Concrete bearing stress

Hello.
I have a plate bearing on top of an existing concrete beam and the plate is loaded downward at one edge. Is it acceptible to calculate the actual concrete stress by using the equation P/A +/- MC/I, assuming the concrete is stress triangularly? Also, is the allowable concrete compressive stress 0.35f'c or .85f'c?

 

[austim]

Firstly - "allowable bearing stress". BOTH values are commonly used, depending on the type of structural assessment used.

If you are designing with actual working loads and ASD (allowable stress design) then 0.35f'c is you value. If you are working with limit state design (LRFD), then you use 0.85f'c (with factored design loads and a reduction factor on the 0.85f'c).

If your plate is loaded outside the 'middle third' then your P/A+M/Z formula is not applicable. If it is loaded at the very edge, without distributed capacity for tension between the plate and the concrete, then you will have an unacceptable bearing stress, and the formula is P/zero, since the only contact area which can provide equilibrium to the applied load (with compression only) is a infinitely narrow strip under the edge.

If you have anchor bolts and your plate is reasonably stiff, then you can analyse the stresses as if you have a reinforced concrete section (with the anchor bolts as reinforcement and the full area of the plate as the effective concrete section).

 

austim,
What I am trying to do is to design the plate. One of the plate's edge is flush with the concrete beam's edge, and the plate is loaded downward at this edge. The plate has full bearing. To analyse the concrete actual bearing stress, I thought using the P/A + - MC/I would give me the max. and min. stress at the plate/concrete beam's edge. On one plate condition, I get a negative stress which means the concrete is in tension. Is this the best or reasonable way to analyse the stress in the concrete? Even though, the concrete is in tension but less than 1/10 of f'c, is it still acceptible?

To get the thickness of the plate, I simply use M/Fb=bt^2/6.
M is the moment of the resultant reaction and the moment arm (ecentricity). Do you agree?

 

[austim]

NO, if you have a calculated tension between the plate and the concrete, and no method of resisting tension (I am assuming that you do not intend to 'glue' the plate to the concrete), then you cannot use P/A+M/Z. (It will give you an underestimate of the true maximum pressure).

You need to go to a foundation engineering text and see how to calculate the bearing pressure under a simple spread footing subject to a resultant load outside "the middle third".

 

[zliazmei]

Vbridge,

IF you have a force outside of "midle tirth " like austim says, you will have a tension stresses. Here where I am from we simply ignore this stress.
What we are doing is.
P/A+M/Z, knowin position of 0 axis we are finding the force in compresion zone.
The force from tension zone must be anchored.
Ptot- Pcomp=Panch. placing the anchor bolts in the centre of gravity of tension zone will give you clear static decision of your problem.

Hope it helps.

Zlia Zmei
(excuse me for my bad english)

 

Thanks for all your replies. I will look into this further. Basically, what I did was applying the trial and error method by extending or increasing the plate size until I nolonger have negative pressure (tension). But, it is much quicker to go straight to the method for tress outside of the middle third.

 

if you perform a P/A +/-Mc/I analysis and get tension on concrete, you have to find the compression by the formula:
qmax= 2*P/(3*b*m)
where P = load
b=width
m= distance from load to edge of foundation on compression side.
Just ignoring the tension is very unconservative !!

 

[100islands]

vbridge,

You can refer to pp 613-620 of "Design of Steel Structures" by Gaylord, Gaylord, and Stallmeyer (3rd Edition) for answers.

 

[breaks]

Also check out the AISC Steel Manual (9th. Edition), pgs. 2-141 to 2-144 for bearing plate design examples. Not sure if your situation is the same, but there are some basic principles that may help you out...

Matt