Selfdual Parametric Method for Linear Programs

A railway hopper car includes a curved roof having a roof sheet provided with lateral edges each joined to the top of a car side sheet by a top chord assembly. Each top chord assembly includes a top chord fully disposed within the car interior and having a vertical leg joined to the interior surface of a side sheet while an opposite inclined or angular leg is joined to the interior surface of the roof sheet. A curved cover overlies both top chord legs and forms, with the roof sheet and side sheet, a smooth continuously descending profile from the top centerline of the car roof to each of the car sides.