1. Concrete Resin Bonded and Mechanical Anchors

2. Purpose: Develop a design procedure for resin bonded and mechanical anchors to be used in the ODOT BDDM

3. Design Codes Used: Mechanical Anchors:
American Concrete Institute (ACI)
Appendix D of ACI
(PCI Design Handbook referenced for conformity)
Resin Bonded Anchors:
International Code Council (ICC)
Section AC308

4. General Description:
Mechanical Anchor: A pre-installed or cast-in-place metal anchor. Pre-installed anchors have headed or hooked ends and are cast in the concrete. Post installed anchors placed in drilled holes and have an expanding mechanism near the bottom of the anchor that applies compressive stress to the surrounding concrete in order to provide tensile resistance of the anchor.
Resin Bonded Anchor: A post-installed metal anchor that is bonded to the concrete with an epoxy resin that is injected into the drilled hole after the anchor is placed.

5. Mechanical Anchors

6. Single Mechanical Anchor Capacities
Nominal Tensile Strength
φNn > Nua
Nn is the design tensile strength of the mechanical anchor based on the critical failure mode.
Nua is the factored applied tensile load to the mechanical anchor.

7. Steel Strength of Anchor in Tension
Nsa = (Ase,N)(futa)
Ase,N is the effective cross sectional area of the anchor.
futa is the steel tensile strength of the anchor = 1.9fya but not more than 125,000 psi.

8. Concrete Breakout Strength – Single Anchor

9. Concrete Breakout Strength – Single Anchor
Ncb = (Anc/Anc0)(ψed,n)(ψc,n)(ψcp,n)(Nb)
Anc is the area of the rectangle with sides located 1.50 hef from the center of the anchor but not beyond the actual edge of concrete.
hef is the effective embedment length of the anchor.
Anc0 is the area of the square with the length of each side equal to 3hef.

10. Concrete Breakout Strength – Single Anchor
Anc Shall not exceed Anc0.
ψed,n = ca,min , ψed,n < 1.0
1.5hef
ca,min = the distance from the center of the anchor to the edge of the concrete.
ψc,n = 1.25 for cast-in anchors, and 1.4 for post-installed anchors.

11. Concrete Breakout Strength – Single Anchor
For post-installed anchors,
ψcp,n = 1.0 if ca,min > cac
ψcp,n = ca,min if ca,min < cac
cac
ψcp,n shall not be taken less than 1.5hef/cac
cac = 2.5 hef for undercut anchors
cac = 4 hef for torque controlled anchors
cac = 4 hef for displacement controlled anchors

12. Concrete Breakout Strength – Single Anchor
For cast-in anchors, ψcp,n = 1.0
___
Nb = (kc)(λ)√f’c (hef)1.5
kc = 24 for cast-in anchors
kc = 17 for post-installed anchors
λ = 1.0 for normal weight concrete

13. Pullout Strength – Single Cast-in Anchors Only
Npn = (ψc,P)(NP)
ψc,P = 1.4 for uncracked concrete
ψc,P = 1.0 for cracked concrete
Np = 8Abrgf’c For headed studs or headed bolts
Np = 0.9f’c ehda For hooked bolts
Abrg = Net bearing area of bolt or stud head
eh = minimum length of hook in hook bolt
da = anchor diameter

14. Blowout Strength – Single Anchor

15. Blowout Strength – Single Anchor
____ __
Nsb = 160ca1 √Abrg λ√f’c
ca1 = Distance from anchor to nearest edge of concrete
Abrg = Net bearing area of bolt or stud head
λ = 1.0 for normal weight concrete

16. Blowout Strength
If the distance (ca2) from the center of the anchor to the edge of the concrete that is perpendicular to the edge for ca1 is less than 3ca1, the value Nsb shall be modified by the factor;
[1+ (ca2/ ca1)]/4
1 < ca2 < 3

17. Strength Provided By Reinforcement
If reinforcement is provided and is developed on both sides of the breakout surface, the design strength of the reinforcement can be used instead of the concrete breakout strength.

