Rectangular Section:

Solid Rectangular Section

Let b be the breadth and d be the depth of a rectangular beam section. The neutral axis coincides along the centroidal axis of beam.

                      Beam Section                          Bending Stress Distribution

      Figure

Moment of inertia, I = (1/12) bd ³

Distance of outermost layer from the neutral axis, ymax = d /2

∴  Section modulus, Z = I / y_max

                                    =(1/12 )bd ³ ×(2/d)

                                      =(1/6)bd²

Assume σ be the maximum bending stress at the outermost layer.

∴          Moment of resistance, M = σ × Z = (1/6 )σ bd ²

We may see the bending stress distribution diagram in Figure.