## Transcribed Text

Problem #1: A steel rod of diameter d=50 mm and yield strength Oy = 300 MPa supports an
axial force P and a vertical force F acting at the end of a 0.8 m-long arm, as shown in Figure 1.
The axial force P is a multiple a of the vertical force F, so that P=aF. Using a safety factor of
n=2, answer the following questions:
a) Based on the maximum shear stress criterion, determine (as a function of a) the largest
permissible value of F.
b) Base on the maximum distortional strain energy criterion, determine (as a function of a)
the largest permissible value of F.
c) Plot the results obtained in parts a) and b) for the range -100 < O < 100, and calculate
the exact numerical results for a=50.
Problem #2: A closed, thin walled cylindrical pressure vessel of mean diameter d = 250 mm
and wall thickness t = 5 mm is subjected to an internal pressure pi = 2.8 MPa, a torque (along
its
longitudinal axis) of T = 31.36 kN-m, and an axial thrust (in tension) of F = 45 kN. The ultimate
strengths of the material are OUT = 210 MPa (in tension) and Ouc = 500 MPa (in compression).
a)
Use the maximum principal stress criterion to determine if the tube will fail by fracture.
b)
Use the Mohr-Coulomb criterion to determine if the tube will fail by fracture.
c) Assume that the value of the torque T was not given. Use the maximum principal stress
criterion to determine the critical value T at which the tube would just fail. (Use all other
parameter values given above.)
d)
Assume that the value of the torque T was not given. Use the Mohr-Coulomb criterion to
determine the critical value of T at which the tube would just fail. (Use all other
parameter values given above.)
1.2 m
d
z
F
,
0.8m
Figure 1

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