Solution: Determine y, which locates the centroidal axis x

Step 1 of 3

Divide the cross-section of the beam into two sections, as shown in the figure below:

Step 2 of 3

Calculate the y coordinate of the centroid measured from the base.

\(\overline y  = \frac{{\sum\limits_i {{{\overline y }_i}{A_i}} }}{{\sum\limits_i {{A_i}} }}\)

\(\overline y  = \frac{{{{\overline y }_1}{A_1} + {{\overline y }_2}{A_2}}}{{{A_1} + {A_2}}}\)

Here, \({\overline y _1}\) is the centroid distance of section 1 measured from the base, \({\overline y _2}\) is the centroid distance of section 2 measured from the base, \({A_1}\) is the area of section 1, and \({A_2}\) is the area of section 2.

Substitute \(\left( {250 + \frac{{50}}{2}} \right)\;{\rm{mm}}\)  for \({\overline y _1}\), \(\left( {\frac{{250}}{2}} \right)\;{\rm{mm}}\) for \({\overline y _2}\), \(\left( {300 \times 50} \right)\;{\rm{m}}{{\rm{m}}^2}\) for \({A_1}\) and \(\left( {250 \times 50} \right)\;{\rm{m}}{{\