Recitation 7

Recitation 7 - Torsion

Prepared By Alexandra Salinas

Important Equations for Today

​Torsional Shear Stress

​Angle of Twist

​Polar Moment of Inertia

​Power, Transmission, and Conversions

​A series of torques are applied to the 6061-T6 aluminum alloy shaft. The diameters and lengths of each section are shown below. Point A is fixed to a wall.

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Question 1: Multiple Segments​

Determine the absolute maximum shear stress due to torsion in the assembly.​

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Question 1a: Multiple Segments​

Determine the angle of twist of Point E relative to point A in the assembly.​

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Question 1b: Multiple Segments​

The drive shaft  AB  of an automobile is made of a steel having an allowable shear stress of  τ_allow  = 6.2 ksi . The outer diameter of the shaft is 2.5 in and the engine delivers 200 hp to the shaft when it is turning at 1140 rev/min. ​

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Write down these given values and do the appropriate conversions!

​Question 2:

Torque and Power​

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​ Determine the torque (lb*in) in the drive shaft AB.​

τ_allow  = 6.2 ksi, d_o = 2.5 inches, P = 200 hp, ω = 1140 rev/min.​

​Question 2a:

Torque and Power​

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​ Determine the minimum thickness for the drive shaft AB.​

τ_allow  = 6.2 ksi, d_o = 2.5 inches, P = 200 hp, ω = 1140 rev/min,

Torque = ​11057.08 lb*in

​Question 2b:

Torque and Power​

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The steel shaft is made from two segments: AC has a diameter of 0.5 in and CB has a diameter of 1 in. The shaft is fixed at A and B and subjected to a torque of 500 lb*ft at D.​​

Question 3: Statically Indeterminate

Determine the maximum shear stress in the shaft.

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Positive sign convention is ​Counter-clockwise. (CCW). d_AC = 0.5 in, d_CB = 1 in.

​Question 3a: Statically Indeterminate

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