Math Foundations -- Sign conventions in this soil pressure graph

[DavidLee24]

Hey guys, so I stumbled across this, and I'm kinda confused on how do they get the sign convention of the value. I've attached the figure and also the soil pressure for better reference. Take for example at C, how do they get the minus and positive sign convention? Thanks a bunch.

P/S : Please do elaborate your answers, thanks!
PP/S : I'm using this example to try to design an actual raft, so please do advice.

 

[Drakkith]

Hi DavidLee. I think it would help if you elaborated on what exactly this is, what q represents, etc.

 

[DavidLee24]

Thanks for the reply, Drakkith. I'm sorry for providing minimal info. I shall edit my post.

EDIT : Not so sure why I couldn't edit my original post, but here's the additional information;

q is the soil pressure; with the formula q = 31 ± 0.6x ± 0.08y (kN/m²) <--- computed
x and y is the direction of moment

I knew how to obtain the distance, eg 8.25m, but not for the sign convention though, which I do believe I'm confusing myself.

 

[Drakkith]

Looks to me like the sign convention corresponds to the X and Y directions from the origin. Since there is a negative sign for the $x$ term for all points to the right of the origin, your equation is:
$q=31-0.6x+0.08y$

 

[DavidLee24]

Thanks again, for the reply. But as for X direction at C, if we divide them into X-Y axis, aren't it be in positive as the X-dir going to the right? I see that for +0.08y <--- it is at above, therefore positive, is it right?

 

[Drakkith]

But as for X direction at C, if we divide them into X-Y axis, aren't it be in positive as the X-dir going to the right?

Nope. You can see that the force in the middle decreases as you go from left to right from 1500 to 1200.

Edit: Hold on. Let me take a closer look at this.

 

[Drakkith]

Okay, this is a bit more complicated than I thought. Notice that from point A to point C the pressure actually has a net increase from 400 to 450, but everywhere else the pressure has a net decrease as you move from left to right. Hence the equation that was solved for has a negative sign for the $x$ term.

The pressure in the $y$ direction has no net increase or decrease except for in the far right edge where it has a net increase, hence the positive sign.

Note that I wouldn't trust this equation. The pressure just under the origin is 1500kN but the equation predicts a pressure only 3% of that.

 

[DavidLee24]

Hi Drakkith, but the value you mentioned eg. 400kN, 450kN ..that isn't the soil pressure as that is the axial load from above into the column. So the soil pressure at A is 36.81 kN/m² and at B, 31.86 kN/m² and finally at C is decrease to 26.91 kN/m² .. The soil pressure is obtained from the formula..

 

[Drakkith]

Hi Drakkith, but the value you mentioned eg. 400kN, 450kN ..that isn't the soil pressure as that is the axial load from above into the column.

My mistake.

So the soil pressure at A is 36.81 kN/m² and at B, 31.86 kN/m² and finally at C is decrease to 26.91 kN/m² .. The soil pressure is obtained from the formula..

I'm not a structural engineer or something, but, like I said, I have my doubts about this formula. It's difficult to trust such a simple formula when the column loads in the middle exceed the edges by a factor of 3 or more yet the calculated soil pressure is often less. Where did you get it?

 

[DavidLee24]

Where did you get it?

Oh, regarding the formula, it is calculated. I will go briefly on how the formula is obtained. Firstly, we calculated the total column load ..Q = Q1 + Q2 + Q3 + ... then, determine the pressure on the soil, q, below the mat at points A, B, C, etc..using the equation q= (Q/A) ± (Myx/Iy) ± (Mxy/Ix) ... and then proceed to calculate the My, Mx, Iy, Ix ..to conclude, that the formula q=31−0.6x+0.08y is obtained by q= (Q/A) ± (Myx/Iy) ± (Mxy/Ix)..