Punching shear

[EricaB]

My company requested a load drop analysis on a reinforced concrete slab to check a 30" pipe 7' below grade for failure. The vendor gives us a report that the pipe will fail. The concrete is subjected to punching shear failure. When I look at the calculation, I notice they do not take into account the rebar in the concrete for energy dissipation. They tell me it does no work. This can't be true! I find it hard to believe but they insist it provides no resistance. We really want to avoid costly modifications to the slab. Any suggestions on rebar contribution to punching shear strength? Thanks for your inputs.

 

[hokie66]

Shear reinforcement in general needs to cross the assumed shear plane, but not near the edge of the concrete. If you are referring to horizontal flexural reinforcing bars, we don't consider that there is a benefit in resisting shear. There is of course some dowel action, but that is not included in our design models.

I do not clearly understand your problem. If you could give some more information, perhaps we could help further.

 

[EricaB]

A load of 360000lb is dropped from 50' over head in a scenario of crane failure. The dropped load can not cause the pipe below grade to leak. The pipe must stay in tact for cooling. The load covers a large area and I can not imagine how over a 20'x20' area the rebar in the slab does nothing. It's an 8" thick, f'c=5000psi with #8's @ 12" oc each way. The slab is located between two turbine buildings. There is a 200 ton gantry crane that could drop the load. I love NUREG-0612.

 

[msquared48]

360 kips (180 tons)from 50 feet? That 8" slab will be toast hands down.

The concrete will locally be broken apart to the extent that the rebar will become of no consequence. Sorry, but my guts tell me that the pipe will fail too.

Mike McCann
MMC Engineering

 

[hokie66]

Agree with Mike. The slab will be of little assistance. It will be broken into little pieces, and the pieces will fall into the crater formed by the pipe collapse. Dynamic compaction gone wild.

 

[EricaB]

Just looking at the magnitude of the kinetic energy that is generated from a drop at that height, I have a feeling we may not be able to avoid costly repairs, period. Concrete does not dissipate energy very well. Thanks for your inputs!!!

 

[ishvaaag]

If the impact force is well determined (at least is a given) and actually subsumes -as compared with static load- the dynamic effects, quite likely it will be effectively applied, given the characteristics of mutual deformation upon impact, on about maybe an area 1/9th of the front of the falling whatever; since something weighing 180 short-tons must be reasonable big (it is something 2.8 m cubic solid steel)it would give 0.87 m2 of loaded front, that at minimum (unlikely) circular perimeter is 1.04 m diameter circumference, on say 15xpix104=4898 cm2 in shear so 29 kgf/cm2 average shear, quite likely 2x29=54 kgf/cm2, a shear stress at a level about what failure if not neccesarily warranted may be suspected. Nawy gives say 20% of fc, 1 ksi shear strength for your case. Solicitation will be somewhat lower on the opposition of underlying soil to the being applied force.

However, except local damage need be suspected locally, the localization of the same and the 7 ft downwards distance for what is a 1 m diameter applied loads may mean that an analyisis of one stabilized pipe underground for a load applied in a sheared circle 1 m diameter with the load (or may be, on half circle, to allow for the eccentrical application), i.e., the effects of such load in the stabilized pipe underground may be enough to reveal the effects in the pipe.

The required understanding is that the 360 kips loads subsumes all the dynamic effects. Then you take a half circle footing 104 cm in diameter and load it with 360 kip. You set a 3D geotechnical model that include the soil layers and your pipe, joints included. You ascertain if the stresses in the pipe or connections are permissible, or if leakage occurs.

You can also make a dynamic analysis including alternatively the slab and the force growing to the (dynamic) design load level of 360 kips ccording to some impact law and look for the same problems.

Inspection of falling load impact books would also be clarifying, to just find simplified statements of the effects; I may be looking for that later.

