Depending on the thickness and f'c of the concrete wall, and the diameter of the bolt, I would expect that shear through the bolt would control the design - even more so with metal side plates.  

Mike McCann
MMC Engineering

I wouldn't worry about bending.  Even though the stress distribution for bearing is probably not consistent through the length of the bolt, I would consider most if not all of the bolt length in bearing. Some of that depends on the hole diameter vs. the bolt diameter.  If tight fit, all of the length, if loose, maybe 2/3 on each half (I'm assuming you have loading on each face of the concrete).

I would consider edge failure as a reasonable potential, even with confinement, since the edge stress is going to create tension in the concrete for a failure wedge.

I think I would start with the bolt's shear capacity, then check bearing.  Ordinarily, I would not check bending of the bolt.

For a 3/4" dia. A307 bolt, (thread included in shear plane) in an 8" thick slab of 4000 psi concrete:

1)  Factored shear 39.6*2 = 79 kN or 17,800#

2)  Bearing area = 0.75*8 = 6.0 in^2.  Shear stress = 2970 psi.  CSA A23 would permit this bearing stress if clearance is adequate all around.

3)  Mf = 17,800 * 8/8 = 17,800"#.
Z = (0.75)^3/6 = 0.0703 in^3 (plastic modulus)
Mr = 0.9 * Z * 36,000 = 2,278"# = 0.128 Mf (No good)

If bending is a valid consideration, the factored load would have to be reduced to 2,278# total, or 1,139# each side.  

This seems ultra conservative, especially when compared to the shear-friction provisions of the CSA code.  As long as the anchorage is adequate to fully develop the ultimate strength of the bar or bolt, I don't believe it is necessary to check bending.

  

BA

I can't picture the bolt failing in bending, so I would check bolt shear and bearing.  For length of bearing, I wouldn't be comfortable using more than 3 times the bolt diameter from each end.  So, with a total shear of 17.8 kips on a 3/4" dia. bolt, I would get a bearing stress of 17.8/2*.75*(3*.75)=5.27 ksi.

I would think that as long the connection is not seen failing under the load (correct lateral cover, normal strength concrete) the conditions of shear-friction are met, since we have the bolts properly anchored to one side of the shear interface. So, assuming the same reduction factor for tension than shear that would give Fi·Ft=29.8 kip for 2 A307 bolts and coefficient of friction = 1 at the interface, that should be normally conservative. However, to keep overall reliability-safety of the structure homogeneous, these connections are usually taking a complementary (dividing) safety factor of 1.7; that would give for the same two bolts 17.52 kips in pure shear.

In case the concrete is old or weak I would also check the bolts as if embedded in masonry, just in case.

I guess I see this a little different. Small diameter members have very small I's which means that the bolt will deflect and move away from the load. As a result the concrete stresses will have to be much larger near the edges. I don't think that there is any way that there will be uniform bearing across the length of the bolt. The free body diagram of the bolt will result in bending moments in the bolts. The bolt bending capacity will govern well before the bolt shear in this condition.

When holes for thru bolts are drilled in the field they won't perfectly match the bolt diameter. Also when trying to match holes in steel members on both sides of a wall the contractor will likely drill from both sides and meet in the middle so there won't even be bearing full width. I have always wished someone would do some tests for this condition.  

I agree that bearing will not be uniform over the length of bolt, but I'm not sure how it varies.  I guess this could be studied using finite element analysis.

If we were talking about drilled holes, I would be inclined to use a higher safety factor, but I thought we were talking about bolts cast in the concrete.

BA

To design this type of connection I normally assume the load distributes over about 1"-1 1/2" and check bearing and bolt bending based on these parameters.

Thanks for all of your comments.  Like ron9878, I wish that there were some applicable research results.

To make things a bit more specific, I am talking about high strength bolts, say A325 or grade 8.8, 1 1/4" or 30 mm, in a wall 10" or 250 mm thick, 50 MPa or 7000 psi concrete.  Cored holes a bit bigger than the bolts and epoxy injected.

