1. A steel box beam of rectangular cross-section has external dimensions of 300 mm x 180 mm. Three of its walls are 12 mm thick but the fourth is a 276 mm x 8 mm steel plate which is welded in. If the beam is to be bent about the major axis, find the major axis plastic section modulus and the shape factor.

2. A simply-supported beam of span L and rectangular cross-section (b x d) is subjected to a point load W at L/4 from the left-hand support. At the ultimate collapse stage, the load corresponds to W_u. Calculate the length of the elasto-plastic zone.

3. A hollow shaft is subjected to a torque of 250 kNm. If the ratio of the internal to the external diameter is 1:3 and the allowable shear stress due to torque is 70 N/mm², determine the required diameters of the shaft and the angle of twist per metre length of shaft. Assume that G = 80 kN/mm².

4. A simply-supported beam with a span of 1500 mm and a cross-section of 50 mm x 75 mm is subjected to an axial tensile load of 25 kN and a lateral point of 3.6 kN acting at 375 mm from the left-hand support. Determine the maximum compressive and tensile bending stresses within the beam assuming that the structural behaviour is linear elastic.

5. A pipe has an internal diameter of 10 cm and is 0.5 cm thick. What is the maximum allowable internal pressure if the maximum shearing stress does not exceed 55 MN/m²? Assume a uniform distribution of stress over the cross-section.

6. A long steel tube, 7.5 cm mean diameter and 0.15 cm thick, is plugged at the ends and subjected to internal fluid pressure such that the maximum direct stress in the tube is 120 MN/m². Assuming that ν = 0.30 and E = 200 GN/m², find the percentage increase in the capacity of the tube.