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本文重点研究了裂纹对薄壁截面偏心受压柱弹性挠度的影响。分析模型假设偏心柱两端铰支 ;截面绕强轴发生单向弯曲变形 ;I型裂纹位于受力最为严重的中间截面内的受拉翼缘上。首先简单介绍了由 Rayleigh- Ritz变分法求得的弹性挠度三角函数级数解 ,该解的优点是可以在裂纹截面满足变形协调条件 ,适应于裂纹在薄壁截面上沿弯矩面外方向扩展的情况。然后针对工字形、箱形两种双轴对称薄壁截面柱 ,具体地分析了在不同荷载、偏心距和长细比条件下裂纹长度对偏心柱挠度的影响规律和范围。理论分析和数值结果表明 :在其它条件不变的情况下 ,柱的长细比越小或偏心距越大 ,裂纹引起的挠度增量越明显。
This paper focuses on the influence of crack on the elastic deflection of eccentric compression columns with thin-walled sections. The analysis model assumes that the eccentric columns are hinged at both ends; the uniaxial bending deformation of the cross section occurs around the strong axis; and the type I crack is located on the tensioned flange in the mid-section with the most severe stress. Firstly, the series solution to the elastic deflection trigonometric function obtained by the Rayleigh-Ritz variational method is introduced briefly. The advantage of the solution is that it can meet the deformation coordination condition at the crack cross section and adapt to the crack propagation along the thin-walled section Extensions. Then, two kinds of biaxial symmetric thin-walled columns with I-shape and box-shape are analyzed in detail. The influences of crack length on the deflection of eccentric columns under different load, eccentricity and slenderness ratio are analyzed in detail. Theoretical analysis and numerical results show that under other conditions, the smaller the slenderness ratio of the column or the larger the eccentricity, the more obvious the increment of the deflection caused by the crack.