Reduction of resultant Moment/Force

[Saladsamurai]

[SOLVED] Reduction of resultant Moment/Force

So I have calculated the resultant force correctly but my solution for distance is incorrect. I keep getting 6.08 ft but the correct solution is 6.57 feet from B.

I found $F_r=798.499$ which is correct. Then I used,

$$\sum M_B=\frac{3}{5}(500)(9)+6(1200)+\frac{12}{13}(260)(4)=4860 lb\cdot ft$$

Then $d=\frac{M_r}{F_r}=6.09 ft$ Where is my error?

 

[Dick]

F_r is the total magnitude of the resulting force, yes. But in the formula d=M/F (where M is the torque, and d is distance from axis), you want the F to be component of the total force that exerts torque. That would be the vertical component only of the total force.