(Solved): Figure Q2.1. The cross section of the beam is \( 100 \mathrm{~mm} \) by \( 200 \mathrm{~mm} \) as ...

Figure Q2.1. The cross section of the beam is \( 100 \mathrm{~mm} \) by \( 200 \mathrm{~mm} \) as hown in Figure Q2.2. The beam is loaded with a single point load of \( 100 \mathrm{kN} \) as shown in Figure Q2.1. i. The imposed load will cause the beam to bend. Calculate the moment of inertia of the beam about its neutral axis. (3 Marks) ii. Determine the maximum bending moment in the beam and the position along the length of the beam where this occurs. (4 Marks) iii. Calculate the normal stress in the beam at point \( \mathrm{A} \) as shown in Figure Q2.2 at the point along the length of the beam where the bending moment is a maximum. (3 Marks) iv. Calculate the shear stress in the beam at point \( \mathrm{A} \) as shown in Figure Q2.2 at a position \( 1 \mathrm{~m} \) from the left hand end of the beam. (5 Marks) Under different loading conditions, the normal stress at a point in the beam is \( 2 \mathrm{MPa} \) in tension and the shear stress is \( 0.5 \mathrm{MPa} \) as shown in Figure Q2.3. Using Mohr's circle of stress, calculate the magnitude of the principal stresses at this point in the beam and their angle relative to the beam. (10 Marks)