S. K. Ghosh Associates Inc. www.skghoshassociates.com 1 -1- Example Problem ½-in. Headed bolts ASTM F 1554 Grade 36 f yt = 36,000 psi f uta = 58,000 psi f’ c = 4000 psi h ef = 12 in. h a = 18 in. SDC C Concrete is assumed cracked at service load 8" 4" 6" 6" 4" 14" 18" 20" Steel base plate Wide flange column -2- Example Problem e Nx = 1 in. e´ Ny = 1 in. 8" 4" 6" 6" 4" 20" e Nx e Ny N ua
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D.5.2.7 – Post-installed Anchors in Uncracked Concrete without Supplementary Reinforcement
In the example problem:
Anchors are cast-in place
ψcp,N = 1.0
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D.5.2.1 – Concrete Breakout Strength of Anchor Group (Tension)
…………(D-5)
In the example problem:
Ncbg = 1020 1296
0.90 x 0.77 x 1.0 x 1.0 x 64.2
= 35.0 kips
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D.5.2.1 – Concrete Breakout Strength of Anchor Group (Tension)
Strength reduction factor, φ:
φ = 0.75 for cast-in headed bolts (assuming Condition A) …….D.4.4(c)
For SDC C or above, a factor of 0.75 is applied..……D.3.3.3
0.75φ = 0.75 x 0.75 = 0.56
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D.5.2.1 – Concrete Breakout Strength of Anchor Group (Tension)
Design strength of the bolt group for concrete breakout in tension:
0.75φNcbg= 0.56 x 35.0 = 19.6 kips
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D.5.3 – Pullout Strength
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D.5.3.6 – Pullout Strength
In the example problem:
Anchors used - 1/2" cast-in headed bolts with Hex head
Abrg = 0.291 in.2
NP = 8 x 0.291 x 4000 / 1000 = 9.31 kips
For cracked concrete under service load, ψc,P = 1.0
Npn = 1.0 x 9.31 = 9.31 kips
This is the pullout strength of one anchor
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D.5.3.6 – Pullout Strength
Strength reduction factor, φ:
φ = 0.70 for cast-in headed studs (Condition B applies for pullout failure) …….D.4.4(c)
For SDC C or above, a factor of 0.75 is applied..……D.3.3.3
0.75φ = 0.75 x 0.70 = 0.53
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D.5.3.6 – Pullout Strength
Design strength of a single bolt for pullout in tension:
0.75φNpng= 0.53 x 9.31 = 4.89 kips
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D.5.3.6 – Pullout Strength
Equating with the maximum demand on a single bolt:
Nua/4 = 4.89 kips
Thus max. Nua = 19.7 kips = 0.75φNpng for the group of bolts
This is the maximum tension demand that the whole bolt formation can support for pullout failure in tension
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D.5.4 – Side-face Blowout
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D.5.4.2 – Side-face Blowout
In the example problem:
Anchors used - Headed boltsMinimum edge distance in X-direction = 4 in. < 0.4hef (= 4.8 in.)Minimum edge distance in Y-direction = 4 in. < 0.4hef (= 4.8 in.)
Side-face blowout possible in both X- and Y-directions.Nsbg needs to be calculated in both directions and the smaller
strength would govern.
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D.5.4.2 – Side-face Blowout
Failure in X-direction
6"
6"
4"
8" 4"
Bolts under consideration
ca1 = 4 in.
Anchor spacing = 6 in. < 6ca1
…......OK
s = 6 + 6 = 12 in.
Abrg = 0.291 in.2
f c = 4000 psi
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D.5.4.2 – Side-face Blowout
Failure in X-direction
Nsbg = 32,752/1000 = 32.8 kips
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D.5.4.2 – Side-face Blowout
Strength reduction factor, Φ:
φ = 0.75 for cast-in headed bolts (assuming Condition A) …….D.4.4(c)
For SDC C or above, a factor of 0.75 is applied..……D.3.3.3
0.75φ = 0.75 x 0.75 = 0.56
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D.5.4.2 – Side-face Blowout
Design strength of the bolt group in side-face blowout under tension:
0.75φNsbg = 0.56 x 32.8 = 18.4 kips
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D.5.4.2 – Side-face Blowout
Nua
Mua = Nua x 1
Nua/2 – Nua/8 = 3Nua/8
Nua/2 + Nua/8 = 5Nua/8
Proportion of tension demand carried by considered column of bolts = 5/8
The maximum tension demand that the whole bolt formation can support in side-face blowout
= 18.4x8/5 = 29.5 kips
Failure in X-direction
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D.5.4.2 – Side-face Blowout
6"
6"
4"
8" 4"
Bolts under consideration
ca1 = 4 in.
