9.11 How would you evaluate circumferential strain
at r = 0?
E
E
2 6 2
a a a
9.13
Axisymmetric model pressure load of 13.26
2
lb
in.
412
9.14 von Mises stresses (with filleted corners)
413
9.15
414
9.18
9.19
Figure 1 Thick walled open-ended cylinder
Theoretical Solution for hoop stress at inner radius
q = 35 106 a = 1.5 b = 1.2 r = 1.2
2 2 2
qb a r
416
Autodesk Results
Theoretical Results
Hoop Stress
159.5 MPa
159.4MPa
Maximum Principal Stress
159.5 MPa
–
Minimum Principal Stress
–35 MPa
–
Deflection in y–direction
0.93mm
–
The Autodesk results for hoop stress and the theoretical solution for hoop stress are very
9.20 A steel cylindrical pressure vessel with flat plate end caps is shown in the figure with
vertical axis of symmetry. Addition of thickened sections helps to reduce stress
concentrations in the corners. Analyze the design and identify the most critically stressed
9.22
9.23 According to the von Mises stress analysis, the average stress through the glass is around
1
5
of the tensile strength of the glass. If the maximum force used with this syringe is 45 N, the
418
the syringe design is indeed safe with this material specification.
9.25 Steel hole punch
419
9.27 a)
420
421
g
b) What speed can the steel flywheel tolerate before yielding based on the maximum
c) Maximum rpm of aluminum alloy 6061-T6 to reach yield:
2
2 2 2 2
2
Sya
a(3 a) b (1 3 a)
a a b a r
8 r 3 a
ωa = 3.427 X 103
ωarpm = ωa·
60
2
ωarpm = 3.272 X 104 rpm
Max speed of disk for aluminum alloy 6061-T6 to reach yield