Methods of forming a semiconductor structure include providing a multi-layer substrate having an epitaxial base layer overlying a strained primary semiconductor layer above a buried oxide layer. Elements within the epitaxial base layer are used to alter a strain state in the primary semiconductor layer within a first region of the multi-layer substrate without altering a strain state in the primary semiconductor layer within a second region of the multi-layer substrate. A first plurality of transistor channel structures are formed that each comprise a portion of the primary semiconductor layer within the first region of the multi-layer substrate, and a second plurality of transistor channel structures are formed that each comprise a portion of the primary semiconductor layer within the second region of the multi-layer substrate. Semiconductor structures fabricated by such methods may include transistor channel structures having differing strain states.