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.

You are making beer. the first step is filling the glass carboy with the liquid wort. the internal diameter of the carboy is 15 in., and you wish to fill it up to a depth of 2 ft. if your wort is drawn from the kettle using a siphon process that flows at 3 gpm, how long will it take to fill?

Prove the equivalence between the two statements of the 2nd law of thermodynamics (i.e., a violation of one statement leads to the violatio the other statement)

Asimply supported beam abc of length l has ab of length hl and second moment of area / and bc of length hl and second moment of area i2. determine the strain energy stored in the beam when it is subject to a vertical load f at its midpoint and the consequential central deflection.