# Torsion

## Helical Springs

When close-coiled helical spring, composed of a wire of round rod of diameter *d* wound into a helix of mean radius *R* with *n* number of turns, is subjected to an axial load *P* produces the following stresses and elongation:

The maximum shearing stress is the sum of the direct shearing stress τ_{1} = *P*/*A* and the torsional shearing stress τ_{2} = *Tr*/*J*, with *T* = *PR*.

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## Solution to Problem 341 | Torsion of thin-walled tube

**Problem 341**

Derive the torsion formula τ = Tρ / J for a solid circular section by assuming the section is composed of a series of concentric thin circular tubes. Assume that the shearing stress at any point is proportional to its radial distance.

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## Solution to Problem 332 | Flanged bolt couplings

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## 310 Strength Comparison of Hollow and Solid Steel Shafts of Equal Outside Diameters

**Problem 310**

Show that the hollow circular shaft whose inner diameter is half the outer diameter has a torsional strength equal to 15/16 of that of a solid shaft of the same outside diameter.

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## 305 Minimum Diameter of Steel Shaft With Allowable Angle of Twist

**Problem 305**

What is the minimum diameter of a solid steel shaft that will not twist through more than 3° in a 6-m length when subjected to a torque of 12 kN·m? What maximum shearing stress is developed? Use G = 83 GPa.

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