Strengths Torsion of Circular Shafts Chapter 12

Introduction A member subjected to twisting moments (torques) is called a shaft Only solid and hollow circular shafts will be considered in this chapter

External and Internal Torques External torque – two equal and opposite forces of magnitude F are applied to the handle. The moment of the couple is T=Fa. This moment has a twisting effect to shaft AB the applied torque at A and the torsional reaction at B are the external torques. Right hand rule – curl the fingers of your right hand in the direction of a torque, the vector representation of the torque is now indicated by the direction of the thumb Internal Torque – at a section of the shaft is the torque within the section required to resist the external torque. Positive internal torque – the internal torque is considered positive if the vector representation of the internal torque in the section is directed outward from the section

Torsion Formula Entire section at the free end rotates through the same angle, while the size and shape of the section and distance to the adjacent section are unchanged. Shaft deforms into a rhombus Since the dimensions of all sides of the element are unchanged there are no normal stresses in the element along the longitudinal and transverse directions. Thus the element is subjected only to shear stresses and is said to be in pure shear torsion formula – if maximum shear stress due to the torque in the circular shaft is with the elastic range of the shaft material, shear stresses vary linearly from the axis of the shaft to the outside surface These shear stresses are perpendicular to the radial direction. The maximum shear stress occurs at points on the periphery of a section.

Shear Stresses on Mutually Perpendicular Planes In this section we shall show that shear stresses exist in the longitudinal planes of a shaft as well The shear stresses on the adjacent faces of an element in a stressed body must have equal magnitude and must be directed either toward or away from a corner of the element

Power Transmission A shaft is subjected to torques that depend on the power transmitted and the angular velocity of the shaft. Power is defined as the work done per unit time. Work done by a torque acting on a rotating shaft is equal to the torque T multiplied by the angular displacement of the shaft 1 hp = 6600 il * in/s 1 rpm = (2pie/60) rad/s When horsepower is used for P and N(rpm ) is used to express the angular velocity 1 kw = 1000w 1 rpm = (2pie/60) rad/s When kw is used for P and n (rpm) is used to express the angular velocity 1 hp =.7457 kW

Angle of Twist Shaft is subjected to torque, two end sections rotate through an angular displacement relative to each other. This relative angular displacement between two sections in the shaft is called the angle of twist.