1. GTSTRUDL Anchor Checking Using ACI 318 Appendix D Rob Abernathy CASE Center GTSUG June, 2011 Delray Beach, FL

2. GTSTRUDL What is “Anchoring to Concrete” GTSUG June, 2011 2 Appendix D, first added to 318 in 2002, “provides design requirements for anchors in concrete used to transmit structural loads…” This presentation is limited to the provisions that are used in anchoring base plates to a bearing surface, although Appendix D can be used in some situations of anchoring to structural members. This presentation is based on ACI 318-05, and includes figures copied from the Appendix D commentary. Many of the formulas and techniques found in Appendix D are based on the paper “Concrete Capacity Design (CCD) …”, ACI Structural Journal, 1995, which is reference D.9 in ACI 318-05 and -08.

3. GTSTRUDL Anchoring to Concrete: Terms and Concepts GTSUG June, 2011 3 F is a reduction factor applied to calculated capacity. y is a modification factor applied when determining capacity. It may be greater than 1.0. h ef is the effective embedment depth of an anchor. Anchor groups are sets of anchors with spacing ≤ 3h ef and having “approximately equal” h ef. Supplementary reinforcement is “reinforcement proportioned to tie a potential concrete failure prism to the structural member”, although the rules for proportioning are not defined in Appendix D.

4. GTSTRUDL Terms and Concepts: Breakout/Failure Cone GTSUG June, 2011 4 The major concern of Appendix D is the failure of the concrete via a “breakout” cone. Tension can cause breakout from the top surface of the concrete as shown to the left or at an edge. Shear can cause breakout on the surface through “pryout” or at an edge. Note that the area involved extends 1.5h ef from the anchor center, hence the 3h ef (1.5 + 1.5) spacing definition of an anchor group.

5. GTSTRUDL What does Appendix D cover? Anchor + concrete capacity only – no base plate provisions Limited to anchors 2” or less diameter and h ef (effective length) of 25” or less. f’ c of 10,000 psi for cast-in anchors and 8,000 psi for post-installed anchors. “Regular” arrangement of similar anchors. Not a formal requirement, but only examples of such are given. GTSUG June, 2011 5

6. GTSTRUDL What is not covered? Plate failures – overstressing of plate material, weld failures, etc. Cyclic (fatigue) or impact loads Through bolts “Irregular” anchor arrangements. Shear lugs and embedded plates. Bearing surface crushing. Individual anchor capacity! Since anchors are evaluated as ‘groups’, the failure of an individual anchor is not necessarily detected. GTSUG June, 2011 6

7. GTSTRUDL Capacity Criteria Seismic reduction (Section D.3.3) Check tension (N) –FN n ≥ N ua (D-1) Check shear (V) –FV n ≥ V ua (D-2) Check interaction if N ua > 0.2FN n and V ua > 0.2FV n : N ua /FN n + V ua /FV n ≤ 1.2 (D-31) Spacing checks –D.8 requirements unless supplemental reinforcement exists. GTSUG June, 2011 7

8. GTSTRUDL The checking process Get characteristics of anchors, base plate and bearing surface concrete plus the location of anchors and edges. Loadings: Section 9.2 or Appendix C load factors Check edge distance and spacing if supplementary reinforcement does not exist. Create groups based on anchor geometry. Check anchor capacity for shear and tension – reduce if seismic requirement Determine F factors based on governing sections Calculate interaction value GTSUG June, 2011 8

9. GTSTRUDL Anchor characteristics Cast-in or post-installed Embedment length h ef Diameter d o Ductility – ductile or brittle, based on test elongation or area reduction. Tensile strength f uta –The use of f uta instead of f ya is to match with AISC LRFD design. A se – effective cross-section area; manufacturer’s value if not pd o 2. GTSUG June, 2011 9

10. GTSTRUDL Anchor Characteristics: Cast-in anchors Headed bolt Hooked bolt Headed stud GTSUG June, 2011 10 Optional data N p pullout strength in cracked concrete A brg bearing area of head if N p not specified, for headed bolts or studs. e h width of hook or L if N p not specified, for hooked bolts Washer – headed anchors, increases h ef.

