9 Contact Stresses
9 Contact Stresses
9 Contact Stresses
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444 TABLE 9-2 Formulas for <strong>Contact</strong> <strong>Stresses</strong><br />
TABLE 9-2 (continued) FORMULAS FOR CONTACT STRESSES, DIMENSIONS, AND CONTACT AREAS, AND RIGID-BODY APPROACHES a<br />
Case Formulas<br />
4b.<br />
Concentrated force on surface<br />
of semi-infinite body<br />
4c.<br />
Uniform pressure p over length ℓ<br />
on surface of semi-infinite body<br />
4d.<br />
Rigid cylindrical die of radius r<br />
on surface of semi-infinite body<br />
At an elemental area perpendicular to z axis of any point Q, the resultant stress is 3F cos2 θ<br />
2πr 2<br />
At surface point O1 outside loaded area<br />
d = 2p<br />
π E<br />
<br />
(ℓ + x1) ln c<br />
ℓ+x1 − x1 ln d x1<br />
<br />
+ pℓ 1−ν<br />
π E<br />
At surface point O2 underneath loaded area<br />
d = 2p<br />
π E<br />
<br />
(ℓ − x2) ln c<br />
ℓ−x2 + x2 ln d x2<br />
<br />
+ pℓ 1−ν<br />
π E<br />
where d = displacement relative to a remote point distance c from edge of loaded area<br />
At any point Q<br />
σc = p<br />
π (α + sin α)<br />
d = F(1 − ν2 )/2RE<br />
At any point Q on surface of contact<br />
F<br />
σc = √<br />
2π R R2−r 2<br />
(σc)max =∞ at edge (σc)min = F/2π R 2 at center
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