concrete breakout cone area for group

huangyhg

concrete breakout cone area for group?
is anyone here familiar with aisc's base plate and anchor rod design 2nd edition?  on page 36, the concrete breakout cone area for group is written as [3(13) + (4)(3)(13) + 4 ] = 1849 in2.  how did they get they this number?  is it a typo?
can anyone provide the concrete breakout cone area for group and use it in a example for a base plate with four anchor rods?  thanks in advance.

this is covered in aci 318-05 appendix d (not this exact example, but the idea of projected areas for concrete breakouts).
yes, it is a typo - it should say "[3(13)+4]*[3(13)+4]=1849 in2"
thank you so much for your prompt response, structuraleit.  your calculation added up.  i was trying to look for an errata for the second edition but could not find out.  there is one for the earlier edition, "column base plates".
can you elaborate some on how the equation was derived, and what do the "3" and "4" refer to?  does the "3" refer to the edge distance, and "4" to the distance between the rods, for instance.  please clarify.
i have referred to my aci-318-05 book on page 391, and the formula i am getting for a 4-rod group is: a nc = (ca1 + s1 + 1.5hef)(ca2 + s2 + 1.5hef).
4 is the spacing.  "3" represents 2*1.5 (for the 1.5hef).
2*1.5hef + 4 = the length of one side of the square for the projected area.  if you square that you will get the projected area.
ca1 on page 391 will be replaced by 1.5hef in the aisc design guide example because they state that edge distance is not an issue.  that ca1 represents a situation where you have less than 1.5hef to the edge of the footing.
the equation was derived based on a concrete breakout cone of about 35 degrees (i believe).  aci also says in the commentary that the surface area of the breakout cone will very closely match the area of the projected square/rectangle given by the equation with 1.5hef.
thanks for the explanation, structuraleit.  it helped me understand how the concrete breakout cone method works.
i understand in the e.g. provided by aisc, edge distance was not a problem.  that was why ca1 on page 391 was replaced by 1.5hef.  now, what if edge distance is an issue?  what if my base plate was near the edge of my foundation?  i guess i would need to input the exact value for ca1, then, right?  what value of ca1 would i use?  most likely, my concrete breakout cone area will be smaller which means concrete pullout strength would be less.  hope you can comment and add something to this.
if you don't have 1.5hef from anchor rod to edge of footing, just use the actual edge distance as shown in the sketch you mentioned in aci.  the area of the projected square/rectangle will be reduced and you will use that area in the calculation for anc instead of the full area.
yes, this will reduce your concrete breakout strength, but this may not be the controlling factor.  
also, be sure to note that if you are considering a column with a base moment, only use the (2) anchors that will be in tension, not all (4).  only use all (4) if there is a tensile reaction at the column base.
thanks again for the prompt response, structuraleit.  you mentioned that the concrete breakout strength might not be the controlling factor.  in the abovementioned aisc design guide example, it seemed that that was what they were looking for.  what other controlling factors do i need to consider?  i have also checked allowable tensile strength of each anchor rod, and also the pullout strength of each anchor rod.  are there other controlling factors i might need to be checking for?  please elaborate.
my columns currently do not have a base moment,because they were designed not to take any moment, but will keep your comments in mind if i have any columns with base moments. btw, how would i know, or how do i ensure that, "there is a tensile reaction at the column base"?
that would really only happen at a column in a braced frame or at a column that may have a beam attached to it that has an upward reaction from a cantilever over another column (or similar).  there may be other situations, but i am not thinking of any at the moment.  
if you don't have any shear in the column, then you won't need to consider shear breakout of the rods in the concrete, but if you do you will.  it seems like you have covered the other criteria.
thanks, structuraleit, you've helped out a lot.  others, please feel free to join in.
i do have some shear at some columns, at the vertical bracing locations, but i am designing shear lugs to take care of those.
i hope i don't ruffle any feathers, but if i have six, or more bolts - instead of just four - do you know what i need to change in the aci 318-02 formulas, or in the aisc example, to suit that condition?
just draw the little diagram for your particular geometry.  draw the 1.5hef sware for each rod and use the outermost lines to calc the areawhen you superimpose all of the swares.  depending on your anchor rod geometry, you can get some pretty odd shapes.  it is usually easiest to keept it to a simple sqare or rectangle unless you really need the extra capacity.
  i doubt the (2) rods in the middle of the baseplate will add much (if anything) to the tensile breakout, but if you need it for the actual steel capacity, then you do.
i think you need more help than just an online forum.  try getting the pca notes on the 318.  they have some examples worked out. also look in the equations in the pci design handbook 6th edition.  it is the same method and theory based on different research.  you are permitted to use the pci instead of the aci.