| Compared with the I-beam,the arbitrarily symmetrical pipe section has no corner points and its bending stiffness is greater.Although the current code in our country proposes the corresponding calculation formula for combined axial and bending capcity by taking the circular tube section as a special section,however,the basis of this formula is identical with the I-beam.It does not highlight the difference between the pipe and the I-beam,and does not reflect the real axial force-bending moment relationship of circular steel tube beam-columns.In this paper,starting from two aspects of theoretical derivation and finite element analysis,the stability behavior of circular steel tube beam-column is studied.Firstly,a finite element model of circular steel tube beam-column considering the initial imperfections of initial bending and residual stress is established.The influence of variables such as initial bending and longitudinal residual stress of hot-rolled circular steel tube,loading sequence,diameter-to-thickness ratio,and diameter on the relationship between axial force and bending moment of circular steel tube beam-column is analyzed.Refferring to this part to determine the calculation model parameters.Secondly,the JEZEK solution of the in-plane stability of circular steel tube beam-column considering only the influence of the initial bending is derived.The solution is derived from the component axial force equilibrium equation,the internal and external bending moment equilibrium equation and the extreme conditions,considering both the unilateral yielding and the bilateral yielding of the section.A finite element model is established to calculate the in-plane ultimate stability bearing capacity of circular steel tube beam-column considering only the influence of initial bending.Compared with the JEZEK solution,the roughness of the JEZEK method,and analyzed relationship between the axial force-bending moment of circular steel tube beam-column is revealed.Then the paper uses finite element calculation software to calculate the stability bearing capacity of circular steel tube beam-columns under unidirectional bending.The FEM results are compared with the calculation results of the current code related formulas,and it is discussed whether the current code related formulas are suitable for calculating stability bearing capacity of circular steel tube beam-columns under unidirectional bending.Starting from the sectional plastic axial force-bending moment interactive equations of the pipe,by substituting the elastic second order bending moment including the geometric imperfection into the cross-sectional interactive equation,the present paper obtained a new equation as upper bounds for the in-plane stability capacity with the codified equivalent moment coefficient,for which a coefficient is modified to be able to agree with the FEM results.The following conclusions are obtained:The calculation results of the relevant formulas of the current code are generally conservative compared with the FEM results,especially when the bending moment changes linearly and is double curvature bending;When the end bending moment ratio is 1,the axial force-bending moment correlation curve of the relevant formula of the current code and the curve of the FEM result show different trends,indicating that the relevant formula of the current code cannot well reflect the actual axial force-bending moment correlation of circular steel tube beam-columns under unidirectional bending;Comparing the upper bounds formula of the stable bearing capacity of circular steel tube unidirectional bending beam-columns derived from the theory with the FEM results,it is found that the formula can well reflect the actual axial force-bending moment curve trend of circular steel tube beam-columns under unidirectional bending;The theoretical derivation formula fitted with reference to the FEM results can more accurately calculate the stable bearing capacity of circular steel tube unidirectional bending beam-columns when the end bending moment ratio is 1,at the same time,the stable bearing capacity of circular steel tube unidirectional bending beam-columns under different end bending moment ratios can also be calculated more accurately after adopting the equivalent bending moment coefficient of the I-beam members.Finally,This paper carries out elastic second-order analysis of the circular steel tube members subject to bidirectional compression-bending.Two cases are analysed separately:(1)the larger end moments about the x-and y-axis occurs at the same end of the member,and(2)they are on separate ends.The elastic second-order bending moments are analysed and then the maximum 2nd order moment is sought to determine equivalent bending moment coefficient.A simple formula for the calculation of equivalent bending moment coefficients is given safely and it is in a consistent form with with the resultant bending moment.Elastic-plastic analysis is carried out for members with different slenderness and end moment ratios to find their buckling capacity.The proposed equivalent moment coefficient for biaxial bending is then used in the derived in-plane buckling equation of beam-column with circular pipe cross-section,an equation is obtained for buckling strength of biaxially loaded pipe columns.The obtained equation is compared with the FE results,the comparison shows that the equation has good accuracy for full ranges of parameters(slenderness,moment ratios)and may be applied in practice. |
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