A composite structure is provided. The structure is formed of rigid composite material in which non-metallic continuous fibers reinforce a polymer matrix. The continuous fibers are electrically conductive. The structure has electrodes electrically connected to the continuous fibers. The composite material contains one or more insulating barriers which electrically divide the structure so that a first portion of the material in electrical contact with one of the electrodes can be held at a different electrical potential to a second portion of the material in electrical contact with the other electrode. In use, an electrical unit can be provided to electrically bridge the first and second portions of the material such that electrical signals can be transmitted between the electrodes and the electrical unit via the continuous fibers.