Concept explainers
A shaft is loaded in bending and torsion such that Ma = 70 N · m, Ta = 45 N · m, Mm = 55 N · m, and Tm = 35 N · m. For the shaft, Su = 700 MPa and Sy = 560 MPa, and a fully corrected endurance limit of Se = 210 MPa is assumed. Let Kf = 2.2 and Kfs = 1.8. With a design factor of 2.0 determine the minimum acceptable diameter of the shaft using the
(a) DE-Gerber criterion.
(b) DE-ASME Elliptic criterion.
(c) DE-Soderberg criterion.
(d) DE-Goodman criterion.
(a) Discuss and compare the results.
(a)
The diameter of shaft of shaft using DE-Gerber criterion.
Answer to Problem 1P
The diameter of shaft is
Explanation of Solution
Write expression for parameter.
Here, fatigue stress concentration factor for bending is
Write expression for parameter.
Here, mid range bending moment is
Write expression for diameter by applying DE-Gerber criterion.
Here, design factor is
Conclusion:
Substitute
Substitute
Substitute
Thus, the diameter of shaft is
(b)
The diameter of shaft using DE-ASME Elliptic criterion.
Answer to Problem 1P
The diameter of shaft is
Explanation of Solution
Write expression for diameter by applying DE-Elliptical criterion.
Here, design factor is
Conclusion:
Substitute
Thus, the diameter of shaft is
(c)
The diameter of shaft using DE-Soderberg criterion.
Answer to Problem 1P
The diameter of shaft is
Explanation of Solution
Write expression for diameter by applying DE-Soderberg criterion.
Here, design factor is
Conclusion:
Substitute
Thus, the diameter of shaft is
(d)
The diameter of shaft using DE-Goodman criterion.
Answer to Problem 1P
The diameter of shaft is
Explanation of Solution
Write expression for diameter by applying DE-Goodman criterion.
Conclusion:
Substitute
Thus, the diameter of shaft is
Comparison with diameter obtained from DE-Geber Criteria.
The diameters obtain from DE-Geber Criteria is
The following table shows the comparison of the diameters obtain from different criterion with respect to DE-Gerber criteria.
Criteria | Diameter |
Percentage (Relative to DE-Geber Criteria) |
DE-Elliptical criterion | ||
DE-Soderberg criterion | ||
DE-Goodman criterion |
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Chapter 7 Solutions
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