Compressive Shear Failure

[pmour]

Situation: A pad/mat foundation is supporting 4 point loads (6" square bearing plates). The foundation thickness has been designed for one way and two way (tension) shear per ACI.

What I was wondering was how to calculate the resistive strength of a compressive type shear failure (see attached)? I would like to be able to calculate how close to the foundation edge is to close? Is this even a factor? This topic was stimulated by a contractor increasing rebar in the foundation and requiring end hooks to meet design strength of ACI 11.7 Shear Friction for the failure mode of breaking off a corner. I would think, if you stay far enough away from the foundation edge the concrete would have enough shear strength to not require the additional rebar or tension development, but how far away is far enough?

 

[cntw1953]

Here are a few leads maybe useful:

1. Determine bearing pressure under pad.
2. Design as a simple beam:
a. flip the lower sketch up-side-down, let point load as reaction on beam support.
b. place the bearing pressure as load applied on the beam.
c. determine critical location and check shear using ACI provision for oneway beams.
3. Design as two way slab:
Steps a & b are identical to above, but use ACI provisions on two way shear (punching shear) to check shear strength of the slab to support/resist the corner loads.

Wish this helps.

 

[cntw1953]

For the condition in upper sketch, use ACI provisions on shear friction. You will need to assume a failure plane (read ACI omments would help) and design for anchorage.

 

[pmour]

The "as a beam" detail was just a comparable example for the "as a foundation" design situation; and I forgot to label the compressive shear failure plan on the "as a foundation" detail, the dashed line top to bottom, left to right. The foundation has been designed as a simple beam for moment and shear, as well as two way shear of a footing. d=14", bearing passes minimum footprint. What I am attempting to determine is what is the minimum distance between the foundation edge and the point load? I have analyzed the point load for two way shear on edge and corner, but was concerned that this other failure mode may control, as shear friction often does.

Given:
18" thick foundation, d=14",
top and bottom rebar with 3" clear cover and no hooks,
6" square bearing plate;

Question: Rather than hooking the rebar for the tension development requirements of shear friction design, how far from the foundation edge must the center of the bearing plate be so that the design is not controlled by shear friction?

Do just need to be far enough from the edge so that the compressive shear failure plane passes thru the entirety of the foundation? What would be the angle from the horizontal for this shear failure, 45 deg, 40 deg, less?

 

[ishvaaag]

One way that can be acceptable to the code is to watch the principal tensile stress, ensuring it keeps limited to the characteristic value that is observed to be extant 95% of the times under the factored load. Depending of the proportions of the footing and the varying point of application (for your investigation) such principal tensile stress will be either in the top or the bottom. What brings to my mind the fact of that you are designing a combined footing for a number of columns and the usual practice is then to have both top and bottom reinforced. Anyway let's think for a moment you are interested in a footing where the top face is without reinforcement, and the bottom has reinforcement. Exceeding the characteristic tensile strength would be uncommon (or should be) for footings, since normally one doesn't want cracks serving as path to the steel for water. Anyway it is a situation ordinarily admitted in reinforced concrete, distributed cracks kept at bay by reinforcement. On the unreinforced top to keep the safety you have not but the tensile strength of the concrete, and if you want to keep the ordinary standards pf safety, its characteristic value. By the way, on making the comparison, I would use likely, conservatively, the value for pure tensile strength, and not flexural tensile strength, we are compared locally for the biggest tensile stresses and it is both locally more accurate and safe to use that value instead of the more lenient for flexural tension. It must be noted that without reinforcement helping to the buildup of stress in the compressive struts, the tensile stress will be directly the limiting one.

So to this effect you may make 3 D models of the different setups to find to where it works for you.

You may also use the same idea with simplified strut and tie schemes, where a compressive strut goes from the bottom of a corner column 45 deg to the bottom of the footing and then for a "tributary" diagonal beam in the footing analyze the tension present, and grossly, the tensile stress. A coarse method yet may give you soon an idea of to where you can go without causing too much tensile stress.

 

[ishvaaag]

As well to add that loading by the soil is not different from loading from distributed loads at floors (except for crack control and inverse direction on the loading) and is one of the more common situations in ordinary buildings. I have practiced it (when in mats) most of the times to the corner itself and the ordinary cautions in design for slabs have lead always that I know to safe and unproblematic designs. Sometimes we have also used recessed columns from the edges, but this has been more on the imposition of the layout or to take some advantage of some cantilever say to extend the footprint of the slab in weak soils.

For multicolumn supports this could be another thing but, then, we are rarely designing the thickness of the footing to be mechanically critical, some minimum depths related to frost or just get to sound soil use to be respected, so if for a design of a multisupport for a bridge or main set of columns in buildings it is unlikely we would decide to be less conservative.

 

[cntw1953]

pmour:

If this is a corner column in two way slab, and there is adequate concrete shear strength through two way action, then you need not to worry about edge distance. The mode - chipping through the corner/edge is not likely to occur. However, you may always assume a failure plan (from highest compressive stress drawn a line towards free edge of the pad), and check using shear friction concepts (similar to corbel for this case).

If design is controlled by shear friction, you need to develop the shear friction bars to achieve yield strength at the critical location, therefore, it controls your edge distance - either for a full development length, or use hooked bars. However, I really do think this (shear friction) is controlling factor.

 

[pmour]

The foundation has top and bottom reinforcement in both directions.

Based on a shear friction design (ACI 11.7) would the minimum distance between the foundation edge and the failure plane be as shown in the attached drawing? 2 to 4 feet seems like a significant oversizing of the foundation? Also, the longitudinal rebar size and spacing will need to be increased to account for shear friction in addition to bending?

Shear friction assumes that the concrete has cracked along this shear plane. What is the plain concrete strength of this plane prior to the failure?

Would it be correct to assume the following: Using Mohr's circle tau max = sigma/2, therefore would the concrete compressive shear strength of 4000 psi concrete be 2000 psi? Can I use this value across my failure plane to determine whether or not the failure would occur in the concrete without accounting for the rebar/shear friction?