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.

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 T_B = 800 - 50 = 750 Nm     From B to C constant torque and at C,

T_C = 750 - 250 = 500 Nm From C to D torque is constant and at D,

T_D = 600 - 500 = 100 Nm 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.

τ_m = 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.