Problem $4$: The rectangular cantilever beam has a cross section

of $20$ mm wide $50mm$ deep and is $1$ m long. It has a through

hole of $20$ mm diameter, with its center $100$ mm from the base,

as shown. The beam carries a transverse load of $1000$ N on its

free end.

a$)(4$ points$)$ Determine the factor of safety guarding the design

against static failure if the yield strength of the material is

$300$ MPa $.$

b$)(4$ points$)$ Find the location of the hole along the beam such

that the stress at the hole section is the same as the stress at

the base of the beam.