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 Ref. 1), 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 were 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 were also discussed. In this paper, "780N/mm^2 grade steels" and "low yield strength steels" are examined. The main results are summarized as follows. (1) The reduction of ductility in CGHAZ of the HT780 by the welding heat-input are almost same as the general mild steels, SN400B and SN490B. (2) Even though the chemical compositions are not so different, the relationship between the Charpy absorbed energies and the equivalent heat-input are quite different to the low yield strength steels. It is inadvisable to fix a type of low yield steel to main structures by welding. (3) The results of Charpy impact test of the low yield steels are clearly divided into very high and very low because of their large grain size. So Charpy impact test is not appropriate for investigating the ductility of the low yield steels.