A component can pass a nominal stress calculation with room to spare and still crack at a shoulder radius, a weld termination, a drilled hole or a machining mark that looked unremarkable on the drawing. The surrounding material appears lightly stressed; the detail governs anyway.
Recognising a stress concentration is not simply a matter of spotting sharp corners. It requires understanding how load enters a component, how geometry and stiffness redistribute that load, and which local stress or strain measure matters for the failure mechanism in question. This article sets out a practical framework for that recognition: separating nominal stress from local amplification, reading FEA results correctly, and matching the assessment to the failure mode that's at risk.
Nominal Stress and Local Amplification Are Different Things
A stress concentration is a local increase in stress caused by a disturbance in the stress field: a change in section, an opening, a notch, a connection, an abrupt change in stiffness. The theoretical stress concentration factor for a given elastic loading case is:
Both the numerator and the denominator need a clearly defined meaning: the stress component, the reference section and the loading mode all matter. A Kt value quoted without them is not usable.
A stepped shaft illustrates why the two effects need separating. The smaller section has higher nominal bending stress simply because its section modulus is lower. That's a structural effect, not a stress concentration. The shoulder fillet adds a further, local amplification on top of it. Confusing the two matters in practice: a design change that reduces the fillet's Kt while removing material can still raise the peak stress, because nominal stress went up faster than the concentration factor came down.
The reverse confusion is just as common. A large bending stress at a cantilever root isn't automatically evidence of a geometric stress concentration. It may simply be the bending moment distribution doing what bending moments do. The attachment detail at the root can then add a genuine local effect on top of that. The question worth asking at every location is: how much of this stress comes from the overall structural response, and how much comes from the specific detail being assessed?
Trace the Load Path Before Inspecting Individual Features
A geometry review is far more effective once the applied forces and moments have been traced through the assembly to its supports. Identify where load enters, where it changes direction, where it splits between members, and where it transfers through a connection between components of different stiffness.
A useful first pass looks specifically at: concentrated load introduction through pins, bolts, bearings and brackets; abrupt terminations of stiffeners, doublers, ribs and gussets; eccentricity between an applied load and the section resisting it; transitions between flexible plate and comparatively rigid attachment; changes in support condition or contact engagement; and anywhere affected by thermal expansion, assembly preload or imposed displacement. A smooth external profile guarantees nothing. A concealed contact edge or a hidden stiffness transition can govern the response entirely.
Loading history matters just as much as geometry. A rotating shaft under a transverse load fixed in space is the classic case: the external load itself is steady, but a material point on the shaft's surface passes through tension and back through compression on every revolution. The local bending stress is fully cyclic even though nothing about the applied load is changing. Before ranking any shoulder, keyway or groove, establish what the material experiences in service (including starts, stops, reversals and the occasional exceptional event) not just what the static load case shows.
Recurring Features Worth Checking Every Time
The following table is a starting point for reviewing drawings, models and physical hardware, a set of candidate locations, not a ranking of severity. A visually prominent feature in a lightly loaded region is frequently less significant than a small defect sitting in a highly stressed area.
| Feature | Where to look | What requires attention |
|---|---|---|
| Holes and cut-outs | Hole boundaries, slot ends, remaining ligaments | Load direction, edge distance, neighbouring openings, bearing loads |
| Stepped shafts and bars | Fillets on the smaller section | Radius, step ratio, relief grooves, loading mode |
| Keyways and splines | Roots, ends, transitions | Local torque transfer, bending, interaction with shoulders |
| Threads | Thread roots, run-outs, head transitions | Root geometry, engagement, non-uniform load transfer |
| Welded attachments | Toes, roots, weld ends, attachment ends | Weld profile, structural restraint, misalignment, local bending |
| Stiffeners and doublers | Terminations, thickness changes | Force transfer into the adjoining material |
| Contacting components | Contact edges, material beneath the contact | Pressure distribution, slip, preload, subsurface stress |
| Damaged surfaces | Pits, scores, dents, fretting | Actual defect geometry relative to loading direction |
Threaded components are a good illustration of why detail matters beyond the obvious. Root radius and thread-forming process affect fatigue performance materially. A threaded connection isn't adequately characterised by nominal diameter alone, and NASA's Fastener Design Manual is a useful reference on exactly how much the manufacturing route changes the picture.
