Abstract: A shell structure for constituting the airflow shaft of a water-cooling tower comprises an upright frame support by ground foundations. The frame consists of a grid having at least three intersecting sets of bars, one of the sets comprising horizontal bars connected as to constitute circumferential girdles vertically distributed along the frame while the other two sets comprises bars which are at opposed angles with said horizontal bars, for defining a grid whose elemental pattern is an equilateral triangle. The bars are connected by nodes each receiving bars of all said sets. A veil defining a substantially continuous airflow stack is located within said frame and maintained in tension by connectons to the nodes of the frame. The frame may have a constant cross-section while the veil has a cross-section which varies along the vertical axis of the structure.