Size a transmission shaft from torque and bending — minimum diameter by the ASME equivalent-torque method, keyway shear and bearing stress, and torsional wind-up, with a stress-versus-diameter plot showing whether strength or stiffness governs.
Tip: this is the driven-shaft torque from the belt tool.
From transverse loads — belt pull, gear separating force, overhung weight.
Rule of thumb: 0.25°/m general, 1°/m for line shafts.
Key checked in shear and bearing at the strength-based shaft diameter.
The von Mises stress (left axis) falls as diameter grows; where it drops below the allowable line, strength is satisfied. Twist (right axis) shows the stiffness limit. The governing diameter is whichever crossing sits further right.
Equivalent torque (ASME). Combine factored bending and torsion: Te = √[(Kb·M)² + (Kt·T)²]. Minimum diameter from allowable shear: D = [16·Te / (π·τ_allow)]^(1/3).
Allowable stress. τ_allow = 0.5·Sy / FoS (distortion-energy shear yield), reduced 25% when a keyway is present. The chart's von Mises curve uses σ = √(σ_b² + 3·τ_t²) with σ_b = 32·Kb·M/(πD³) and τ_t = 16·Kt·T/(πD³), compared against Sy/FoS.
Stiffness. Angle of twist θ = 32·T·L / (G·π·D⁴). The stiffness diameter is the D that keeps θ within your deg/metre limit.
Key checks. Shear stress in the key τ_k = F/(w·L_k) and bearing stress σ_br = 2F/(h·L_k), where the tangential force F = 2T/D at the shaft surface. Both are reported as a factor of safety against yield.
Standard size. The recommended diameter rounds the governing value up to the next preferred metric shaft size (ISO R20-ish set).
This is a static/quasi-static design check. Fatigue-critical shafts need a full endurance analysis (Soderberg/Goodman) with size, surface, and reliability factors, which this tool does not perform.