Page 383 - Marks Calculation for Machine Design

P1: Sanjay
15:14
January 4, 2005
Brown.cls
Brown˙C08
U.S. Customary MACHINE ASSEMBLY SI/Metric 365
Step 8. Substitute the shear stress (τ shear ) Step 8. Substitute the shear stress (τ shear )
found in step 1, the shear stress (τ torsion ) found found in step 1, the shear stress (τ torsion ) found
in step 5, and the angle (β) found in step 7 in step 5, and the angle (β) found in step 7
in Eq. (8.78) to determine the maximum shear in Eq. (8.78) to determine the maximum shear
stress (τ max ) as stress (τ max ) as
2
2
2
2
2
2
τ max = τ shear + τ torsion τ max = τ shear + τ torsion
−2 (τ shear )(τ torsion ) cos β −2 (τ shear )(τ torsion ) cos β
 2 2   2 2 
(0.9) + (2.9) (0.16) + (0.50)
=  −2 (0.9)(2.9)  ( kpsi · in ) 2 =  −2 (0.16)(0.50)  ( MPa · m ) 2
◦
◦
×(cos 143 ) ×(cos 143 )

(0.81) + (8.41) 2 (0.0256) + (0.25) 2
= ( kpsi · in ) = ( MPa · m )
−(5.22)(− 0.799) −(0.16)(− 0.799)
= (0.81 + 8.41 + 4.17) ( kpsi · in ) 2 = (0.0256 + 0.25 + 0.1278) ( MPa · m ) 2
= 13.39 (kpsi · in) 2 = 0.4034 (MPa · m) 2
τ max = 3.7 kpsi · in τ max = 0.64 MPa · m
Step 9. Substitute the maximum shear stress Step 9. Substitute the maximum shear stress
(τ max ) found in step 8 and the given weld (τ max ) found in step 8 and the given weld
strength (S weld ) in Eq. (8.89) to determine the strength (S weld ) in Eq. (8.89) to determine the
weld throat (H) as weld throat (H) as
τ max 3.7 kpsi · in τ max 0.64 MPa · m
(weld throat) H = = (weld throat) H = =
S weld 18.0 kpsi S weld 126.0MPa
= 0.206 in = 0.005 m
Step 10. Substitute the weld throat (H) found Step 10. Substitute the weld throat (H) found
in step 9 in Eq. (8.90) to determine the weld in step 9 in Eq. (8.90) to determine the weld
size (t) as size (t) as
H 0.206 in H 0.005 m
(weld size) t = = (weld size) t = =
cos 45 ◦ cos 45 ◦ cos 45 ◦ cos 45 ◦
5
= 0.2907 in < = 0.007 m < 1mm
16 in
Note that the next larger fillet weld size was Note that the next larger fillet weld size was
chosen. chosen.

8.3.5 Fatigue Loading
Designing a weld for dynamic loading is similar to that presented in Chap. 7 for fluctuating
shear loading. The appropriate design theory is the Goodman theory, stated mathematically
in Eq. (7.34), and repeated here as

τ a τ m 1
+ = (7.34)
S e S us n