in the name of allah

1. Lecture by : LT “Sayed Dawod karimi” dawodkarimi2007@gmail.com 0799560376 in the name of allah For NMAA and Kardan University Faculty of Engineering

2. Lecture #5 Elastic Torsion Theory • 1. Learning Objectives • After this lecture you should be able to: • Understand the assumptions inherent in the elastic torsion equations. • Construct a torque diagram for a shaft in torsion. • Understand the mathematical and physical meaning of the polar moment of inertia.

3. 2. Orientation • Thus far we have learned how to analyze and design structural members subjected to axial loads. Axial loads are just one of many types of loads that real structural members are subjected to. Over the course of the next several lessons, we will investigate the effects of another type of loading: Torque. Examples of torsional shafts abound. In a typical automobile, the drive shaft, flywheel, axle, and transmission are all examples of torsional shafts. Later in the course, we will learn to combine the effects of axial loading and torsion as we analyze and design members subjected to combined loading.

4. 3. Reading Assignment • 7.1, 7.2, 7.3

5. 4. Key Definitions • Torsional Shaft: A device capable of transmitting torque from one plane to a parallel plane. • Angle of Twist: Denoted by the symbol θ, angle of twist represents the amount of rotation undergone by a plane perpendicular to the longitudinal axis of a torsional shaft. See figure 7-4. • Torsional Shearing Strain: Your text makes reference to two measures of torsional shearing strain. The first, γc, represents the shearing strain at the surface of the shaft. The second, γp, represents the shearing strain at a distance ρ from the center of the shaft. • Shear Modulus: Represented by the letter G, and also know as the modulus of rigidity, the shear modulus is a material property that relates shearing strain to shearing stress. • Annulus: A disk with a concentric hole (a ring). • Polar Second Moment of Area: Represented by the letter J, is a measure of an object’s ability to resist torsion.

6. 5. Study Problems 7.1(a), 7.2(a)

7. 6. Challenge Problems 7.18(a)

8. End of lesson Question