# Homework Help: Determine x and y coordinates of resultant force through object

1. Oct 3, 2012

### Northbysouth

1. The problem statement, all variables and given/known data
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

2. Relevant equations

3. 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:

Rz = 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.

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2. Oct 4, 2012

### 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?

3. Oct 4, 2012

### Northbysouth

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

Rz = -212 kN

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

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

Mz = 0

M = 1166.224 kNm

Rz*y = -1027.1
y = 4.8448

Rzx = 552.4
x = -2.60566