huangyhg

slab punshing shear and steel cap plate
will the punching shear in a concrete slab supported by a steel cap plate be reduced if the cap plate edges were chamfered 45 degress?
the chamfering will provide a transition in the slab thickness from say 7.25 above the plate to a full slab thickness of 8.0 in. the cap plate thickness being 0.75".
thanks
the equations and assumptions for punching shear are too general to make a meaningful analysis at that level of precision. even if they were that accurate, normal construction tolerances and variations in material properties would make detailed theoretical calculations suspect.
the actual punching shear is determined away from the edge of the plate, so it won't make any difference in the calculations how the plate edge is arranged.
making the plate wider will help your punching shear by increasing the perimeter bo (aci term). the thickness of the plate will then increase because of the increased moment in the plate itself but increasing the thickness of the plate alone will not help your punching shear in the concrete slab. i would stick with a standard square-cut edge. so, my answer to your question is no.
after a quick trsearch, aci318 section 15.4.2(c) specifically determine the location of the punshing shear critical section.
now, the question is: what "d" value should be used in the punshing shear equation?
1. should "d" be based on slab thickness - plate thickness
or
2. "d" based on total slab thickness?
thanks.
it is actually section 15.5.2
my answer is #2. the idealized assumption is that a punching shear failure will occur at the location of the critical section - far away from the plate. this is not "true", but has stood the "test of time" as a reasonably accurate way to predict concrete behavior with simple (pre-calculator/computer) math.
sliderulera, that is well understood, however, we usually repeat this task of punshing shear calculation on buildings on a daily basis. as with everything else all calculations are well documented and presented as a backup to show that the slab column connection is acceptable and code compliant. after discussing this issue with others, i conclude this:
"d" is be based on the diagonal crack due to shear.
1. if the cap plate edges are not chamfered then the diagonal crack will initiate from the top corner of the plate edge. in this case "d" should be based on the slab thickness minus the plate thickness.
2. if the plate edges are chamfered then the diagonal crack is forced to initiate from the bottom of the slab. hence, in this case "d" is based on the total slab thickness.
to me this make sense since. as an extreme example, it is not logical to base "d" on the total slab thickness for an 8" slab with a 5" thick cap plate. in this unrealistic but acadamically viable case the crack line will initiate at 3" below the top of the slab. so in general i think that a cap plate does reduces the effective slab thickness in ressisting punshing shear.

the punching shear capacity based on the shear stress in the concrete, the 4(f'c)^0.5*bo*d and others, imply that punching shear resistance comes from concrete alone in those cases. note that the only material properties in these equations are those of concrete, no fy is involved. it doesn't make any sense to add steel thickness when the stress is all in the concrete. your questions suggest you don't understand this. "d" is also defined in the aci at the beginning of the chapters in which it appears as the strutural depth of the slab, i.e. the distance from the extreme compression fiber to the centroid of the tension steel. with this definition, you can't add the steel thickness either. note that "d" is less than "h"=total slab thickness.
the theory behind taking the critical section at d/2 from the support face comes from the assumption that the stress between the support face and the distance d/2 will go directly into the support through arching action in the concrete instead of through shear stress as does the rest of the load. sliderule pointed out that is has withstood the test of time and is therefore a good assumption.
with these things in mind, if you need more shear capacity you need to reduce the shear stress in the concrete, by having say a larger base plate to increase the perimeter distance bo, a drop panel or steel reinforcing with the slab itself. the base plate will not help you with punching shear by taking the shear stress or adding it's thickness to the structural depth.
punching shear failure is sudden and brittle by nature. if you are close enough to capacity that you are trying to justify the addition of 0.75" worth of plate then you need to just add shear reinforcing or preferably a drop panel and be safe. messing around with punching shear and doing it wrong is a good way to get people hurt or worse.
ucfse, what you wrote is not accurate. you got the whole thing backward.
"d" is not the total thickness of the footing/concrete slab. "d" is the distance from the compression side of the concrete to the center of the tensile reinforcement and does not include the base/bearing plate thickness.

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