Page 272 - Marks Calculation for Machine Design

P1: Shibu
January 4, 2005
14:56
Brown˙C06
Brown.cls
254
STRENGTH OF MACHINES
As stated in step 2, the maximum-normal-stress theory gives the most accurate informa-
tion for points 1, 2, 3, and 4, so use Eq. (6.14) to make the following calculations for these
combinations.
Point 1:
σ 1 1 40
= = = 1.33
S ut n 30
1
n = = 0.75 (unsafe)
1.33
Point 2:
σ 1 1 30
= = = 1.0
S ut n 30
1
n = = 1.0 (okay, but marginal)
1.0
Point 3:
σ 1 1 20
= = = 0.67
S ut n 30
1
n = = 1.5 (safe)
0.67
Point 4:

σ 1 1 25
= = = 0.83
S ut n 30
1
n = = 1.2 (safe)
0.83
Also stated in step 2, the modified Coulomb-Mohr theory gives the most accurate infor-
mation for point 5, so use the first expression in Eq. (6.18) to make the following calculation
for this combination.
Point 5:

σ 1 S ut σ 2 1 15 30 −55
1 − − = = 1 − −
S ut S uc S uc n 30 90 90

1 15 30 −55 1 60 55 30 55 85
= 1 − − = + = + = = 0.94
n 30 90 90 2 90 90 90 90 90
1
n = = 1.06 (safe, but just barely)
0.94
Step 4. Compare the factors-of-safety found in step 3 for Points 4 and 5 with the Coulomb-
Mohr theory given in the first expression of Eq. (6.16).