The article investigates by finite elements the bending stresses around a centre transverse circular hole in straight bars with rectangular or circular cross-section. Four loading conditions are considered, pure bending and three variants of three-point bending (load concentrated on the bar surface above the hole, load directly applied to the hole as uniform pressure, load applied to the hole through a connecting pin). Mostly, the hole diameter is one-third of the section height and one-twentieth of the beam length. Holes of one-fourth and one half of the section on several beam lengths are also investigated for the flat bar in three-point bending to appraise the sensitivity to aspect ratios. The results show that, in all cases, the notch effect is mildly detrimental to the stress distribution and can even be beneficial in comparison with the unperforated bar. This is because the hole increases the stresses around the neutral axis, where the stresses are naturally low, thus taking away stresses from the surface where the bending stresses are naturally highest. The design of pivoted flexural machine elements like levers, yokes and balance arms can take advantage from this evidence.

中文翻译：

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具有横向中心孔的直棒中的弯曲应力：有益缺口效应的案例？

本文通过有限元研究了矩形或圆形截面直杆中心横向圆孔周围的弯曲应力。考虑四种载荷条件，纯弯曲和三点弯曲的三种变体（载荷集中在孔上方的杆表面上，载荷作为均匀压力直接施加到孔上，载荷通过连接销施加到孔上）。大多数情况下，孔径是截面高度的三分之一和梁长度的二十分之一。还对三点弯曲中的扁钢在几个梁长度上的四分之一和二分之一截面的孔进行了研究，以评估对纵横比的敏感性。结果表明，在所有情况下，缺口效应对应力分布都有轻微的损害，与未穿孔的钢筋相比甚至可能是有益的。这是因为孔增加了中性轴周围的应力，而中性轴周围的应力自然较低，从而消除了弯曲应力自然最高的表面的应力。杠杆、轭和平衡臂等枢轴弯曲机器元件的设计可以利用这一证据。