3.0. TORSION

A shaft (usually circular rod or bar) experiences torsion when torque is applied. Torque is moment, which rotates certain segments of the shaft.

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3.1. TORSIONAL STRESS

Torque is due to a shear load which makes the shaft rotate. This is the reason why torsional stress uses  (tau). This torsional stress is given by the formula:

                                  

where:
               torsional stress, Pa or psi

           torque, N-m or lb-ft

          distance from the center of the shaft to point of consideration, (for maximum stress, c=r), m or in

          polar moment of inertia,  or



EXAMPLE 3.1.1. SOLID SHAFT
EXAMPLE 3.1.2. HOLLOW SHAFTS
EXAMPLE 3.1.3. MULTIPLE GEARS

3.2. POLAR MOMENT OF INERTIA

Polar moment of inertia, J, is the resistance of the material from twisting, contrary to area moment of inertia, I, which is the resistance of a material to bending.

For solid shaft:

                                    (using shaft radius, R)

                                   (using shaft diameter, D)


For hollow shaft:

                       (with shaft's inner radius, r)

                     (with shaft's inner diameter, d)

3.3. ANGLE OF TWIST

The angle of twist is the rotational measurement of the twist the shaft experienced.

                          

where:
                         

                          angle of twist, rad

                         torque, N-m or lb-ft

                  polar moment of inertia,  or 

                        length, m

                 shear modulus, in  or Pa



EXAMPLE 3.3.1. TORQUE FOR A GIVEN ANGLE OF TWIST

3.4. POWER TRANSMITTED BY THE SHAFT

Occasionally, power is applied to gears or bearings instead of torque, this will require one to convert power into torque before being able to solve for stress or angle of twist.

                       
                         

where:
         
               power, watts or    

               torque, N-m or lb-ft

           angular velocity,

               frequency, rpm

3.5. FLANGED BOLT COUPLING

There are times when long shafts are needed. Although fabrication is easy, transport might have problems. This is the main reason why flanged bolt couplings are used. Couplings are small mechanical devices used to connect shafts. To lengthen a shaft, two couplings are needed where ends of two shafts are inserted. A key would be inserted for the efficient rotation of the shafts. These couplings are then joined by bolts.

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where:
          
                 shear load, N or lb
   
                 distance from center of flange to circle of bolts, m
                 
                 number of bolts



EXAMPLE 3.5.1. TORQUE CAPACITY OF A FLANGED BOLT COUPLING
EXAMPLE 3.5.2. TORQUE CAPACITY OF TWO-ROW BOLT COUPLING

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