A wood beam ABC with simple supports at A and B and an overhang BC has height h = 300 mm (see figure). The length of the main span of the beam is L = 3.6 m and the length of the overhang is L/3 = 1.2 m. The beam supports a concentrated load 3P = 18 kN at the midpoint of the main span and a moment PL/2 = 10.8 kN ˆ™ m at the free end of the overhang. The wood has weight density γ = 5.5 kN/m3.
(a) Determine the required width b of the beam based upon an allowable bending stress of 8.2 MPa.
(b) Determine the required width based upon an allowable shear stress of 0.7 MPa.

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