Page 332 - Shigley's Mechanical Engineering Design

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Fatigue Failure Resulting from Variable Loading 307
The failure criteria are used in conjunction with a load line, r = S a /S m = σ a /σ m .
Principal intersections are tabulated in Tables 6–6 to 6–8. Formal expressions for
fatigue factor of safety are given in the lower panel of Tables 6–6 to 6–8. The first row
of each table corresponds to the fatigue criterion, the second row is the static Langer
criterion, and the third row corresponds to the intersection of the static and fatigue

Table 6–6 Intersecting Equations Intersection Coordinates
Amplitude and Steady S a S m rS e S ut
+ = 1 S a =
Coordinates of Strength S e S ut rS ut + S e
and Important S a S a
Load line r = S m =
Intersections in First S m r
Quadrant for Modified S a S m rS y
+ = 1 S a =
Goodman and Langer S y S y 1 + r
Failure Criteria S a S y
Load line r = S m =
S m 1 + r

S a S m S y − S e S ut
+ = 1 S m =
S e S ut S ut − S e
S a S m
+ = 1 S a = S y − S m ,r crit = S a /S m
S y S y
Fatigue factor of safety
1
n f =
σ a σ m
+
S e S ut

Table 6–7 Intersecting Equations Intersection Coordinates
Amplitude and Steady 2 2 2 ⎡ 2 ⎤
S a S m r S ut 2S e
Coordinates of Strength + = 1 S a = ⎣ −1 + 1 + ⎦
S e S ut 2S e rS ut
and Important
Intersections in First S a S a
Load line r = S m =
Quadrant for Gerber and S m r
Langer Failure Criteria S a S m rS y
+ = 1 S a =
S y S y 1 + r
S a S y
Load line r = S m =
S m 1 + r
⎡ ⎤

2
2 2
S a S m S ut 2S e S y
+ = 1 S m = ⎣ 1 − 1 + 1 − ⎦
S e S ut 2S e S ut S e
S a S m
+ = 1 S a = S y − S m ,r crit = S a /S m
S y S y
Fatigue factor of safety
⎡ ⎤

1 S ut 2 σ a 2σ m S e 2
n f = ⎣ −1 + 1 + ⎦ σ m > 0
2 σ m S e S ut σ a