mathematical relationship between the energy stored in a solid torsion bar twisted by an angle

Questions
Students are required to do library and internet research, and to consult textbooks on solid mechanics, to answer some questions.
1. Describe the mathematical relationship between the energy stored in a solid torsion bar twisted by an angle ? the torque T, shear modulus G amd moment of inertia I.
2. A solid steel bar 38mm in diameter must transmit a torque of 903 N.m over a length of 2.5 metres. Given that the shear modulus is 76GPa, find the maximum (i) shear stress, (ii) the angular twist in the bar, and (iii) the energy stored in the steel bar.
3. Explain, using diagrams, how a torsion bar automotive suspension works.
4. An aluminium alloy bar was tested in tension and torsion. The tension test on one portion of 20 mm diameter showed an extension of 0.34 mm with a load of 40 kN measured on a gauge length of 200 mm. The torsion test on a second portion of 14 mm diameter showed an angle of twist of 0.125 radians on a gauge length of 250 mm when the torque was 35 N.m. Find E and G for the material.

5. Explain what is meant by factor of safety in structural engineering. The propeller shaft of an aircraft engine is steel tubing of 75 mm external diameter and 60 mm internal diameter. The shaft is to transmit 150 kW at 1600 RPM.The failure stress in shear for this shaft is 140 MPa. What is the factor of safety?