Note: This answers refers to the original version of the question, which was about replacing cellulose with chitin.
The structural material in tree mechanics is not cellulose, but lignin.
Lignin is a class of complex organic polymers that form key structural materials in the support tissues of vascular plants and some algae. Lignins are particularly important in the formation of cell walls, especially in wood and bark, because they lend rigidity and do not rot easily. Chemically, lignins are cross-linked phenolic polymers.
The chemical structures of chitin (left) and cellulose (right). See how similar they are. Pictures from Wikipedia.
Chemically, cellulose and chitin are very similar; they are both simple polymers, derived from glucose. Lignin (from Latin lignum, "wood") is entirely different:
A possible chemical structure of lignin. Note the aromatic rings, utterly absent from chitin and cellulose, and the numerous and irregular cross-links between units. Picture by Karol Głąb, available on Wikimedia under multiple licenses including a public domain dedication.
As a biopolymer, lignin is unusual because of its heterogeneity and lack of a defined primary structure. Its most commonly noted function is the support through strengthening of wood (mainly composed of xylem cells and lignified sclerenchyma fibres) in vascular plants. (Wikipedia, s.v. Lignin)
The conclusion is that replacing cellulose with chitin is immaterial; the strength of the mechanical structure is given by another material entirely.