A tubular dashboard beam (100) has a circular cross-section and extends transversely between vertical pillars of a motor vehicle. The beam is formed in one piece and has at least two different diameters (d1, d2, d3) between the two ends thereof, a larger diameter (d1) of the beam being in the region of an end (101, 102) of the beam which is intended to be located in the region of a driver's seat of the motor vehicle. At least the end at the driver's seat side which must be fixed to a vertical pillar of the motor vehicle is partially crushed so as to have a cross-section in the form of a circular arc whose chord (105) which closes the cross-section extends at one side and the other of the circular arc (106), providing a planar face whose lateral edges (109) surround the curved face of the circular arc.