KEVOS® MAKEOS · Strength
Shaft Diameter for Brittle Materials and Hollow Shafts
What diameter does this shaft need by the maximum-normal-stress theory, and how does a hollow shaft compare?
Shaft diameter for brittle materials (cast iron, hardened steel) by the maximum-normal-stress theory with shock factors, the hollow-shaft factor B, and the outside diameter of a hollow shaft equal in strength to a solid one.
Open the calculatorRuns in your browser. No account needed.
How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Bending moment | N·m | Maximum bending moment at the section. |
| Torque | N·m | Torque at the section. |
| Shock factor, bending | Combined shock and fatigue factor for bending. | |
| Shock factor, torsion | Combined shock and fatigue factor for torsion. | |
| Allowable tensile stress | MPa | Allowable tensile stress of the brittle material (well below its tensile strength). |
| Bore ratio (inside ÷ outside, 0 = solid) | Ratio of bore to outside diameter for a hollow shaft; 0 for solid. |
Method and formulas
- Solid: D = ∛(5.1 ÷ St × [Km M + √((Km M)² + (Kt T)²)]).
- Hollow factor B = ∛(1 ÷ (1 − k⁴)); outside diameter = B × solid diameter.
- Weight ratio = B²(1 − k²); torsional stiffness ratio = B⁴(1 − k⁴).
- Example: the default loads need 52.311 mm solid, or 54.788 mm outside × 32.873 mm bore hollow.
Limitations
- Brittle materials only (elongation under about 5%); ductile shafts use the maximum-shear method (shaft diameter tool).
- Stress concentrations and fatigue need separate checks.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Size shafts of cast iron or hardened steel
- Replace a solid shaft with a lighter hollow one
- Compare weight and stiffness of hollow and solid shafts
Who it is for
- Design engineers
- Structural and mechanical engineers
- Engineering students
What you get
- Solid shaft diameter (maximum normal stress)
- Hollow shaft outside and inside diameters
- Weight and stiffness compared with the solid shaft
Interpreting the result
- A hollow shaft with k = 0.6 is about 4% larger in diameter but roughly 30% lighter.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 295–303. Topic reference; no source tables or recommended settings are reproduced.
WORKOS tools are screening and decision-support utilities. Verify important financial, engineering, safety, legal or operational decisions using appropriate professional standards and your organisation’s approved data.
Open the Shaft Diameter for Brittle Materials and Hollow Shafts calculator
