Determine x and y coordinates of resultant force through object

[Northbysouth]

Homework Statement

The concrete slab supports the six vertical loads shown. Determine the x- and y-coordinates of the point on the slab through with the resultant of the loading system passes.

Image attached

Homework Equations

The Attempt at a Solution

I started off by finding the resultant force. Seeing as how all the forces in the system act in only the z direction I summed them to get:

R_z = 69Kn - 69kN -42kN - 44kN - 67kN - 59kN
= -212 kN

But I'm not sure how I should proceed from this step. I would appreciate any suggestions.

 

[tiny-tim]

Hi Northbysouth!

Assume that it goes through the position (x,y).

You know it's -212 kN, so what is the moment of that about the x-axis or the y-axis?

 

[Northbysouth]

I've managed to solve it now. I did the following:

R_z = -212 kN

M_x = (69kN)(2.3) -(67kN)(3.1+2.3) -(44)(8) -59*(2.3+3.1+2.6)
= -1027. kNm

M_y = 67*2.3 + 44*6.7 + 69*6.7 -69*5.2
= 552.4 kNm

M_z = 0

M = 1166.224 kNm

R_z*y = -1027.1
y = 4.8448

R_zx = 552.4
x = -2.60566

Thanks for your help.