18. Group Mechanical Anchors in Tension
The following design specifications are from Appendix D of the American Concrete Institute (ACI) Manual of Concrete Practice, 2008, Part 3.
General Equation for Mechanical Anchor Tension Capacity for Group Anchors
Nominal Tensile Strength
φNn > Nua
Nn is the design tensile strength of the mechanical anchors based on the critical failure mode.
Nua is the factored applied tensile load to the mechanical anchors.

19. Group Mechanical Anchors in Tension
Steel Strength of Anchors in Tension
Nsa = (n)(Ase,N)(futa)
n = Number of anchors in a group
Ase,N is the effective cross sectional area of a single anchor.
futa is the steel tensile strength of the anchor = 1.9fya but not more than 125,000 psi.

20. Concrete Breakout Strength in Tension – Group Anchors
Ncbg = Anc (ψec,n)(ψed,n)(ψc,n)(ψcp,n)Nb
Anc0
Anc is the area of the rectangle with sides located 1.50 hef from the centerline of the outside anchors of the group but not beyond the actual edge of concrete.
Anc shall not exceed nAnc0 where n is the number of tensioned anchors in the group.
hef is the effective embedment length of the anchor.
Anc0 is the area of a single anchor failure zone which is a square with the length of each side equal to 3hef.

21. Concrete Breakout Strength in Tension – Group Anchors
___1___
ψec,N = e’N < 1
3hef
e’N = eccentricity of the load on tension anchors
ψed,n = ca,min , ψed,n < 1.0
1.5hef
ca,min = the distance from the center of the anchor to the edge of the concrete.
ψc,n = 1.25 for cast-in anchors, and 1.4 for post-installed anchors.

22. Concrete Breakout Strength in Tension – Group Anchors
For post-installed anchors,
ψcp,n = 1.0 if ca,min > cac
ψcp,n = ca,min if ca,min < cac
cac
ψcp,n shall not be taken less than 1.5hef/cac
cac = 2.5 hef for undercut anchors
cac = 4 hef for torque controlled anchors
cac = 4 hef for displacement controlled anchors

23. Concrete Breakout Strength in Tension – Group Anchors
For cast-in anchors, ψcp,n = 1.0
___
Nb = kcλ√f’c ( hef)1.5
kc = 24 for cast-in anchors
kc = 17 for post-installed anchors
λ = 1.0 for normal weight concrete

24. Pullout Strength – Cast-in Anchors Only
Npn = (ψc,P)NP
Npn = Pullout strength of a single anchor
ψc, P = 1.4 for uncracked concrete
ψc,P = 1.0 for cracked concrete
Np = 8Abrgf’c For headed studs or headed bolts

25. Pullout Strength – Cast-in Anchors Only
Np = 0.9f’c ehda For hooked bolts
Abrg = Net bearing area of bolt or stud head
eh = minimum length of hook in hook bolt
da = anchor diameter

26. Blowout Strength – Group Anchors
Nsbg = (1+ s/6ca1) Nsb
Nsbg is the nominal blowout strength of a single anchor in a group of anchors.
s = the distance between the outer anchors along the edge.
___ ___
Nsb = 160ca1 √Abrg λ√f’c
ca1 = Distance from anchor to nearest edge of concrete

27. Blowout Strength – Group Anchors
Abrg = Net bearing area of bolt or stud head
λ = 1.0 for normal weight concrete
If the distance (ca2) from the center of the anchor to the edge of the concrete that is perpendicular to the edge for ca1 is less than 3ca1, the value Nsb shall be modified by the factor;
(1+ ca2 )/4
ca1
1 < ca2 < 3

28. Strength Provided by Reinforcement
If reinforcement is provided and is developed on both sides of the breakout surface, the design strength of the reinforcement can be used instead of the concrete breakout strength.

29. Mechanical Anchor – Single Anchor Shear
General Equation for Shear Strength of Anchor
φVn > Vua
Vn is the design shear strength of the mechanical anchor based on the critical failure mode.
Vua is the factored applied shear load to the mechanical anchor.

