Abstract:
Based on existing methods for calculating the maximum second-order bending moment (MSOM) of members under combined axial compression and bending, and assuming that the MSOMs of the original member and the equivalent length member under combined axial compression and bending are equal, this paper derives a general expression for the equivalent length coefficient (ELC), a calculation formula for ELC based on the maximum first-order bending moment of the member, a practical calculation formula for ELC of members under combined axial compression and typical bending, and a simplified calculation formula for ELC under transverse loads. The accuracy and application range of the proposed practical formulas are checked by employing the calculated amplification coefficient of moment or first-order maximum moment. The results show that, the minimum and maximum ELC values for end moments are 0 and 1 respectively, and the ELC of a member under combined axial compression and transverse load can be expressed as a function of the ratio of axial compressive force to the critical flexural buckling force. For common load conditions, the ELC in this paper has high accuracy and wide applicability; while the ELC in the national standard GB 50936−2014 may be significantly unsafe or overly safe.