Question

Distributed Loads Question

Can someone explain to me how this resultant force (400lb) is broken into a 200lb force in each of the sectioned diagrams (from the picture below) and the distances to follow.

Can someone show me this mathematically?

Answer 1

Notice that up the top it shows 50lb/ft and all the arrows along the bar - ie each foot of the bar weighs 50lb, the total bar is 8ft so it's mass is 400lb.

The 400lb in the center would be where the center of mass of the bar acts. But since they want to determine forces acting at point B, they're taking the forces acting to the left and right of B, and each section to the left or right is 4ft (so the centre of mass of those 4ft sections will be right in the middle of each), so each has mass 200lb (4ft times 50lb/ft).

Note that for the first part of the solution, they aren't using any of that - they're just using equilibrium equations for torque, and forces in the x and y directions. I'm guessing the next part of the solution is using the sectioned diagrams.

Answer 2

Yes, the resultant force acting on the 8 ft span is 50 pounds per foot. And the center of a square/rectangle is dead smack in the geometric center.

The Free Body Diagram was cut in a section. The author then moved the force to the center of each sectioned cut. I get this but I was under the impression that the resultant force can not be broken apart by just dividing it by two. (The sections in question)

Ah, I think I see. If I consider the evenly distributed load acting onl on the left section I will have 50lbs/ft across 4ft = 200 lbs/ft and place it in the center.

Thanks. I needed to review this once more and you helped make the confusion clear.

Answer 3

Yeah, i think he's just imagining the center as the reference point, to find the forces acting there.