A floorplate lifting system includes a lift bridle and a lift system. The lift system includes a plurality of strand jacks, a plurality of static strand bundles, a plurality of strand anchors, and a plurality of strand mounting brackets. The plurality of strand mounting brackets are detachably affixed to a vertical support core. First ends of the plurality of static strand bundles are attached to the plurality of strand anchors, and the plurality of static strand bundles are suspended from the plurality of strand mounting brackets via the plurality of strand anchors. Second ends of the plurality of static strand bundles are suspended from the plurality of strand jacks. The strand jacks are attachable to the lift bridle.