"In this chapter we will discuss the effects of applying a torsional loading to a long straight member such as a shaft or a tube. Initially we will consider the member to have a circular cross section. We will show how to determine both the stress distribution within the member and the angle of twist, when the material behaves in a linear-elastic manner and also when it is inelastic. Statically indeterminate analysis of shafts and tubes will also be discussed, along with special topics that include those members having noncircular cross sections. Lastly, stress concentrations and residual stress caused by torsional loadings will be given special consideration."

INERTIA
A PROPERTY OF A BODY THAT RESISTS ANY CHANGE IN MOTION. FOR TRANSLATION MOTION, MASS IS A MEASURE OF THE BODY INERTIA. IT IS HARD TO CHANGE THE STATE OF MOTION OF A HIGH MASS OBJECT. FOR ROTATION, THE MOMENT OF INERTIA OF A BODY IS A MEASURE OF BODY INERTIA.

LINEAR
PROPERTY OF SYSTEMS WHERE THE SYSTEM OUTPUT OR RESPONSE IS IN DIRECT PROPORTION TO THE INPUT. DOUBLING THE INPUT (LOAD, FORCE, ENERGY, TENSION,...) HAS THE EFFECT OF DOUBLING THE OUTPUT (STRETCH, COMPRESSION, DISPLACEMENT,...)

LINEAR VARIATION
A CHANGE IN PARAMETERS THAT FOLLOWS A DIRECTLY PROPORTIONAL RELATION. LINEAR VARIATIONS ARE DEMONSTRATED BY SHOWING THAT THE DATA FOLLOW A STRAIGHT LINE GRAPH.

MOMENT
A FORCE APPLIED TO AN OBJECT AT SOME DISTANCE FROM THE ROTATION AXIS THAT MAY CAUSE THE OBJECT TO ROTATE. THIS IS THE SAME AS A TORQUE. THE MOMENT IS CALCULATED AS THE PRODUCT OF A FORCE TIMES THE DIRSTANCE OF ITS POINT OF APPLICATION FROM THE AXIS OF ROTATION.

MOMENT OF INERTIA
THE RESISTANCE OF A BODY TO ANY CHANGE IN ROTATIONAL MOTION. THIS IS CALCULATED AS A PRODUCT OF MASS TIMES THE SQUARE OF THE DISTANCE FROM THE MASS TO THE AXIS.

SHEAR

SHEAR STRAIN

SHEAR STRESS

STRAIN

STRESS

STRESS

TORQUE