Page 259 - Marks Calculation for Machine Design

P1: Shibu
14:56
January 4, 2005
Brown˙C06
Brown.cls
STATIC DESIGN AND COLUMN BUCKLING
s 2 241
Boundary of allowable Biaxial where
s = s > 0
combinations 3 1 2
12
Biaxial where
s = 2s > 0
1
2
2
–12
s 1
12
Uniaxial where
> 0, s = 0
s 1
5 2
4
–12
Pure shear where
s > 0, s = –s 1
2
1
Scale: 1 kpsi ¥ 1 kpsi
FIGURE 6.8 Principal stress combinations in Example 1 (U.S. Customary).
for Example 3 (Sec. 5.3) falls on the (σ 1 = 2σ 2 > 0) biaxial load line outside the boundary,
and the combination for Example 3 (Sec. 5.3) falls on the pure shear load line outside the
boundary.
Step 2. Identify which theory is appropriate for each combination.
For all the examples the distortion-energy theory gives the most accurate information.
However, for Example 5 (Sec. 5.2) and Example 4 (Sec. 5.3) the maximum-shear-stress
theory would be okay, but would be more conservative. For Example 3 (Sec. 5.3), the
maximum-normal-stress theory would be okay, but would be more conservative. For
Example 2 (Sec. 5.3), all three theories are appropriate as they intersect at a point on
the (σ 1 ) axis.
Step 3. Calculate the factor-of-safety for each combination, using the appropriate static
design theory.
As stated in step 2, the distortion-energy theory gives the most accurate information, so
use Eq. (6.9) to make the following calculations for each combination.
Example 5 (Sec. 5.2):
1/2
2 2 2 2 1/2

σ + σ − σ 1 σ 2 1 ((11) + (−4) − (11)(−4))
1 2
= =
S y n 12
1 (121 + 16 + 44) 1/2 (181) 1/2 13.45
= = = = 1.12
n 12 12 12
1
n = = 0.89 (unsafe)
1.12