1 concrete resin bonded and mechanical anchors. 2 purpose: develop a design procedure for resin...

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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 318-08

(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 StrengthφNn > 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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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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Anc Shall not exceed Anc0.

ψed,n = 0.7 + 0.3ca,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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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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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



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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 StrengthφNn > 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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___1___ψec,N = 1+ 2e’N < 1 3hef

e’N = eccentricity of the load on tension anchors




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cac





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For cast-in anchors, ψcp,n = 1.0 ___Nb = kcλ√f’c ( hef)1.5

kc = 24 for cast-in anchors



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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


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



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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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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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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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 = 0.70 + 0.30 ca2 < 1.0 1.5ca1

ψcV = 1.4 for anchors located in a region where analysis shows no concrete cracking at service loads.

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ψcV = 1.0 for anchors in cracked concrete with no supplementary reinforcement or edge reinforcement smaller than a #4 bar.

ψcV = 1.2 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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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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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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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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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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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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ψed,V = 0.70 + 0.30 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 = 1.4 for anchors located in a region where analysis shows no concrete cracking at service loads.

ψcV = 1.0 for anchors in cracked concrete with no supplementary reinforcement or edge reinforcement smaller than a #4 bar.

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ψcV = 1.2 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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___ ___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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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/1450 < 3 hef

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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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ANa0 = (scr,Na)2 = the projected area of failure surface of a single anchor

ANa shall not be greater than ANa0.

ψed,Na = 0.70 + 0.30ca,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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cac = 1.50 hef if hef < 8d

d = anchor diameter

cac = hef2 + 1.33 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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_________ scr,Na = 20d √τk,uncr /1450 < 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


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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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_____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.

1 _ψec,Na = 1+ 2e’N

scr,Na

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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



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d = anchor diameter




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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ccr,Na = scr,Na

2 _________ scr,Na = 20d √τk,uncr/1450 < 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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kc,uncr = 24

ANa0 = (scr,Na)2 = the projected area of failure surface of a single anchor.





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d = anchor diameter





Ncb = ANc . ψed,N . ψc,N . ψcp,N .Nb

ANc0

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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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cac


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__Nb = kcλ √f’c hef1.5

kc = 24


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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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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/1450 < 3 hef

hef = effective embedment depth of anchor

d = anchor diameter

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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


ANa shall not be greater than nANa0 where n is the number of anchors in tension in the group.

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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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kc,cr = 17

ψec,Na = 1/[1+(2e’N/scr,Na)]




d = anchor diameter, hef = embedment depth

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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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ψec,N = 1/[1+(2e’N/3hef)]

e’N = eccentricity of tension anchors



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ψc,N = 1.4 for post installed anchors



cac

ψcp,n shall not be taken less than 1.5hef/cac _Nb = kcλ √f’c hef1.5



1 concrete resin bonded and mechanical anchors. 2 purpose: develop a design procedure for resin...

Documents

n f uta n

concrete n p

p n p c

c f c h ef

h ef e n

uncracked concrete c

c a2 c a1

tension group anchors