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Moment distribution

Moment distribution

Moment distribution

(OP)
A few times I have encountered the problem of a structure, rectangular in plan view, which is supported at its four corners by piles (I guess from a conceptual level they could be columns instead). If V-Hx-Hy-Mx-My-T loading is given at the centre of the rectangular structure, how would you go about resolving the moment taken at each of the corners?

I think it's okay to assume the V, H and T components could be divided equally between the four corners. For the moments, what I have seen in the past is to assume a 'push-pull' mechanism whereby one corner goes up and the opposite goes down; the other two corners would have to be treated as pivots which practically don't move, which probably isn't quite right. This means the Mx and My get resolved as additional vertical loads. I've been led to believe that the 'push-pull' resolution is conservative which is probably why it has been used.

Are there better ways of resolving the moments? Are there any better simple methods out there? I don't mind if it's iterative - I can program something up. Similarly if it requires some basic FE code. I just wanted to know what you guys would do and whether there are any better methods out there (short of doing a full in-place structural analysis)

RE: Moment distribution

I think your "by hand" method is just fine.

Personally, I would model the pile cap on RISA-3D, with a support near each corner.

DaveAtkins

RE: Moment distribution

"push and pull" means replace the moment with a couple. depending on the the attachment, I suspect that it is redundant and then it depends on the stiffness of the base ... do "plane sections remain plane" ?

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

RE: Moment distribution

(OP)
What do you mean by 'couple'? I realise this is an engineering forum but jargon is as useless here as it is everywhere else - different engineers have different jargon.

An alternative visualisation could be to consider a slab supported at its corners by columns.

RE: Moment distribution

(OP)
Thanks for the link. From reading that article I am more familiar with the term 'pure moment' - I would argue this technical term is more widely understood too.

Given the above, the comment by rb1957 seems to suggest replacing a moment at the centre with a 'couple' (i.e. a pure moment) at the supports. I don't understand that. Can anyone else explain?

RE: Moment distribution

A couple is simply two equal and opposite forces a distance apart. A moment can always be replaced with an equivalent couple.

In your case a moment at the center of the pile cap is the same thing as a couple, with the equal and opposite couple forces acting at the piles. Just like you said in your original post.

DaveAtkins

RE: Moment distribution

(OP)
Ah I see. Thanks for explaining.

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