Page 269 - Marks Calculation for Machine Design

P1: Shibu
January 4, 2005
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Brown˙C06
Brown.cls
STATIC DESIGN AND COLUMN BUCKLING
Remember that for brittle materials, the ultimate strength in compression is significantly
greater than the ultimate strength in tension. 251
Recommendations for Brittle Materials. Based on the closeness of the fit of the experi-
mental data shown in Fig. 6.13, the following are the recommendations as to which theory
best predicts whether a design is safe or not, specifically in the first (I) and fourth (IV)
quadrants.
First (I): (σ 1 > 0 and σ 2 > 0)
Maximum-normal-stress theory is the most accurate. Coulomb-Mohr theory does not
apply. Modified Coulomb-Mohr theory does not apply.
Fourth (IV): (σ 1 > 0 and 0 >σ 2 > −S ut )
Maximum-normal-stress theory is the most accurate. Coulomb-Mohr theory is okay,
but conservative. Modified Coulomb-Mohr theory does not apply.
Fourth (IV): (σ 1 > 0 and −S ut >σ 2 > −S uc )
Modified Coulomb-Mohr theory is the most accurate. Coulomb-Mohr theory is okay, but
conservative. Maximum-normal-stress theory does not apply.
Graphically, these recommendations are shown in Fig. 6.14.
◦
The line at 45 passing through the origin of the coordinate system in Fig. 6.14 establishes
the left boundary of the possible combinations of the principal stresses (σ 1 , σ 2 ). The vertical
line in the first (I) quadrant that extends downward to (−S ut ) in the fourth (IV) quadrant, and

s 2
Boundary of allowable
combinations
Maximum-normal-stress
theory
S ut

II I S
ut
s 1
–S uc
IV
–S ut
Coulomb-Mohr
theory
III

Modified Coulomb-Mohr
–S uc theory
Maximum-normal-stress
theory

FIGURE 6.14 Summary of recommendations (brittle).