16.20 Handed Out: Lecture 25
Due: Lecture 29
HOME ASSIGNMENT #6
Warm-Up Exercises
The behavior of a torsional rod with an equilateral cross-section with height of a
can be described via the following stress function:
φ = C1 (x – √—
3 y – 2/3 a) (x + √—
3 y – 2/3 a) (x + 1/3 a)
1. Indicate why this is a valid torsion stress function.
2. Determine the torsional constant for this cross-section.
3. Find the rate of twist for such a cross-section.
4. Determine the iso-resultant stress contours and the magnitude of the
maximum resultant stress.
Practice Problems
5. Two aluminum cantilevered beams (E = 70 GPa, ν = 0.30) are each 2 meters in
length and subjected to end-torques of 40 N-m. One has a channel cross-
section, the other an I cross-section as illustrated below. Both have an overall
height of 90 mm, width of 35 mm, and with thicknesses of all sections of 5
mm.
y
x
a 2/3 a
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