## HSS statics problem

## HSS statics problem

(OP)

If I have a piece of rectangular HSS, with another formed channel resting on top with spacer blocks on the inside, how do I find the reactions of the blocks on the sides that resist the moment shown? I'm not sure if my convention of the angle of the reactions is correct. I believe for the block on the right, its corner follows the path traced by the circle with the center at the pivot point of the moment. For the block on the left, the corner that contacts the HSS does so only after the one on the right makes contact, and starts pivoting at that location.

So that leaves me with the question, how to find the reactionary forces if I know the magnitude of the moment and all the dimensions? Its not a force couple because they aren't parallel (although their x-y components would be I suppose), unless I have their direction screwed up then its a simple M/d = F situation, but I'm not sure if that is the case.

So that leaves me with the question, how to find the reactionary forces if I know the magnitude of the moment and all the dimensions? Its not a force couple because they aren't parallel (although their x-y components would be I suppose), unless I have their direction screwed up then its a simple M/d = F situation, but I'm not sure if that is the case.

## RE: HSS statics problem

1) why two of three ?

2) why different arcs/centers of rotation ? (wouldn't the outer part rotate about a center ?)

3) why tangential ?

this looks to be a highly redundant reaction set. Whilst you know the three forces form a closed polygon(triangle), I don't think you can readily set the direction of magnitude of any of them. Sure you can make assumptions, but ...

The stiffness of the channel will also affect the solution.

another day in paradise, or is paradise one day closer ?

## RE: HSS statics problem

And since immediately flattening of the contact locations L(eft) en R(ight) will occur we can say that these forces are equal and opposit working forming a moment since then are at a vertical parallel distance y being the width of the spacers.

So the forces can be calculated.

Note with a real wench there the hand force on the wrench will plays its role in the horizontal Equilibrium (when the hand force is hor)

## RE: HSS statics problem

If that is what you are suggesting that is how I initially approached the problem, but then I thought about an eccentrically loaded bolt pattern and how the reaction forces are perpendicular to a line drawn from the pivot point to the bolt, and figured this must be similar.

## RE: HSS statics problem

That said with tolerance build up in the components how are you going to guarantee that hen the top block pivots the wo side plates will touchdown on the rectangular section simultaneosly?

If the above doesn't happen then the u section is taking the load all on one side.

“Do not worry about your problems with mathematics, I assure you mine are far greater.” Albert Einstein

## RE: HSS statics problem

desertfox: the OP has not mentioned any vertical forces up till now, so we can assume the friction in the 'pivot' point to be low, therefore as soon as one side touches its reaction force will overcome that friction and slide the top U until the other side also touches.

Actually it isn't a real pivot but more a slidable contact which may not even be there as with the wrench example.

Ofcoarse with a vertical weight in the game it would be different.

## RE: HSS statics problem

## RE: HSS statics problem

another day in paradise, or is paradise one day closer ?

## RE: HSS statics problem

Imagine that we push the U section either left or right so that one of the side plates contacts the rectangular section the other side having all the clearence between the two faces, now apply a moment to the U section does the U section rotate? Or is it prevented from rotating by the side wall in full contact with the side plate on the U section? Now move the U section so that the clearence is equal on both sides and apply the moment just as you have in your diagram, now it may well rotate till one or both side plates come into contact with box section but the reactions depending on what actually happens in practice will be different in each case.

You can make simplifying assumptions and calculate theoretical reactions but they may be far from the truth.

“Do not worry about your problems with mathematics, I assure you mine are far greater.” Albert Einstein

## RE: HSS statics problem