I know, the use of higher strength (which may not help) and larger bolts aggravates the problem, and I think means the concrete will always control rather than the bolt strength, but it differs from a one-sided connection, so I don't know of any actual design guide which fits.

hokie66, what design procedure did you follow in the end?  

I have a similar condition to check...

1 1/2" diameter grade 8 high strength bolt to be installed in a cast 1 5/8" diameter hole placed in a 14" thick wall subject to shear on one-side only.

I agree that bolt shear and bending, and concrete bearing are to be checked.  The bearing length on concrete to resist bolt shear is likely going to be the within the first couple of inches of the wall.

I am not aware of a specific design guide for this condition of a thru-bolt subject to shear placed in cast or drilled hole

Well, to consider bending, go back to fundammentals: You have to have a lever arm, a force on that lever arm, and a "pivot point" (a point where the object to be bent will actually start its turn).

So, start with an ideal case: the bolt is in perfectly "hard/rigid concrete" and cannot "wiggle" in the hole (it is cast in place or fastened with epoxy filler in the hole or inserted into a very tight hole, the load is applied in pure shear (in parallel to the surface of the concrete), and that load is applied very close to the surface of the concrete.   

What can bend?   How can it bend?  It's simply not possible.

--

Real world:  The hole is oversized or the concrete around the cast-in-place bolt deforms, the epoxy yields a little.  The baseplate is pulled sideways and "up" away from the concrete (which yields a little bit) and thus there is a bending action on the baseplate.  This pries up one half of the bolts on the "high side", and bends the bolts closest to the bend in the baseplate on the "low side".

Real world, the loads are applied up above the surface of the concrete, and those loads have a vertical component: usually much smaller than the shear component, but it is there.  The baseplate holes are larger than the bolts = which allows the bolt to yield sideways a little bit, and so the bolt will be able to bend at the surface of the concrete: it can't be kept perfectly vertical.

But it is the prying action of a "flexible" baseplate in soft (or cracking) concrete that will cause the most problems.  

With a sufficiently rigid baseplate, the yielding (failure) is usually in pulling the bolts up out of a hole out of their anchor (that, in this case, is resisted because the bolts are through the concrete slab), or in stripping the threads and pulling through the bolts on the high side.  

Then the sign or post fails by fallin down, thus bending the bolts on the low (downwind) side.   Yes, they bent, but after the initial failure.

eamonnc,
My design issue has not yet been resolved.  Your problem with one-sided shear is more like a post installed anchor, and you can probably use Hilti's design methods.

racookpe,
The concrete failure in my case will control, but I would still like to have a design guide rather than depend on my own assumptions.  The load is not a wind load, and the bolts are in pure shear.  The small moment is taken in another way.

Consider the ultimate stress block, similar to the way we consider a concrete beam.  If the bolt diameter is 'd' and the factored load is 'P', then 2*a*d*0.85f'c = P, where a is the required length of bearing at each face.

The resulting moment is P/2*a/2 or Pa/4 which is the factored moment required to be resisted by the bolt.  

That is consistent with ultimate strength theory.

BA

I think your way is appropriate, BA.  I will have to include a strength reduction factor, 0.6 for bearing.

hokie66,

Put another wallaby on the barbie!

BA

We're running out of those.  What about some nice emu steaks?

That would be fine.  Or I could send you a couple of caribou, elk or wapiti.

BA

I could send you a couple of reindeer too, but Santa could be in short supply come December, so maybe I had better not.

BA

Heck...  Down under Barbie is a Wallaby.  

 

Mike McCann
MMC Engineering

I tend to chemically anchor these in, so I conservatively treat it as a chemset of the same length.

I disagree that bending can be completely ignored as therecould be spalling at the edges. I usually allow for an inch of spalling. All these things are included in the chemical anchor capacities.

wedge failure is likely if there is no confining plate present, thus it would be good to include in your calcs, the ais "design of structural connections" has a diagram on it, page 248.  

When in doubt, just take the next small step.
 

thanks for the responses!  i will throw another wallaby, emu, caribou, elk, wapiti, and reindeer on the barbie!