cantilever hollow beam of 2 m long is shown in Figure 1. The hollow section is consisted of one rectangle and two half circles.

 cantilever hollow beam of 2 m long is shown in Figure 1. The hollow section is consisted of one rectangle and two half circles. The thickness of the outer wall is 10mm while that for the inner walls is 5mm. The dimensions of the hollow section are shown in Figure 2. The beam is subjected to torsional moment of 50kN.m and bending moment of 40 kN.m. Consider G= 83 GPa.

(1) Determine the normal and shear stresses at points A and B on the outer surface of the beam and show them on sketches.

(2) Calculate the angle of twist of the tube at point C.

(3) Calculate the principal stresses, maximum shear stress and the orientation of principal planes and shear plane at the same points as in part (1). Show also the principal stresses and the maximum shear stress on sketches.