Solid circular point-stress screen
Shaft bending + torsion
Inputs
Moment at the stated critical solid-shaft section; use a signed convention consistently.
Steady torque at the same shaft section; use a signed convention consistently.
Nominal solid circular diameter at the same section.
Results
Outer-fiber bending stressσb
71.62
Outer-fiber torsional shearτt
23.873
Maximum principal stressσ₁
78.848
Minimum principal stressσ₂
-7.2282
Plane-stress von Mises equivalentσvm
82.699
σb = 32M/(πd³); τt = 16T/(πd³); σvm = √(σb² + 3τt²)
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
Calculate outer-fiber bending stress, torsional shear, plane-stress principal values, and a von Mises equivalent for one solid shaft section.
σb = 32M/(πd³); τt = 16T/(πd³); σvm = √(σb² + 3τt²)
When
- Solid circular shaft
- Single section
- Elastic point stress
- No local concentration
Don’t
- This is an elastic outer-fiber point-stress screen for one solid circular shaft section. It excludes axial load, stress concentrations, keyways, fillets, fluctuating loading, fatigue, material allowables, deflection, bearing reaction, torsional vibration, buckling, and design approval.
Shigley's Mechanical Engineering Design