11. GTSTRUDL Anchor Characteristics: Post-installed anchors Type: UC (undercut), TC (torque- controlled), DC (displacement- controlled) Pullout strength N p Category: 1, 2 or 3 – low to high sensitivity. GTSUG June, 2011 11

12. GTSTRUDL Anchor Characteristics: Post-installed anchors Optional data c ac : Manufacturer’s critical edge distance or taken from D.8.3. V sa : Shear strength in lieu of D-20 k c and y c,N – Concrete breakout strength coefficient + cracked concrete modification factor. If k c from the manufacturer is used, the specified y c,N must also be used. GTSUG June, 2011 12

13. GTSTRUDL Anchor Configuration and Base Plate Conditions Anchor and edge locations –In general, edges > 1.5*h ef may be ignored –Without supplement reinforcement, other criteria should be checked and may be up to 4.0*h ef for post-installed anchors. Grout pad under plate – affects y factors GTSUG June, 2011 13

14. GTSTRUDL Concrete Characteristics f’c Cracked/Uncracked Supplementary reinforcement –Outside the scope of Appendix D in ’05. Note: ’08 adds “Anchor reinforcement” with specific design guides. Thickness –In general, > h ef *1.333 or h ef +4” for post- installed without supplemental reinforcement. GTSUG June, 2011 14

15. GTSTRUDL Tension capacity: Section D.5 GTSUG June, 2011 15 Tension capacity is determined using “Section D.5 – Design requirements for tensile loading”, with four types of strength measures specified in sections D.5.1 to D.5.4. The lowest value of N n calculated is used in equation D-1 and its type will be used when determining F for tension. Processing must be done on a load-by-load basis, since not all anchors will be in tension for all loads and this will affect capacity calculations, especially y ec,N, the modification factor for loading eccentricity.

16. GTSTRUDL D.5.1 Steel Strength of Anchor GTSUG June, 2011 16 The simplest check! For all loaded anchors in each load case: N sa = n*A se *f uta (D-3) n= number of loaded anchors A se = cross-section area from d o or manufacturer specified Note that the calculated value is for the sum of all loaded anchors, without a specified check on individual anchors.

17. GTSTRUDL GTSUG June, 2011 17 D.5.2 Concrete Breakout N cb = (A Nc /A Nco )*y ec,N *y ed,N *y c,N *y cp,N *N b y ec,N : Eccentricity factor from D-9 (single anchor = 1.0) y ed,N : Edge proximity factor y c,N : Cracked concrete factor y cp,N : Post-installed c ac reinforcement factor (cast-in = 1.0) N b = Concrete breakout for a single anchor, no edges From D-7, D-8 or manufacturer’s specs

18. GTSTRUDL D.5.2 Concrete Breakout: (A Nc /A Nco ) GTSUG June, 2011 18 A Nco = Maximum area of single breakout cone = 9.0*h ef 2 A Nc, the total projected concrete failure area of an anchor group, is affected by anchor spacing and edge distance.

19. GTSTRUDL D.5.2 Concrete Breakout: y ec,N GTSUG June, 2011 19 If eccentricity exists in both X and Y, y ec,N is the product of y ec,N_X and y ec,N_Y.

20. GTSTRUDL D.5.3 Pullout Strength GTSUG June, 2011 20 For each anchor in tension – no grouping: N pn = y c,P *N p Cast-in anchors: N p from D-15 or D-16 N p = 8*A brg *f’ c (D-15) N p = 0.9*f’ c *e h *d o (D-16) Post-installed anchors: N p specified y c,P = 1.0 for cracked concrete = 1.4 for uncracked concrete

21. GTSTRUDL D.5.4 Concrete side-face blowout GTSUG June, 2011 21 Only cast-in, headed anchors with c a1 < 0.4*h ef : N sb = 160*c a1 *sqrt(A brg )*sqrt(f’ c ) If there are multiple anchors, Nsb is modified by: 1.0 + s/(6*c a1 )

22. GTSTRUDL Shear capacity: Section D.6 GTSUG June, 2011 22 Shear capacity is determined using “Section D.6 – Design requirements for shear loading”, with three types of strength measures specified in sections D.6.1 to D.6.3. The lowest value of V ua calculated is used in equation D-2 and its section will be used when determining F. Processing must be done on a load-by-load basis, even though all anchors tend to share the shear load, since y ec,N, the modification factor for loading eccentricity, will vary. If edges are present, processing for shear becomes very complicated, since c a1, the minimum edge distance, is measured “in the direction of the applied shear”, and may in fact be different for every anchor if in-plane rotation exists. One solution is to separate the shear into (X, Y) components and process separately, but ACI does not address this issue directly. Non-orthogonal edges would complicate the problem even more.