30. Nominal Steel Shear Strength
For cast-in headed stud anchors:
Vsa = Ase,vfuta
For post-installed anchors:
Vsa = 0.6Ase,vfuta

31. Nominal Steel Shear Strength
Ase,V = cross-sectional area of anchor in shear
futa = material strength of the anchor = 1.9 fya but not more than 125,000 psi
fya = the specified yield strength of the anchor material
Where anchors are used with built-up grout pads, the nominal strength shall be multiplied by 0.80.

32. Concrete Breakout Strength of Anchor in Shear

33. Concrete Breakout Strength of Anchor in Shear
Vcb = AVc (ψed,V)(ψc,V)(ψh,V)(Vb)
AVc0
AVc is the area of the exposed vertical face of the concrete failure section.
The maximum area of this surface is equal to 3ca1 x 1.5ca1 = 4.5ca12
ca1 is the distance from the centerline of the anchor to the exposed face of concrete.
AVc is limited by the existing edges of concrete that encroach into the fundamental failure area.

34. Concrete Breakout Strength of Anchor in Shear
Ca2 is the distance along the exposed surface from the edge of the concrete to the centerline of the anchor.
AVc0 = 4.5ca12
ψed,V = ca2 < 1.0
1.5ca1
ψcV = for anchors located in a region where analysis shows no concrete cracking at service loads.

35. Concrete Breakout Strength of Anchor in Shear
ψcV = for anchors in cracked concrete with no supplementary reinforcement or edge reinforcement smaller than a #4 bar.
ψcV = for anchors in cracked concrete with reinforcement of a #4 bar or larger between the anchor and the edge of concrete.
ψcV = 1.4 for anchors in cracked concrete with reinforcement of a #4 bar or greater between the anchor and the edge of concrete, and with the reinforcement enclosed within stirrups spaced at no more than 4 inches.
________
ψh,V = √1.5ca1/ ha > 1.0

36. Concrete Breakout Strength of Anchor in Shear
ha is the thickness of the member in which the anchor is located, measured parallel to the anchor axis.
___ ___
Vb = [7(le/da)0.2 √ da ] λ √ f’c (ca1)1.5
le = Load bearing length of the anchor for shear
da = Anchor diameter
λ = Light weight concrete factor

37. Concrete Pryout Strength of Anchor in Shear

38. Concrete Pryout Strength of Anchor in Shear
Vcp = kcpNcb
kcp = 1.0 for hef < 2.50 “
kcp = 2.0 for hef > 2.50 “
Ncb = concrete breakout strength in tension for anchor

39. Strength Provided By Reinforcement
If reinforcement is provided and is developed on both sides of the breakout surface, or encloses the anchor and is developed beyond the breakout surface, the design strength of the reinforcement can be used instead of the concrete breakout strength.

40. Mechanical Anchor Group Shear
General Equation for Shear Strength of Anchors
φVn > Vua
Vn is the design shear strength of the mechanical anchors based on the critical failure mode.
Vua is the factored applied shear load to the mechanical anchors.

41. Nominal Steel Shear Strength
For cast-in headed stud anchors:
Vsa = n(Ase,V)(futa)
For post-installed anchors:
Vsa = n0.6(Ase,V)(futa)
n = number of anchors

42. Nominal Steel Shear Strength
Ase,V = cross-sectional area of anchor in shear
futa = material strength of the anchor = 1.9 fya but not more than 125,000 psi
fya = the specified yield strength of the anchor material
Where anchors are used with built-up grout pads, the nominal strength shall be multiplied by 0.80.

43. Concrete Breakout Shear Strength of Anchors
Vcbg = AVc (ψec,V)(ψed,V)(ψc,V)(ψh,V)Vb
AVc0
AVc is the area of the exposed vertical face of the concrete failure section.
The maximum area of this surface is equal to (3ca1+s1)(1.5ca1)
ca1 is the distance parallel to the shear force from the centerline of the outside anchors to the exposed face of concrete.
s1 is the spacing between the outside anchors in the group measured parallel to the failure plain.