Judging Sharpness Relative to the Surrounding Geometry
An absolute radius on its own rarely establishes severity. For a stepped shaft, the relevant parameters are typically the diameter ratio D/d and the relative fillet radius r/d together, not the radius in isolation. For a plate with an opening, hole size relative to plate width and distance to nearby boundaries matter just as much.
The loading mode has to match the reference solution being used. A concentration factor derived for axial tension cannot be carried across to bending or torsion on the same geometry. A shaft under combined bending and torque generally needs separate elastic concentration factors evaluated before the combined local stress state can be assessed properly, and orientation matters too. An elongated opening can behave very differently as the principal loading direction changes relative to it.
Neighbouring features deserve particular scrutiny. A keyway ending near a shoulder, two closely spaced holes, or a weld termination beside a cut-out can create an interacting stress field that a simple multiplication of isolated handbook factors will not represent correctly. That shortcut is only valid where the specific assessment method explicitly supports it. For interacting geometry, use a validated solution for the combined arrangement or a properly verified numerical model instead.
The Nominal-Stress Convention Is Part of the Factor
Gross-section and net-section reference stresses produce different numerical Kt values for the same physical peak stress, and mixing them is one of the more common ways a handbook lookup goes wrong. A worked example makes the point concrete.
Take a plate 100 mm wide and 10 mm thick, with a central 20 mm hole, carrying 100 kN in tension. Gross-section nominal stress is 100,000 / (100×10) = 100 MPa. Net-section nominal stress is 100,000 / ((100−20)×10) = 125 MPa. For illustration only (not a derived solution for this specific geometry) assume the actual local elastic peak is 320 MPa:
| Reference convention | Nominal stress | Corresponding Kt | Recovered peak |
|---|---|---|---|
| Gross section | 100 MPa | 3.20 | 320 MPa |
| Net section | 125 MPa | 2.56 | 320 MPa |
Both factors describe the identical physical peak, correctly paired. Apply the gross-section factor of 3.20 to the net-section stress of 125 MPa instead, and the result is 400 MPa, a 25% overestimate purely from mismatching the convention, with no error in either individual number. The convention has to travel with every quoted factor, spreadsheet entry and calculation sheet, not just the number.
The familiar "Kt = 3" result for a circular hole deserves the same care. It applies specifically to an isolated circular hole in an effectively infinite, isotropic, linear-elastic plate under remote uniaxial tension, referenced to the far-field stress. The classical Kirsch solution. It is not a general-purpose factor for bolt holes, finite-width plates, or anywhere bearing contact or nearby openings are present; those conditions need their own appropriate treatment.
Match the Assessment to the Failure Mechanism
The same elastic concentration carries different consequences depending on whether the governing failure mode is monotonic yielding, fatigue, or crack growth. Treating them interchangeably is a common source of both over- and under-conservative assessments.
In a ductile component under monotonic loading, local yielding can redistribute stress, so an elastic peak above yield doesn't by itself establish global plastic collapse. It can still violate a no-yield requirement or cause unacceptable permanent set, and where redistribution is being relied on, the assessment needs to consider available ductility, constraint and the extent of plasticity, not simply assume it because the material happens to be described as ductile.
For fatigue, the governing quantity is the local cyclic response, not the peak of an occasional static case. A component can survive an occasional overload and still accumulate meaningful damage under repeated lower loads that never approach yield. Passing a static proof test says nothing about the required fatigue life. Where local cyclic plasticity becomes significant, an elastic Kt alone can't describe the strain history; a suitable notch approximation or a cyclic elastic-plastic analysis with compatible fatigue data becomes necessary instead.
An existing crack is a different problem again. Fracture mechanics stress intensity factors such as KI describe the crack-tip field and are not interchangeable with the dimensionless elastic concentration factor Kt: once a crack is present, crack size, orientation, material toughness and loading history become the governing parameters, assessed under a framework such as BS 7910 rather than a stress concentration handbook.
