Page 275 - Marks Calculation for Machine Design

P1: Shibu
January 4, 2005
14:56
Brown.cls
Brown˙C06
STATIC DESIGN AND COLUMN BUCKLING
Point 2:
σ 1 1 210 257
= = = 1.0
S ut n 210
1
n = = 1.0 (okay, but marginal)
1.0
Point 3:
σ 1 1 140
= = = 0.67
S ut n 210
1
n = = 1.5 (safe)
0.67
Point 4:
σ 1 1 175
= = = 0.83
S ut n 210
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 1 105 210 −385
1 − − = = 1 − −
S ut S uc S uc n 210 630 630
1 105 210 −385 1 420 385 210 385 595
= 1 − − = + = + = = 0.94
n 210 630 630 2 630 630 630 630 630
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).
Point 4:
σ 1 σ 2 1 175 −175
− = = −
S ut S uc n 210 630
1 175 −175 175 175 525 175 700
= − = + = + = = 1.11
n 210 630 210 630 630 630 630
1
n = = 0.90 (unsafe)
1.11
Point 5:
σ 1 σ 2 1 105 −385
− = = −
S ut S uc n 210 630
1 105 −385 105 385 315 385 700
= − = + = + = = 1.11
n 210 630 210 630 630 630 630
1
n = = 0.90 (unsafe)
1.11