Page 271 - Marks Calculation for Machine Design

P1: Shibu
January 4, 2005
14:56
Brown.cls
Brown˙C06
STATIC DESIGN AND COLUMN BUCKLING
Biaxial where 253
s = s > 0
2
1
s 2
Boundary of allowable
combinations 3
30
Biaxial where
2 s 1 = 2s > 0
2
s
–90 30 1
1
–30 Uniaxial where
4 s > 0, s = 0
1
2
5

Pure shear where
–90 s > 0, s = –s 1
1
2
Scale: 5 kpsi ¥ 5 kpsi

FIGURE 6.16 Principal stress combinations in Example 2 (U.S. Customary).

solution
Step 1. Plot the combinations of principal stresses from the given table.
This is shown in Fig. 6.16. Notice that the combination of principal stresses for point
1 falls outside the boundary in the fourth (IV) quadrant, the combination for point 2 falls
on the uniaxial load line directly on the boundary, the combination for point 3 falls on the
(σ 1 = σ 2 > 0) biaxial load line inside the boundary, the combination for point 4 falls on
the pure shear load line outside the boundary defined by the Coulomb-Mohr theory, but
inside the boundary defined by the maximum-normal-stress theory, and the combination
for point 5 falls outside the boundary defined by the Coulomb-Mohr theory, but inside the
boundary defined by the modified Coulomb-Mohr theory.
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.