Finger beam moment capacity

[youngstructural]

Hello All;

I need to know the bending moment capacity for a finger beam I'm working with. The beam is 600mm wide, 2700mm long (and 400mm deep) and is bearing on 100kPa Safe Bearing Pressure soil. The vertical load veries, but I would need it for 25kN and 40kN. The load and moment look like:

| N | Axial Load (N) & Moment (M) act about the Dot, 400mm from LHS
| M |
___·____________________
| |
|_______________________|

My problem is that I don't do enough geotechnical work to be 100% confident in my methodology. I have the following two fomulae for qmin and qmax,

qmin = N/A - M/S ; qmax = N/A + M/S

where S = (Width*Length^2)/6
and A = Area under Footing (0.6*2.7 = 1.62m^2)

BUT, qmin turns out negative, so I use the following formula for solving for the point where the slope of the stress envelop crosses zero stress:

x = 3(N*Width - 2M)/(2N)
and then
qmax = 2N/(x*Length)

This yields a very small moment capacity... In the order of 10 to 20 kN·m. I believe that what I've done is correct, that it is rational to restrict the moment to this low a load. However, I am not 100% confident, and would greatly appreciate some advice!

Is it as simple as recognizing that the slope of the stress field cannot change? Because if I try the first two formulae for qmin and qmax with a high moment and set qmin to zero, solving for qmax gives me 30kN·m!!! I would think this is not realistic, because the back of the footing would lift up before acheiving this stress distribution, but am I right?

Your thoughts are appreciated,
Regards,

YS

B.Eng (Carleton)
Working in New Zealand, thinking of my snow covered home...

 

[youngstructural]

Anybody willing to take a look???

Thanks,

YS

B.Eng (Carleton)
Working in New Zealand, thinking of my snow covered home...

 

[civilperson]

Bending moment capacity is a function of the amount of reinforcing and the the strength of the concrete. The amount of capacity needs to be greater than the moments produced by the soil pressures. Take the soil pressure, (100 kPa), times the area (2300 x 600), acting at the centroid of the area (2300/2) as maximum moment experienced by this foundation at the face of the column. Put in reinforcement at this location sufficient to have moment strength greater than the calculated moment. Check that this moment is less than the imposed moment.

 

[youngstructural]

I understand that shortcut very well, but I am worried it is not applicable in my case... The structure is so light that I have doubt about the foundation being able to develop the moment without overturning occuring.... Hence the use of a fomula to solve for the point where the line of stress crosses the line of zero shear (x-axis).

I just would like someone to reaffirm my belief that it's an overturning issue at work here. I'm pretty confident it is, because if I do a sum of moments about the work point, it shows a balanced condition for the reduced moment capacity...


B.Eng (Carleton)
Working in New Zealand, thinking of my snow covered home...