F= M x D

How do I solve for X in this problem? Given the dead load (100 lbs/ft) and a force coming from the right (50 ).

Do I set overturning and stabilizing moments equal to each other?

For instance, is the solution:

50 x 12 = 100 x (x/2) ?

I know this must be a moment arm type of issue.

Take moment about he bottom right corner. 

Are you saying that the load from the top is dependent on the width "X"?  The load applied to the top is 100*x with a moment arm of x/2 and is in the negative direction.  The side moment is fixed at 50 with a moment arm of 12 ft and is positive.

Solve for equilibrium -(100x)(x/2)+(50)(12) = 0  x= sqrt(12)

Thank you!!! This is helpful. Is there a reason you took the moment about the bottom right corner?

I could have picked the bottom left corner, and it would have been the same concept and result, right?

What was the problem statement for this question?  Wouldn't you have to account for reaction forces to the 2 loads shown in the diagram?

youngmotivatedengineer said:

What was the problem statement for this question?  Wouldn't you have to account for reaction forces to the 2 loads shown in the diagram?

Click to expand...

you are 100% correct.  All forces need to be balanced.  I think in my haste I over-simplified the problem,

The problem statement is to solve for X, given the three variables that are already provided (50, 100, 12').

No reaction forces needed, I think?

Would the way you have shown, can it be done about the left point and still yield the same answer?

About left point, it is

100' x [x/2] = 50 x 12 ? (No negative or clockwise moments in this case?)

agree if information regarding what the question reads exactly would be helpful. if the question is asking what's the minimum "x" for this structure to be stable (not overturning) given the shown loads, then yes, x would be 12. the reaction forces wouldn't affect the overturning unless they were doing more than resisting the loads shown. 

but in my experience, what I interpret from the question vs what the question is actually asking is sometimes not exactly aligned. 

synchronized posting

(also, the title of this post bothers me. it should be F = M/d or M = Fd but F does not equal Md) - just for clarification