Torsion · stiffness · first-mode speed
Solid shaft design
Inputs
Stated steady torque for the solid-shaft screening model.
Nominal solid circular diameter used for stress, twist, and stiffness calculations.
User-entered allowable basis; this screen does not select material allowables or safety factors.
Stated simply-supported span and torsion length for this narrow screen.
User-entered shear modulus at the stated condition.
User-entered Young’s modulus at the stated condition.
Single stated central force for simply-supported deflection only.
User-entered uniform mass per unit length for the first-mode speed screen.
Results
Minimum torsion-only diameter
23.351
Torsional shear stress
32.595
Torsional twist
1.1205
Central-load deflection
0.58671
First-mode critical-speed estimate
18,126
dmin = ∛(16T/πτallow); τ = 16T/(πd³); θ = TL/(GJ); δcenter = FL³/(48EI); ω₁ = (π²/L²)√(EI/m′)
A first-pass number, not a code check, certification, or approval. Read the method and its limits below. What this is and is not.
Nearby: Axial response · Beam deflection & reactions · Elastic stability · Solid-shaft torsion
Method
Formula, when it applies, and when it does not
Screen torsion-only sizing, stress, twist, central-load deflection, and first-mode critical speed for a solid shaft model.
dmin = ∛(16T/πτallow); τ = 16T/(πd³); θ = TL/(GJ); δcenter = FL³/(48EI); ω₁ = (π²/L²)√(EI/m′)
When
- Solid circular shaft
- User-entered allowables
- Central point load
- Uniform simply-supported speed model
Don’t
- This is a solid circular shaft screen: torsion-only allowable sizing, Saint-Venant twist, a simply-supported single central-load deflection, and a uniform simply-supported first-mode speed estimate. It excludes combined fatigue, stress concentrations, keyway effects, bearing/support flexibility, damping, unbalance, couplings, attached disks, distributed auxiliary masses, thermal effects, buckling, alignment, and rotor-dynamics validation.
Shigley's Mechanical Engineering Design — shaft design, deflection and critical speed