Elastic Concentration and Fatigue Notch Effect Are Not the Same Number
Kt describes elastic stress amplification. The fatigue notch factor Kf describes the reduction in fatigue strength a notch causes under specified conditions, and the two are related (not identical) through:
q is notch sensitivity, conventionally ranging from 0 (no fatigue-strength reduction regardless of Kt) to 1 (Kf = Kt, full sensitivity). It reflects that measured fatigue strength reduction doesn't always match the elastic peak-stress amplification: material, notch dimensions and the local stress gradient all influence the actual response. This is a modelling relationship to apply with the appropriate data for the material and detail in question, not a universal constant.
Combined or changing loads add a further trap: an unsigned von Mises contour cannot distinguish tension from compression on its own. Fully reversed uniaxial stresses of +100 MPa and −100 MPa both produce a von Mises magnitude of 100 MPa. Subtracting those two equivalent-stress values gives zero, when the actual stress range experienced by the material is 200 MPa. Multiaxial fatigue assessment generally needs the signed stress or strain history and a critical-plane method, not a single equivalent-stress plot read at two points in the cycle.
Welded Joints Carry Concentrations at Several Scales at Once
A welded attachment typically contains a structural concentration from the connection geometry, additional local bending from any misalignment, and a further notch effect at the weld toe or root on top of both. Inspecting the toe transition, undercut, root configuration, penetration, weld ends and attachment termination all matter. A neat-looking weld can still sit on a poor structural detail, and reshaping the weld profile alone can leave the dominant local bending mechanism completely unaddressed.
Which stresses belong in the calculation depends on which of three established method families is being used, and they are not interchangeable within a single assessment:
- Nominal-stress methods pair a defined nominal stress with a fatigue detail category whose S-N curve already incorporates the typical local effects for that joint type.
- Structural hot-spot methods include the structural stress concentration from the connection geometry while deliberately excluding the local weld-notch peak, extrapolating from defined reference points near the weld toe.
- Effective-notch methods model a prescribed fictitious notch radius (typically 1 mm) at the weld toe or root and evaluate it against a fatigue curve derived specifically for that notch representation.
Comparing an arbitrary peak stress from a sharply modelled weld toe against a nominal-stress fatigue curve double-counts the local effect and produces a meaningless result. Record which method was used, the exact stress extraction procedure, and the resistance curve it's paired with, all together, EN 13445-3 Annex B and the equivalent IIW recommendations exist precisely because stress definition and fatigue resistance data have to travel as a matched pair.
Look Beneath Contact Surfaces, Not Just Around Geometric Notches
Bearings, gears, pins, press fits and clamped interfaces introduce concentrated load transfer that doesn't resemble a conventional shoulder or hole problem at all. The critical response depends on contact pressure, friction, clearance, preload and local slip, and the critical location can move during a load cycle as engagement changes.
In rolling contact specifically, fatigue damage often originates below the surface, at the depth where the governing shear stress from Hertzian contact theory peaks, not at the surface itself, which a surface-only review will miss entirely. Fretting introduces a further mechanism where contacting surfaces undergo small relative movement under nominally static load. The practical recognition cue is concentrated force transfer through a limited contact area, present even when both mating components have smooth, unremarkable profiles.
Reading FEA Peaks Before Treating Them as Design Values
A contour plot shows where the model predicts high stress. It does not establish that the displayed maximum is physically meaningful or appropriate for the assessment being carried out. That distinction is where a large share of FEA misuse happens.
Start with the global response: equilibrium, reactions, deformation and load transfer. No amount of local mesh refinement compensates for an incorrect support condition or an unrealistic connection upstream of it. Then check the local geometry and result extraction. Confirm the model includes the radius, thickness transition, contact or eccentricity responsible for the expected concentration, and review the relevant stress components and through-thickness behaviour rather than relying on a single equivalent-stress contour.
A genuine finite-radius elastic concentration approaches a bounded peak as the mesh adequately resolves it. An idealised sharp re-entrant corner, a point load, or an abrupt constraint termination instead produces a mathematical singularity, where the reported peak keeps rising as the mesh refines further. The distinction matters because a rising value on its own doesn't prove singular behaviour. An under-resolved but finite concentration also rises as the mesh improves. The way to tell them apart is to examine successive mesh refinements and stress at fixed physical locations, watching for convergence to a bounded value versus continued unbounded growth.
