Page 273 - Marks Calculation for Machine Design

P1: Shibu
14:56
January 4, 2005
Brown˙C06
Brown.cls
Point 4:
−25
1
25
σ 1 σ 2 STATIC DESIGN AND COLUMN BUCKLING 255
− = = −
S ut S uc n 30 90
1 25 −25 25 25 75 25 100
= − = + = + = = 1.11
n 30 90 30 90 90 90 90
1
n = = 0.90 (unsafe)
1.11
Point 5:
σ 1 σ 2 1 15 −55
− = = −
S ut S uc n 30 90
1 15 −55 15 55 45 55 100
= − = + = + = = 1.11
n 30 90 30 90 90 90 90
1
n = = 0.90 (unsafe)
1.11
where the factors-of-safety found are less than one and indicates an unsafe static condition.
This is why the Coulomb-Mohr theory is more conservative, or more restrictive, in this
region of the diagram.
SI/Metric
Example 2. Plot the combinations given in the table below of the principal stresses (σ 1 , σ 2 )
on a static design coordinate system for brittle materials. Show the boundaries of the recom-
mended theories for determining if the combinations are safe, along with the four special
load lines shown in Fig. 6.15. Also, determine the factor-of-safety for each combination. Use
an ultimate strength in tension (S ut ) of 210 MPa and an ultimate strength in compression
(S uc ) of 630 MPa that are typical values for cast iron.
Principal stresses (in MPa)
Point Principal stress (σ 1 ) Principal stress (σ 2 )
1 280 −105
2 210 0
3 140 140
4 175 −175
5 105 −385

solution
Step 1. Plot the combinations of principal stresses from the given table.
This is shown in Fig. 6.17. 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.