Bending stresses in straight bars with a transverse centre hole: A case of beneficial notch effect?

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.