(ii) A simply supported beam with an IPE 400 (S275) cross-section (Figure 1) and a span L= 4 m, is subjected to a centrally located point load of 200 kN, and a uniformly distributed load of w kN/m, applied along the top flange of the beam.

(a) Determine the maximum value of w kN/m that the beam can carry, when considering in-plane restrained major axis bending failure (about the Y-Y axis). [8 marks]

(b) Determine the maximum value of w kN/m the beam can carry when considering vertical shear failure of the beam. [8 marks]

(c) Identify the critical mode of failure from the two modes checked above.