A simply supported timber beam is to be designed to support a distributed load. The length and width of the beam are known, along with the allowable normal stress values. The depth of the beam needs to be determined.

To solve this, the entire beam is considered as a free body, and the moment and force balances are written to determine the reactions at the supports.

The shear force and bending moment diagrams for the beam are then drawn. The bending moment value is zero at both ends.

The maximum absolute bending moment value is then determined by considering the area under the shear curve.

The minimum allowable section modulus is now calculated using the absolute bending moment value and the given allowable stress.

The minimum depth required in the timber beam is finally determined using the relationship between the dimensions of the beam and the minimum allowable section modulus.

This depth is the minimum necessary to ensure that the beam can safely carry the imposed loads without exceeding the allowable stress.