Example 04: Required depth of rectangular beam based on allowable bending, shear, and deflection

A beam 100 mm wide is to be loaded with 3 kN concentrated loads spaced uniformly at 0.40 m on centers throughout the 5 m span. The following data are given:

Allowable bending stress = 24 MPa
Allowable shear stress = 1.24 MPa
Allowable deflection = 1/240 of span
Modulus of elasticity = 18,600 MPa
Weight of wood = 8 kN/m3
  1. Find the depth "d" considering bending stress only.
  2. Determine the depth "d" considering shear stress only.
  3. Calculate the depth "d" considering deflection only.