A building structure has a plurality of elongated flexible compression arches or ribs to which a flexible membrane is operatively connected to span spaces between the arches in a folded pattern with the arches located at the apices of the folds and valleys formed between the apices. A plurality of cables are operatively associated with the membranes by prestressing and are located in the valleys formed between the arches in order to maintain the membrane in tension under substantially all load conditions so that the flexible arches are braced against buckling by the membrane. As a result, the flexible components of the structure cooperate to form a relatively rigid structural system capable of spanning relatively long distances for covering sports stadiums and the like.