Torsion of rectangular cross section rotated at an angle?

In summary, the speaker wants to use a rectangular cross section to act as a torsion spring that can be adjusted by rotating it at an angle theta. However, calculating the polar moment of inertia for non-circular cross sections is more complicated than for circular cross sections, and the parallel-axis theorem may not be applicable. This is why most torsion springs and anti-roll bars are circular in cross-section.
  • #1
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I want to use a rectangular cross section to act as a torsion spring that can be adjusted. The idea is that the adjustment would be made via rotating the rectangular cross section about it's center at an angle theta. I've used parallel axis theorem before, but I don't think that is applicable here since it is just one shape. How can I calculate the polar moment of inertia so that I can then use other stress equations? If you're curious for what it's for, it's intended to be a blade type anti-roll bar.

Thanks for the help!
 
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  • #2
The torsion of non-circular cross sections is way more complicated than for circular cross sections. That's why torsion springs and anti-roll bars are usually circular in cross-section.

The torsion constant J is no longer equal to the polar moment of inertia for non-circular sections, and the calculation of stress is also no longer a simple procedure.

http://en.wikipedia.org/wiki/Torsion_constant
 
  • #3
The parallel-axis theorem can be used with one shape if you break that shape down to smaller, more elementary shapes. For example, an I-beam can be broken down into 3 rectangles and determining the moment of inertia of the flanges from the simple formula bh^3/12 will require the parallel-axis theorem since the rotation axis isn't at the center of mass of the object (which the formula assumes).
 

1. What is torsion of a rectangular cross section rotated at an angle?

Torsion refers to the twisting or rotation of an object around its axis. When a rectangular cross section is rotated at an angle, it experiences a twisting force that causes it to deform.

2. What factors affect the torsion of a rectangular cross section?

The torsion of a rectangular cross section can be affected by several factors including the material properties, the cross sectional dimensions, and the angle of rotation.

3. How is the torsion of a rectangular cross section calculated?

The torsion of a rectangular cross section can be calculated using the formula T = k * G * theta * b * h3, where T is the torsional stress, k is a constant, G is the shear modulus, theta is the angle of rotation, b is the width of the cross section, and h is the height of the cross section.

4. What are the applications of studying torsion of rectangular cross sections?

The study of torsion in rectangular cross sections has various applications in engineering and science, such as in the design of structural elements, mechanical systems, and in understanding the behavior of materials under twisting forces.

5. How does the torsion of a rectangular cross section affect the structural integrity of a building?

If the torsion of a rectangular cross section is not accounted for in the design of a building, it can lead to structural instability and failure. Therefore, it is important to consider torsional forces when designing structural elements in order to ensure the safety and stability of the building.

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