This example demonstrates how to calculate the appropriate machine shaft size so that the shaft can safely withstand both torque and bending moments without failing or deforming during operation.
A machine shaft is made of steel with a yield strength () of 200 MPa. This shaft must simultaneously withstand a torque () of 250 N·m and a bending moment () of 150 N·m. Calculate the safe shaft diameter () according to the Maximum Shear Stress Theory, given a safety factor () of 2.5. (Note: You can modify the variables in the input data section)
There is no fixed value, but for preliminary design, it is often considered approximately:
| Application Type | Approximate Safety Factor (SF) |
|---|---|
| Constant known load, controlled material | 1.5 - 2.0 |
| General machinery, varying loads | 2.0 - 3.0 |
| Impact loads, uncertain loads, or high consequence of failure | 3.0 - 5.0 |
| Rotating shafts requiring fatigue analysis | Usually start with 2.0 - 3.0 and analyze fatigue separately |
Step 1: Calculate the theoretical minimum diameter () (This is the shaft size where the shear stress exactly reaches the yield point, without any safety factor applied)
💡 Calculator Tip: If you input (in ) and (in ) directly into a calculator, the result will be , which is in centimeters (cm) . Converting this to millimeters (multiplying by 10) gives the result of mm.
Step 2: Calculate the design shaft size () (Compensate for uncertainties in actual usage by applying the safety factor )
From the first step calculation, the Minimum Theoretical Diameter is mm, which means if a shaft of this size is built, it will exactly reach the yield point (the onset of failure) when subjected to maximum loads.
Therefore, in the second step, when designing using the Maximum Shear Stress Theory combined with a safety factor of , the required shaft diameter is mm. Using a safety factor compensates for material uncertainties, actual loading conditions, and manufacturing limitations. In actual design, engineers will use this value to select a standard shaft size available in the market, which will always be larger than the calculated value (e.g., 35 mm or 40 mm) to ensure maximum safety.