Problem #$1(40$ points$).$ The section of the sealed joint shown in Figure $1-1$ is subjected to a cyclic force that alternates between $4$ kips and $6$ kips $.$ The members of the joint have a modulus of elasticity $(E)$ of $16$ Mpsi $.$ All bolts are carefully preloaded to a force of $F_i=25$kip each.

Determine the following:

$(10$ points$).$ The yielding factor of safety.

$(10$ points$).$ The overload factor of safety.

$(10$ points$).$ The factor of safety against joint separation.

$(10$ points$).$ The fatigue factor of safety using the Goodman criterion.

Figure $1-1$ Section of the Sealed Joint for Problem #$2.$