In mechanical and structural design — especially for shafts, axles, and beams in mining machinery — two critical stress types must be carefully evaluated: bending stress and shear stress.
Though both occur simultaneously in many components, confusing or misapplying them can result in flawed calculations, reduced fatigue life, or even catastrophic failure.
This blog clarifies the differences between bending and shear stresses, and how each is applied in real-world engineering scenarios.
1. What Is Bending Stress (σ<sub>b</sub>)?
Bending stress occurs when an external moment tries to bend a structural member, causing the material on one side to stretch (tension) and the other to compress.
σb=M⋅yIσ_b = \frac{M \cdot y}{I}
Where:
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MM = Bending moment (Nm)
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yy = Distance from the neutral axis
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II = Moment of inertia
✅ Max bending stress occurs at the outermost fiber of a section.
🛠️ Common in:
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Shafts supporting gears/pulleys
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Crane booms under vertical load
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Mining truck axles
2. What Is Shear Stress (τ)?
Shear stress occurs when a force tries to slide one part of a material over another. It’s greatest at the neutral axis of a rectangular cross-section and more evenly distributed in circular shafts.
τ=V⋅QI⋅bτ = \frac{V \cdot Q}{I \cdot b}
Where:
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VV = Shear force
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QQ = First moment of area
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bb = Width of the cross-section at the point of interest
✅ Shear is highest at mid-height and zero at outer surfaces in beams.
🛠️ Common in:
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Keyways and pinned connections
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Shear pins in conveyors
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Bolts, rivets, and load-bearing welds
Comparison Table
| Feature | Bending Stress (σ<sub>b</sub>) | Shear Stress (τ) |
|---|---|---|
| Load Direction | Perpendicular to axis | Parallel to cross-section |
| Peak Location | Outer fibers | Neutral axis or mid-line |
| Causes | Moments (torques, lever arms) | Direct force (V) |
| Failure Mode | Cracking, deformation | Sliding, shear fracture |
| Real-World Example | Shaft with pulley load | Keyway under torque |
Combined Stress Considerations
In mining and industrial shafts, both bending and shear occur together. That’s why engineers often use the Von Mises stress equation to evaluate combined effects:
σeq=σb2+3τ2σ_{eq} = \sqrt{σ_b^2 + 3τ^2}
This allows a single, comparable stress value to be used in fatigue and yield checks.
Mining-Specific Example
Imagine a mining conveyor shaft:
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Pulley weight introduces bending
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Torque from the motor causes shear
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Keyway amplifies local shear stress
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The combined stress must be below material yield strength, considering safety factor and fatigue
Best Practices for Design Engineers
✅ Always evaluate both stress types even if one dominates
✅ Use FEM analysis for complex geometries
✅ Apply fillets or radii to reduce peak bending stress
✅ Avoid abrupt section changes that raise shear stress
✅ For fatigue-loaded parts, use modified Goodman diagrams
Bending and shear stresses are foundational concepts — but they become powerful tools when applied correctly. In mining, construction, and heavy machinery, where equipment works under dynamic, combined loads, distinguishing and addressing each stress type ensures reliability, safety, and long-term performance.