Question 1:
(i) Using Prandtl's membrane analogy, describe the effect of a longitudinal crack in a circular shaft under torsion.
(ii) A Thick-walled cylinder is subjected to both internal and external pressures (pi and po). How do the radial stresses relate to these pressures at the internal and external radii?
(iii) Describe what situation and why you would apply:
a. Tresca failure criteria,
b. von Mises failure criterion.
Question 2:
The following cross-section is subjected to torsion of 1 kN.m. Find the maximum shear stress and identify the section in which it occurs. All dimensions in mm and G = 27 GPa.
Figure 1
Question 3:
Decompose this tensor into a set of dilatational stresses and a set of deviator stresses. Determine the principle deviator stresses.
|
40
|
10
|
42
|
|
[10
|
25
|
-28] ??????
|
|
42
|
-28
|
35
|
Compare the von Mises stress of the original tensor and the deviator tensor and interpret the outcome.
Question 4:
The structural element shown below (Figure 2) supports an axial load P and a vertical load R at the end of the long bar. The relationship between the loads is P = 40R, the diameter of the steel rod is 50 mm and its yield strength is 260 MPa.
(a) At what point in the rod will the failure occur?
(b) What is the largest allowable value of load P in accordance with maximum distortion energy theory. Assume of a factor of safety k = 2.
Figure 2