Moment distribution

[LRJ]

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-H_x-H_y-M_x-M_y-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 M_x and M_y 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)

 

[DaveAtkins]

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

 

[rb1957]

"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 ?

 

[LRJ]

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.

 

[hokie66]

The word "couple" is not jargon. It is fundamental to physics and engineering.

https://en.wikipedia.org/wiki/Couple_(mechanics)

 

[LRJ]

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?

 

[DaveAtkins]

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

 

[LRJ]

Ah I see. Thanks for explaining.