Do not resolve a suspect peak by simply ignoring the hottest element or reading stress "two elements away" without a defined, validated basis for doing so. The physical location that phrase points to changes with mesh density, and the resulting value has no established relationship to any actual failure criterion. A defensible treatment instead means representing the real radius, improving the load or support modelling, or adopting an established structural-stress, notch-stress or fracture-mechanics method, with the extraction procedure that method specifies. Submodelling can provide useful local resolution, provided the global model supplies reliable boundary displacements and the local refinement doesn't materially change the assembly's overall stiffness.
Compare the Model Against the Manufactured, Operated Component
Stress concentrations are influenced by dimensions and conditions frequently absent from the nominal CAD model entirely. A physical review should record actual radii, machining marks, weld undercut, misalignment, corrosion pits, fretting, dents and any previous repair, including inaccessible faces and concealed interfaces the load path makes relevant.
Document findings with dimensions, orientation and location. "surface damage near the shoulder" is far less useful than a measured score at a defined position relative to the fillet and the bending direction. Inspection establishes the physical condition of the component; it does not by itself measure the operating stress, and equally, the absence of a visible crack does not establish acceptable fatigue performance on its own.
Select non-destructive examination for the defect type and material expected: penetrant testing for discontinuities open to a properly prepared surface, magnetic particle testing for ferromagnetic materials where surface or near-surface discontinuities are the concern, access, geometry and expected flaw orientation drive the right choice between them.
Experimental validation has its own spatial limitations worth remembering. A strain gauge averages strain over its active grid, and a gauge spanning a steep gradient near a concentration will systematically under-report the true local maximum. A meaningful comparison matches a measurement against a model result at the same position, orientation and averaging area. Agreement with a nearby nodal peak that doesn't share those characteristics isn't a meaningful validation target.
Reducing Concentrations Properly
Increasing a fillet radius is often useful, but the more effective change frequently lies in the surrounding structure rather than the local detail itself: smoother section transitions, better alignment, relocating openings, separating interacting features, or a more gradual transfer of force at an attachment end.
Consider a welded bracket carrying a transverse load at an offset. A short stiffener can reduce overall deflection while creating a new critical region exactly where the stiffener ends. The force it carries has to transfer back into the adjoining plate somewhere, and that somewhere becomes the new thing to check. The revised design needs assessment at both the original attachment and the new stiffener termination; reduced deflection on its own says nothing about fatigue performance at the new detail.
The same logic applies to increasing a shaft fillet radius. It requires checking adjacent bearing or hub clearance, since a beneficial nominal geometry can be undermined if the mating component ends up bearing against the fillet itself or forcing an unsuitable relief detail. Specify the dimensions that support the assessment: minimum radius, transition profile, surface condition, permissible misalignment, required finishing, and confirm they survive manufacturing, inspection and maintenance intact. After any modification, reassess the full assembly: a lower concentration factor at one location is only useful once the complete response, and the resistance it's being checked against, both support the revised design.
Summary
Recognising a stress concentration is an engineering judgement, not a geometry checklist. It requires separating nominal stress from local amplification, tracing the actual load path before ranking individual features, matching the assessment method to the governing failure mechanism, and treating an FEA contour plot as a starting point for investigation rather than a finished answer.
The review record that supports a design decision should let another engineer reconstruct the reasoning without relying on a coloured plot: the governing load history, the physical cause of the concentration, the reference stress convention, the local geometric representation and its limitations, the applicable failure mechanism, a compatible assessment method, and the supporting evidence, analytical checks, mesh convergence, measurement and inspection findings. That record is what turns a red spot on a screen into a defined engineering decision: a located detail, a credible mechanism, an appropriate method, and a design that can be manufactured and inspected as intended.
Forgepoint provides stress analysis and FEA as part of our mechanical design service, including detailed fatigue assessment of welded and bolted structures. If a detail on your design needs a proper concentration or fatigue assessment, get in touch to discuss your requirements.
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