A preliminary design on the use of a cantilever prismatic timber beam indicated that a beam with a rectangular cross section 2 in. wide and 10 in. deep would be required to safely support the load shown in part a of the figure. It was then decided to replace that beam with a built-up beam obtained by gluing together, as shown in part b of the figure, five pieces of the same timber as the original beam and of 2 X 2-in. cross section. Determine the respective lengths l1 and l2 of the two inner and outer pieces of timber that will yield the same factor of safety as the original design.
