Maximum shear stress and angle of twist, Mechanical Engineering

Maximum shear stress and angle of twist:

Torques are applied on the shaft as illustrated in Figure. Discover in which portion of the shaft, maximum shear stress & angle of twist takes place.

139_Maximum shear stress and angle of twist.png

Figure: Torque Diagram

Solution

 Torque diagram is drawn below the shaft. For the cause a zero line is selected and clockwise torque is plotted above this line, that means upward and anticlockwise torque is plotted downward.

At A raise 50 Nm up, A to B the constant torque and 800 Nm down. Thus at section B

the torque TB = 800 - 50 = 750 Nm  924_Maximum shear stress and angle of twist1.png   From B to C constant torque and at C,

TC = 750 - 250 = 500 Nm924_Maximum shear stress and angle of twist1.png From C to D torque is constant and at D,

TD = 600 - 500 = 100 Nm668_Maximum shear stress and angle of twist2.png At E the torque is 100 -100 = 0. Therefore, highest torque acts on portion BC and TB = 750 Nm. For discover maximum stressed T/ d 3 portion check for . These values are written on torque diagram below zero line.

By Verifying the highest stress shall occur in portion CD.

τm = 16TC / π d 3 = 16 × 500 × 103/ π (75)3

= 6.036 N/mm2

The largest angle of twist is decided by largest value of Tl/ J or Tl/ d 4 . These values are written below the values of T/d3 on torque diagram.

 The largest twist occurs in portion AB.

θ max         = TA l / J G

=50 × 103 × 1200/ (π/32) (40)4 × 80 × 103

= 2.984 × 10- 3  rad = 0.171 deg.

= 10′ 15.5′′ C.

Posted Date: 1/21/2013 4:23:23 AM | Location : United States







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