Page 446 - Shigley's Mechanical Engineering Design

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Screws, Fasteners, and the Design of Nonpermanent Joints 421
Alternatively, you can determine the principal stresses and then use Eq. (5–12) to find
the von Mises stress. This would prove helpful in evaluating τ max as well. The prin-
cipal stresses can be found from Eq. (3–15); however, sketch the stress element and
note that there are no shear stresses on the x face. This means that σ x is a principal
stress. The remaining stresses can be transformed by using the plane stress equation,
Eq. (3–13). Thus, the remaining principal stresses are

−10.39 −10.39 2
2
± + 6.07 = 2.79, −13.18 MPa
2 2
Ordering the principal stresses gives σ 1 , σ 2 , σ 3 = 41.5, 2.79, −13.18 MPa. Substi-
tuting these into Eq. (5–12) yields

[41.5 − 2.79] + [2.79 − (−13.18)] + [−13.18 − 41.5]
2 2 2 1/2
Answer σ =

2
= 48.7MPa
(h) The maximum shear stress is given by Eq. (3–16), where τ max = τ 1/3 , giving

σ 1 − σ 3 41.5 − (−13.18)
Answer τ max = = = 27.3MPa
2 2

Table 8–4 Screw Nut
Screw Bearing Material Material Safe p b , psi Notes
Steel Bronze 2500–3500 Low speed
Pressure p b
Source: H. A. Rothbart and Steel Bronze 1600–2500 ≤10 fpm
T. H. Brown, Jr., Mechanical Cast iron 1800–2500 ≤8 fpm
Design Handbook, 2nd ed.,
McGraw-Hill, New York, 2006. Steel Bronze 800–1400 20–40 fpm
Cast iron 600–1000 20–40 fpm
Steel Bronze 150–240 ≥50 fpm

1
Ham and Ryan showed that the coefficient of friction in screw threads is inde-
pendent of axial load, practically independent of speed, decreases with heavier lubri-
cants, shows little variation with combinations of materials, and is best for steel on
bronze. Sliding coefficients of friction in power screws are about 0.10–0.15.
Table 8–4 shows safe bearing pressures on threads, to protect the moving sur-
faces from abnormal wear. Table 8–5 shows the coefficients of sliding friction for

1 Ham and Ryan, An Experimental Investigation of the Friction of Screw-threads, Bulletin 247, University of
Illinois Experiment Station, Champaign-Urbana, Ill., June 7, 1932.