Dashboard cross member for an automobile vehicle, tubular and composite, characterized in that: it comprises a tube, generally rectilinear, comprising a succession of concentric layers, each consisting of glass yarns coated with a polymerized thermoplastic resin or carbon yarns coated with a compatible polymerized thermoplastic resin, with all the yarns joined over approximately the entire length of the tube by hot melting then solidification of the polymerized thermoplastic resins; and in that this tube includes in succession, from the center of the tube towards its periphery, at the least: • a first layer comprising at least one winding having a winding angle included between 30° and 90° with respect to the general direction of the tube, of glass yarns coated with polymerized thermoplastic resin; • a second layer comprising glass yarns set out essentially longitudinal with respect to the general direction of the tube, that is at an angle included between 0° and 10° with respect to the general direction of the tube, and coated with polymerized thermoplastic resin; • a third layer comprising at least two cross-laid windings, inclined at an angle included between 40° and 60° with respect to the general direction of the tube, of carbon yarns coated with compatible polymerized thermoplastic resin; • a fourth layer comprising at least one winding having an angle included between 70° and 90° with respect to the general direction of the tube, of glass yarns coated with polymerized thermoplastic resin. it comprises a tube, generally rectilinear, comprising a succession of concentric layers, each consisting of glass yarns coated with a polymerized thermoplastic resin or carbon yarns coated with a compatible polymerized thermoplastic resin, with all the yarns joined over approximately the entire length of the tube by hot melting then solidification of the polymerized thermoplastic resins; and in that this tube includes in succession, from the center of the tube towards its periphery, at the least: • a first layer comprising at least one winding having a winding angle included between 30° and 90° with respect to the general direction of the tube, of glass yarns coated with polymerized thermoplastic resin; • a second layer comprising glass yarns set out essentially longitudinal with respect to the general direction of the tube, that is at an angle included between 0° and 10° with respect to the general direction of the tube, and coated with polymerized thermoplastic resin; • a third layer comprising at least two cross-laid windings, inclined at an angle included between 40° and 60° with respect to the general direction of the tube, of carbon yarns coated with compatible polymerized thermoplastic resin; • a fourth layer comprising at least one winding having an angle included between 70° and 90° with respect to the general direction of the tube, of glass yarns coated with polymerized thermoplastic resin. • a first layer comprising at least one winding having a winding angle included between 30° and 90° with respect to the general direction of the tube, of glass yarns coated with polymerized thermoplastic resin; • a second layer comprising glass yarns set out essentially longitudinal with respect to the general direction of the tube, that is at an angle included between 0° and 10° with respect to the general direction of the tube, and coated with polymerized thermoplastic resin; • a third layer comprising at least two cross-laid windings, inclined at an angle included between 40° and 60° with respect to the general direction of the tube, of carbon yarns coated with compatible polymerized thermoplastic resin; • a fourth layer comprising at least one winding having an angle included between 70° and 90° with respect to the general direction of the tube, of glass yarns coated with polymerized thermoplastic resin.