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**Concrete Resin Bonded and Mechanical Anchors**

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

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**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

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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.

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Mechanical Anchors

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**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.

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**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.

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**Concrete Breakout Strength – Single Anchor**

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**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.

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**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.

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**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

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**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

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**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

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**Blowout Strength – Single Anchor**

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**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

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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

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**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.

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**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.

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**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.

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**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.

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**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.

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**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

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**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

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**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

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**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

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**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

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**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

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**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.

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**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.

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**Nominal Steel Shear Strength**

For cast-in headed stud anchors: Vsa = Ase,vfuta For post-installed anchors: Vsa = 0.6Ase,vfuta

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**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.

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**Concrete Breakout Strength of Anchor in Shear**

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**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.

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**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.

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**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

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**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

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**Concrete Pryout Strength of Anchor in Shear**

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**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

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**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.

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**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.

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**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

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**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.

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**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.

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**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

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**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.

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**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.

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**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

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**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

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**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.

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**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.

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**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

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**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

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**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

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**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)

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**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

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**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

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**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

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**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

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**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

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**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)

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**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.

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**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

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**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

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**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

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**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.

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**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

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**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

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**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

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**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

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**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.

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**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)

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**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

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**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.

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**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.

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**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

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