Anchor spacing = 8 in. < 6ca1
…......OK
s = 8 in.
Abrg = 0.291 in.2
f c = 4000 psi
Failure in Y-direction
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D.5.4.2 – Side-face Blowout
Nsbg = 29,106/1000 = 29.1 kips
Failure in Y-direction
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D.5.4.2 – Side-face Blowout
Failure in Y-direction
Design strength of the bolt group in side-face blowout under tension:
0.75φNsbg = 0.56 x 29.1 = 16.4 kips
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D.5.4.2 – Side-face Blowout
Nua
Mua = Nua x 1
Nua/2 + Nua/8 = 5Nua/8
Proportion of tension demand carried by considered row of bolts = 5/12
The maximum tension demand that the whole bolt formation can support in side-face blowout
= 16.4x12/5 = 39.3 kips
Nua
Mua = Nua x 1
Nua/3 + Nua/12 = 5Nua/12Nua/3
Nua/3 - Nua/12 = Nua/4
Failure in Y-direction
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D.5.4.2 – Side-face Blowout
Governing side-face blowout strength of the whole bolt formation is the smaller of those computed by considering failure in X-direction (29.5 kips) and in Y-direction (39.3 kips)
Failure Mode 1: Concrete breakout occurs from the anchors closest to the edge
AVc = [1.5ca1 +6+6+4][Min(ha, 1.5ca1)]
= [1.5x4 + 6 + 6 + 4][1.5x4] = 132 in.2
AVco = 4.5ca12 = 4.5x42 = 72 in.2
Number of bolts, n = 3AVc < nAVco ……………OK
AVc/AVco = 1.83
8" 4"
4"
1.5ca1
6"
6"
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Shear in X-Direction
Failure Mode 1: Concrete breakout occurs from the anchors closest to the edge
le = hef = 12 in. > 8do = 4 in. le = 4 in.
= 3796/ 1000 = 3.8 kips
Basic concrete breakout strength
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Shear in X-Direction
Failure Mode 1: Concrete breakout occurs from the anchors closest to the edge
Eccentricity factor
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Shear in X-Direction
Failure Mode 1: Concrete breakout occurs from the anchors closest to the edge
Edge factorca2, bottom = 4 in. < 1.5ca1 (= 6 in.)
= 0.90
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Shear in X-Direction
Failure Mode 1: Concrete breakout occurs from the anchors closest to the edge
Cracking factor
Concrete is cracked at service load. It is assumed that supplementary reinforcement comprising of No. 4 bars is present between the anchors and the edges. No stirrup is used to enclose the reinforcement.
ψc,V = 1.2
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Shear in X-Direction
………(D-22)
Vcbg = 132 72
1.0 x 0.90 x 1.2 x 3.8
= 7.52 kips
Failure Mode 1: Concrete breakout occurs from the anchors closest to the edge
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Shear in X-Direction
φ = 0.75 for Condition A …….D.4.4(c) For SDC C or above, a factor of 0.75 is applied
..……D.3.3.30.75φ = 0.75 x 0.75 = 0.56
Failure Mode 1: Concrete breakout occurs from the anchors closest to the edge
Strength reduction factor, φ
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Shear in X-Direction
Design strength of the first row in concrete breakout in shear:
0.75φVcbg= 0.56 x 7.52 = 4.21 kips
This needs to be compared against the fraction of the total shear demand causing this failure
Failure Mode 1: Concrete breakout occurs from the anchors closest to the edge
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Shear in X-Direction
Failure Mode 1: Concrete breakout occurs from the anchors closest to the edge
Vuax/2 = 4.21 kips Vuax = 8.42 kips
This is the total shear demand that the whole group can support before Mode 1 failure takes place
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Shear in X-Direction
Failure Mode 2: Concrete breakout occurs from the anchors in the 2nd column from the edge
Failure Mode 2: Concrete breakout occurs from the anchors in the 2nd column from the edge
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Shear in X-Direction
Cracking factorConcrete is cracked at service load. It is assumed that supplementary reinforcement comprising of No. 4 bars is present between the anchors and the edges. No stirrup is used to enclose the reinforcement.
