The vehicle has a door column (4), i.e. the B column, in which an external shaped element with a reinforcing element (8) in it fit. The reinforcement element joins the roof of the bodywork at the top. The top end of the reinforcement element is T-shaped, with two arms (21,22) extending in opposite directions. Both arms have an end cut at an angle so that they are longer at the top than at the bottom. These arms are connected to the edge of the roof to provide greater rigidity of the bodywork round the door apertures.