A laminated wood beam on simple supports (figure part a) is built up by gluing together four 50 mm x 100 mm boards (actual dimensions) to form a solid beam 100 mm x 200 mm in cross section, as shown in the figure part b. The allowable shear stress in the glued joints is 425 kPa, the allowable shear stress in the wood is 1.2 MPa, and the allowable bending stress in the wood is 11.4 MPa.

(a) If the beam is 3.6 m long, what is the allowable load P acting at the one-third point along the beam, as shown? (Include the effects of the beam's own weight, assuming that the wood weighs 5.5 kN/m'.)

(b) Repeat part (a) if the beam is assembled by gluing together two 75 mm x 100 mm boards and a 50 mm x 100 mm board (see figure part c).