Slide 3

We will now review the derivation and interpretation of the theory of torsion of circular shafts. We start by looking at a small section of length dx of a circular shaft under torsion. During twisting, one end of the shaft will rotate about the longitudinal axis with respect to the other end. The magnitude of this rotation is measured in terms of the angle in radians by which one end rotates relative to the other. This is called the ‘Angle of Twist’. It can be seen that the line ab, which was initially horizontal, rotates through an angle gamma, and moves to the line ab’. Here d phi is the angle of twist. The shear strain, gamma is the angle between ab and ab'. It is found by the distance bb' divided by the distance ab. Using geometry, the arc length rho*d phi equals gamma*dx. Thus we can write the strain as gamma = rho d phi over dx. Let's assume that we are dealing with a shaft of uniform cross section and materials, thus the total twist, phi over a length L is simply phi=L times the slope of twist, d phi dx. Combining the third and fourth equations we get the final equation, giving the relation of shear strain to twist (phi), radial distance (rho), and shaft length (L). Note that all the relations here, are based solely on the geometry of the circular shaft. Hence they are valid for any type of material. This is not so in what follows, the calculation of stresses based on linear elastic material behavior.

Introduction

Chalk Talks
•Basic theory
•Testing
  system
•Engineered   materials
•Turkey bone

Virtual Tests
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•Turkey bone
•PMMA
•Cast iron

Test Data
•Aluminum
•Turkey bone
•PMMA
•Cast iron

Lab Manual
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-Instructions
-Data sheets
•Turkey bone
-Instructions
-Data sheets
•Entire lab
  manual (.doc) (.pdf)

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