capacity of through bolts in concrete

huangyhg

capacity of through bolts in concrete
for bolts through concrete, loaded in double shear (equal both sides), and far from any edge, what design procedure would you follow?  assuming the bolt is cast in, or otherwise completely encased within the concrete matrix, would bending of the bolt have to be considered?  concrete bearing would obviously be important, but over what length of the bolt?  would edge failure of the concrete control, even if steel side plates restrain the concrete?  sorry to be so general, but just looking for advice on how others would approach the design.   
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   
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