NCEES practice MD&M #124 and 125

Im hoping someone can help my mom-brain fog on these two. My answers are not matching.

For #124, I get the area of the bolt to be .196in^2 but the book gets .142

For #125, I'm not sure what this equation they are using for secondary shear force is coming from. I was thinking I would use the polar moment of inertia equation with J=sum(r^2*A) but not sure how their J=6*36?

thanks!!

posting both questions and answers below, or I will try to

#124: 0.142 in² is the tensile stress area for a 1/2-13 bolt. It's a table lookup. See Table 53.5 in MERM13.

#125: Direct Shear is from the 500# load applied downward, divided by all three bolts. Secondary shear is based on the forces required to balance the moment of the offset load. 500#*19in (to center of bolts)... since you have a simple pattern, you might recognize that reax forces on A and C form a couple to balance the moment load. I have no idea where their actual equation comes from, but I used: 500#/3x + 500#*19in/(6in*2x) = 958.3 lbf.

Thank you so much. I am using MERM12 and the table is 51.5 on page 51-10 if anyone else reads this and needs it.

Have a great day and I appreciate the guidance!