Let $I\subseteq\mathbb{R}$ be an open interval. Consider $B=\mathbb{R}^{2}\times I$ and $\Delta=\{0\}\times I$. On $B_{0}=(\mathbb{R}^{2}-0)\times I$ we take the product affine structure between the affine structure on $\mathbb{R}^{2}-0$ described in the previous example and the standard affine structure on $I$.