A laminated plastic beam with a square cross section is built up by gluing together three strips, each 10 mm × 30 mm in cross section. It must carry a load P at its midpoint.
a. The beam has a total weight W and a length L. Considering the weight of the beam as a distributed load in addition to the applied load P, draw the shearing force and bending moment diagrams, indicating magnitudes in terms of W, L, and P.
b. If the beam has a total weight of 4 N and a length of 400 mm, calculate the maximum permissible load P that may be placed at the midpoint if the maximum allowable tensile stress in the plastic is 8 MPa and the maximum allowable shear stress in the glued joints is 0.3 MPa.
