In this paper, the requirements of the column-overdesign factors for forming the weak-beam plastic mechanisms are investigated in 3, 6 and 12 story steel frame models subjected to strong ground accelerations. In order to take the account of randomness in the yield strength of each member, the Monte-Carlo method is adopted. A slight plastification in columns could be allowed in a steel frame because of a rather stable hysteresis in the interstory shear-drift relation. Therefore, the plastic mechanism could be judged as the weak-beam type for the frame, in which the average of accumulated plastic rotations in all columns never exceeded a specified tolerance. The probability of the mechanism formation is shown corresponding with the column-overdesign factor.
