A hollow shaft of 30-mm inner diameter and 60-mm outer diameter is acted on by an axial tensile load of 50 kN, a torque of 500 N-m and a bending moment of 200 N-m. Determine the principal stresses and their directions.

Amass of 1.5 kg of air at 120 kpa and 24°c is contained in a gas-tight, frictionless piston-cylinder device. the air is now compressed to a final pressure of 720 kpa. during the process, heat is transferred from the air such that the temperature inside the cylinder remains constant. calculate the boundary work input during this process.

The force on a cutting tool are 2600n vertically downward and 2100 horizontal. determine the resultant force acting on the tool and the angle at which it acts.

Ajournal bearing has a journal diameter of 3.250 in with a unilateral tolerance of 20.003 in. the bushing bore has a diameter of 3.256 in and a unilateral tolerance of 0.004 in. the bushing is 2.8 in long and supports a 700-lbf load. the journal speed is 900 rev/min. find the minimum oil film thickness and the maximum film pressure for both sae 20 and sae 20w-30 lubricants, for the tightest assembly if the operating film temperature is 160°f. a computer code is appropriate for solving this problem.