Mechanical Design

Shaft Stress — Torsion

Torsional shear stress for solid and hollow shafts — applied stress vs. material allowable, max torque capacity, ANSI B17.1 keyway sizing, and keyway stress concentration.

Inputs

Typically 0.35–0.60 of UTS for steel

Keyway (optional)

Set to 0 to omit keyway effects
Same unit as keyway width
Keyway stress concentration factor k'w applied: k'w = 1 + 1.5·(b/d) + (h/d) per AGMA approximation.

Results

Shear stress — no keyway

—

psi

Shear stress — with keyway

—

psi

k'w factor

—

stress concentration

Max torque — no keyway

—

in·lb

Max torque — with keyway

—

in·lb

Allowable shear stress

—

psi

Inputs

Same unit as outside diameter
Typically 0.35–0.60 of UTS for steel

Keyway (optional)

Set to 0 to omit keyway effects
Same unit as keyway width
Keyway stress concentration factor k'w applied: k'w = 1 + 1.5·(b/d) + (h/d) per AGMA approximation.

Results

Shear stress — no keyway

—

psi

Shear stress — with keyway

—

psi

Polar moment (J)

—

in⁴

Max torque — no keyway

—

in·lb

Max torque — with keyway

—

in·lb

Allowable shear stress

—

psi

Material reference table

Material ↕ YS (ksi) ↓ TS (ksi) τ_allow (psi) (SF=1.5)

Torsional Shear Stress — Solid & Hollow Shafts

Solid shaft: τ = 16T / (π·d³) Hollow shaft: τ = T·(D/2) / J   where J = π(D⁴ − d⁴) / 32 k'w = 1 + 1.5·(b/d) + (h/d)   [AGMA keyway SCF] τ_allow = YS / (2 · SF)   [von Mises shear yield] T_max = τ_allow · J / c   [max torque from allowable stress]
T = applied torque (in·lb) d = solid shaft diameter D / d = hollow OD / ID J = polar moment of inertia c = outer radius b = keyway width h = keyway depth SF = safety factor YS = material yield strength