Static analysis will be done at a location on the shaft where we have either torque or moment. By using the Maximum shear stress theory and using the equation (18-10) in the text book, we do static analysis on diameters d_3, d₂, d₄ respectively. We assume the diameter d₁ = 0.8 (d₂).

For fatigue analysis, first identify the critical locations.

A critical location is defined as a point where the shaft is more likely to fail, such as a Stress concentrated area with a high bending moment. Stress concentration can occur if there is a sudden change in the cross sectional area (Case 1) or if there is any non-uniformity (Case 2).

1. Diameter d₁ at shoulder – ignore fatigue analysis. Case 1, but low moment.
2. Diameter d₂ at shoulder – perform fatigue analysis ( eqn. 18-28). Case 1 and high moment.
3. Diameter d₂ at keyway – perform fatigue analysis ( eqn. 18-28). Case 2 and high moment.
4. Diameter d₃ at shoulder – perform fatigue analysis (eqn 18-28). Case 1 and high moment.
5. Diameter d₄ at keyway – ignore fatigue analysis (eqn 18-28). Case 2 but low moment.

Note: In eqn 18-28 ignore factor K_f in the numerator.

S_e = k_ak_bk_ck_dk_e S_e^’

All the factors can be found out from Chapter 7 in the text book.

You can assume k_t for the keyways to be 2.5 and for the shoulders you have to calculate it from Fig (A-15-9) in the text book.

Notch radius

0£ r £ 0.08 (For sharp corners)

0.08 £ r £ 0.16 ( For rounded corners)

Wherever there is a bearing fitted on to the shaft, the fillet is taken as well rounded and if there is no bearing then the fillet is taken as sharp..

Calculate the notch sensitivity (q) from fig. 5-16.

After the analysis, select the maximum diameters to be the final diameters of the shaft.