44. Concrete Breakout Shear Strength of Anchors
AVc is limited by the existing edges of concrete that encroach into the fundamental failure area.
AVc0 is the projected failure area for a single anchor
AVc0 = 3ca1 x 1.5ca1
ψec,V = 1/[1+ (2e’v/3ca1)]
e’v = the eccentricity of anchors loaded in shear in the same direction

45. Concrete Breakout Shear Strength of Anchors
ψed,V = ca2 < 1.0
1.5ca1
ca2 is the distance perpendicular to the shear force along the exposed concrete surface from the edge of the concrete to the centerline of the nearest anchor.
ψcV = for anchors located in a region where analysis shows no concrete cracking at service loads.
ψcV = for anchors in cracked concrete with no supplementary reinforcement or edge reinforcement smaller than a #4 bar.

46. Concrete Breakout Shear Strength of Anchors
ψcV = for anchors in cracked concrete with reinforcement of a #4 bar or larger between the anchor and the edge of concrete.
ψcV = 1.4 for anchors in cracked concrete with reinforcement of a No. 4 bar or greater between the anchor and the edge of concrete, and with the reinforcement enclosed within stirrups spaced at no more than 4 inches.
________
ψh,V = √1.5ca1/ ha > 1.0
ha is the thickness of the member in which the anchor is located, measured parallel to the anchor axis.

47. Concrete Breakout Shear Strength of Anchors
___ ___
Vb = [7(le/da)0.2 √ da ] λ √ f’c (ca1)1.5
le = Load bearing length of the anchor for shear
le = hef for anchors with constant stiffness over the full length of the embedded section.
le shall be no greater than 8da
da = Anchor diameter
λ = Light weight concrete factor according to ACI 8.6.1

48. Concrete Pryout Shear Strength of Anchors
Vcpg = kcpNcbg
kcp = 1.0 for hef < 2.50 “
kcp = 2.0 for hef > 2.50 “
Ncbg = concrete breakout strength in tension for group anchors

49. Strength Provided By Reinforcement
If reinforcement is provided and is developed on both sides of the breakout surface, or encloses the anchor and is developed beyond the breakout surface, the design strength of the reinforcement can be used instead of the concrete breakout strength.

50. Single Resin Bonded Anchor in Tension
The following design specifications are from the Acceptance Criteria for Post-Installed Adhesive Anchors in Concrete Elements published by the International Code Council (ICC). These specifications are planned to be incorporated into the 2011 edition of the American Concrete Institute (ACI) Building Code.

51. Single Resin Anchor Tensile Strength
Na = ANa (ψed,Na) (ψp,Na)(Na0)
ANa0
ANa = the actual horizontal base surface area under the resin bonded anchor.
It is a rectangle with sides limited to a distance of ccr,Na or ca,min from the anchor which ever is least.
ca,min = minimum edge distance
ccr,Na = scr,Na 2
_________
scr,Na = 20d √τk,uncr/ < 3 hef

52. Single Resin Anchor Tensile Strength
hef = embedment depth
d = anchor diameter
τk,uncr is the bond strength of the resin based on uncracked concrete.
______
τk,uncr = kc,uncr √ hef f’c < Manufacturers value for resin πd
kc,uncr = 24

53. Single Resin Anchor Tensile Strength
ANa0 = (scr,Na)2 = the projected area of failure surface of a single anchor
ANa shall not be greater than ANa0.
ψed,Na = ca,min < 1.0
ccr,Na
ψp,Na = max(ca,min ; ccr.Na)
cac
ψp,Na = 1.0 if ca,min > cac

54. Single Resin Anchor Tensile Strength
cac = 1.50 hef if hef < 8d
d = anchor diameter
cac = hef hef if hef > 8d
48d
Na0 = (τk,uncr )(π)(d)(hef)

