Page 274 - Marks Calculation for Machine Design

P1: Shibu
January 4, 2005
14:56
Brown˙C06
Brown.cls
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STRENGTH OF MACHINES
Biaxial where
s = s > 0
2
1
s 2
Boundary of allowable
combinations 3
210
Biaxial where
2 s 1 = 2s > 0
2
s
–630 210 1
1
–30 Uniaxial where
4 s > 0, s = 0
1
2
5
Pure shear where
–630 s > 0, s = –s 1
2
1
Scale: 35 MPa × 35 MPa

FIGURE 6.17 Principal stress combinations in Example 2 (SI/metric).

Step 2. Identify which theory is appropriate for each combination.
For points 1, 2, 3, and 4, the maximum-normal-stress theory gives the most accurate
information, and for point 5 the modified Coulomb-Mohr theory gives the most accurate
information. However, for points 4 and 5 the Coulomb-Mohr theory would be okay, but
would be more conservative. For point 2, either the maximum-normal-stress theory or the
Coulomb-Mohr theory 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 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 1 280
= = = 1.33
S ut n 210
1
n = = 0.75 (unsafe)
1.33