concrete bearing

huangyhg

concrete bearing
i'm trying to understand the reasoning in the bearing capacity calculations used in a number of concrete codes, where confinement can be taken to aid the bearing capacity (i.e. by a factor of sqrt(a2/a1), within limits).
does anyone have any papers/tech info in regards to the testing (or similar research) which has been carried out to formulate the american aci / australian as3600 approach to concrete bearing surfaces?
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i don't have any papers, but it's a result of the confinement that the additional concrete provides.
you can give a look to bidimensional confinement enhancement of concrete compressive strength in many classical texts on reinforced concrete, park & paulay, montoya-meseguer-morán between others. aisc lrfd code uses that and may give references.
the concept is easy to understand, the lateral confinement of the surrounding concrete creates a triaxial state of compressive stresses under a column applying compression. f'c and fck are derived from unconfined compression tests at which the average value of compression attained before rupture is lesser than in the confined state.
by the way it is the same reason because coefficients of conversion between 8" cube strength and 6"x12" cylinders' stregth is required, the cube being stubbier shows bigger restraint at its core and its enhanced compressive strength there pushes up the average strength.

i cannot recall the specific research papers that lead to this conclusion; however, i do offer the following insight.
the allowable bearing pressure is 0.35fc due to shear cone failure of the supporting concrete, say below a column base plate for example.
this was proven via sample testing and thus the sqrt(a2/a1) which is limited to 2.0 maximum.
the 0.35fc can be increased to 0.70fc upper limit based on the additional concrete confinement created by the additional concrete around the bearing contact surface. why? because the diagonal shear failure plane has increased with the increase of the additional concrete confinement.
a similar behavior is footings on soil, look at boussinesq influence charts for spread footings on soil for example to understand how the footing bearing stress can be reduced by taking some of the isobars around the footing out. the isobars are contributing to the bearing capacity. a similar approach for the concrete bearing stress applies.

the research which leads to bearing pressure increase due to confinement would be quite old, as it has been in the codes as far back as i can re  
hokie66,
there are three types of concrete failures
1) diagonal tension failure in long span beams.
2) shear compression failure in short span beams.
3) splitting or true shear failure which almost eleminates the diagonal tension concept.
in the above case, i believe we are closer to 3) than 1)
see pages 6) & 7) in the following url
allow me to reiterate and expound on my last post:
1) diagonal tension failure in long span beams.
2) shear compression failure in short span beams.
3) splitting or true shear failure which almost eleminates the diagonal tension concept. based on which the 0.35fc was established.
4) the upper crushing limit is what hokie66 is referring to which is the 0.70fc
between 3) and 4) is where the sqrt(a2/a1) factor applies.

ahaddad1,
not sure which code you are quoting with the .35 and .70 factors.  aci?
the australian code as3600, depending on the area ratio, allows ultimate bearing stress to be increased up to a limit of 1.2 fc'.
again, i think the op was asking about bearing, not shear.  it is the same reason that you can pass column loads through floors of lower strength concrete than the columns, within limits.
concrete strength fc' is based on testing specimens, which fail in shear, but these are unconfined.  bearing is different from shear.  
hokie66,
slendebeam was asking about the factor sqrt(a2/a1)
where,
yes, that agrees with our concrete code.  allowable stress design is no longer used in the australian concrete or steel codes.
i think slenderbeam understands how to use the code, but he was asking for references to research on which the bearing provisions are based.  i don't think we have answered that.
hokie66,
the factor formula sqrt(a2/a1) derivation is very simple but may have research papers that i am not aware of.
i will draw you a sketch and attach it in my next post when i have some time to show how the formula can easily be derived.