55. Group Resin Anchor Tensile Strength
Nominal Tensile Strength
Na = Ana(ψed,Na)(ψg,Na)(ψec,Na)(ψp,Na)Na0
ANa0
ANa = the actual horizontal base surface area under the resin bonded anchor group.
It is a rectangle with sides limited to a distance of ccr,Na or ca,min , which ever is least, from a line through the outside rows of anchors
ccr,Na = scr,Na 2

56. Group Resin Anchor Tensile Strength
_________
scr,Na = 20d √τk,uncr / < 3 hef
d = anchor diameter
τk,uncr is the bond strength of the resin based on uncracked concrete.
______
τk,uncr = kc,uncr √ hef f’c < Manufacturers value for resin πd
ANa0 = (scr,Na)2 = the projected area of failure surface of a single anchor

57. Group Resin Anchor Tensile Strength
ANa shall not be greater than ANa0.
ψed,Na = ca,min < 1.0
ccr,Na
ψg,Na = ψg,Na0 + [ (s/scr,Na)0.5 (1- ψg,Na0)]
ψg,Na is the group failure surface factor
__ __
ψg,Na0 = √n – [ (√n – 1) (τk,cr/ τk,max,cr)1.5] > 1.0
n is the number of tension loaded anchors in a group

58. Group Resin Anchor Tensile Strength
_____
τk,max,cr = kc,cr √ hef f’c πd
kc,cr = 17 for cracked concrete
ψec,Na is a modification factor for eccentrically loaded anchor groups. _
ψec,Na = e’N
scr,Na

59. Group Resin Anchor Tensile Strength
e’N is the eccentricity of the load on the group of anchors
This equation is valid for e’N < s/2
s = Anchor spacing
ψp,Na = max(ca,min ; ccr.Na)
cac
ψp,Na = 1.0 if ca,min > cac

60. Group Resin Anchor Tensile Strength
cac = 1.50 hef if hef < 8d
d = anchor diameter
hef = embedment depth
cac = hef hef if hef > 8d
48d
ca,min = minimum edge distance
Na0 = (τk,cr )(π)(d)(hef)

61. Single Resin Anchor Shear Strength
Nominal Shear Strength
Vcp = min [ (kcp)(Na) ; (kcp)(Ncb) ]
kcp = 1.0 for hef < 2.5 in.
kcp = 2.0 for hef > 2.5 in.
Na = ANa (ψed,Na)(ψp,Na)Na0
ANa0
ANa = the actual horizontal base surface area under the resin bonded anchor. It is a rectangle with sides limited to a distance of ccr,Na or ca,min from the anchor which ever is least.

62. Single Resin Anchor Shear Strength
ccr,Na = scr,Na 2
_________
scr,Na = 20d √τk,uncr/ < 3 hef
hef = effective embedment depth of anchor
d = anchor diameter
τk,uncr is the bond strength of the resin based on uncracked concrete.
______
τk,uncr = kc,uncr √ hef f’c < Manufacturers value for resin
π d

63. Single Resin Anchor Shear Strength
kc,uncr = 24
ANa0 = (scr,Na)2 = the projected area of failure surface of a single anchor.
ANa shall not be greater than ANa0.
ψed,Na = ca,min < 1.0
ccr,Na
ψp,Na = max(ca,min ; ccr.Na)
cac
ψp,Na = 1.0 if ca,min > cac

64. Single Resin Anchor Shear Strength
cac = 1.50 hef if hef < 8d
d = anchor diameter
hef = embedment depth
cac = hef hef if hef > 8d
48d
ca,min = minimum edge distance
Na0 = (τk,uncr )(π)(d)(hef)
Ncb = ANc . ψed,N . ψc,N . ψcp,N .Nb
ANc0

65. Single Resin Anchor Shear Strength
ANc = is the area of the rectangle with sides located 1.50 hef from the center of the anchor but not beyond the actual edge of concrete.
Anc0 is the area of the square with the length of each side equal to 3hef.
Anc Shall not exceed Anc0.
ψed,n = ca,min , ψed,n < 1.0
1.5hef
ca,min = the distance from the center of the anchor to the edge of the concrete.

