How do I solve this challenging mechanic statics problem?

[paul11273]

I have a problem for HW that is driving me crazy!
A copy of the original problem from the text is attached.

Here is what I have done so far...

First, I split the area under the force horizontally into two triangles and found the centroid of each.
Centroid of upper triangle is 3m from left side.
Centroid of lower tri is 6 m from left side.

Area force of triangle 1 is 15.75 kN
Area force of triangle 2 is 6.75 kN

Total area force is 22.5 kN

Location to place this equivalent force is 3.9m from left side.

I believe I am good to this point. Now, to find the reactions at point B and C, I have setup the following equations:

Sum Fy = By + Cy - 22.5kN - 50kNm/2m - 50kNm/8m = 0
and
Sum Ma = 2m*By + 8m*Cy - 22.5kN(3.9m) - 50kNm = 0

Solving these equations simultaneously I end up with
Cy = 5.04kN
By = 48.71kN

According to the answers in the back of the book (Vector Mechanics for Engineers, 7th ed - Beer, Johnston & Eisenberg) the answers are
Cy = 15.46 kN
By = 7.04 kN

Any help would be greatly appreciated. I am spent on this problem and just cannot see where I am going wrong. I suspect my problem is how I am dealing with the 50kNm torque shown on the diagram.
Thanks.

 

[jamesrc]

You've got some extra terms in your force balance equation:

$$\Sigma F_y = 0 = B_y + C_y - 22.5 {\rm kN}$$

You shouldn't have any terms from your applied moment - it's an applied moment. You'd only consider forces there if you resolved it into a couple or something.

 

[paul11273]

OK, I got it now. Thanks Jamesrc. I treated the moment all wrong. You pushed me in the right direction.
Thanks again.