QUESTION 1. The segment of shaft shown in Figure 1 is made of AISI 1095 annealed steel. The shaft is fine turned with a diameter of D=20 mm and with a transverse hole of d=3 mm diameter. The segment as shown is part of a drive shaft for a mixing machine.
Under normal operating conditions the shaft segment rotates at 60 rpm and is subject to the following fluctuating loads:
- A torque that varies from -120 Nm to +120 Nm once every five seconds;
- An axial tensile load that varies from 0 to 8 kN at the same rate as the torque variation; and
- A bending moment that varies between 10 Nm and 40 Nm once every second.
Determine the expected life of this segment of shaft.
(If you determine life in excess of the Endurance limit then determine the factor of safety).
Figure 1. Shaft segment
QUESTION 2. The end-cap of a pressure vessel as shown in Figure 2 is secured by 10 off M12 x SAE class 8.8 bolts (with rolled threads). A soft gasket is used such that the clamped member stiffness is one third of the bolt stiffness. The internal diameter of the pressure vessel is 300 mm and the pressure in the vessel varies from 0 to P kPa gauge. Assuming that the bolts are initially tightened to 80% of their yield strength determine :
(a) the maximum value of P that would not cause separation of the joint;
(b) the maximum value of P that would not cause eventual fatigue failure of the bolts; and
(c) the wall thickness required for the pressure vessel for this maximum pressure P.
Figure 2. Pressure vessel end-cap