3. Figure 1 shows a T-beam fabricated by welding two plates, both 60 mm x 6 mm in

section. The section is symmetric about its vertical axis.

(a) Locate the centroid of the section, relative to the corner marked O in the figure.

[2 marks]

(b) Calculate the centroidal second moments of area (Iz and ly) and the product

moment of area (lyz) of this beam cross-section.

[6 marks]

(c) If two bending moments about its centroidal axes are applied on the beam (Mz

= 10 kN-m and My = 10 kN-m), find the location of the maximum compressive

longitudinal direct stress and determine its magnitude.

[10 marks]

(d) Suppose now the beam is loaded differently, so that a downward shear force of

5 kN is generated in this section, using the formula given in the attached

formulae sheets, calculate the shear stress in the weld bead.

[7 marks]