Moment on Mat Foundation

[kirei17]

Hey,
Here is just a simple question (but i believe the answer would be very critical).
I just want to know if my assumption of moment diagram is correct.
My case is a mat foundation. Here i just drew it two dimension. I showed column as a load only, while for the foundation i drew it exactly as it was designed.

 

[DST148]

@kirei17> Moment diagram with concentrated moments(same signs) at each end of the mat would look
something like a bow-tie, traingle on each side of horizontal, with max ordinate at each end.

 

[kirei17]

about the concentrated moment, i dont get it, bow tie has max positive and max negative in one section. How can that be possible?
I thought mine is already correct looking at the possible bent form of the foundation.

 

[SteelPE]

DST is correct, the moment diagram should look more like a bow-tie. Figure your bearing pressures and then sum moments at any given point, plot and you will see that it looks similar to a bow-tie.

 

[paddingtongreen]

Your diagram is false, without a net downward load to counter the overturning moment your foundation will fly away. You need to show the soil pressure gradient and then take moments. Then, if you want to understand, you need to calculate moments at intervals from one end to the other.

In foundations like this, because there is no adhesion between the soil and the foundation (no tension)the two cases are not additive, the loads must be combined into a single case.

Michael.
"Science adjusts its views based on what's observed. Faith is the denial of observation so that belief can be preserved." ~ Tim Minchin

 

[kirei17]

Sorry, perhaps i wrote it falsely.

Of course in one section when there is negative moment at one side (whether it is top or bottom), there is always going to be positive moment at the other side, and so does the opposite.

But from what i learned is that moment diagram only show the tension side of a section. If the bottom goes tensioned then the graphic show positive value below the line. If the top goes tensioned then the graphic show negative value above the line.
So what you guys mean about bow-tie should match my understanding about the moment diagram.
Please address me if my understanding is still uncorrect.

@paddingtongreen
You are right. the moment diagram should be an envelope. I only focus at the shape of moment diagram from two concentrated moment with spring support along the "2D beam". In reality i do consider the selfweight of the structure, which i assure you, quite adequate to ensure the foundation stay in touch.

Anyway, for the soil pressure, as i consider the mat foundation to be rigid, i tend to go with the uniformly distributed pressure. Of course, it may not be rigid enough with a 55cm thick foundation covering 15.0m x 8.0m size area with quite a huge load (the ultimate moment could reach > 20 ton.m/m).

 

[kirei17]

To further explaining, actually my objective here is to know in what part of section should rebar lap splice be placed. So it would not be placed at the section with maximum tension but at minimum tension.

 

[kirei17]

Wait a minute. How to merge or edit a post?? Im new to this forum, so pardon me for multiple reply.

Sorry, i misinterpret the bow-tie shape. Now i think it is different with my understanding of moment diagram, but i still think that my assumption is the correct one. How could the moment at the edge of the foundation be maximum, when it is free end at each edge? Spring support (subgrade modulus of the soil) is not vertically non-moving support, so even when it is compressed at the edge, i consider the edge to be free end. So when the column, which is place a little bit at the inner side of the foundation, get rotated, the edge of foundation is free end, thus at the edge the moment is zero.

Anyway, still, feel free to correct me if my understanding is not correct. I know i am not too god at this part of knowledge.

 

[SteelPE]

kirei17

Once you enter a post you can not edit it. Being a technical forum, with people asking complex questions and receiving complex answers, it's important to keep the exact text people post to help others who might read your post years after it was written (1 year, 2 years, 10 years from now).

Attached you will find the diagram I believe you are looking at with your concentrated moments. The diagram comes from a spreadsheet I wrote a while back for combined footings (basically what you have here). You will be able to see that the diagram is a bow-tie as discussed above (the moments are applied at 2 and 12 of the diagram). Now, in this spreadsheet, I added the weight of the footing to the analysis because the footing is used to resist the "overturning" generated by the moments.

 

[kirei17]

Thanks SteelPE

Now i see why it is being called bow-tie. But its different from what i am expecting. Actually my diagram is not far from what you shown, but mine didn't have sudden drop (change of sign) at the point of application of conc moment (it's like the drop in shear diagram?). Maybe because i don't consider the selfweight factor?? And to be honest i didn't calculate just guess.

Now would you mind on further explaining me, like, what are the moments that are added to obtain sigmaMu ?
In case 2, in 0.2s distance, when i add sigmaMu from Mu, col + Mu, ftg+fill + Mu, soil (-16 + 16 + (-9) = -9), i don't get the same value to sigmaMu value (-10).

Also, what case is case 2 and what is for case 3 ?

You're being very helpful.

 

[kirei17]

Now if the combined moment shape should look like the one that you sent, that means in my previous attached drawing (re-attach below for scanned, better quality drawing), my assumption of normal condition (normal operation vertical load) is false. Because if it is true, then the combined moment shape (or envelope shape) when it is added seismic concentrated moment will have a negative (top tension) moment at the middle/between column, when, in your sent diagram, it is obviously not the case.

Maybe it is because i don't really consider selfweight of the foundation. I just focus on the column load (which is from operating equipment load). That's why my moment diagram assume maximum tensile at top part of middle/between column section. But then, even if i do consider foundation selfweight, the model is not supported at both edge (despite the key form at both footing ends), so there would be no top compression at middle section to zero the tensile from normal operation vertical load.

 

[SteelPE]

kirel17

The page you saw is part of a larger spreadsheet with a few different load cases. In this instance, both diagrams looked the same.... but they don't always. I just used this as an example to show you what was going on. You should concentrate on the diagram and not the chart. All the chart is doing is keeping track of the loads and moment applied to the footing (dead and live point loads, footing weight, surcharge weight, lateral loads etc...) and then summing them up at the bottom to create the diagrams.

I sill disagree with your new diagram. Just like a shear diagram, where you have loads applied, you will have a sudden increase or decrease in the diagram. In this instance you get a sharp drop at the location were the moment is applied. This is a very basic concept and something you should be familiar with already, I don't understand the confusion.

 

[kirei17]

SteelPE,

no, no, i already remembered about the sudden change (it's a point moment, point force hence sudden drop). How the heck could i miss that? Of course your diagram is true. I don't do much of this kind of thing anymore since university. By the way, the new diagram is not new. I only scan it for a better view, not the camera photo view i first sent.

or probably because usually it's only rigid support, and now it is spring support along the beam. i remember the first step is to determine support reaction. now with these spring, i become confused as to what is right and not.

Anyway, at least i got it right for the maximum moment and and where the moment were zero.

What i am still confusing is about the top diagram. I have two diagram. One is vertical load only diagram (the top diagram which i shown above) and the other is concentrated moment diagram (the bottom one). I already get the answer for the concentrated moment diagram, which in yours, is already combination of moment. What do you think about the top diagram? Let's just say i ignore the moments and foundation weight. Would the vertical load from column create a maximum negative (top tension) moment at middle of the two columns?

 

[SteelPE]

kirei17

You responded to your own post before I was able to put my response.

To answer your question about the top moment diagram. Depending on the magnitude of the vertical reactions and whether or not hey are equal..... the maximum moment will occur in between the two point loads..... but not necessarily in the middle.

I can tell you that I would never attempt to design a mat foundation as I have no experience with these types of structures. The spreadsheet I showed you was prepared for a combined footing (two columns on the same footing). The diagrams are similar which is why I show them to you. I think you may need to run these questions by your supervisor as it appears you might be over you head.