00:01
So in this problem, we're going to look at how to decompose a set of forces into a single resultant.
00:06
And one of the reason why we want to do this is because if we wanted to say find the reactions at each location here at the end, reaction a and then whatever at the roller, we could use the one force that we found instead of having to consider all three forces.
00:23
Now, this doesn't work if you want to, say, find the deflection in the beam.
00:27
But for reactions it does work.
00:31
And five feet and finally eight feet between the forces.
00:40
So the principle we're going to use here is sum of forces.
00:43
So we have our system that we have, and we're going to find an equivalent system where we have one applied force, some distance d from point a here.
00:57
And what we can do is use moment equivalents so that the moment, sum of moments on the top figure is equal to the sum of moments in the bottom figure.
01:07
And in that way, we'll have equivalence as well as using that sum of forces in the top is equal to some forces in the bottom.
01:17
So i guess the first thing we can do is fine what the force is equal to.
01:20
And the force is just going to be the sum of all the forces.
01:24
So 300 plus 450 plus 200.
01:31
And so our force works out.
01:34
We would it be what? 500 and 450.
01:36
So that would be our force.
01:42
And then we can find what its location is with the moments.
01:48
Because, of course, a moment is a force times a distance in general if these are perpendicular to each other.
01:54
And so we'll use that to locate where the force should be.
01:58
We'll take moments about point a.
02:00
And so for example here, we have 300 pounds at 3 feet, 450 pounds at 3 plus 5 feet, 8 feet, and so forth.
02:09
We'll take a clockwise moment to be positive, just so we see that if we had a pinned and took one of these forces and extended it around a at the same distance, same radius from a, we'd see that tends to be a clock rest rotation.
02:27
Now this is true for every one of our forces here...
