Maximum Shear Stress
Maximum shear stress is the highest internal shear stress at a point in a part. In 3D stress analysis it equals half the greatest absolute difference between principal stresses. For ductile metal design, it is the basis of the Tresca failure criterion, which predicts yielding when shear reaches about half the tensile yield strength. This makes it more conservative than von Mises, which predicts yielding at roughly 0.577 of yield strength in pure shear.
On the shop floor, maximum shear stress governs the durability of toolholders, spindles, arbors, shafts, keyways, and bearing supports. The highest torsional shear stress sits at the outer surface of a circular shaft, so a modest increase in torque, cutter stick-out, or an interrupted-cut impact can cause a sudden spike at that critical diameter. That is why spindle diameters and holder engagement lengths are sized for peak cutting-force events, not average load. In fasteners, dowels, and millwork joints, the same principle appears as sliding failure across a plane under clamping or service loads. The designer checks whether internal shear resistance stays below the allowable limit. Using maximum shear stress in finite-element checks or hand calculations prevents shaft twist, toolholder slip, screw-body shear, and joint slip. In ductile parts, Tresca’s conservative nature catches local stress concentrations near key seats and thread roots before production release.
What is the governing equation for maximum shear stress in principal-stress form?
The maximum shear stress is given by τ_max = (σ_1 - σ_3)/2. Under the maximum shear stress criterion, yielding begins when this value reaches the material’s allowable shear limit.
Where is the maximum shear stress located in a round shaft under torque?
It is located at the outer radius of the shaft. Torsional shear stress increases with distance from the center, so the surface experiences the greatest shear stress.
How does Tresca differ from von Mises stress?
Tresca is based on maximum shear stress and is more conservative. In pure shear, Tresca predicts yielding at about 0.5 times the tensile yield strength, while von Mises predicts yielding at about 0.577 times the tensile yield strength.