 

[ishvaaag]

From this site

http://www.livephysics.com/tools/cl...ated-to-impact-force-from-falling-object.html

one can ascertain that the falling object needs be stopped in an average downwards stopping length of 15.2 mm if the average impact force has to equal its weight. Even if this does not warrant on StVenant dissipation of localized effects the local effects can be averaged at even the 7 feet depth (giving our estimate of at least a 104 cm diameter circle being the averaged front of the impact, but it may be bigger and so the impact effects might not be averaged at the depth), it gives us what the average deformation needs be at the surface (be it obtained from rupture or deformation). So we have now both an impact force and an average deformation that we need to match in our model.

 

[ishvaaag]

Hmmm, I see a contradiction above, I mean, the impact effects need not of neccesity be averaged at 7 ft depth, given that the loaded front may be in the same order of magnitude. Yet we can make some estimates.

 

[ishvaaag]

The "elastic" properties of soils...

 

[ishvaaag]

The settlement just under the applied load at the depth of the top of the pipe...

 

[ishvaaag]

And the elastic settlement at the same depth just 3 meters away along the buried pipe...

 

[ishvaaag]

Just as a convenience to estimate the added flexural stresses in the buried pipe, assume it answers to the law of a doubly fixed constant section beam with a point load amidst. The differential descent of about 2 mm will require some such load from which we can derive stresses.

We derive the notional central load P by making the deflection equal to 2mm.

 

[ishvaaag]

By making such derivation for a 780 mm outer diameter 15 mm wall thickness pipe, the load degrades from the value at the surface of about 160 ton to 95.65 ton at the buried depth. This causes in the pipe additional flexural stresses of about 1060 kgf/cm2, that may still be actually bearable accidentally.

In short, by these calculations, if the pipe is buried in thoroughly compacted material on as much resistant deeper layers of soil, and the thickness of the steel pipe is not too thin, not severy tight to limit strength without consideration of the accidental loading, these calculations give the pipe some chance of survival.

Later we will try to confirm more or less the same with a (still, non geotechnical) FEM 3D model.

 

[ishvaaag]

The FEM analysis reveals the circular section becoming somewhat ellipsoidal; descent atop the pipe is about 1 mm and at its bottom about 0.8 mm

 

[ishvaaag]

Given the squashing the maximum principal attains about the same value above calculated only at the sides (note the descent at the bent pipe is lower)

 

[ishvaaag]

And the worse vonMises stress is where we had the worse longitudinal stress of our simplified analysis; it reaches (same dimensions and properties of soil) about 1500 kgf/cm2.

All along the FEM analysis materials have been rendered weightless to just assess the added stresses of the force at the surface over the slab.

So more or less the insight above stands, if corrected, and if the impact is of the imparted magnitude.

Remaining tasks:
Proper assessment of impact force.
Proper modelling in geotechnical package.

But I think what above gives an idea on how to attack the problem with just FEM packages dealing with continuous materials.

 

[ishvaaag]

We have not extolled the max info of our model. We have seen that we needed 15.2 mm to limit the load about the 160 ton level. The response at 160 ton level gives only under 3 mm descent, hence even if the actual stopping of the load is go be held at around 15 mm, the initial load at impact must show to be higher, and only through rupture of the slab then progress to be held at the average value of 160 ton. So now we can conclude our slab needs to break for the force be held at the 160 ton, average.

 

[ishvaaag]

This is more or less confirmed by the fact of the maximum principal tensile stress under the loaded zone being in the model already at the 104 kgf/cm2, a level of stress that more or less already requires the quoted mesh of 1 inch diameter rebar at 12 in between centers just a bit under the centerline of the 8 in thick slab for a decent reinforcement. Since we have derived above the initial impact force needs be bigger to keep the average value, we may think the slab needs to break as well on that account.

Another insight is that the physics statement on the web site of the force is not quite likely good enough to portrait the imparted force even for one indeformable body along time, particularly at max value, from an engineering viewpoint (if not flawed, what I have not examined). We may try to examine the question from a quantity of movement viewpoint, then by the still demurred examination of impact formula statements from enginering design tests. This I plan to do later.

 

[ishvaaag]

I include now my re-estimate of the imparted force ... with the result of that I simply badly read the website given output force by a 1000 times less the magnitude. That's a nice level of error, heh.

Since however the conclusion of that damage to the buried pipe is by now well established, I suspend any further work on this humbling and yet to me interesting thread.