Method of constructing a building, and a building construction system therefor

A method of constructing a building, the method comprising:

• constructing a vertical support core of the building;
• attaching a climbing rail to an exterior surface of the vertical support core, wherein the climbing rail extends vertically and is substantially parallel with the vertical support core;
• constructing a first floor plate around a periphery of the vertical support core at a ground elevation;
• constructing a structural support system of the first floor plate including a plurality of frame members attached together and at least one connecting rail fixedly attached to the frame members, the at least one connecting rail positioned adjacent to and substantially parallel with the climbing rail, wherein each of the climbing rail and the at least one connecting rail include a plurality of holes spaced apart vertically relative to each other;
• attaching a climbing jack to the climbing rail at an initial jack elevation below the first floor plate, such that the climbing jack supports the first floor plate;
• moving the climbing jack vertically upward on the climbing rail to raise the first floor plate to a first floor final elevation;
• and
• attaching the first floor plate to the climbing rail at the first floor final elevation by inserting a pin through aligned said holes in each of the climbing rail and the at least one connecting rail.