Question

Problem 6-10 A rotating shaft of 25-mm diameter is simply supported by bearing reaction forces $R_1$ and $R_2$. The shaft is loaded with a transverse load of 13 kN as shown in the figure. The shaft is made from AISI 1045 machine finished steel whose strengths are $S_{ut} = 570$ MPa and $S_y = 310$ MPa. The surface has been machined. Determine (a) the minimum static factor of safety based on yielding. (b) the endurance limit, adjusted by factors discussed in class. (hint: do not consider temperature and reliability factors because the information about temperature and reliability is not given.) (c) the minimum fatigue factor of safety based on achieving infinite life. (hint: $n_f = \frac{S_e}{\sigma_{max}}$) (d) If the fatigue factor of safety is less than 1 (hint: it should be for this problem), then estimate the life of the part in number of rotations. Ans: $n_y = 0.98$, $S_e = 192$ MPa, $n_f = 0.6$, $N \approx 25000$ cycles Hint: Use Fig. 6-23, $f = 0.87$ If you use Eq. (6-11), $f = 0.875$, and N will be slightly different.

          Problem 6-10
A rotating shaft of 25-mm diameter is simply supported by bearing reaction forces $R_1$ and $R_2$. The
shaft is loaded with a transverse load of 13 kN as shown in the figure. The shaft is made from AISI
1045 machine finished steel whose strengths are $S_{ut} = 570$ MPa and $S_y = 310$ MPa. The surface has
been machined. Determine
(a) the minimum static factor of safety based on yielding.
(b) the endurance limit, adjusted by factors discussed in class. (hint: do not consider temperature
and reliability factors because the information about temperature and reliability is not given.)
(c) the minimum fatigue factor of safety based on achieving infinite life. (hint: $n_f = \frac{S_e}{\sigma_{max}}$)
(d) If the fatigue factor of safety is less than 1 (hint: it should be for this problem), then estimate
the life of the part in number of rotations.
Ans: $n_y = 0.98$, $S_e = 192$ MPa, $n_f = 0.6$, $N \approx 25000$ cycles
Hint: Use Fig. 6-23, $f = 0.87$
If you use Eq. (6-11), $f = 0.875$, and N will be slightly different.

Problem 6-10
A rotating shaft of 25-mm diameter is simply supported by bearing reaction forces R1 and R2. The
shaft is loaded with a transverse load of 13 kN as shown in the figure. The shaft is made from AISI
1045 machine finished steel whose strengths are Sut = 570 MPa and Sy = 310 MPa. The surface has
been machined. Determine
(a) the minimum static factor of safety based on yielding.
(b) the endurance limit, adjusted by factors discussed in class. (hint: do not consider temperature
and reliability factors because the information about temperature and reliability is not given.)
(c) the minimum fatigue factor of safety based on achieving infinite life. (hint: nf = (Se)/(σmax))
(d) If the fatigue factor of safety is less than 1 (hint: it should be for this problem), then estimate
the life of the part in number of rotations.
Ans: ny = 0.98, Se = 192 MPa, nf = 0.6, N ≈ 25000 cycles
Hint: Use Fig. 6-23, f = 0.87
If you use Eq. (6-11), f = 0.875, and N will be slightly different.

Added by James A.

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