A building framework includes metal columns (e.g., tubular or I-beam), wood-product beams, and bracket connectors for joining the beams to the columns to form a building joint of sufficient strength and durability for buildings suitable for human occupation. First mechanical fasteners (such as bolts and nuts) secure a selected connector to the column, and second mechanical fasteners (such as lag bolts) secure a selected beam to the connector. The columns include double rows of holes. A plurality of different connectors with differently angled flanges are provided, such that beams can be connected at a wide variety of different angles. Further, the system allows columns and/or beams to be cut at the construction site, or at a building supply company. Thus, basic building components can be inventoried in a manner not previously possible, yet the system supports a wide variety of different building frames for on-site customization and adaptability.