Corner or Interior Column?

[L775]

A corner rectangular column in a multi-story building with 8" P/T floor slabs is being analyzed for punching shear. The column has overhangs on the outside in x and y directions in a plan view.
Question:
How much of an overhang or a cantilevered slab length should be provided so that the column is considered interior for punching shear resistance?
ACI-318 is pretty silent on this issue.

Thanks for your thoughts,

 

[JAE]

I would suppose it would depend on the perimeter critical section location with regard to the edge of concrete.

The commentary for 11.12.1.2 states: "For edge columns at points where the slab cantilevers beyond the column, the critical perimeter will either be three-sided or four-sided."

This implies that cantilevers do indeed affect the size of the critical section. If your critical section is beyond the cantilever length, then ignore the cantilever.

 

[miecz]

Even if you have the requisite overhangs, consider if your shear load is carried uniformly by all four sides. Think of a continuous beam with a short cantilever. Does the beam have twice the shear resistance of one with no cantilever?

 

[WillisV]

For the moment (pardon the pun) ignoring moment transfer and just focusing on direct punching shear the controlling (shortest) critical perimeter for a 3-sided or 4-sided column would control. For example consider a c"xc" square column with a slab depth of "d". For a true interior condition the critical perimeter would be 4sides x (c+ 2*(d/2)) = 4(c+d). At an edge column with cantilevered slab, the critical perimeter would still be c + 2*d/2 for the inside face, however the perimeter would simply run straight out the the slab edge on the sides. Saying "z" equals the slab edge distance from the back of the column, the total critical perimeter then equals [c+2*d/2]+2sides *[c+d/2+z] = 3c+2d+2z. Equating the expressions for interior and exterior with cantilevered perimeters and solving for z yields z = d+(c/2). Therefore for an edge distance greater than d+(c/2) the expression for interior columns governs, and for an edge distance less than that, the expression for exterior columns governs.

This same logic can easily be applied to rectangular columns etc. For columns with large moment transfer it is usually easiest to simply run them both ways and see which is worse!

 

[haynewp]

I was thinking the same thing as jmiec. Be careful about just meeting what the code defines as area required for an interior column if you can't develop a four sided punching shear.

 

[jen4950]

Stepping back a little bit...

Conceptually, what is the failure mode? Is the slab going to break off and leave the column with a piece of cantilevered slab stuck to it, or is the slab going to slide off the column on all 4 sides?

Keep in mind punching shear is a brittle failure- and one of the most dangerous failure modes in modern construction- virtually no warning.

Come to think of it, what are the -quote- dangerous failure modes of materials, sections and means and methods used in modern construction?

I'd say the following:

1) Punching shear of a flat plate; especially multistory construction with the possibility of pancaking. I'm sure everyone remembers that failure of L'Ambiance Plaza and the "lift-slab" technique.

2) Shoring or improper sequencing

3) "Piano Wire" Concrete Beams. Not enough reinforcement, so when the beam is loaded past the concrete's tensile (rupture) stress it cracks, and the reinforcement goes straight to yield stress.

4) Non-ductile behavior of columns - i.e. crushing (and failure) when overloaded as opposed to yielding of the reinforcement.

5) Excessive or unanticipated temporary loading

6) Wrong connection for the application and material. For instance, welded liberty ships. The welded connection allowed the hull steel that was unacceptably brittle at cold (North Atlantic ocean cold) temperatures to propogate cracks in an uncontrolled manner. One huge advantage of rivets and bolts- next time you get on an airplane, notice there are no welds on the fuselage; all rivets. Gets back to fatigue (left all of that theory back in Grad school- but it is important!)


7) Anything post-tensioned in the hands of inexperienced contractors or engineers.

 

[Ingenuity]

L775,

ACI 318 and Canadian codes are silent on the subject, but the European CEB-FIP (now called FIP) Model Code of 1978 suggests a distance of 5d (d = effective depth) to consider a edge or corner column as interior. CAN3-A23.3 1984 Figure N11.27 duplicates the CEB procedure/suggestion if you can get your hands on a copy.

Since this is a PT slab, you also have to think about if indeed you will have the beneficial effects of the axial prestress (P/A) at such locations. P/A effects are produced from the PT anchorages that may not have distributed their actions into the slab under certain tendon/free edge arrangments.

HTH