Estimate the required length of thread engagement that will ensure tensile failure of the cap screw before the threads are stripped in the aluminum block.

1.A -20 UNF-2A SAE Grade 2 steel cap screw is being considered for use in attaching a cylinder head to an engine block made of 356.0 cast aluminum . It is being proposed to engage the cap screw into an internally threaded hole tapped directly into the aluminum block. Estimate the required length of thread engagement that will ensure tensile failure of the cap screw before the threads are stripped in the aluminum block. Assume that all engaged threads participate equally in carrying the load. Base your estimate on direct shear of the aluminum threads at the major thread diameter, and use the distortion energy theory of failure to estimate the shear yield strength for the aluminum block.