The present invention provides a space frame structure, such as a dome, for covering an open space, which structure is assembled from beam members which intersect at rigid node joints. The beam members and other structural components used in the skeleton of the space frame are made from pre-cast concrete which has not been subjected to pre-tensioning and the rigid node joints ar formed in situ, for example by casting concrete joints incoroporating the ends of beam members. The loads imposed by the weight of the beam members on the beams and the node joints effectively simulate pre-stressing of the components which act within the assembled structure as pre-stressed concrete. The invention also provides a method for fabricating a space frame structure made from pre-cast concrete beams and other components.