引用本文: 黄可, 郭昱均, 郝泱, 李栋栋, 范钦珊. 由一张A4纸引发的思考1)[J]. 力学与实践, 2021, 43(5): 801-805.
HUANG Ke, GUO Yujun, HAO Yang, LI Dongdong, FAN Qinshan. INSPIRATION OF A SHEET OF A4 PAPER1)[J]. MECHANICS IN ENGINEERING, 2021, 43(5): 801-805.
 Citation: HUANG Ke, GUO Yujun, HAO Yang, LI Dongdong, FAN Qinshan. INSPIRATION OF A SHEET OF A4 PAPER1)[J]. MECHANICS IN ENGINEERING, 2021, 43(5): 801-805.

## INSPIRATION OF A SHEET OF A4 PAPER1)

• 摘要: 为了从力学角度解释"一张打印纸平着立不起来,而弯曲一定弧度后就可以"这一现象,本文通过数学手段对两种状态下横截面几何性质进行演算,得到了截面形心主惯性矩的计算公式,并结合计算机分析进行验证,证明了公式的适用性。通过对纸张稳定性的讨论,把该问题抽象为自重状态下的压杆稳定性分析,发现弯曲弧度对于稳定性影响很大,当弧度为2.52时,圆柱面状A4纸均布轴向载荷的临界值约为平面状A4纸的3.7\times 10^5倍。

Abstract: In order to explain the phenomenon that "a sheet of printing paper cannot be erected, while a certain degree curved one can" in terms of mechanics, the geometric properties of the cross section under two different states are analyzed to form a formula for the principal centroidal moments of inertia, which is verified by numerical simulations. The stability of the sheet of paper or a curved one is reduced into the stability of a column under its own weight. It is found that the curvature of the arc has a great influence on the stability. When the arc is 2.52, the critical value of the evenly distributed axial load of the cylindrical A4 paper is about 3.7\times10^5 times of that of the planar one.

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