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Torsional Rod-Material and Structures-Assignment, Exercises of Structures and Materials

This is assignment for Material and Structures course. To cover following points, Prof. Aparijita Singh assigned this task at Andhra University to engineering students: Torsional, Rod, Equilateral, Cross-section, Stress, Function, Constant, Rate, Twist, Contours, Magnitude, Cantilever, Beam, Thickness, End-torque

Typology: Exercises

2011/2012

Uploaded on 07/26/2012

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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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16.20 Handed Out: Lecture 25

Due: Lecture 29

HOME ASSIGNMENT

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 = C 1 (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

  1. 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

16.20 Home Assignment #6 Page 2 Fall, 2002

For the two beams, determine and compare:

(a) The angle of twist, α, (in degrees) between the two endfaces.

(b) The maximum resultant shear, τ, developed (assume possible stress

concentrations near corners have been relieved by adequate fillets).

(c) A T-section of the same height of 90 mm is also being considered in this case. What length would the top of the “T” need to have in order for the resistance to torsion be the same as for the channel section? As for the I cross- section? All pieces continue to have a thickness of 5 mm.

Application Tasks

  1. A four-foot long aluminum (E = 10.5 Msi, ν = 0.30) rod has an elliptical cross- section, as shown with a major axis, 2a, of 5 inches and a minor axis, 2b, of 2

90 mm

5 mm

35 mm

5 mm

35 mm

5 mm

5 mm

90 mm

5 mm

5 mm

5 mm 5 mm