This paper presents a study of the electrical and mechanical behavior of several continuous carbon fibers epoxy composites for both strengthening and monitoring of structures. In these composites, the arrangement of fibers was deliberately diversified to test and understand the ability of the composites for self-sensing low strains. Composites with different arrangements of fibers and textile weaves, mainly unidirectional continuous carbon reinforced composites, were tested at the dynamometer. A two-probe method was considered to measure the relative electrical resistance of these composites during loading. The measured relative electrical resistance includes volume and contact electrical resistances. For all tested specimens, it increases with an increase in tensile strain, at low strain values. This is explained by the improved alignment of fibers and resulting reduction of the number of possible contacts between fibers during loading, increasing as a consequence the contact electrical resistance of the composite. Laboratory tests on strengthening of structural elements were also performed, making hand-made composites by the "wet process", which is commonly used in civil engineering for the strengthening of all types of structures in-situ. Results show that the woven epoxy composite, used for strengthening of concrete elements is also able to sense low deformations, below 1%. Moreover, results clearly show that this textile sensor also improves the mechanical work of the strengthened structural elements, increasing their bearing capacity. Finally, the set of obtained results supports the concept of a textile fabric capable of both structural upgrade and self-monitoring of structures, especially large structures of difficult access and needing constant, sometimes very expensive, health monitoring.