PROBLEM $8\mathrm{.}13$

The wooden members $\backslash ($ A $\backslash )$ and $\backslash ($ B $\backslash )$ are to be joined by plywood splice plates which will be fully glued on the surfaces in contact. As part of the design of the joint, and knowing that the clearance between the ends of the members is to be $8$ mm $,$ determine the smallest allowable length $\backslash ($ L $\backslash )$ if the average shearing stress in the glue is not to exceed $800$ kPa $.$