this mean that the bends or folds of the sheet are unstable? Why would negative $\Delta f_{\beta}$ and U make the sheet fall to pieces?