Abstract: Design methods of centrally loaded member for AISC 360-16 are explained and comparison is make between AISC 360-16 and GB 50017-2017. Design considerations and differences of flexure buckling, torsion buckling and flexure-torsion buckling for two country's codes are introduced. These will be helpful to understand design accomplishments for three kinds of buckling.
The stability strength calculation of axial compression member is listed in Chapter E of AISC 360-16, in which the design compressive strength is φ_cP_n; the compressive coefficient of drag is φ_c=0.9; the nominal compressive strength P_n shall be the lowest value obtained based on the applicable limit states of flexural buckling, torsional buckling, and flexural-torsional buckling.
For flexural buckling, the number of column curves in AISC 360-16 decreases from three to one. The flexural buckling strength of axial compression member is P_n=F_crA_g, where there are F_cr=0.658^F_y/F_eF_y or F_cr=0.877F_e, and F_e=((π²E)/((L_c/r)²)).
The column curve in AISC 360-16 can be divided into two segments, with the limit slenderness ratio of 137 (F_y=235 MPa) and the normalized slenderness ratio of λ_c=(L_c/πr)√F_y/E=1.5. In the elastic stage, the Euler's critical force is taken as the reference, and the reduction factor 0.877 is introduced to consider the influence of the geometric imperfections of the member, which is clear in concept and consistent with Euler's formula. In the inelastic stage, the nonlinear properties of the generalized Euler's formula are taken into account after the material strength exceeds the proportional limit, and the geometric imperfections and the residual stresses of the member are also considered.
GB 50017-2017 adopts four column curves, flexural buckling strength of which can be calculated by N/φAf ≤ 1.0. Considering the initial imperfections and the residual stresses of the member, stability factor φ is determined by the critical force of flexural buckling of axial compression member and is applicable in both elastic and inelastic zones. The slenderness ratios in both main axes are first calculated and then the larger slenderness ratio is substituted into φ=(1/2λ_n²)[(α₂+α₃λ_n+λ_n²)-√(α₂+α₃λ_n+λ_n²)²-4λ_n²] or i>φ=1-α₁λ_n² to calculate stability factor φ.
When analyzing torsional buckling and flexural-torsional buckling, torsional buckling may occur for biaxial symmetric cross-section. For cross-sections with single symmetric axis or without symmetric axis, flexural-torsional buckling may happen. The buckling strength of torsional buckling or flexural-torsional buckling is P_n=F_crA_g, where there are F_cr=0.658^F_y/F_eF_y or F_cr=0.877F_e, and F_e takes the critical stress of torsional buckling or flexural-torsional buckling.
Thus it can be seen, torsional buckling and flexural-torsional buckling of AISC 360-16 are calculated according to the column curve of flexural buckling after the computation of the corresponding elastic critical force.
The critical force of torsional buckling in GB 50017-2017 is N_z=(1/i₀²)(GI_t+((π²EI_ω)/l²)), by which divided A is consistent with that in AISC 360-16.
In specific applications, GB 50017-2017 adopts the concept of equivalent slenderness ratio, and the slenderness ratio for torsional buckling is calculated by λ_z=√I₀/(I_t/25.7+I_ω/l_ω²) and considered as the slenderness ratio for flexural buckling. The stability factor φ is then computed based on the above method, which is the same as the method adopted in AISC 360-16. The difference is that the elastic segment of column curve in AISC 360-16 is determined by the product of Euler's critical load and reduction factor, and the inelastic segment is closer to the test curve, while GB 50017-2017 takes the regression curve from test data as the column curve.
GB 50017-2017 adopts (N_Ey-N_yz)(N_z-N_yz)=N_yz²(y_s²/i₀²) to calculate the critical flexural-torsional buckling force N_yz. In AISC 360-16, supposing x_o=0, flexural-torsional buckling equation of uniaxial symmetric cross-section is (F_e-F_ey)(F_e-F_ez)=F_e²(y_o/[r_o)². Essentially, the above two equations are consistent. In other words, the calculation formulas of flexural-torsional buckling strength in GB 50017-2017 and AISC 360-16 are the same.
For axial compression member, both AISC 360-16 and GB 50017-2017 present design formulas for flexural buckling, torsional buckling, and flexural-torsional buckling. Both the two specifications determine the stability factor φ of three buckling modes based on column curve of flexural buckling. AISC 360-16 adopts one column curve and GB 50017-2017 uses four column curves, both of which consider the influences of geometric imperfection and residual stress and agree well with relevant tests in different countries. Torsional buckling and flexural-torsional buckling in AISC 360-16 and GB 50017-2017 come from the elastic stability equilibrium equation, which are transformed into the critical force of flexural buckling through equivalent critical force and designed by column curve of flexural buckling.