Chapter 10 Torsion Torsion A complex stress that

Chapter 10 Torsion

Torsion • A complex stress that is developed to resist twisting motion • Is expressed in units of length and force – Inch-kips, Newton-meters • Typically it is applied to a shaft through pulleys and gears

Torsion on a Circular Shaft • A circular shaft that is subjected to torque will develop no tensile, compression, or bending stresses. It is placed in a state of pure shear

Torsion on a Circular Shaft (Cont’d) Torsional shear on the outside of a shaft • Equation 10 -7 – = T(c) / J • = Torsional shear on the outside of a shaft • T = Applied torque • J = polar moment of inertia

Torsion on a Circular Shaft (Cont’d)

Torsion on a Circular Shaft (Cont’d) Pulley A • T = (800 * 5) – (400 * 5) = 2, 000 in. lbs CW Pulley B • T = (900 * 15) – (50 * 15) = 12, 750 in. lbs CW Pulley C • T = (700 * 10) – (300 * 10) = 4, 000 in. lbs CCW Pulley D • T = (900 * 7) – (400 * 7) = 3, 500 in. lbs CCW

Torsion on a Circular Shaft (Cont’d) • • • T = 2, 000 in. lbs j = 24 * 3. 14 / 32 J = 1. 57 C=1 σ = (2, 000)(1)/1. 57 σ = 1273. 8853 The maximum shear stress created at pulley A • Note this torsional shear stress is calculated in the shaft for the portion before pulley A

The Torsion Test • Typically performed on a specimen with a hollow shaft • The torque is incrementally changed while the angle of twist is simultaneously measured

Transmitting Power Through Shafts • Power is commonly transmitted from one rotating shaft to another by either pulleys or gears • Power is facilitated from one shaft to another by applied torque

Transmitting Power Through Shafts (Cont’d) • Work is defined as the product of force moving a distance • Work = Force * Distance • For a shaft work is defined as:

Transmitting Power Through Shafts (Cont’d) • Power is defined as work per unit time • Horsepower = (torque * rpm) / 63, 000