Page 365 - Marks Calculation for Machine Design

P1: Sanjay
January 4, 2005
15:14
Brown.cls
Brown˙C08
U.S. Customary MACHINE ASSEMBLY SI/Metric 347
Step 17. Substitute the bolt preload (F preload ) Step 17. Substitute the bolt preload (F preload )
from step 13, and the given tensile-stress from step 13, and the given tensile-stress
area (A T ), ultimate tensile strength (S ut ), and area (A T ), ultimate tensile strength (S ut ), and
endurance limit (S e ) in Eq. (8.60) to determine endurance limit (S e ) in Eq. (8.60) to determine
the alternating strength of the bolt (S a ) as the alternating strength of the bolt (S a ) as
F preload F preload
S ut − S ut −
A T A T
S a = S a =
S ut S ut
1 + 1 +
S e S e
17,280 lb 84,780 N
(120 kpsi) − (830 MPa) −
2.26 × 10 −1 in 2 1.57 × 10 −4 m 2
= =
120 kpsi 830 MPa
1 + 1 +
18.6 kpsi 129 MPa
(120 kpsi) − (76.5 kpsi) (830 MPa) − (540 MPa)
= = 1 + 6.43
1 + 6.45
43.5 kpsi 290 MPa = 39.0MPa
= = 5.84 kpsi = 7.43
7.45
Step 18. Substitute the alternating stress on the Step 18. Substitute the alternating stress on the
bolt (σ a ) found in step 16 and the alternating bolt (σ a ) found in step 16 and the alternating
strength of the bolt (S a ) found in step 17 in strength of the bolt (S a ) found in step 17 in
Eq. (8.57) to determine the fatigue factor-of- Eq. (8.57) to determine the fatigue factor-of-
safety (n fatigue ) as safety (n fatigue ) as
S a 5.84 kpsi S a 39.0MPa
n fatigue = = = 2.4 n fatigue = = = 2.4
σ a 2.39 kpsi σ a 16.1MPa
Step 19. Substitute the alternating stress on Step 19. Substitute the alternating stress on
the bolt (σ a ) found in step 16, the bolt preload the bolt (σ a ) found in step 16, the bolt preload
(F preload ) found in step 13, and the given tensile- (F preload ) found in step 13, and the given tensile-
stress area (A T ) in Eq. (8.56) to determine the stress area (A T ) in Eq. (8.56) to determine the
mean stress on the bolt (σ m ) as mean stress on the bolt (σ m ) as
F preload F preload
σ m = σ a + σ m = σ a +
A T A T
17,280 lb 84,780 N
= (2.39 kpsi) + 2 = (16.1MPa) + −4 2
2.26 × 10 −1 in 1.57 × 10 m
= (2.39 kpsi) + (76.46 kpsi) = (16.1MPa) + (540.0MPa)
= 78.85 kpsi = 556.1MPa
Step 20. Substitute the alternating stress on the Step 20. Substitute the alternating stress on the
bolt (σ a ) found in step 16, the mean stress on bolt (σ a ) found in step 16, the mean stress on
the bolt (σ m ) found in step 19, and the given the bolt (σ m ) found in step 19, and the given
yield strength (S y ) in Eq. (8.61) to determine yield strength (S y ) in Eq. (8.61) to determine
the factor-of-safety against yielding (n yield ) as the factor-of-safety against yielding (n yield ) as
S y S y
n yield = n yield =
σ m + σ a σ m + σ a
92 kpsi 660 MPa
= =
(78.85 kpsi) + (2.39 kpsi) (556.1MPa) + (16.1MPa)
92 kpsi 660 MPa
= = 1.13 = = 1.15
81.24 kpsi 572.2MPa