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Design of Anchor bolt  circular bolt pattern ACI 31805 AppendixD(3)

I am designing anchor bolts for vertical vessels seated on an octagon pier ( with pile cap/piles). The vessel anchor bolts are in a circular pattern. The max shear and tension at the base of vessel is given by the vendor
I want to use headed anchor rods and comply with ACI31805 Appendix D In determining Anc = projected concrete failure area of (single)/group of anchors. For my model I am using ca1= the edge distance from anchor to edge of concrete – measured in a radial direction.
I am confused with the parameters ca2 which is defined as the edge distance in a perpendicular direction to ca1.
Since the bolts are in a circular pattern I do not have a edge distance ca2 perpendicular to ca1 I used PIP STE05121 – anchor bolt design guide. But this does not provide much guidance for a circular bolt pattern
Can any one help? 

Yes, you do have a distance to concrete edge at right angles to ca1, just not a edge at right angles to ca2. Use circular ties around the anchor bolts to use strength of the steel rather than the concrete shear strength of the breakout surface. (With a phi of 0.75, D5.2.9 and D6.2.9) 

Teguci (Structural) 
28 May 08 17:00 
I suggest using the edge distance C1 for the one direction, 1.5 Heff or half the distance to the adjacent bolt in the perpendicular direction and 1.5 Heff for the direction towards the center. Then calculate the pullout strength of one anchor based on this area.
Alternatively, you can offset a circle 1.5 Heff inward from the anchor ring and calculate the area between the inside circle and a circle c1 distance to the outside of the anchor ring (this assumes that the distance between anchors is less than 3 Heff) and use that area for An 

Thanks to both of you. Attached is sketch with the parameters c1, c2, C3, and c4. Am I correct in my understanding?
Is is ok to consider only one bolt with the design tension? 

Opps attached is the sketch that I am refering Thanks a lot 

Teguci (Structural) 
29 May 08 8:10 
Start with using the minimum C1 distance (from the anchor to the edge of the octogon and not the circumscribed circle). If this doesn't work then average several anchors offset distances together, which might give you what you have shown.
If you look at the anchorage equation, you can consider all of the anchors at the same time, or, with some basic math, using the average area per anchor times the number of anchors and get the same result. An / n = Average An per anchor. Therefore, Average An per anchor times n = An 

csd72 (Structural) 
29 May 08 10:10 
A few notes:
You should use the actual edge distances not the theoretical circle.
Your edge distances are tiny compared to your anchor bolt size so your best option is to utilise steel ties for shear strength. 

The tension given by vendor is probably due to horizontal loads,(seismic or wind), and will effect each bolt differently in relation to its location with respect to the direction of the horizontal load. Thus the maximum tension will effect one or two bolts along the load axis and will decrease as the distance from the centroid of the bolt area decreases,(P/A  Mc/I). "c" will range from the radius to zero and then back to radius. A 3 foot deep anchor embedment will have 4.5 foot breakout cone which over laps the adjacent and second bolt's cone. If you use the same maximum tension for five adjacent bolts with the center bolt under analysis for breakout with overlapping cones, this is a small bit conservative. Probably will require reinforcement steel for mental comfort since the research on which the Appendix D was based stopped at 24" depth of embedment. 

I thank all of you very much for the input. Attached are some sketches regarding my design ( 2 emails). The anchor bolts are in the pier. The pier is reinforced with #7 vertical bars at 7" o.c along the octagon face and # 3 ties at 18in oc. horizontally. The embedment length of anchor bolt that I come up with is 46 in. I am assuming that only ONE bolt will carry all the tension and 2 bolts carry the shear (conservative). My thinking was that The tension from the bolt is transferred to the vertical rebar of the pier by providing min the development length of 23" for the vertical rebar (# 7 bar f'c =5000 psi, fy 60ksi Ld=23") (see sketch 3 /3) I require a min of 4 #7 rebar adjacent to the single bolt to transfer this tension from bolt to the rebar. Then this tension from the bolt is transferred to the rebar and again transferred to the pile cap by providing adequate development length below this 23" that is required. By providing this length on the rebar I come up with an embedment length of 3.84'=46" If I do this do I still need to consider using ACI 31805/AppendixD. Just for mental peace I wanted to comply with ACI318/AppendixD and ran into this problem Attached is a PIP spread sheet and a mathcad sheet computing the lengths. Please let me know your input 

This is rest of the sketches and calcs Thanks 

The rule states that you must use 0.6 of dead load with overturning due to full siesmic force, (not logical but still it is the rule). This will raise the tension value for the anchor bolt in worst case. 

sdz (Structural) 
29 May 08 23:35 
If you had a pure tension load on all anchors you would have to use h'ef instead of hef. See Clause D.5.2.3.
With small edge distance you also need to check for lateral bursting. Clause D.5.4. If this is OK then you can use vertical reinf as supplementary reinf, making sure you have development length both sides of potential failure planes.
Alternatively consider threading the end of a reinforcing bar. The embedded part of the bar can be treated the same as other reinforcing.