66. Single Resin Anchor Shear Strength
ψc,n = 1.25 for cast-in anchors, and 1.4 for post-installed anchors.
For post-installed anchors,
ψcp,n = 1.0 if ca,min > cac
ψcp,n = ca,min if ca,min < cac
cac
ψcp,n shall not be taken less than 1.5hef/cac

67. Single Resin Anchor Shear Strength
cac = 2.5 hef for undercut anchors
cac = 4 hef for torque controlled anchors
cac = 4 hef for displacement controlled anchors __
Nb = kcλ √f’c hef1.5
kc = 24
λ = 1.0 for normal weight concrete

68. Group Resin Anchor Shear Strength
Nominal Shear Strength
Vcpg = min [ (kcp)(Nag) ; (kcp)(Ncbg) ]
kcp = 1.0 for hef < 2.5 in.
kcp = 2.0 for hef > 2.5 in.
Nag = Ana(ψed,Na)(ψg,Na)(ψec,Na)(ψp,Na)Na0
ANa0

69. Group Resin Anchor Shear Strength
ANa = the actual horizontal base surface area under the resin bonded anchor group. It is a rectangle with sides limited to a distance of ccr,Na or ca,min from the outside rows of anchors, which ever is least.
ccr,Na = scr,Na 2
__________
scr,Na = 20d √τk,uncr/ < 3 hef
hef = effective embedment depth of anchor
d = anchor diameter

70. Group Resin Anchor Shear Strength
τk,uncr is the bond strength of the resin based on uncracked concrete.
______
τk,uncr = kc,uncr √ hef f’c < Manufacturers value for resin πd
kc,uncr = 24
ANa0 = (scr,Na)2 = the projected area of failure surface of a single anchor
ANa shall not be greater than nANa0 where n is the number of anchors in tension in the group.

71. Group Resin Anchor Shear Strength
ψed,Na = ca,min < 1.0
ccr,Na
ψg,Na = ψg,Na0 + [(s/scr,Na)0.5 (1- ψg,Na0)]
__ __
ψg,Na0 = √n – [(√n – 1)(τk,cr/τk,max,cr)1.5] > 1.0
s = Anchor spacing
τk,cr = Bond strength in cracked concrete
_______
τk,max,cr = kc,cr √(hef)(f’c)

72. Group Resin Anchor Shear Strength
kc,cr = 17
ψec,Na = 1/[1+(2e’N/scr,Na)]
ψp,Na = max(ca,min ; ccr.Na)
cac
ψp,Na = 1.0 if ca,min > cac
cac = 1.50 hef if hef < 8d
d = anchor diameter, hef = embedment depth

73. Group Resin Anchor Shear Strength
cac = hef hef if hef > 8d
48d
ca,min = minimum edge distance
Na0 = (τk,uncr )(π)(d)(hef)
Ncbg = ANc (ψec,N)(ψed,N)(ψc,N)(ψcp,N)Nb
ANc0
ANc = is the area of the rectangle with sides located 1.50 hef from the center of the anchor but not beyond the actual edge of concrete.

74. Group Resin Anchor Shear Strength
Anc0 is the area of the square with the length of each side equal to 3hef.
Anc Shall not exceed Anc0.
ψec,N = 1/[1+(2e’N/3hef)]
e’N = eccentricity of tension anchors
ψed,n = ca,min , ψed,n < 1.0
1.5hef
ca,min = the distance from the center of the anchor to the edge of the concrete.

75. Group Resin Anchor Shear Strength
ψc,N = 1.4 for post installed anchors
ψcp,n = 1.0 if ca,min > cac
ψcp,n = ca,min if ca,min < cac
cac
ψcp,n shall not be taken less than 1.5hef/cac _
Nb = kcλ √f’c hef1.5
kc = 17 for post-installed anchors
λ = 1.0 for normal weight concrete