23. GTSTRUDL D.6.1 Steel shear strength GTSUG June, 2011 23 For all loaded anchors in each load case, For cast-in headed studs: V sa = n*A se *f uta (D-19) For cast-in headed and hooked bolts, plus post-installed anchors without sleeves in the shear plane: V sa = n*0.6*A se *f uta (D-20) Else: Manufacturer’s specified value n= number of loaded anchors A se = cross-section area from d o or manufacturer specified Use resultant shear for 6.1

24. GTSTRUDL D.6.2 Concrete breakout in shear GTSUG June, 2011 24 V cb = (A Vc /A Vco ) *y ec,V *y ed,V *y c,V *V b (D-22) y ec,V = Eccentricity factor, = 1.0 for single anchors y ed,V = Edge proximity factor y c,V = Cracked concrete factor V b = Single anchor breakout strength in cracked concrete This is the most complicated provision, but only applies to anchors “near” an edge, such that 4.5*c a1 3.5 *sqrt(f’ c ) approaches A se *f uta (D-19).

25. GTSTRUDL D.6.2 (con’t) GTSUG June, 2011 25 A Vco = max. single anchor shear breakout area = 4.5*c a1 2 (D-23) (D-24)

26. GTSTRUDL D.6.3 Concrete pryout GTSUG June, 2011 26 V cp = k cp *N cb (D-29) V cp = k cp *N cbg (D-30) k cp =1.0 if h ef < 2.5 inches 2.0 if h ef ≥ 2.5 inches Note the back-reference to N cb – hopefully D.5.2.1 (concrete breakout strength) was not limited by n N *A Nco (n N = # of loaded anchors in tension), or D.5.2.1 will need to be re- calculated for the shear group.

27. GTSTRUDL Determining F values: Section D.4.4, loads from Section 9.2 GTSUG June, 2011 27 Determine governing failure mode: If steel element governs, Ductile: F = 0.75 for tension, 0.65 for shear Brittle: F = 0.65 for tension, 0.60 for shear If concrete governs, but not D.5.3 or D.6.3, and supplementary reinforcement exists, F = 0.75 for shear, all anchors F = 0.75 for tension, cast-in & post-installed Cat 1 -0.10 for Category 2, -0.20 for Category 3 If concrete governs but not the above conditions F = 0.70 for shear, all anchors F = 0.70 for tension, cast-in F = 0.65 for tension, post-installed Category 1 -0.10 for Category 2, -0.20 for Category 3

28. GTSTRUDL Determining F values: Section D.4.5, loads from Appendix C GTSUG June, 2011 28 Determine governing failure mode: If steel element governs, Ductile: F = 0.80 for tension, 0.75 for shear Brittle: F = 0.70 for tension, 0.65 for shear If concrete governs, but not D.5.3 or D.6.3, and supplementary reinforcement exists, F = 0.85 for shear, all anchors F = 0.85 for tension, cast-in & post-installed Cat 1 -0.10 for Category 2, -0.20 for Category 3 If concrete governs and no supplementary reinforcement, F = 0.75 for shear, all anchors F = 0.75 for tension, cast-in & post-installed Cat 1 -0.10 for Category 2, -0.20 for Category 3

29. GTSTRUDL Seismic Loads, Section D.3.3 GTSUG June, 2011 29 D.3.3.3 If seismic loads are used and in regions of moderate to high seismic risk, an additional reduction factor of 0.75 must be applied to FN n and FV n. 0.75FN n ≥ N ua D.3.3.4 N n and V n must be governed by ductile steel elements or D.3.3.5 The “attachment” must undergo ductile yielding at loads below failure of the anchors. No guidance is offered as to making this determination.

30. GTSTRUDL Section D.8 – Edge distances, spacings and thickness GTSUG June, 2011 30 If no supplementary reinforcement exists: Min c-to-c spacing:4*d o for cast-in, untorqued anchors 6*d o for all other anchors Minimum edge distance: Cover requirements for cast-in, untorqued 6*do (or cover) for cast-in, torqued 6*do for post-installed UC 8*do for post-installed TC 10*do for post-installed DC Minimum concrete thickness for post-installed anchors t ≥ 1.5*h ef t ≥ h ef +4”