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以单轴对称工字截面压杆为对象,针对截面几何尺寸不同的上、下翼缘分别设定相应的剪滞翘曲函数,利用能量变分原理并结合微分方程组降阶法,推导了单轴对称截面压杆考虑剪力滞效应的临界荷载的闭合解,由此考察了欧拉临界荷载公式的可靠性和适用条件.结果表明,欧拉公式高估了薄壁压杆的临界荷载;翼缘惯性矩与全截面惯性矩之比和跨宽比对临界荷载有一定影响,其中后者的影响更明显;欧拉临界荷载公式只适用于跨宽比较大的压杆.
Taking the uniaxial symmetrical I-section bar as object, the corresponding shear lag warping function was set for the upper and lower flanges with different section geometries, respectively. By using the energy variational principle and the reduced-order method of differential equations, The reliability of the Euler critical load formula and the applicable conditions are investigated by considering the closed solution of the critical load of the shear lag effect for the uniaxially symmetric section compression bar.The results show that the Euler formula overestimates the critical load of the thin- ; The ratio of the moment of inertia of the flange and the moment of inertia of the full cross-section and the ratio of span to span have an impact on the critical load, of which the latter is more obvious. The Euler’s critical load formula is only applicable to the strut with wide span.