ψc,V = 1.2
Failure Mode 2: Concrete breakout occurs from the anchors in the 2nd column from the edge
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Shear in X-Direction
………(D-22)
Vcbg = 612 648 1.0 x 0.77 x 1.2 x 19.7
= 17.19 kips
Failure Mode 2: Concrete breakout occurs from the anchors in the 2nd column from the edge
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Shear in X-Direction
φ = 0.75 for Condition A …….D.4.4(c) For SDC C or above, a factor of 0.75 is applied
..……D.3.3.30.75φ = 0.75 x 0.75 = 0.56
Strength reduction factor, φ
Failure Mode 2: Concrete breakout occurs from the anchors in the 2nd column from the edge
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Shear in X-Direction
Design strength of the first row in concrete breakout in shear:
0.75φVcbg= 0.56 x 17.19 = 9.62 kips
This needs to be compared against the fraction of the total shear demand causing this failure
Failure Mode 2: Concrete breakout occurs from the anchors in the 2nd column from the edge
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Shear in X-Direction
Vuax = 9.62 kips
This is the total shear demand that the whole group can support before Mode 2 failure takes place
Failure Mode 2: Concrete breakout occurs from the anchors in the 2nd column from the edge
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Shear in X-Direction
Design concrete breakout strength of the anchor group based on two failure modes:
1st Mode: 8.42 kips2nd Mode: 9.62 kips
0.75φVcbg,x = 8.42 kips
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Shear in Y-Direction
8" 4"
6"
6"
4"
e Vx = 1"
vuay
20"
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Shear in Y-Direction
Failure Mode 1: Concrete breakout occurs from the anchors closest to the edge
8" 4"
4"
1.5ca1
ca1 = 4 in.ha = 18 in. > 1.5ca1 …….OKca2,right = 4 in. < 1.5ca1
ca2,left = 20 in. > 1.5ca1 ……OK
Only one edge distance < 1.5ca1
ca1 need not be revised
Vuay/3
20"
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Shear in Y-Direction
Failure Mode 1: Concrete breakout occurs from the anchors closest to the edge
Failure Mode 1: Concrete breakout occurs from the anchors closest to the edge
le = hef = 12 in. > 8do = 4 in. le = 4 in.
= 3796/ 1000 = 3.8 kips
Basic concrete breakout strength
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Shear in Y-Direction
Failure Mode 1: Concrete breakout occurs from the anchors closest to the edge
Eccentricity factor
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Shear in Y-Direction
Failure Mode 1: Concrete breakout occurs from the anchors closest to the edge
Edge factorca2, right = 4 in. < 1.5ca1 (= 6 in.)
= 0.90
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Shear in Y-Direction
Failure Mode 1: Concrete breakout occurs from the anchors closest to the edge
Cracking factorConcrete is cracked at service load. It is assumed that supplementary reinforcement comprising of No. 4 bars is present between the anchors and the edges. No stirrup is used to enclose the reinforcement.
ψc,V = 1.2
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Shear in Y-Direction
Failure Mode 1: Concrete breakout occurs from the anchors closest to the edge
………(D-22)
Vcbg = 10872 0.86 x 0.90 x 1.2 x 3.8
= 5.29 kips
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Shear in Y-Direction
Failure Mode 1: Concrete breakout occurs from the anchors closest to the edge
φ = 0.75 for Condition A…….D.4.4(c)
For SDC C or above, a factor of 0.75 is applied..……D.3.3.3
0.75φ = 0.75 x 0.75 = 0.56
Strength reduction factor, φ
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Shear in Y-Direction
Failure Mode 1: Concrete breakout occurs from the anchors closest to the edge
Design strength of the first row for concrete breakout in shear:
0.75φVcbg= 0.56 x 5.29 = 2.96 kips This needs to be compared against the fraction of the
total shear demand causing this failure
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Shear in Y-Direction
Failure Mode 1: Concrete breakout occurs from the anchors closest to the edge
Vuay/3 = 2.96 kips Vuay = 8.88 kips
This is the total shear demand that the whole group can support before Mode 1 failure takes place
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Shear in Y-Direction
Failure Mode 2: Concrete breakout occurs from the anchors in the 2nd row from the edge
ca1 = 4 + 6 = 10 in.ha = 18 in. > 1.5ca1 …….OKca2,right = 4 in. < 1.5ca1
Failure Mode 2: Concrete breakout occurs from the anchors in the 2nd row from the edge
20"
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Shear in Y-Direction
le = hef = 12 in. > 8do = 4 in. le = 4 in.
= 15,005 / 1000 = 15 kips
Basic concrete breakout strength
Failure Mode 2: Concrete breakout occurs from the anchors in the 2nd row from the edge
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Shear in Y-Direction
Eccentricity factor
Failure Mode 2: Concrete breakout occurs from the anchors in the 2nd row from the edge
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Shear in Y-Direction
Edge factor
ca2, right = 4 in. < 1.5ca1 (= 15 in.)
