FINAL MAE 343, Fall 2022
′
Sf′ = σF′ N b ; Sf′ = aN b ; Sf′ = SU T N c
1
σ′
1 σ′
b′ = −
log F′ = − log F′
logNe
Se
6
Se
′
σF = SU T + 50 kpsi or SU T + 345 MPa; do not use if data is available
′
′
σ′ N b
σ ′ 103b
f= F t = F
SU T
SU T
Se ′ = 0.5SU T if SU T < 200 kpsi, else = 100 kpsi
Se ′ = 0.5SU T if SU T < 1380 MPa, else = 690 kpsi; do not use if data is available
(f SU T )2
a=
Se
1
f SU T
1 f SU T
b=−
log
= − log
logNt
Se
3
Se
1
c = log f
3
b
ka = aSut
kb : see Table 6-2, p. 296
kc : bending only=1.0, axial only=0.85, torsion only =0.59
kd = 0.975 + 0.432 10−3 T − 0.115 10−5 T 2 + 0.10410−8 T 3 − 0.59510−12 T 4 ; T in o F, p. 299
Kf = 1 + q(Kt − 1) (notch sensitivity)
√ −1
a
q = 1+ √
r
√
2
3
a = 0.246 − 3.08 10−3 Sut + 1.51 10−5 Sut
− 2.67 10−8 Sut
(axial and bending)
√
−3
−5 2
−8 3
a = 0.19 − 2.51 10 Sut + 1.35 10 Sut − 2.67 10 Sut (torsion)
Sf = aN b
σa
σm
1
=
+
ηf
Se SU T
Sy
S
ηy =
or = y may give dierent values
σa + σm
σmax
o
o
F = 9/5 C + 32
1
#1/2
2
1
σa′ =
Kf,b σa,b +
Kf,a σa,a + 3 (Kf,s τa )2
0.85
1/2
′
σm
= (Kf,b σm,b + Kf,a σm,a )2 + 3 (Kf,s τm )2
"
Goodman
1
σ′
|σ ′ |
= a+ m
ηf
Se
Sut
Soderberg
σ′
|σ ′ |
1
= a+ m
ηf
Se
Sy
Gerber
ηf =
1
2
Sut
′
σm
2
σa′
Se
s
 1+
′ S
2σm
e
Sut σa′
2
ASME elliptic
"
ηf =
σa′
Se
2
+
′
σm
2 #−1/2
Sy
Langer
ηy =
Sy
′
; σ ′ = σm
+ σa′
′
|σmax
| max
2

− 1