Complementary shear stress failures

JUNE 2018

So often in engineering we express concerns about whether a component is ‘strong enough’ to do the task for which it has been designed. But ‘strength’ is not always the critical parameter that needs to be considered, as our recent Tech Tips have highlighted failures are exacerbated by, for example, corrosion, cyclic loading (fatigue), temperature and/or material microstructure. There is also the question of whether ‘strength’ is the appropriate parameter to consider when toughness or resistance to fatigue crack initiation may be more appropriate, or when loading direction should specifically be taken into account. Frequently our perception of strength in materials refers to tensile strength, and indeed this is vital, but may not always be the limiting factor in a failure and in some cases both compressive strength and resistance to shear should be assessed. Although often discounted, components can and indeed do fail in shear.

A well-known manifestation of shear failure occurs in shafts loaded in torsion which induces torsional shear stresses in the transverse plane of the shaft.  As an additional consequence of the transverse shear, there is also a so-called ‘complementary shear stress’ induced in the longitudinal direction which is not always appreciated by the designer, manufacturer or operator.  These shear stresses can readily cause longitudinal cracking (at right angles to the perceived applied shear stress).  The potential for cracking due to complementary shear stress is exacerbated in cases where any ‘preferred orientation effects’ or other defects induced during the fabrication of the steel (that are typically orientated in the longitudinal direction) provide planes of weakness.  It is not only in cases where the steel has substantial microstructural features such as stringers or laminations that this type of failure occurs.  Simple grain orientation is sufficient to result in strength and toughness differences, as a function of orientation, of up to 25%.  In splined shafts, the effects of the complementary shear stresses are compounded by the stress concentrations at the root of the spline which promotes the initiation of longitudinal cracks that propagate readily by fatigue mechanisms.  

While such shear failures are clearly apparent in torsional loading situations, similar complementary shear effects manifest in conventional bending structures as well.  In structural steelwork, it is important that structural elements have sufficient moment resistance in bending (typically afforded by having substantial flanges at a distance from the neutral axis).  However, in I-beams such benefits can easily be nullified if the web strength is too low causing the web to buckle or it being unable to transfer the direct and complementary shear loading.

In bending, complementary shear stresses, developed in the longitudinal direction, need to be opposed to prevent the planes within the beam running parallel to the axis separating like an unconnected stack of planks (which would have significantly less bending resistance than an integral beam of similar size).  Such shear loading can be of sufficient magnitude to cause longitudinal cracking of the web.  Once cracks develop in the web, they often change direction and propagate by fatigue into flanges and can ultimately lead to failure of the beam.  
The message is clear; be aware that shear stress has both direct and complementary shear components or risk premature failure.

Published in Technical Tips by Origen Engineering Solutions on 1 June 2018