= 0.78
Failure Mode 2: Concrete breakout occurs from the anchors in the 2nd row from the edge
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Shear in Y-Direction
Cracking factorConcrete is cracked at service load. It is assumed that supplementary reinforcement comprising of No. 4 bars is present between the anchors and the edges. No stirrup is used to enclose the reinforcement.
ψc,V = 1.2
Failure Mode 2: Concrete breakout occurs from the anchors in the 2nd row from the edge
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Shear in Y-Direction
………(D-22)
Vcbg = 405 450
0.94 x 0.78 x 1.2 x 15
= 11.88 kips
Failure Mode 2: Concrete breakout occurs from the anchors in the 2nd row from the edge
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Shear in Y-Direction
φ = 0.75 for Condition A …….D.4.4(c) For SDC C or above, a factor of 0.75 is applied
..……D.3.3.30.75φ = 0.75 x 0.75 = 0.56
Strength reduction factor, φ
Failure Mode 2: Concrete breakout occurs from the anchors in the 2nd row from the edge
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Shear in Y-Direction
Design strength of the 2nd row for concrete breakout in shear:
0.75φVcbg= 0.56 x 11.88 = 6.65 kips
This needs to be compared against the fraction of the total shear demand causing this failure
Failure Mode 2: Concrete breakout occurs from the anchors in the 2nd row from the edge
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Shear in Y-Direction
2Vuay/3 = 6.65 kips Vuay = 9.98 kips
This is the total shear demand that the whole group can support before Mode 2 failure takes place
Failure Mode 2: Concrete breakout occurs from the anchors in the 2nd row from the edge
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Shear in Y-Direction
Failure Mode 3: Concrete breakout occurs from the anchors in the 3rd row from the edge
ca1 = 4 + 6 + 6 = 16 in.ha = 18 in. < 1.5ca1
ca2,right = 4 in. < 1.5ca1
ca2,left = 20 in. < 1.5ca1
3 edge distances < 1.5ca1
ca1 needs to be revised
8" 4"
Ca2,left = 20 in.
4"
6"
Vuay
6"
20"
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Shear in Y-Direction
Failure Mode 3: Concrete breakout occurs from the anchors in the 3rd row from the edge
Failure Mode 3: Concrete breakout occurs from the anchors in the 3rd row from the edge
8" 4"
1.5ca1 = 20 in.
4"
6"
6"
20"
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Shear in Y-Direction
le = hef = 12 in. > 8do = 4 in. le = 4 in.
= 23,093 / 1000 = 23.1 kips
Basic concrete breakout strength
Failure Mode 3: Concrete breakout occurs from the anchors in the 3rd row from the edge
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Shear in Y-Direction
Eccentricity factor
Failure Mode 3: Concrete breakout occurs from the anchors in the 3rd row from the edge
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Shear in Y-Direction
Edge factor
ca2, right = 4 in. < 1.5ca1 (= 20 in.)
= 0.76
Failure Mode 3: Concrete breakout occurs from the anchors in the 3rd row from the edge
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Shear in Y-Direction
Cracking factorConcrete is cracked at service load. It is assumed that supplementary reinforcement comprising of No. 4 bars is present between the anchors and the edges. No stirrup is used to enclose the reinforcement.
ψc,V = 1.2
Failure Mode 3: Concrete breakout occurs from the anchors in the 3rd row from the edge
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Shear in Y-Direction
………(D-22)
Vcbg = 576800 0.95 x 0.76 x 1.2 x 23.1
= 14.4 kips
Failure Mode 3: Concrete breakout occurs from the anchors in the 3rd row from the edge
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Shear in Y-Direction
φ = 0.75 for Condition A ..….D.4.4(c) For SDC C or above, a factor of 0.75 is applied
..……D.3.3.30.75φ = 0.75 x 0.75 = 0.56
Strength reduction factor, φ
Failure Mode 3: Concrete breakout occurs from the anchors in the 3rd row from the edge
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Shear in Y-Direction
Design strength of the 3rd row in concrete breakout in shear:
0.75φVcbg= 0.56 x 14.4 = 8.10 kips
This needs to be compared against the fraction of the total shear demand causing this failure
Failure Mode 3: Concrete breakout occurs from the anchors in the 3rd row from the edge
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Shear in Y-Direction
Vuay = 8.10 kips
This is the total shear demand that the whole group can support before Mode 3 failure takes place
Failure Mode 3: Concrete breakout occurs from the anchors in the 3rd row from the edge
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Shear in Y-Direction
Design concrete breakout strength of the anchor group based on three failure modes: