Torque on an open-ended rectangle

[Zula110100100]

I was at work and we build a "fence" on a trailor to keep the load in place, and we got into a disagreement about how much stress would be on each corner if we hit a bump and the boards moved up unequally. Now, there's a lot more physics in that scenario than the one I am describing but I think this simplified version answers my question.

Which point would have more stress in this example:

I would imagine the only force we'd be calling stress on a corner would be the torque. Since lbs is a weight it already takes gravity into account so it would be 4 ft-lbs of torque on pt. A. On point be we would figure out the distance to weight with

a²+b² = c²

4+4 = 8

c = 2.8284271247461900976033774484194

But the force of gravity is at a 45° angle to the radius so we use c sin 45 which is 2 ft.

So for pt. B, 2 lbs at 2 ft = 4 ft-lbs the same as A.

I tried with a couple of other rectangles and it was always the same...is that true?

Also, I am less sure of the physics but I think with a 4 sided rectangle if a force is applied parallel to one of the sides the torque on each corner would be equal?

 

[LightHero]

Or maybe it would be the same as the above but with an additional force applied perpendicular that is equal to the force parallel?Yes, this is true. If a force is applied parallel to one of the sides, the torque on each corner will be equal. Additionally, if you apply a force perpendicular to the side, the torque on each corner will also be equal.

 

[astrokreng]

First of all, it is important to clarify that torque is not the same as stress. Torque is a measure of rotational force, while stress is a measure of the internal forces within a material. In this scenario, the torque on each corner of the rectangle would be the same, as you correctly calculated. However, the stress on the corners would depend on the material of the fence and how it is attached to the trailer. If the material is strong and securely attached, the stress on the corners would be minimal. However, if the material is weak or poorly attached, the stress on the corners could be significant and could potentially lead to failure of the fence.

Additionally, if a force is applied parallel to one of the sides of a rectangle, the torque on each corner would not necessarily be equal. It would depend on the exact location of the force and the distribution of weight along the sides of the rectangle. It is important to consider the specific geometry and forces involved in each scenario to accurately determine the torque and stress on each corner.