The maximum bending moment occurs in the midlength (second-order moment) in a simply supported beam-column subjected to compression and end moments, depending on the slenderness ratio and the level of the axial force. In AIJ Recommendation for Limit State Design of Steel Structures, the second-order moments are evaluated by multiplying an amplification factor by the first-order moments. The amplification factor of linear elastic beam-columns can be calculated, however, the initial deflection

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... not considered.In connection with the design method of steel beam-columns, objective of this study is to clarify the dimensionless factors which define the amplification factor and the effect of the dimensionless factors on the amplification factor is discussed.The analytical model is the simply supported linear elastic beam-column subjected to axial force and end moments. The amplification factor is obtained by solving the differential equation. It has found that parameters which affects the amplification factors were the initial deflection, the axial force ratio and the ratio of end moments. The analysis was carried out with these parameters. It has become clear from the analysis that: 1) the amplification factors increases as the amplitude of the initial deflection increases and 2) the maximum bending moment is not always equal to the end moment, which is the first-order bending moment, when the moment distribution is anti-symmetric bending and the initial deflection is considered.