We describe a combined experimental and theoretical investigation of shape-morphing structures assembled by actuating composite (Janus) fibers, taking into account multiple relevant factors affecting shape transformations, such as strain rate, composition, and geometry of the structures. Starting with simple bending experiments, we demonstrate the ways to attain multiple out-of-plane shapes of closed rings and square frames. Through combining theory and simulation, we examine how the mechanical properties of Janus fibers affect shape transitions. This allows us to control shape changes and to attain target 3D shapes by precise tuning of the material properties and geometry of the fibers. Our results open new perspectives of design of advanced mechanical metamaterials capable to create elaborate structures through sophisticated actuation modes.