In The Great Hanshin-Awaji Earthquake, the general yield brittle fractures were observed in beam-column connections of steel building frames. Among many influencing factors which affect the general yield brittle fracture, it can be considered that fracture toughness has substantial effects. Some studies are making clear the required toughness for the base metal and the weld metal, but general values are not proposed. Moreover, it seems that it is also important to pay attention to the toughness decrease in the weld heat affected zone (weld HAZ), because the toughness decrease occurs in the HAZs of mild steel. In this paper, the relationship between toughness of simulated HAZs of "the rolled steels for building structures (SN)" and the weld heat-input limit of the SN steel are investigated, in an attempt to provide the required toughness for HAZs. The relationships between the increase of the hardness value and toughness, and changes of microstructure after weld heat-input are also discussed. The main results are summarized as follows. 1) The SN400B can keep its toughness at higher heat-inputs compare to the SN490Bs. 2) The steel grade, which becomes harder than other steel grades at the same heat-input, has smaller absorbed energy and smaller limit of heat-input. 3) The weld heat-input limit of the SN400B and the SN490B are proposed separately for some required toughness values.