Hollow Rectangular Section:

A hollow rectangular section with total breadth B and depth D is illustrated in Figure.

                           Beam Section                         Bending Stress Distribution

 Figure

Assume the breath & depth of the central rectangular hole be b and d, respectively.

∴          Moment of inertia, I = (BD³ /12 ) - (bd ³/12)

Distance of outermost layer from the neutral axis, y_max = D/2

∴  Section modulus, Z = I / y_max

= (1/12) [BD ³ - bd ³] ×   2

= [(BD³ - bd ³)/ 6D]

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

∴          Moment of resistance, M = σ × Z = (σ/6D)   [BD ³ - bd ³]

The bending stress distribution is illustrated in Figure.