This paper describes experimental and theoretical studies of the mechanics of free-standing nanoribbons and membranes of single-crystallne silicon transfer printed onto patterned dielectric layers. The results show that analytical descriptions of the mechanics agree well with experimental data,and they explicitly reveal how the geometry of dielectric layers (i.e., the width and depth of the features of relief) and the silicon (Le. the thickness and widths of the robbons) affect mechanical bowing (i.e., "sagging") in the suspended regions of them silicon. This system is of practical importance in the use of semiconductor nanomaterials for electronic devices, because incomplete sagging near defects in gate dielectrics provides a level of robustness against electrical shorting in those regions which exceeds that associated with conventional deposition techniques for thin films. Field effect transistors formed using silicon nanoribbons transferred onto a range of ultrathin gate dielectrics, including patterned epoxy, organic self-assembled monolayers, and HfO2, demonstrate these concepts.